Design and Fabrication of Acousto-optic Devices (Optical Science and Engineering)

DESlGn AND

C.

editor of Russian contributions rny of Aerospace instrumentation

Library of Congress Cataloging-in-Publication Data Design and fabrication of acousto-optic devices edited by Akis P. Goutzoulis, Dennis R. Pape; editor of Russian contributions, Sergei V. Kulakov. p.cm. - (Opticalengineering; v. 41) Includes bibliographical references and index. ISBN 0-8247-8930-X Acoustoopticaldevices--Congresses.2. I. Goutzoulis,Akis P. II. Pape,DennisR. m. Kulakov, V.(SergeiViktorovich) N.Series: Optical engineering (Marcel Dekker, Inc.); v. 41. TA1770.D47 1994 621.36’9--d~20 93-40794 CIP

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Neither this book nor any part may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying, microfilming, and recording, or by any information storage and retrieval system, without permission in writing from the publisher. MARCEL DEKKER, INC. 270 Madison Avenue, New York, New York

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Current printing (last digit): l 0 9 8 7 6 5 4 3 2 1 PRINTED IN THE UNITED STATES OF AMERICA

Series Introduction

The philosophy of the Optical Engineering series is to discuss topics in optical engineering at a level useful to those working in the field or attempting to design subsystemsthat arebased on optical techniques or that have significant optical subsystems. The concept is not to provide detailed monographs on narrow subject areas but to deal with the material at a level that makes it immediately useful to the practicing scientist and engineer. We expect that workersin optical research will also find them extremely valuable. As editor of the series, I am pleased to bring you this book, which is the latest in a number of volumes that relate to acousto-optics: for example Acousto-Optic Signal Processing, edited by Berg and Lee (vol. ElectroOptic and Acousto-Optic Scanning and Deflection, by Gottlieb et al. (vol. Acousto-Optics, by Korpel (vol. and sections of Optical Scanning, by Marshall (vol. 31). Acousto-optics is perhaps a confusing term to the uninitiated, but, in fact, it refers to a well-known subfield of both optics and acoustics. It refers, of course, to theinteraction between light and sound;between light waves and sound waves; between photons and phonons. Perhaps more specifically, it refers to the control and modification of a light beam by means of an acoustic beam. It was LCon Brillouin who first suggested, in the very early that light could be scattered by a sound wave. But, ten years went by before iii

iv these types of effects were demonstrated by Debye and Sears and by Lucas and Biquard. Thus, certain fundamental effects in acousto-optics have been known for some time. However, the surge in applications of these effects has occurred much more recently, brought about in part by the development and application of lasers. Thus, we are now fortunate tohave devices that can use sound to modulate, deflect, refract, and diffract light. This volume in our series is devoted to the design, fabrication, and testing of such devices. I acknowledge and appreciate the work of the editors and authorswho have contributed to this volume. Brian J. Thompson University Rochester Rochester, New York

Preface

Acousto-optic (AO) devices have played a centralrole in the development and recent proliferation of activity in the fields of optical information processing, optical computing, optical communications, and optical sensing. The interaction of light and sound, the A 0 effect, was primarily a subject of academic interest until the invention of the laser in 1960. The need then arose for the modulation and deflection of laser beams. Lightmodulating and -deflecting devices based on theA 0 effect were developed and A 0 technology wasborn. In the late 1960s tunable filter devices which use the A 0 effect to filter polychromatic light were developed. Optical processing arose in the 1970swith the realization that information could be manipulated spatially using optics. Acousto-optic modulator and deflector devices found early application in optical signal processing systems as the means by which time-varying electrical information could be imparted onto light waves in real time. As the use of optics to process image and digital information developed throughout the 1970s and 1980s, A 0 technology matured into thedevice technology of choice for electrical to optical information conversion. More recently,A 0 tunable filter (AOTF) devices have begun to have a major impact on the development of optical sensing and optical communication systems. As thefield of acousto-optics has evolved from having primarily scientific interest to technological significance, the design and fabrication of A 0 devices has evolved into ahighly refined engineering specialty at anumber of industrial firms and technical facilities throughout theworld. The growing importance of these devices for commercial and military applications in the late 1970s and 1980s led to restrictions on publishing specific A 0 design and fabrication details. The large amount of work in this field in the former Soviet Union was, until recently, virtually unknown inthe West.

vi

PREFACE

The book offers, for the first time and in a single volume, a systematic and detailed look at A 0 device design, fabrication, and testing. It includes all the necessary technical information (including proven computer-aided design programs) for the design and manufacture A 0 deflectors, modulators, and AOTFs. It also includes major contributions from authors from the leading institutionof acousto-optic technologyin the former Soviet Union (St. Petersburg State Academy of Aerospace Instrumentation, formerly known as Leningrad Institute of Aviation Instrumentation). This book will be an invaluable aid to a wide audience of readers, including teachers in physicsand engineering at both the undergraduate and graduate levels, students wishing to learn about the practicalities of these devices (providing them with enough information to actually fabricate a device), practicing acousto-optic device designers and fabricators in manufacturing wishing to learn techniques by others, and optical engineers designing and fabricating optical systems wishing to learn how to enhance system performance through device design and fabrication. While other books have been published on acousto-optic theory by electrical engineers and optical signal processing and optical computing architectures and applications by optical engineers, this book fills the gap between theory and application by describing the details of device design and fabrication from the perspective of authors with years of practical experience both in working in A 0 device fabrication facilities and in building practical A 0 devicebased systems. This book consists of seven chapters, written by different authors, and describes the principles of AO, the design of deflectors, modulators, and AOTFs, the design the transducer structure, the fabrication of A 0 devices, and the device testing. The first chapter, “Principles of Acousto-Optics” (by Akis P. Goutzoulis and Victor V. Kludzin), reviews the theory and principles A 0 in order to prepare the readerfor the various device design issues discussed in the following chapters. There are threetypes of A 0 devices (deflectors, modulators, and AOTFs), which can use different types of light and sound interaction. The type A 0 interaction depends on the geometry of the A 0 interaction and theoptical and acoustic properties of the A 0 material. All A 0 interactions are based on the photoelastic effect, and they can be either isotropic or anisotropic depending on the optical properties of the A 0 crystal. The theory, characteristics, and types of the various A 0 interactions are discussed inSection 2. The device performance also depends on the inherent properties of the A 0 material used. In many cases the device requirements call for high diffraction efficiency and large number of resolution spots or time-bandwidth product (TBWP). Such issues are discussed in Section along with techniques for evaluating the potential

PREFACE

vii

TBWP of a given material. In the same section the authors present data for several common A 0 materials measured by scientists of the St. Petersburg State Academy of Aerospace Instrumentation. The diffraction efficiency and the bandwidth of any A 0 device can improve if a phased array rather than a single-element transducer is used. These transducers steer the acoustic wave such that the A 0 Bragg matching condition is satisfied over a wide frequency range. The characteristics, types, and basic design procedure of these transducers are discussed in Section An important requirement in high-performance deflectors and A O F s is large spuriousfree dynamic range. This is often limited either by nonlinear acoustics or by multiple A 0 diffractions when multiple tones are present in the A 0 crystal. The degree of acoustic nonlinearities is determined by both the applied power density and the nonlinearcharacteristics the A 0 crystal. Section 5 contains a simplified analysis of nonlinear acoustics, along with experimental data that will help the reader comprehend the overall problem and its implications. The same section also contains a discussion and a comparison of the mechanisms and thecharacteristics of the spurious thirdorder intermodulation products. Section 6 describes the characteristics of acoustic collimation, which cansignificantlyreduce the acoustic spread due to thefinite transducer aperture,resulting in longer aperture, moreefficient A 0 devices, and multichannel deflectors with greatly reduced acoustic crosstalk. The chapter closes with Section 7, whichdiscusses a simple geometrical technique that can be used to transform pure longitudinal waves into pure shearwaves. The second chapter, “Design of Acousto-Optic Deflectors” (by Dennis R. Pape, Oleg B. Gusev, Sergei V. Kulakov, and Victor V. Molotok), describes the detailed design of A 0 deflectors. Section 2 discusses the characteristics of A 0 deflectors, which include bandwidth, diffraction efficiency, and time aperture, and links these characteristics to thekey system operational parameters in scanning and information-processing applications. Section 3 describes the dependence of deflector efficiency on the chief device design parameters of material and acoustic mode selection and transducer geometry length and height specification. Section discusses various materials issues and their desired characteristics (such as strong A 0 interaction, low acoustic attenuation, low acoustic velocity, and small acoustic curvature), andit develops an A 0 figure of merit that relates the material parameters to theproduct of time aperture andthe squareof the device operating frequency. Based on this analysis a nomograph is produced that aids in materialselection. Section 5 contains a discussion of transducer geometry design guidelines. Four major classes of A 0 interaction geometries are discussed: isotropic, anisotropic, phased array, and anisotropic phased array. For each interaction the optimum transducer

viii

PREFACE

length is determined. In the same section a detailed procedure for optimizing the transducer height is presented along with a discussion on nonrectangular transducerconfigurations. Sections 6 and 7 are concerned with the total A 0 efficiency of the deflector, which depends, among other things, on the degree to which the acoustic energy launched at the transducer remains in the optical illumination aperture. Losses in acoustic energy from acoustic diffraction and attenuation are discussed in those two sections respectively. summary of the overall deflectordesign methodology is presented in Section 8, and is followed by five deflector design examples, which are described in Section 9. These examples include (1) 500-MHz isotropic Gap, (2) 1-GHz anisotropic LiNbO,, 32-MHz opticallyactive anisotropic Te02, 500-MHz phased array longitudinal LiNbO,, and 60-MHz phased array anisotropic slow shear TeOz deflector. For each of the preceding examples the authors provide proven computer programs that are based on the design methodology described earlier and that calculate optimal transducer parameters and the expected diffraction efficiency. In Appendix A, Oleg B. Gusev provides a computer program which combines the overall design methodology with electrical impedance design, that the electrical impedance-matching network can be modified interactively with the bandshape to achieve a desired frequency-dependent A 0 diffraction efficiency response. The third chapter, “Design of Acousto-Optic Modulators’’ by Richard V. Johnson), elucidates design principles for A 0 modulators. The first section reviews the major markets A for0 modulators in order to determine the performance measures that are most critical for practical applications. In Section 2 the author describes the fundamental principles and characteristics of modulators, which include the typical modulator head, drive electronics, optical diffraction characteristics, intensity modulation and transfer function, temporal response, and limits to which the incidentlight beam can be focused. Section contains derivations for calculating the RF power requirements of the modulator and a discussion on modulator materials and figures of merit. The requirementsof the incident light source for best modulator operation arereviewed in Section In thesame section the static contrast ratio is calculated for a lowest order T E M , Gaussian profile laser beam. A simple model the modulator’s temporal response isgivenin Section where a single-parameter measure of modulator performance is defined with respect to risetime,and a numerical algorithm is presented for calculating the modulator response to an arbitrary video signal. The effects of transducer length on the modulator performance, including diffraction efficiency, optical beam profile distortion, and degradation in temporal response, are described in Section 6. A typical mod-

PREFACE

ix

ulator design strategy is then. described in Section 7. Such a strategy, involving arbitration between conflicting performance requirements, embodies conventional modulator design wisdom as well as techniques for obtaining even more performance from a modulator. The closing section contains a review of four different approaches for maximizing the performance of a laser scanning system using an A 0 modulator. The fourth chapter, “Acousto-Optic Tunable Filters” (by Milton Gottlieb), provides a comprehensive review of the theory, operation, design, and fabrication of AOTFs along with the description of several AOTF applications. Section 2 discusses the theory and operation of AOTFs. This includes collinear AOTFs and the required crystal symmetries, noncollinear AOTFs and theircharacteristics such as phase-matching conditions, passband, calculation of their angular aperture, and etendue. The same section contains a discussion on the features and advantages of AOTFs such as their agility and internal modulation. Section 3 discusses the materials and A 0 interactions that are appropriate for AOTFs. A general design procedure for both collinear and noncollinear AOTFs is also described along with configurations for separating the diffracted and-undiffracted optical beams and techniques for suppressing the sidelobes and improving and imaging through the AOTF. In Section the author presents a review of the AOTF fabrication procedure, and he emphasizes several fabrication issues that are unique for AOTFs. Section 5 deals with a multitude of AOTF-based systems and applications. These systems include laser cavity tuning, spectrometry, spectropolarimetry, astronomical spectrophotometry, fluorescence spectroscopy, spectral imaging, semiconductor laser tuning for communications, fiberoptic wavelength multiplexing, and coherence detection. For each application the author describes the specifications and characteristics of the AOTF used and provides actual experimental data. The final section contains a brief description of waveguide AOTFs. The fifth chapter,“Transducer Design” (by Akis P. Goutzoulisand William R. Beaudet),addresses the design and theinterfacing of the transducer structure that launches the acoustic wave into the A 0 device. A typical transducer structureconsists of a metal top electrode, a piezoelectric crystal, and one (or more) metal bonding layer that attaches the piezoelectric crystal to the A 0 substrate and is used as the bottom electrode. The performance of the A 0 device-as measured by its bandwidth, impedance, conversion efficiency, and VSWR-depends largely on the characteristics of the transducer structure used. These characteristics are determined by, among other things, the number, composition, dimensions, and natural properties (e.g., mechanical impedance) of the various layers and

PREFACE of the A 0 substrate. Section 2 contains a comprehensive analysis of the transducer structure.The analysis of the various bonding layers is presented via equivalent circuits through the use of a transmission line equivalent matrix analysis to predict the device electrical impedance and transducer conversion efficiency. The effects of the various layers in simple transducer configurations are also described along with techniques that allow broadband operation with minimum conversion loss. The same section also contains a discussion of the various materials issues, where the emphasis is on bonding materials because they dramatically affect the amount of acoustic energy transferredfrom the transducer into the A 0 substrate. InAppendix B, Akis P. Goutzoulis presents a proven computer program based on the analysis presented in Section 2. They use this program in conjunction with three design examples covering the 20-40 MHz, MHz, and1.352.7 GHz frequency ranges, in order to show the use of the design methodology as well as of the program itself, for thestudy and analysis ofsimple and complex transducer structures. Actual experimental results are also presented in order toshow the agreement between theory andexperiment. The final section completes the transducer design by describing the electrical matching and power delivery networks. Impedance-matching techniques appropriate for simple transducers structures, phased array transducers, and multichannel devices are presented alongwith actual data obtained from prototype devices. The sixth chapter, “Acousto-Optic Device Manufacturing” (by Vjacheslav G. Nefedov and Dennis R. Pape), discusses techniques and procedures for fabricating A 0 devices. Section 2 discusses the manufacturing of the A 0 device optical window block. A brief description of typical crystal growth techniques is presented followed by procedures for crystal orientation, sawing of the optical window block, surface polishing, and optical antireflection coating. Section 3 discusses in detail the manufacturing of the piezoelectric transducer and several issues associated with internal stresses. The section begins with a description of thin-film transducer fabrication, including ZnO deposition technology, sputtering configurations, ZnO film characteristics, film quality, and several issues related to thedeposition parameters. This is followed by a discussion of the ZnO transducer performance and characteristics. The second part of Section 3 deals with the platelet transducer fabrication. This includes transducer bonding techniques (such as adhesive bonding, thermocompression bonding, cold vacuum compression bonding and optical contact bonding) ,platelet transducer reduction (such as mechanical reduction and ion milling), and top electrode definition. This chapter closes with a discussion of the final device assembly. This consists the impedance-matching network, wiring bonding, acoustic absorber, and device housing.

PREFACE

xi

The last chapter, “Testing of Acousto-Optic Devices” (by Akis P. Goutzoulis, Milton Gottlieb, and Dennis R. Pape), addresses the testing of the various types of A 0 devices. Device testing is the step thatfollows the device fabrication, and its main purpose is to determine the degree to which the design goals have been achieved. The detailed testing of experimental A 0 devices, which is based on new designs or fabrication techniques, is often of crucial importance because it may reveal performance issues and/or effects not previously estimated or even known. Similarly, testing is important for characterizing new A 0 materials and estimating their performance when used in conjunction with specific device designs and applications. Since all A 0 devices involve electric, acoustic, and optical parameters, the tests must cover allthree domains to the degree necessary dictated by the device type and the application. Tests common to all types of A 0 devices involve (1) the acoustic pulse echo, which shows the transducer bond quality, (2) the Schlieren imaging, which showsthe quality and characteristics of the propagating acoustic field, (3) the electric impedance, reflection loss, and VSWR, the optical scattering, which determines the quality of the A 0 crystal used, and (5) the acoustic attenuation of the A 0 crystal. Section 2 covers the tests appropriate for deflectors, which include frequency response, diffraction efficiency, third-order intermodulation products, single- and two-tone dynamic range, and the TBWP. Section discusses the additional tests necessary for multichannel deflectors, which include channel-to-channel performance uniformity, channelto-channel isolation, and the channel-to-channel phase and time uniformity of the input signal. Section 4 describes the modulator tests, which include risetime, modulation bandwidth, modulation transfer function, and the modulation contrast ratio. In Section 5 the authorsdiscuss the AOTFtests, which include the determination of the tuning relation, optical bandwidth, spectral resolution, the out-of-band transmission, the RF power dependence of transmission, polarization rejection ratio, spectral dependence of the spatial separation of the various orders, angular aperture or field of view, and the spatial resolution of spectral images. This book is an outgrowth of an international conference on A 0 held in the former Soviet Union in Leningrad (now St. Petersburg) in the summer of 1990. Western scientists learned for the first time many details about the development of A 0 technology in the former Soviet Union at this meeting. Drs. Goutzoulis and Pape met the conference organizer Professor Kulakov and his colleagues from the Leningrad Institute of Aviation Instrumentation (now the St. Petersburg State Academy of Aerospace Instrumentation). From this initial meeting the idea for a book that would describe the practical details of A 0 device design and fabrication was suggested by Professor Kulakov. The editors andcontributors are indebted

xii

PREFACE

to the manyscientistsandengineersin the United States,Russia,and throughout the world who have contributed to the development and our understanding technology.

Akis P. Goutzoulis Dennis R. Pape Sergei V . Kulakov

Contents

Series Introduction

iii

Preface

V

Contributors Principles of Acousto-Optics Akis P. Goutzoulis and Victor V . Kludzin Design of Acousto-Optic Deflectors Dennis R. Pape, Oleg B. Gusev, Sergei V . Kulakov, and Victor V . Molotok

xv 1

69

Design of Acousto-Optic Modulators Richard V . Johnson

123

Acousto-Optic Tunable Filters Milton S. Gottlieb

197

Transducer Design Akis P. Goutzoulis and William R . Beaudet

285

Acousto-Optic Device Manufacturing Vjacheslav G. Nefedov and Dennis R. Pape

339

Testing of Acousto-Optic Devices Akis P. Goutzoulis, Milton S. Gottlieb, and Dennis R. Pape

403

xiii

xiv

CONTENTS

Appendix A: Computer-Aided Design Program for Acowto-Optic Deflectors Oleg B. Gwev Appendix B: A Computer Program for the Analysis and Design of Transducer Structures Akis P. Goutzoulis

479

Index

485

Contributors

William Milton

Beaudet Harris Corporation, Melbourne, Florida Gottlieb Westinghouse Scienceand Technology Center, Pitts-

burgh, Pennsylvania Akis P. Goutzoulis Westinghouse Science and Technology Center, Pit&

burgh, Pennsylvania Oleg B.Gusev St. Petersburg State Academy tation, St. Petersburg, Russia Richard V. Johnson

Aerospace Znstrumen-

Crystal Technology, Inc., Palo Alto, California

St.PetersburgState mentation, St. Petersburg, Russia

Academy

Aerospace Znstru-

Sergei V. Kulakov

St. PetersburgState Academy mentation, St. Petersburg, Russia

Aerospace Znstru-

Victor V. Molotok St. Petersburg State Academy

Aerospace Znstru-

VictorV.Kludzin

mentation, St. Petersburg, Russia Vjacheslav G. Nefedov St. Petersburg State Academy strumentation, St. Petersburg, Russia Dennis

Aerospace Zn-

Pape Photonic System Zncorporated, Melbourne, Florida

xv

This Page Intentionally Left Blank

Principles of Acousto-Optics Westinghouse Science and Technology Center Pittsburgh, Pennsylvania

St. Petersburg State Academy of Aerospace Instrumentation St. Petersburg, Russia

INTRODUCTION The objective of this chapter is to review the theory of acousto-optics (AO) in order to prepare the reader for the various device design issues discussed in the following chapters. In general, there are three types of A 0 devices (deflectors, modulators, and tunable filters or AOTFs), each of which can use different types of light and sound interactions. The type of the A 0 interaction is determined by the light-sound geometry and the optical and acoustic properties of the A 0 material. All A 0 .interactions are based on the photoelastic effect, and they can be either isotropic or anisotropic, depending on the optical properties of the A 0 crystal. Isotropic A 0 interactions do not change the polarization of the optical beam, and they can result in either multiple or single diffracted optical beams (or orders). The multiple-order isotropic diffraction is called Raman-Nath, and because of its low diffraction efficiency it is not frequently used inpractical devices. The single-order isotropic diffraction is called Bragg; it is much more efficient and thereforeit is widely used inpractical devices. Anisotropic A 0 interactions change the polarization of the optical beam, and they result in a single diffracted order. They offer higher efficiencies and larger acoustic and optical bandwidths than the isotropic A 0 interactions. Most highperformance deflectors and AOTFs are actually based on anisotropic interactions. The theory, characteristics, and types of A 0 interactions are

l

2

KLUDZIN

AND

GOUTZOULIS

reviewed in Section 2. For each interaction we discuss the mathematical formulation and we derive expressions for the diffraction efficiency and the AO. Such expressions are used routinely in the device design. Aside fromthe actual A 0 interaction employed, the device performance also depends on the inherent properties of the A 0 material used. In general, different properties are required by different devices, however, in almost all cases the requirements call for high diffraction efficiency which translates to a specific figure of merit. For deflectors and for some types of AOTFs an important material-related parameter is the number of resolution spots or time-bandwidth product (TBWP). This parameter is affected mostly by acoustic attenuation, although in certain cases the crystal length may also be the limiting factor. In Section 3 we briefly discuss the A 0 material properties, and we describe techniques for evaluating the potential TBWP of a given material. For several common A 0 materials we present data which have been measured by scientists of the St. Petersburg State Academy of Aerospace Instrumentation (St. Petersburg, Russia) over the last several years. The diffraction efficiency and the bandwidth of any A 0 device can be improved if a phased array rather than a single-element transducer is used. Such transducers steer the acoustic wave such that the A 0 interaction geometry is satisfied over a wide frequency range. For a given acoustic frequency the phased array transducer radiates a greater amountof acoustic power in the desired direction, thereby increasing the overall diffraction efficiency. The characteristics, types, and the basic design procedure of these transducers are discussed in Section 4. An important requirement in high-performance deflectors and AOTFs is large spurious-free dynamic range. This is often limited by either nonlinear acoustics or by multiple A 0 diffractions when multiple tones are present in the A 0 crystal. The degree of acoustic nonlinearities is determined by both the applied power density and the nonlinear characteristics of the A 0 crystal. In Section 5 we present a simplified analysis of the nonlinear acoustics, along with their effects and properties, andwe present experimental data which willhelp the readercomprehend the overall problem and its implications. In the same section we also discuss and compare the mechanisms and the characteristics of the spurious third-order intermodulation products. These types of spurious signals are of interest because they appear within the octave bandwidth of the A 0 device, and therefore they decrease the overall dynamic range. Two important acoustic properties which are very useful in various A 0 devices are the acoustic collimation and the acoustic mode conversion. Acoustic collimation can significantly reduce the acoustic spread due to the finite transducer aperture, and it results in longer aperture, more ef-

PRINCIPLES OF ACOUSTO-OPTICS

3

ficient A 0 devices as well as multichannel deflectors with greatly reduced acoustic crosstalk. The characteristics and the advantages of acoustic collimation are discussed in Section 6 along with examples of acoustically anisotropic A 0 materials which support it. Acoustic wave transformation refers to a simple geometrical technique which can be used to transform pure longitudinal waves into pure shearwaves. In Section 7 we discuss the basics of this acoustic property, and we describe a simple procedure for the design of an acoustic mode converter.

2 ACOUSTO-OPTICINTERACTIONS 2.1 Acousto-optic devices are based on the photoelastic or elasto-optic effect [l-61 according to which an acoustic signal applied on an A 0 crystal produces a strain which changes the optical properties of the crystal. The acoustic signal is injected into thecrystal by means of a piezoelectric transducer, and as it propagates it produces regions of compression and rarefraction. When an optical beam passes through the crystal it may be deflected or modulated, and is frequency shifted. The changes in the optical properties of the crystal are the result of the changes in the index of refraction of the crystal produced by the strain.The complete mathematical description of the photoelastic effect depends on thedirectional properties of the A 0 material and requiresa tensor relation between the elastic strain and the photoelastic coefficients, and is

where AB, is the change in the tensor components of the dielectric impermeability, A(l/nz)ijis the change in the (l/n2)ijcomponent of the optical index ellispoid, pijk1 is a fourth-rank photoelastic tensor, and S,, are the strain components. The strain-induced changes in the optical properties of the crystal result from changes in the material index of refraction and may lead to rotation of the light polarization. The optical changes are best studied via the index ellipsoid by dalculating the difference of the ellipsoid equations for the unperturbed and perturbed states. This results in expressions for the change, Anij, in the refractive index, nij, as a function of the photoelastic coefficients and the strain. The form of these expressions is Anij = O.k$pijk&l,

i,j,k,l = 1,2,3

(2)

The crystal symmetry of any particular material determines which of the Pijkr components are nonzero andwh.ich components are related to others.

GOUTZOULIS AND KLUDZIN The coefficientsPijkl are assumed symmetrical withrespect to indices ij and kl, and can be contracted to p,,,,, (m,n = 1, 2, . . . , 6). However, this is not the case for optically anisotropic materials [4] where a microscopic body rotation in the medium disturbs the symmetry of the p o k l tensor, and thus p j j k l is not necessarily equal to p j j l k . In this case Eq. (1) must be slightly modified to account for these effects. detailed treatment of the index ellipsoid procedure can be found in [6] and In practice the term “acousto-optic interaction” refers to the effect of the acoustic wave on an incident optical wave, because in most cases the presence of the optical wave does not change the acoustic properties of the medium. From this point of view, the interaction can be treated as a parametric process, in which the acoustic field changes the refractive index of the medium. Usingthe methods of classical optics, we candescribe the interaction as the diffraction of the optical wave by a periodical phase grating induced by an acoustic wave. The fundamental difference between an ordinary grating and thephase grating generated by the acoustic wave is that the latter is not stationary; it travels with the speed of sound in the medium and its parameters can vary with time. This traveling phase grating Doppler-shifts the optical frequency, and it can be used to deflect, modulate, or filter the optical beam. Devices basedon these properties of the traveling phase grating are called deflectors, modulators, and tunable filters respectively. Examples of such devices are shown in Figs. 1, 2, and respectively. Although the design of these devices varies significantly, the underlying phenomena are the same and is based on isotropic or anisotropic interactions.

2.2 IsotropicAcousto-opticInteractions The characteristics of the diffracted light beams resulting from an interaction can be determinedby solving the wave equation that describes the optical wavepropagation in the A 0 crystal. Raman and Nath [5] analyzed the case of isotropic interactions which occur when the crystal is isotropic. In this case the refractive indices for the incident and the diffracted optical beams are thesame. (Note thatin an anisotropic interaction the refractive indices for the incident and diffracted optical beams are different, and the polarizations of the two beams are orthogonal.) For an isotropic interaction when an acoustic wave propagates along the x axis and a planeoptical beam propagates in the x-z plane at anangle (inside the medium) from the z axis, the wave equation can be written as

1 Example of a TeO, acousto-optic deflector. (Courtesy Technology.)

Crystal

where is the refractive index in the region of the A 0 interaction, is the speed of light, and E is the electric field. When the acoustic wave is planar, sinusoidal traveling wave, n(.x,t) can be described by = n

+ An sin(Ck,t

- K,x)

(4)

where n is the average refractive index of the medium, An is the amplitude of the refractive index change due to the acoustic strain, and K , and Ck, are the wave number and frequency of the acoustic wave, respectively. The solutions of the wave equation cannot beexpressed in analytical form, however, because is periodic in both space and time, the perturbed optical field E can be expanded in a Fourier series:

2 Example a Tl,AsS, acousto-optic modulator.(Courtesy inghouse Electric Corporation.)

West-

where

. r = ki(z cos - x sin

+ mK$

(6)

where Emand are the amplitude and the wave vector of the mth diffracted light beam respectively, and wi and kiare the frequency and the wave number of the incident light respectively. Equations (5) and (6) represent an expansion in plane waves of the output light distribution, which shows that the frequency, of the zkrnth diffracted order will be equal to = oi

* ma,

which means that the optical frequency of the mth diffracted order will be up- or downshifted by an amount equal to the frequency of the mth harmonic of the acoustic signal. Substituting Eqs. into Eq.(3), we obtain a set coupled-wave equations which describe the interaction of optical and acoustic waves in

PRINCIPLES OF ACOUSTO-OPTICS

7

3 Example of a TAS acousto-optic tunable filter. (Courtesy of Westinghouse Electric Corporation.) the medium. These equations were derived by Raman and Nath [5] and can be written as

where U1 =

- ko AnL COS

eo

and ko = 2dA0 is the wave number of the incident optical beam in free space, with A,, being the optical wavelength in free space. The solutions of Eq. (8) describe the electric field of the optical waves in the various diffraction orders. In interpreting these equations we can applybasic coupledmode theory [S] and assume that different optical waves propagate in the crystal and energy exchange takes place between them. If sinusoidal acoustic waves are used, the optical waves can exchange energy only with adjacent waves. In this case the variable u1 can be viewed as the coupling constant between the adjacent waves. The amount of energy transferred

GOUTZOULIS AND KLUDZIN

8

depends on thecoupling constant andthe degree of synchronization of the waves. The factor m2Ka/2ki cos 0, on the right side of Eq. (8) indicates the degree of synchronization. The larger the value of this factor the.less the synchronization (or thelarger the phase difference between the waves) and therefore the less the amount of energy transferred. We can proceed with Eq. (8) by examining A 0 interaction geometries in which an appreciable amount of light can be transferred outof the zero order into the diffracted orders. This can be accomplished by using the Klein and Cook [2] parameter defined as Q

= ki cos 0,

-

21~hoL nA2 cos 0,

where L is the A 0 interaction length along the direction of propagation of light and A is the acoustic wavelength. The parameter Q is appropriate because it measures the differences in phase of the various partial waves due to thedifferent directions of propagation. Using the parameter Q we can write Eq. (8) as

From Eq. (11) we cansee thatan appreciable amount of light is transferred out of the zeroth orderif either orboth coefficients of the right-hand side are small for m = ? 1. This can be accomplished if (1) Q is small and 0, is about OD, or (2) if Q is large and the two terms on the right-hand side of Eq. (11) are equal. When Q 0.3 the A 0 diffraction is called Raman-Nath and results in multiple diffraction orders similar to those produced by a thin diffraction grating. Figure shows the basic geometry of the Raman-Nath interaction and the resulting multiple diffraction orders. In this case light is transferred from the zeroth orderto thefirst order, from the first order to thesecond order, etc. The mth diffracted order is separated from the undiffracted order by an angle Om which can be approximated by

Since Q 0.3, the first term on the right-hand side of Eq. (11)can be neglected, and byusing the boundary conditions E,(O) = E,, and Ern(0)= 0 we obtain the following solutions: E,,,(z) = Eoe-irnXJ,,,

2ui sin X

PRINCIPLES OF ACOUSTO-OPTICS

m=+N

L Qa

Raman-Nath acousto-optic diffraction geometry showing multiple diffracted orders. where X = (K,z tan and J,,, is the Bessel function of the mth order. By setting = L in Eq. and by calculating the productE,(L)E,,,(L)*, where the asterisk denotes thecomplex conjugate, we obtain anexpression for the normalized intensity, Q = Zm/Io, of the mth diffracted order at = L: sin(K,L tan (K,L tan Using the identity J-,,,(u) = (- l)mJ,,,(u)we find from Eq. (14) that the diffraction pattern is symmetricfor all angles of incidence. As Raman and Nath noted, an examination of the output light intensity shows that phase rather than amplitude modulation is possible, the depth of which is measured by the parameterul. This acousticallyinduced phase modulation can be transformed into amplitude modulation via well-known Schlieren imaging techniques. For Q > 7, the acoustic grating is nolonger thin, andthe A 0 interaction becomes sensitive to theangle of the incident optical beam. This diffraction regime is called Bragg and is most widely used in practical applications. Since energy transfer is most effective between optical waves withthe same phase term, thediffracted light willappear predominantly in a single order. Figure 5 shows the basic geometry for the Bragg diffraction and the resulting single diffraction order. The amount light in the.diffraction order

KLUDZIN

10

AND GOUTZOULIS

OPTICAL

"a

L

t "a

A

T I

z

5 Bragg acousto-optic diffraction geometry showinga single diffracted order.

is maximized when the two terms on the right-hand side of Eq. (11) are equal; i.e., when tan Oo = mQ/2KUL.For m = 1 this condition reduces tQ

K, = sin Bo = sin O B = 2ki 2nA where OB is known as the Bragg angle. In practice O B is small, around a few degrees; e.g., for A. = 0.63 km and for an A 0 crystal with sound velocity V = 2 k d s e c and n = 2.5, the Bragg angle inside the crystal for a frequency of l GHz is 3.6". For thesame example the Bragg angle outside the crystal (i.e., n = 1 in Eq. (15)) is 9.1". The Bragg condition given by Eq. (15) can also be derived by considering the Bragg interaction as a collision between photons and phonons [ 9 ] .From this point of view, a photon with energy and momentum hki interacts with a phonon of frequency flu and momentum hK,, where h is Planck's constant, The interaction produces a new photon at frequency and momentum hkd and a phonon at frequency 0, with momentum hK,. Application of the energy and momentum conservation laws yields the fol-

PRINCIPLES OF ACOUSTO-OPTICS

l1

lowing relationships:

where the + or - sign applies when the optical wave is moving against or with the acoustic wave respectively. Equation (16a) shows that the frequency of the diffracted optical beam will be Doppler-shifted, up or down, depending onthe relative direction of the optical and acoustic beams. Since oi>> r R ,(e.g., 1015 Hz versus lo9 Hz respectively), the magnitude of kd is approximately that of ki, i.e., (kd(= Iki(.This is shown graphically in Fig. 6, and since (kdl = (ki(the diffraction triangle is always isosceles. This means that the magnitude of the acoustic wave vector must satisfy lK,l = 21kil sin eB, which reduces to Eq. (15). From Fig. 6 we note that when the Bragg condition is satisfied, the angle between the incident optical beam and the diffracted beam is We also note that the wave vectors lie on one circle because for the isotropic interaction the refractive indices of the incident and the diffracted light beams are equal. For the ideal isotropic Bragg diffraction wecanassume that energy exchange takes place between the incident optical wave Eo and the diffracted optical wave E,. In this case when is close to eB, the set of equations given by Eq. (11) reduces to the following two equations: dE0 U -+-"E,=O 2L

6 Wave vector diagram for isotropic Bragg diffraction.

12

GOUTZOULIS AND KLUDZZN

and dEl dz

U1 -Eo 2L,

"

where =

=

jx2q El

is given by KoL sin 0, - KoL tan 2 cos e, 2

eo

Phariseau [lo] solved Eqs. (17) and (18) andobtained the following solutions:

The normalized intensity of the diffracted beam, I d , can be calculated by setting = L in Eqs.(20)and(21) and calculating the quantity 1 - Eo(L)Eo(L)*,to get

where Zi is the intensity of the incident optical beam. When the Bragg condition is satisfied, eo = BB and thus = 0; the diffracted beam intensity is maximized and Eq. (22) reduces to

It is of interest to compare the normalized diffraction efficiencies for the Raman-Nath (Eq. (14)) and the Bragg (Eq. (23)) regimes. For normal incidence Eq. (14) reduces to ZT = Pm(ul),and since for m = 1 the maximum value of Jl(ul) = 0.58, the maximum normalizeddiffracted beam intensity or maximum diffraction efficiency possible is 33.6%. On the other hand, the Bragg diffraction can result in 100% diffraction efficiency, since for = IT the normalized intensity Id,,, is equal to 1. The limited diffraction efficiency in conjunction with the appearance multiple diffracted orders restricts the usefulness of Raman-Nath devices.

PRINCIPLES OF ACOUSTO-OPTICS

13

The parameter u1can be expressed as a function of practical parameters via the following relationship of the strain S,, and the acoustic power P,

P,

SkJz, LH

=

where is the density of the A 0 crystal, is the acoustic velocity, and H is the height of the acoustic beam. Using the expression for the strain obtained by substituting Eq. into Eq. and substituting the result for An into Eq. (9), we obtain u1 = COS

eo

Substituting Eq. into Eq. we obtain the following expression for the normalized maximum diffracted intensity:

Equation is important because it relates the normalized diffracted beam intensity to the physical and geometrical characteristics of the A 0 device and the input acoustic power P,. In practice the term “diffraction efficiency,” rather than “normalized maximum diffraction intensity” is used, and Eq. is approximated by the expression:

We emphasize that Eq. is valid only for small values of u1 and that is expressed in percent per watt of the applied acoustic power P,. In Eqs. and the quantity

M2

=

n6p2 -

is called the figure of merit and determines the inherent efficiency of the material regardless of the interaction geometry. As Eq. shows, high-efficiency materials must havea high refractive index and a low acoustic velocity. The geometrical characteristics of the A 0 device are given by the ratio LIH. In practice, M2 is used almost exclusively for AOTFs, as well as for scanners and low-bandwidth, high-resolution deflectors. Another parameter of importance forpractical Bragg diffraction-based devices is the 3-dB A 0 bandwidth, Af, defined as the difference between

KLUDZIN

14

AND GOUTZOULIS

the highest and lowest frequencies at which the normalkfed diffracted intensity I d drops by 50%. To calculate Af we first rewrite Eq. (22) as

where sinc = sin(TA)/TA. When ( ~ ~ 1 2 is ) ' small compared to Eq. (29) is well approximated by [9]

Id

in

From Eq. (19)we see that the parameter used in Eq. (30), is proportional to K , and thus to the acoustic frequency. Therefore Eq. (30) shows that the intensity of the diffracted order follows a sinc2-type behavior as the frequency changes. If the acoustic power is constant with frequency, the 3-dB bandwidth will extend up to thefrequencies for which Id = 0.5. This occurs when the argument of the sinc' function is equal to 2 0 . 4 5 ~ .By using Eq. (19) and = 0.45~,.we can write this condition as KaL (sin BB 2 COS eo

-

sin

=

0.45~

By substituting K, = 2 d A , and sin OB = K,/2ki = Ad2nAC, where A, is the center wavelength, and sin eo = Ad2nA, where A # A,, and by using the relations A, = V!fcand A = V/f, we can write Eq. (31) as fJA0

2nV2 COS eo

(f, -

=

0.45

Since the sinc function is symmetric around the center frequency, we can use the definition Af12 = f , - f , solve for Af, and obtain the following expression for the 3-dB bandwidth: COS

Af = 1.8nCR AoLfc

(33)

Observe that Af is inversely proportional to the interaction length L. This is an important point anda consequence of the fact that for a fixed angle of the incident optical beam and a fixed acoustic direction, an isotropic Bragg device will onlyoperate at one particular length of the acoustic wave vector, i.e., at oneacoustic frequency (or alternatively, the diffracted light wave vector kd must be equal to that of the incident light beam ki). If the direction of the diffracted beam is to be changed, we must change both the direction and the magnitude of the acoustic vector. For operationover a range of acoustic frequencies it is necessary to have a spread of the acoustic wave vector directions from the transducer. This is accomplished

PRINCIPLES OF ACOUSTO-OPTICS

15

by using the acoustic diffraction resulting from a transducer of width L . Since the angular spread of the acoustic beam is N L , the larger the device bandwidth Af, the larger the required wave vector spread and, therefore, the smaller the transducer length L . This situation is shown graphically in Figure 7. Note, however, that the diffraction efficiency q (Eq. (27)) is proportional to L, and therefore there is a bandwidth-efficiency trade-off. Equation (33) shows that the bandwidth is proportional to nVL. This gives rise [l31 to a different figure of merit, MI, which is used when the efficiency-bandwidth performance an A 0 device is of interest. M, is appropriate for weak interactions (i.e., q << 1) and is defined as

-

Using M, we can approximate q Af by

There is yet another figure

merit, MS,which is defined as [l41

M3 = nVM2

and which is useful for applications where the height of the transducer H is made as small as the size of the optical beam, i.e., H = V/Af.

7 Wave vector diagramfor isotropic Bragg diffraction showing wideband operation by using a transducer with angular acoustic beam spreadof

GOUTZOULIS AND KLUDZIN

Anisotropic A 0 interactions takeplace in optically anisotropic crystals and involve diffraction between ordinary and extraordinray optical beams. these beams face different refractive indices, this type of A 0 interaction is often called birefringent and involves rotation of the polarization of the diffracted beam by 90" with respect to that of the incident beam. This is an important feature of the anisotropic diffraction, because polarization filtering can be used to reduce optical noise and/or separate the diffracted and undiffracted beams. In a birefringent crystal the diffracted light wave vector kdcan differ in magnitude from k, if the polarization is changed in the diffraction process. Figure 8 shows the wave vector diagram for the birefringent diffraction in a negative uniaxial crystal (where no > ne with n, = no and nd = ne). For a given acoustic direction there exist two distinct acoustic frequencies which satisfy exact momentum-matching conditions. From Fig. 8 we see that a change in the direction of the diffracted wave vector kd to kb can be obtained by a change in the magnitude of the acoustic wave vector K, to K:. Thus an optical beam can be deflected simply byvarying the frequency of a well-collimated acoustic beam which remains fixed in direction. This implies that the angular spread of the acoustic wave vector required for phase matching across a particular acoustic bandwidth needs to be much less for the anisotropic than for the isotropic interaction. As we will see,

8 Wave vector diagram for the general case of anisotropic diffraction.

PRINCIPLES OF ACOUSTO-OPTICS

17

this represents an advantage of the anisotropic interaction over the isotropic, because it allows us to design A 0 devices with much wider bandwidths (for fixed diffraction efficiency) or with higher diffraction efficiencies (for fixed bandwidth). Harris and Wallace [l51 treated theoretically the anisotropic Bragg diffraction for collinear light-sound propagation, whereas Chang [9] treated the general noncollinear case. Chang, following a procedure similar to the one described in the previous section, obtained the following differential equations for an optical wave propagating at an angle from the axis and an acoustic wave propagating in the plane at an angle from the axis;

where AK, is the magnitude of the momentum mismatch (i.e., AK, = ki + mKa - km) givenby

is the frequency of the mth order, = cos + m(Ka/ki)cos n, is the refractive index for the mth order,X , is the appropriate component of the acoustically induced nonlinear susceptibility given by X , = e, Xwhere e, is a unit vector in the direction of the electric field of mth order, X is the nonlinear susceptibility tensor that describes the photoelastic effect, S is the unit strain tensor for the acoustic wave, and S is the strain of the acoustic wave. The coupled-wave equation for zero order can be obtained by observing that AK, = 0, = cos eo, E - , = 0, and X, = -n2n?p, where p is the appropriate photoelastic coefficient, and where n, = nd and no = nidenote the refractive indices for the diffracted beam andincident beams respectively. Substituting these relationships into Eq. (37) and using the relation ki = (wdc)n,,we obtain the coupled-wave equation

W,

dEo - j -kin;pS* dz 4 cos El "

(39)

In a similar manner we can obtain the first-order coupled-wave equation:

Note that for collinear propagation (i.e., = 0') Eqs. (39) and (40) are the same as those derived by Harris and Wallace The form of Eqs.

18

KLUDZIN GOUTZOULIS AND

and is similar to the form of Eqs. (17) and ( B ) , and therefore their solutions are similar. This means that the normalized intensity of the first diffracted order has a sinc2-type profile and isgivenby Eq. (22). However, the variables and u1 are different: 4

AKIL = 2 2 3 3 2

'IT n i n d p

Is[ 2L 2

Note thatq and u1 as derived from the Chang differential equations coincide with the variables derived by Harris and Wallace for the collinear case. (For a detailed derivation of Eqs. and see To calculate the normalized anisotropic diffraction efficiency, we follow the procedure used for the isotropic Bragg diffraction efficiency. For small values of u1 we find that is approximated by

A comparison of the expressions for the isotropic and anisotropic Bragg diffraction efficiencies (Eqs. and (43) respectively) shows that since for all practical purposes eo is small, cos eo = 1 and therefore the two expressions are similar. Note, however, that the factorn6 for the isotropic case has been substituted by n)n: for theanisotropic case. This means that, given the definition of the figure of merit M,, the anisotropic figure of merit, M,, is slightly different from M,:

Although the factor u1 is similar for the isotropic and anisotropic Bragg interactions, the factor is quite different, and as a result we obtain substantially different bandwidths for a given interaction length. To see this let us calculate the anisotropic interaction length L,. This can be achieved by following a proceduresimilar to the one used for theisotropic interaction length, and setting q = Using Eqs. (41) and we can write

+

(?),}

=

PRINCIPLES OF ACOUSTO-OPTICS

-

For 90" we find that cl = cos we write Eq. (45) as

19

and cos(O0 +

=

-sin eo, and

As we will see in detail, in the anisotropic interaction there is a natural center frequency, fc, which defines a frequency bandwhere the momentummatching conditions are matched overa broadband of acousticfrequencies. By defining this center frequency as fc = V(nj - n2,)ln/X0,by substituting this expression in Eq. (46), and by using the relation V = Af we obtain the relation 2niV cos eo

) + f)

2niVf sin eo

LOX0

-

(

=

0.45

(47)

When sin eo = Xo/niAcand V = Acfc, we obtain the relationship LJO cfc - f )' = 0.45 2n,v* COS eo Substituting in Eq. (48) the 3-dB bandwidth definition (i.e., Aj72 = fc - f) and solving for Af, we obtain 3.6niV2 cos eo (49) LJO Equation (49) defines the bandwidth achievable with the anisotropic A 0 interaction as afunction of the interaction length L,. To compare the anisotropic bandwidth, Af,, with the isotropic bandwidth, A&, we must compare Eqs. (49) and (33) when the same interactionlength is used, i.e., when L, = L . This gives (Af)' =

(Afa)' = 2fcAf (50) which shows that for the same interactionlength a significant bandwidth advantage is possible with the anisotropic interaction. This advantage is due to the fact that the required change in the Bragg angle around the center frequency is much smaller in the anisotropic than in the isotropic diffraction. We note that the bandwidth advantage increases the fractional bandwidth decreases; e.g., for25% fractional bandwidth (or Aflf, = 0.25) the advantage is a factor of 2.83 (i.e., Afa = 2.83 AA), whereas for 50% fractional bandwidth the advantage is a factor of 2 (i.e., Afa = 2 Af). We also note that the above calculations were performed under the assumption that the bandwidth is symmetric around the center frequency and the peak occurs at the center frequency. However, since for a given

20

K L UDZIN

GO UTZOULIS

acoustic direction there exist two momentum-matching frequencies, it is possible to choose momentum matching at two frequencies on opposite sides of f c and allow a 3-dB dip at f c . This phase-matching approach [9] will further increase the bandwidth by a factor of V?!. The bandwidth advantage of the anisotropic interaction also translates into larger interaction lengths when the same bandwidth is used; using Af, = Ah = Afand equating Eqs. (33) and (49),we find that the isotropic and anisotropic interactions lengths are related by 2fcL L, = Af Once again the advantage is a function of the fractional bandwidth; e.g., for 25% bandwidth L, = 8Li, whereas for 50% bandwidth L, = 4Li. The interaction length advantage translates in larger diffraction efficiencies, since for a fixed H the diffraction efficiency is proportional to L . In anisotropic crystals, two anisotropic diffraction geometries are possible [ (1) an ordinarily polarized kiwill result in an extraordinarily polarized kd, and (2) an extraordinarily polarized ki will result in an ordinarily polarized k,. In either case the frequency of the diffracted beam can be up- or downshifted depending on (1)the type crystal used, i.e., whether ne > no or ne < no, and (2) the direction of the acoustic wave. The polarization rotation makes multiple diffraction impossible, which means that Raman-Nath diffraction cannot occur in anisotropic media. The frequency dependence of the angles of the incident and diffracted optical beams, as measured withrespeci to theperpendicular to theacoustic wave vector, are very important in the design of anisotropic devices, and they can be calculated from the wave vector diagrams. With the aid of Figure 8 we see that theperpendicular to K, satisfies kd

COS 8 d

= ki

COS

0;

Components parallel to the acoustic wave vector (with negative) satisfy kd sin

ed

Od

positive and

Oi

+ ki sin Oi = K,

Squaring Eq. (52), solving with respect to sin2 Od, and equating this result with the expression for sin2 0d obtained from the square of Eq. (53), we obtain an expression for sin Oi as a function of ki, kd,and K,. Substituting the values ki = 2nni/Xo,k, = 2.rmd/X0,and K, = 2mf/V, we obtain the following relation of sin Oi and f:

PRINCIPLES OF ACOUSTO-OPTICS

21

Repeating the above procedure (while solving for sin2 0J, we obtain

Note that thefirst terms in Eqs. and (55) are similar to those occurring in isotropic Bragg diffraction (i.e., Eq. whereas the second terms are due to the anisotropic diffraction. The angles of incidence and diffraction are plotted in Figure 9 as a function of frequency. We note two specific regions: (1) the low-frequency region, for which the angular frequency selectivity is maximum if d0/af+ and which is determined by the frequency of the collinear interaction fk (it is discussed next), and (2) the middle-frequency region, for which the angular frequency selectivity is minimum if a0/af --f 0, and which is used for wideband deflectors. The center frequency, fo, of this region can be calculated by equating the two terms inside the brackets of Eq.

9 Plot of the angles of incidence and diffractionas a function of frequency for the anisotropic diffraction.

KLUDZIN

22

AND GOUTZOULIS

With reference to Fig. 8 we note that the general cseof anisotropic diffraction has two limitingcases. The first case (Fig. 10) involvesa collinear anisotropic interaction; i.e.,ki, and K, propagate in the same direction. In this case there exists a lower critical frequency fmi, below which Bragg diffraction cannot occur. This frequency is given by [l61 fk

= (ni -

V

Vhn -

A0

h0

nd) - =

(57)

This case is interesting because it allows phase matching of a given acoustic. frequency over a wide range of incident light directions. This is important in AOTFs because it allows large angular apertures [15, 171. The second case (Fig. 11)involves the degenerationof the two matching solutions and is called 90" or tangential birefringent phase matching. In this case K, is tangential to the inner circle, and phase matching can take place over a wide range of acoustic frequencies [l61 because, to the first order, the direction of K, does not change as theacoustic frequency changes. Two different types of tangential birefringent bandshapes are possible, and they are designated as single- and double peaked. see this, consider the general expression for the birefringent bandshape as a function of frequency given by [l81

Wave vector diagram for anisotropic diffraction with collinear propagation of light and sound.

PRINCIPLES OF ACOUSTO-OPTICS

23

Wave vector diagram for tangential birefringent diffraction. + where Lo = A2n/A, is a characteristic interaction length, Afm = f; wheref; andf; are the frequencies at which the Bragg angle is matched, andf, is the tangential frequency around which the birefringent bandshape is symmetrical. When Afm = 0, the bandshape has a single broad peak and no ripple within the passband. This case corresponds to exact phase matching at the tangential frequency. When Afh # 0, the bandshape has two peaks at = fo ? Afm/2, and it corresponds to the case where exact phase matchingoccurs at two symmetricfrequencies aroundf,. By choosing the two frequencies properly, we can maximize the bandwidth at the expense of a midband dip. In general, the double-peak approach results in maximum bandwidth and is most often used for wideband deflectors. The advantage of the double-peaked approach depends on the crystal characteristics and the device design. For example, Hecht [l91 using the double-peak approach with a 3-dB midbanddip, has demonstrated a bandwidth increase of about 35% over that of the single-peak approach. For.most birefringent materials, fo is in the GHz range; e.g., for shear propagation in LiNbO, fo 2.7 GHz at A = 633 nm, whereas for shear propagation in Ti02fo is 10.7 GHz, also at A = 633 nm. For many applications these high fo values are not useful, and therefore frequency tuning would be desirable. Such frequency tuning is possible, and it can be accomplished by tilting the interaction plane with respect to the crystal optic axis until the desired center frequency lies at the tangential phase match point in that plane 211. We note that the optical rotation approach usually results in input and outplrt optical beams with linear po-

fz

-

~

24

KLUDZIN

AND GOUTZOULIS

larization; however, some ellipticity may be possible depending on the rotation angle necessary and the optical wavelength. Note that for certain materials (e.g., TeO,) superior performance may be achieved when, in addition to optical rotation, acoustic rotation is used as well. In some cases the performance improvements include increased diffraction efficiency, increased dynamic range, and decreased acoustic attenuation. Unfortunately for TeO, these improvements come at the expense of shorter optical apertures because of increased energy walkoff produced by the acoustic rotation. Anisotropic diffraction is also possible in crystals exhibiting optical activity (e.g., TeO,) and in conjunction withcircularly polarized optical beams In such crystals right-handed and left-handed circularly polarized lightbeams face different refractive indices. When these waves interact with shear acoustic waves, the right-handed polarized light willbe diffracted and it will have its polarization changed to left-handed mode, and vice versa. This type of anisotropic interaction can be treated just like the birefringent case, with the differrence that the birefringence is interpreted in terms of optical activity. In this case however, Eqs. (54) and (55) must be modified as shown in The best-known example of an anisotropic optically active A 0 device is TeO, with shear-wave propagation along [110]. In closing this section we note thatanisotropic diffraction is possible in noncubic crystal classes and usually in conjunction with shear acoustic waves. The photoelastic coefficients involved are p - , p55, and p M . Note that shear waves can produce rotation of polarization even in optically isotropic materials (e.g., cubic crystals). However, we do not consider this as anisotropic diffraction because in these cases there is no birefringence. Anisotropic ,diffraction with longitudinal acoustic waves is also possible [24] if p41or an equivalent photoelastic coefficient is used.

3 ACOUSTO-OPTICMATERIALS An important stage in the design of any A 0 device is the choice of the A 0 material. The material choice is affected by several factors, which include the type of the A 0 device, the application requirements, and the quality of the available A 0 materials. In thefollowing sections we examine the effects of the A 0 materials on the design of A 0 deflectors (Chapter 2), A 0 modulators (Chapter and A 0 tunable filters (Chapter 4) for various applications and design approaches. In this brief review we discuss only those A 0 materials that are readily available and present minimum difficulties in terms of crystal growth and device processing. These materials and their most important properties are shown in Table 1. With the ex-

PRINCIPLES OF ACOUSTO-OPTICS

25

26

KLUDZIN

AND GOUTZOULIS

ception of Tl,AsSe3, the data shown in Table 1 have been measured by scientists of the St. Petersburg State Academy of Aerospace Instrumentation (St. Petersburg, Russia) over the last several years. These data are the average values over many samples, and thus they may differ from the data reported for the best samples elsewhere in the Russian literature. It may be of interest for the reader to compare these data with those reported in the Western literature [27-301 in order to evaluate the relative stage of material development. Table 1includes data (orestimates) for theacoustic nonlinearity constant (see Section which is of major importance in high-performance A 0 deflectors, because in most cases it determines the level of the third-order intermodulation products and thus the dynamic range of the device. Note that for glasslike materials, where the practical frequency band is limited by acoustic attenuation, the attenuation constant with reference to = '100 MHz is used. Also note that in crystals of the interesting materials KRS-5 (TIBr-TlI) and KRS-6 (TlCl-TlBr), the Russian scientists have observed a serious spread in the values of the optical absorption, the acoustic attenuation, and the M 2figure of merit. The information capacity of the A 0 deflectors and AOTFS isdetermined by the time-bandwidth product (TBWP), which is defined as the product of the device time aperture (T,) and the bandwidth Af. The TBWP is equivalent to the number of resolvable elements, defined as the ratio of maximum deflection angle over the angular spread of the diffraction-limited optical beam. As such, TBWP is an important parameterin A 0 deflectors, A 0 scanners, and AOTFs. In A 0 deflectors it determines the frequency resolution (when used in spectrum analyzers), the processing gain (spaceintegrating correlators), orthe number of parallel correlations (timeintegrating correlators). In A 0 scanners it determines the maximum number of different scanning positions, and in AOTFs it determines thespatial and spectral resolutions. In general, the maximum Af is determined by the octave AYf0 = 0.67, where fo is thecenter frequency. The maximum time aperture, T, = D/V, is determined by the maximum usable crystal length D,which in most cases is determined by the maximum acceptable acoustic attenuation at distance D from the transducer. Different acoustic attenuation critieria can be employed for different applications. For example, D can be determined by the distance at which fo drops by 3 dB, or the distance at which the difference between the highest and lowest frequency over Af is no larger than 3 dB, or yet the distance at which the highest frequency drops by no more than 3 dB. The acoustic attenuation in crystals has been studied extensively 321. It has been foundthat in room temperature the dominant mechanism

PRINCIPLES OF ACOUSTO-OPTICS

27

of acoustic attenuation is the Akhieser loss caused by relaxation of the thermal phonondistribution toward equilibrium. Woodruff and Ehrenreich [31] have derived a formula which describes the acoustic attenuation as a function of the acoustic frequency and temperature (T), and which measures the attenuation, a,in nepers per unit time:

where is the Gruneisen constant andkt is the thermal conductivity. From Eq. (59) we see that theacoustic attenuation is proportional to the square of the acoustic frequency and varies linearly with the thermal conductivity. In practice, however, it has been found [33,34] that for several popular materials the acoustic attenuation varies as a f", where n is a factor between 1 and 2 and which often depends on the frequency range used and thespecificsample. This is a notable point especiallyfor high-frequency A 0 deflectors where acoustic attenuation may become a major limitation. Chang [35] has reported that samples of GaP used with shear propagation along [l,- 1,0] have shown consistently a frequency dependence factor n of 1.5. In the Western literature, the acoustic attenuation is most often defined as

-

(60)

a(f) = aof"

where a. is the attenuation constant per unit length at 1 GHz, f is the frequency in GHz, and is a constant, which isequal to 2 for most crystals of interest. On the other hand, in the Russian literature, the acoustic attenuation is frequently described by .(nf) = n"a(f)

(61)

where x is a material-dependent constant typically from 1 to 2.5, and a(f) is the attenuation factor fora reference frequency. For example, for glasslike crystals, x 1 over a considerable frequency range. In large-aperature A 0 devices (such as deflectors and some types of AOTFs), acoustic attenuation acts as anexponential decay weightingacross To,which can be described by.

-

w(t) = exp[ -

(62)

The parameter a' is measured in nepers per second and is [36]

where r is the material acoustic loss constant in dBlcm-GHz*. We emphasize that in practical devices the acoustic attenuation along a propa-

28

GOUTZOULIS AND KLUDZIN

gation path is often higher than that predicted by Eqs. (62) and The additional losses may be attributed to (1) acoustic diffraction losses, (2) losses due toscattering from crystal impurities, acoustic beam walkoff, and (4) acoustic harmonic losses due to acoustic nonlinearities. In Fig. 12 we show a plot of the potential TBWP of the most common materials as a function of frequency. For this plot we used the Russianmeasured material parameters shown in Table 1 and the expression TBWP =

0.46E lo?*

--x

where fn is the frequency at which the acoustic attenuation coefficient has been measured. Furthermore,we have set a minimum acceptable level of diffraction efficiency -q = 1%/Win conjunction with a maximum input acoustic power density of 10 W/cm2. In Fig. 12 the frequency, f, beyond which q drops to unacceptable levels is denoted with an asterisk. Dashed lines show the TBWP as the frequency increases beyond fmax. Figure 12 shows that beyond fmax the TBWP decreases as a result of the increased

4

\

\ \

E

\ \

\

I

\

KRS *\

\

.- \

rI

\

*\ \

.o

\

I

+

12 Time-bandwidth productsas a function frequency for common A 0 materials. The material parameters used this plot are the average figures measured by scientists at the St. Petersburg State Academy Aerospace Instrumentation (St. Petersburg, Russia).

PRINCIPLES OF ACOUSTO-OPTICS

29

acoustic attenuation. It also shows that at the low-frequency region TeO, dominates (TBWP 3500), whereas at thehigh-frequency region LiNb03 dominates (TBWP An accurate estimateof deflector TBWP can also be obtainedusing the procedure developed by Youngand Yao [38]. They showedthat theTBWP available is determined by three key factors: (1) acoustic attenuation, optical aperture D,and (3) the acoustic beam spread determined by the transducer width L. The limitations imposed on theTBWP by these factors are described by the following equations:

-

lSh,

rh: TBWP TBWP

D’

2AC

[&l

2

where is the attenuation in dB per unit length at 1 GHz, and h,, h, are the acoustic wavelengths at the centerfrequency and 1 GHz respectively. This formulation assumes that the maximum fractional bandwidth is Af = f,/2,and that the transducer width L is related to the near-field distance D,,by D,,= L2/2A,,which is a validassumptiononly for acoustically isotropic crystals (see Section 7). We note that this formulation does not take intoaccount the acoustic spread along the transducer height; however, this effect can be minimized if anisotropic acoustic focusing or apodized transducer electrodes are used. The results of this procedure are best studied via a specific example. One such example is shown in Fig. 13 for a shear [l101 Hg2C12Bragg cell [39] with V = 347 and = 230.5 dB/cm-GHz2. This is an interesting example because Hg2C12is a very promising material in terms of (1) large TBWP, (2)long Tu,(3) large M2 (640 10-18s3/g), and (4) wide optical frequency range (UV to 20 km). As such, this material is well suited for long Tu, large TBWP l-D or 2-D A 0 deflectors, as well as noncollinear for large spectral transmission applications. Figure 13 shows how the crystal length, transducer interaction length, and acoustic attenuation limit the TBWP. It can be seen that the main limitations are imposed by the combination of acoustic attenuation andmaximum crystal length which for ourcase has been setto 10 cm. Fig. 13 shows, the maximum TBWP = 5184 is achieved for D = 10 cm, L 2 1.5 mm, and fo = 36 MHz. For higher frequencies TBWP is reduced because of attenuation, whereas for lower frequencies TBWP is reduced becauseof limited time aperture. Note

30

GOUTZOULIS AND KLUDZIN

10, ooo 9. OOO

t

Center Frequency (MHz)

13 Hg2C12Bragg cell resolution for shear propagation along [l101 as a function of frequency for various values of crystal length D and transducer width L,with acoustic attenuation constant r = 230.5 dB/cm-GHz2 8 dBIpsecGHz2).

that the TI3WP = resu1t.k based on Af = fo/2 = MHz and T, = psec (for D = cm), as well as the criterion that fo 'drops no more than dB cm away from the transducer. We emphasize that different TBWPs are possible if different criteria are used: (I) If an octave bandwidth is used, i.e., Af = and fo = MHz, covering the MHz band, the resulting TI3WP will be which is significantly larger than However, in this case the highest MHz) and lowest MHz) frequencies will undergo significant differential attenuation (5.3 and 1.3 dB respectively), which may not be acceptable in some applications. (11) reduce the differential attenuation, we can impose the condition that the

PRINCIPLESOF ACOUSTO-OPTICS

31

differential attenuation be kept to dB at the endof the crystal. In this case Af = 21 MHz and the TBWP figure becomes 6048 spots. When the acoustic attenuation is not the limiting factor, TBWP can be increased by folding the acoustic beam several times in the plane perpendicular to the interaction plane [40]. An example of this approach is shown in Fig. 14, where 45" comer reflectors are used to fold the acoustic beam so that thereflected acoustic beams propagate parallel to each other. An example [41] of such a device is shown in Fig. 15, where the original acoustic beam is folded 11 times that the resulting time aperture, Tf,is equal to 12T,, where T, is the time aperture resulting from a single, unfolded acoustic beam. To avoid acoustic mode conversion at each reflector, shear waves in high-quality fused quartz were used and resulted in a Tf of 250 psec anda 2.1-dB bandwidth of -20 MHz, i.e., a TBWP of 5000. This design can be extended to T, 1 msec for Af = 10 MHz, in which case TBWP = Note that the acoustic phase undergoes a change of 1~ upon reflection, and since each acoustic wave undergoes two reflections per folding the various acoustic beams are in phase withthe original beam.

-

""*"""" " " "

" " "

+""

" " "

14 Geometry of an device employing corner reflections for acoustic beam folding and increased time aperture.

32

KLUDZIN

AND GOUTZOULIS

15 Twelve-branch 2-D folded acoustic beam A 0 deflector employing shear waves in fused quartz with time aperture of 250 psec and a TBWP of 5000. (Courtesy of Westinghouse Electric Corporation.)

PRINCIPLES OF ACOUSTO-OPTICS

33

The advantages .of the corner approach are (1) more efficient use of the A 0 aperture, and (2) the path is folded in a nearly square-type format which allows the use of round optics with modest apertures. The disadvantages are (1) the loss of a part of the signal between successive reflections in a corner (i.e., where the acoustic signal propagates perpendicular to the original acoustic beam), and (2) the difficulty of fabrication. The 2-D acoustic beam folding can be extended to 3-D folding with the third dimension being along the optic axis. The aperture areaoccupied by a single channel in 2-D can accommodate as many channels as can practically be folded along the third dimension, and therefore3-D folding may increase the overall Tf by an order of magnitude. An example [41] of this type of device is shown in Fig. 16, where six planes are used, each containing five channels stacked along the optical axis. The width of each channel is 1 cm, and with D,,, = 10 cm the resulting Tf is about Fsec. In closing this section we note that in some cases acoustic beam folding is the only

16 Example of an deflector employing 3-D acoustic beam folding. This device uses six planes each containing five channels for a total time aperture of 0.6 msec. (Courtesy of Westinghouse Electric Corporation.)

34

KLUDZIN GOUTZOULIS AND

practical solution for achieving a large T,, given that nonfolded implementations may require pathlengths of the orderof a meter. For example, without folding the device of Fig. 15 would require a path length of 92 cm.

In Section 2 we showed that the Bragg angle changes with frequency, and therefore for wideband devices it is necessary to use a sufficiently narrow transducer that the resulting acoustic beam spread satisfies the Bragg angle requirements over the band of interest. Unfortunately this solution results in relatively small interaction lengths which limit the diffraction efficiency, especially in isotropic interactions. The alternative lution for maximizing the bandwidth-efficiencyproduct of any device is to steer the acoustic beam as a function of frequency. This can be accomplished via the use of a phased array transducer, which consists of multiple piezoelectric elements with fixed interelement phase shifts. By proper choice of the number of transducer elements ( N ) , array element size ( D ) , spacing (S), and phase (+), the acoustic beam will closely track the Bragg angle as the frequency changes. Thus, for a given frequency, the phased array transducer will radiate a greater portion the acoustic power in the desired direction, therebyincreasing significantlythe diffraction efficiency over a single-element transducer. Therefore phased array transducers are preferred, since they require less acoustic power and lower power densities to produce anequivalent effect with asingle-element transducer. The reduced power density also leads to reduced thermal gradients and reduced elastic intermodulation products and thus to increased dynamic range. The acoustic pattern resulting from a phased array transducer can be calculated bysolving the scalar wave equation for the givenboundary conditions However, since the same wave equation is applicable to either RF oroptical propagation, the acoustic pattern is similar to the RF pattern generated by a phased array antenna used to electronically steer a radar beam or to the optical pattern generated by a diffraction grating illuminated by an optical plane wave. Use of either approach shows that the acoustic beam profile can be determined by the convolution of the single-element transducer beam profile (element pattern) and the array diffraction field (array pattern). The geometry of a phased array transducer is shown in Figure 17 and involves a multielement transducer made on a single piezoelectric plate. Each transducer element is driven by an equal-amplitude signal whose phase is increased from element to element by an amount In practice, the incremental phase shift is equal to and it is achieved by connecting

+.

PRINCIPLES OF ACOUSTO-OPTICS DRIVE

3R

22

"""

-

35 42

"""

"""

"""

""" """

""" """

1 X

Planar phased array piezoelectric transducer geometry. the elements in series via alternating top and bottom connections. This type of phased array is called planar and allows the convenient manipulation of the total input impedance by combinations of series and parallel connections among elements. This is an important featurebecause it allows for relatively easy, wideband impedance matching even at high frequencies. The acoustic pattern the phased array is symmetrical with angle, 8, and frequency and it may have several sidelobes. The normalized power of this pattern, T(Of), can be calculated from standard diffraction grating theory or from phased array antenna theory [44] and is described by 1 sin(NTS(sin 8 - sin 8,)/A) sinc[ sin(.rrS(sin N 8 - sin 8,)/A) (68)

TDr 1'

where 8, is the beam steering angle and 8 is measured from the boresight. In Eq.(68) the ratio of sines represents the array pattern,whereas the sinc function represents the element pattern.An analysis of the acoustic pattern reveals some interesting properties the planar array which place some restrictions in the overall design. The element pattern represents the effect of a single transducer element and is symmetric with a single lobe that occurs at 8 = 0 and a series of decreasing sidelobes which cross zero at (TDsin 8)/A = mm for m = & 1, 2, . . . . The array pattern represents

GOUTZOULIS AND KLUDZIN the effect of acoustic interference from different elements andhas maxima (often called grating lobes) each of value W which occur when the denominator of the array pattern becomes zero, i.e., when sin 8 - sin 8, = mNS for m = 0, 1, 2, . . . . The array pattern will have a single lobe as long as S/A < [l + [sinO31]-l, which is always true if S < N2. In practice, however, S >> A, and therefore grating lobes will occur at angles 8' given by

*

sin 8' = sin 8,

* mA S

where m is an integer. Since the complete acoustic pattern is the product of the array and element patterns, the location of the grating lobes and the width of the element lobe are of primary importance in designing an efficient phased array transducer. In general, it is desirable to choose D small enough that the values of sinc[(nD sin 8)/A] are large for values of 8 that satisfy the Bragg angle conditions over the desired bandwidth. The array pattern is then steered as a function of frequency that the element pattern is enhanced by a factor of W . However, since for practical devices S >> A, the array patternwill exhibit multiple symmetric grating lobes. By properly choosing the width of the element lobe, we can weight down all but two of these lobes, that the final acoustic pattern will consist of two main lobes inclined in opposite directions with respect to the array plane. The angles of both acoustic lobes and e,,- for m = + 1 and m = - 1 respectively) vary as the inverse of the acoustic frequency; however, only one of these lobes is used for tracking the desired Bragg angle. The other acoustic lobe is generally undesirable because it consumes acoustic power, and it may result in a second parasitic Bragg diffraction, which in turn consumes a small part of the optical power [45], and it may increase the intermodulation products. Figure 18 shows the geometry of the acoustic lobes and the Bragg interaction, with the arrows showing the change in the direction of the lobes as the frequency increases. To minimize the parasitic Bragg diffraction and thereforeminimize the loss of light, a bevel is usually set at the acoustic face that at the center frequency, fo, the desired lobe propagates parallel to the crystal length. By setting the angle between the device and the input optical beam equal to the Bragg angle (atfo) we perfectly satisfy the Bragg condition for thedesired lobe, whereas we maximize the mismatch for the undesirable lobe, thereby minimizing the parasitic Bragg diffraction. To maximize the performance of the array, we require that 8, tracks the Bragg angle OB. Since in practice 8, is small, we can use the geometry

PRINCIPLES OF ACOUSTO-OPTICS Transducers

k-S-l

Geometry of the acoustic lobes and the Bragg interaction in a planar phased array transducer. The arrows show the change in the direction of the two main acoustic lobes as the frequency increases.

of Figure 17 to calculate 0, in terms 0, = tan 0, =

the phase shift 4 as

4 -

KaS where K, = 2 d A is the acoustic wave number. When 0 = IT,Eq. (70) becomes

e,

=

V -

2fS which shows that the steering angle is inversely proportional to the frequency. Unfortunately, the Bragg angle is a linear function of frequency and therefore steering errors will occur. Assuming that theincident optical beam makes an angle (inside the material) with respect to the plane of the transducer, we can define the steering error A0, as the difference between the total angle of incidence and the Bragg angle:

38

KLUDZIN

AND GOUTZOULIS

From Eq. (72) we find that for AOe = 0, the phase shift per element must satisfy

which shows that the phase shift required for perfect beam steering is a quadratic function of frequency and therefore thephased array will track the Bragg angle only over some frequencyrange. To minimize the steering error we can reason as follows [45]. Assuming that 8, = A/2A0, the total angle between the incident light and the composite acoustic pattern at the center frequency fo is W2A0 + A,,/2S. As the frequency changes, the total angle changes, and in order to make the Bragg angle increment equal to the angular increment of the acoustic wave front we should have

d d A [2A l+L]=O

(74)

Eq. (74) is satisfied at A = A,, when S = which shows that ideal matching exists only atf = fo. For any other frequency f,the steering angle is smaller by - fo)/f0]’. Given that the error is alwaysin one direction, it can be partially corrected by changing Oi such that there are two frequencies, fL and fH, on opposite sides of fo, for which perfect matching occurs. This is demonstrated in Figure 19, which shows the Bragg angle and the phased array steering angle as a function frequency. The maximum error occurs at frequency fi,which is equal to 0.5(fL + fH). If fL and fH are selected that the mismatch is symmetric around the center frequency, the midband mismatch can be compensated by the peak of the element pattern, which is also symmetric around the midband. The result is that the overall bandwidth is flatter than that of a sigle-element device. Procedures for determining the design parameter S and the adjustable parameter Oi as a function of fL and fH have been developed by Xu [7]. Once a set of fL and fH has been selected, the design proceeds with the calculation of S, D , and the optimal number N . Pinnow [46] has shown that the elementwidth D is given by 2cnw1 D =where the adjustable parameterC isdefined such that theargument of the element pattern in Eq. (68) isCT.Cischosensuch that the aperture pattern, sinc2(C7r), whenevaluated atfL and fH is large. Once the optimal

39

PRINCIPLES OF ACOUSTO-OPTICS

f

L

fl

f

”

Frequency

19 Bragg angle andphasedarray steering angle as a function of frequency. At frequencies fL and fH the error is zero, whereas at frequency f, the error is maximum.

D has been selected, the element spacing S can be determined as

The madmum mismatch that occurs at f i can then be determined [47]:

The mismatch at and around the midband results in a reduced efficiency interaction and, therefore,in a dip. Equations (77) and (68) show that since the mismatch effects the array pattern only, the number of elements N must be adjusted so that the resulting ripple is kept within a desired level. For a ripple level of P dB within the passband the optimal number of elements N is [48]

GOUTZOULIS A N D KLUDZIN

40

where the parameter E can be found from the magnitude P , expressed in dB, of the ripple at the midband given by

P

=

10 log

[ ~

si:G7cJ

(79)

Once N is determined the diffraction efficiency performance of the phased array transducer can be calculated. This can be accomplished by first calculating the ratio of the phased array interaction length, N D , to the interaction length Ls of a single-element transducer:

L

ND Ls

=-

The performance advantage, A,, of the phased array transducer with each element driven by 1/N of the total power is then [46]

where in practice the factor T ( O , f ) / wis somewhat less than 1 over the bandwidth of interest. Several planar phased arrays have been reported in the literature with the most notable being an A 0 deflector with a dual phased array structure [49] on X-propagating LiNbO,. In that device, the first array consisted of 31 elements and covered the 1.31-1.93 GHz range, whereas the second array consisted of 52 elements and covered the 1.92-2.60 GHz range. The diffraction efficiency improvement was about 6~ over that of a single element device. In practice, most reported planar phased array A 0 devices with single arrays have achieved efficiency improvements in the 2 x -5 x range for fractional bandwidths up to 50%, the performance being determined by (1) the parasitic acoustic lobe loss of 3 dB, and (2) the restricted number of elements in order to avoid more than 3 dB in-band ripple. In the stepped phased array structure [45] of Fig. 20 each step is driven separately by a transducer attached to its surface. Adjacent transducers are driven 7c radians out of phase via alternating top and bottom connections. The step height is such that at the center frequencyf, the acoustic wave front produced by all the transducers is perpendicular to the x direction. Given that each element is offset by 180" from its neighbor, this can be achieved by setting the step height equal to h = Ro/2,and it results ?n steps with an overall slope of Ro/2S. As the frequency changes, the combined acoustic wave front tilts so that the slope of the resulting wave front is h/2S, and therefore acoustic beam steering is possible. From Fig.

PRINCIPLES OF A CO USTO-OPTICS TRANSDUCERS

i

Figure 20 Stepped phased array piezoelectric transducer geometry.

20 we find that the steering angle 8, is 8, = tan 8,

. r r h KS S

= --

and for h = Ao/2 it becomes 8,

=

[A I]

I2s f

fo

From Eq. (83) we see that the ideal phase shift is, once again, a quadratic function of frequency, and since in practice this is not possible, errors will occur. The errors can be minimized and the array design can be optimized by following a procedure similar to that of the planar array. The stepped array has an advantage over the planar array in that a single acoustic lobe is generated and therefore the acoustic and parasitic optical losses are eliminated. This advantage is similar to the advantage gained by the use of an optical blazed grating which concentrates the diffracted light in a single order. The disadvantage lies in the difficulty of its fabrication, especially at high frequencies (>1 GHz) where A/2 is a few micrometers for most common A 0 materials. Most of the stepped arrays reported to date have 2-10 elements [50]. One of the highest-frequency stepped array transducers ever reported [47] is the N = 3 element array fabricated on PbMoO,, which exhibited a 3-dB bandwidth of 250 MHz covering the 140-

42

KLUDZIN

AND GOUTZOULIS

390 MHz frequency range, with a diffraction efficiency of 8%/100 mW. Chen and Yao have demonstrated a novel quasi-planar phased array with a center frequency of 2 GHz and a bandwidth of 700 MHz. The device was novel because it was fabricated on a planar transducer surface; however, it almost completely eliminated the second parasitic acoustic lobe, i.e. , it almost acted as a stepped array. The quasi-steps were accomplished by using an etched periodic silver substrate and consisted of 20 elements whose incremental phase was The resulting acoustic pattern consisted of a single acoustic lobe which contained about80% of the acoustic power. In closing this section we note that planarphased array transducers can be combined with birefringent phase matching in order to improve the performance of A 0 deflectors [52,52a]. For example [52], a 1.9-3.5 GHz LiNbO, with N = 6 and element spacing twice the size that is used in isotropic designs was demonstrated, with a peak diffraction efficiency of 7%iW at 0.83 pm.

5 ACOUSTO-OPTICNONLlNEARlTlES Acousto-optic devices can produce nonlinear responses which are due to acoustic nonlinearities and/or multiple linear A 0 diffractions. The acoustic nonlinearities occur mainly as a result of crystal lattice anharmonicities and distort the acoustic signal(s). Thus, an initially sinusoidal signal becomes distorted as it propagates, and this distortion is the source of harmonic generation. In general, the nth harmonic grows nonlinearly as a function of distance, it reaches a maximum, and then it decays. The exact form of this behavior depends critically upon the initial level of the signal, the nonlinearity of the crystal, and the acoustic attenuation of the crystal. Because the harmonics appear at frequencies which are integer multiples of the frequency of the original sinusoidal signal, they can be avoided by using an octave bandwidth, and thus their only effect is the depletion of power from the fundamental. However, when two sinusoidal signals at different frequencies fl and fi are propagating in a crystal, not only the harmonics of each but also the sums and differences of these harmonics will be generated. Inpractice, only two of these intermodulationproducts have appreciable levels and lie within the octave bandwidth. These are known as theelastic two-tone third-order intermodulation products (IMPs) and appear at frequencies 2f1 - f2 and 2f2 - fi. Third-order IMPs can also be produced from multiple linear A 0 diffractions and are known as the dynamic third-order IMPs. Light diffracted by the first signal can be rediffracted by the second signal and then rediffracted by the first signal. Both elastic and dynamic IMPS represent unwanted, spurious signals which degrade the spurious-free dynamic range

PRINCIPLES OF ACOUSTO-OPTICS

43

(SFDR) of the A 0 device, and thus they must be carefully analyzed when designing high-performance devices. In this section we discuss the behavior and the effects of the nonlinear responses. We first present a simplified analysisof the acoustic nonlinearities (Section 5.1) in order to give the reader a general understanding of the behavior of the harmonics generated by a sinusoidal acoustic signal as it propagates in an A 0 crystal. This is followed by a discussion of the thirdorder IMPS (Section 5.2) and their effects on the SFDR of an A 0 device.

5.1 AcousticNonlinearities Acoustic nonlinearities are produced when finite-amplitude waves are distorted as they propagate in the A 0 crystal. The spatial dependence of these nonlinearities can be calculated by solving the equation of motion for the simple case of a sinusoidal acoustic wave. To determine the equation of motion we must first relate the stress, T, and strain, S, produced in the A 0 crystal due to the presence of the acoustic field. For small acoustic amplitudes this relationship is linear and is described by Hooke’s law, which in tensor notation can be written as T = where is the elastic stiffness tensor. The tensor relationship can be also be written as Tij = Cijk,&, i,j,k,l = where a repeated index implies a summation over the index and where c+/ are the elastic stiffness constants. A further simplification in this expression is possible by using the abbreviated subscript notation, according to which Hooke’s law can be written as Ti = ci,.Sj,where i, j = 1, 4, 5, 6. (A detailed treatment of Hooke’s law, the transformation properties and theabbreviated subscript notation can be found in [64] and [65].) For large acoustic amplitudes the stress and strain are no longer linearly related, and we must modify Hooke’s law to take into account the higher-order elastic stiffness constants. In this case cijksk

cijklsksl

l+-+-+--* Cij c,

1

where Ti are the components of the stress, Sj are the components of the strain, and C,, c,,, CijkI, . . . are the second, third, fourth, . . . etc., order elastic constants respectively. For a longitudinal sinusoidal wave only the third-order elastic constants, c i j k , are significant and Eq. (84) reduces to

44

where Ir is the acoustic velocity and TNLis the nonlinear part of the stress, which can be calculated from Eq. (85). As mentioned, the acoustic nonlinearities result from the fact that an originally harmonic wave, while it propagates through a nonlinear medium, undergoes waveform distortions. These distortions result in a waveform whose leading-edge slope is much greater than that of the trailing edge and which asymptotically reaches a sawtooth shape. This propagating sinusoidal acoustic signal can be viewed as a sum of harmonics whose parameters depend not only on the nonlinear characteristics of the crystal and the power density at the fundamental, but also on the power absorption coefficients of the harmonics. The exact form of the various harmonics can be analyzed via Eq. (86) by (1) expanding the displacement into spectral components at the fundamental and harmonic frequencies, and (2) separating the terms with equal phase and frequency. This will result in two coupled-wave equations, the solutions of which will fully describe the harmonics as a function of distance, power density, crystal nonlinearities, and acoustic attenuation. ~nfortunatelythe exact derivation of these equations is complicated and lengthy, and therefore it is beyond the scope of this owever, we can present a simplified, approximate analysis [S5] which will give a qualitative understand in^ of the overall harmonic generation process. Let us assume that in the AO crystal there exist an infinite number of harmonics which constantly exchange energy. This process is illustrated graphically in'Fig. 21, in which the arrows connecting the various acoustic modes show the possible paths and directions of the energy exchange. As Fig. 21 shows, the most significant energy exchange occurs from the fundamental acoustic mode S1 to the harmonics s, (m = 2, 3, . . .). reference to Fig. 21 let us consider a thin layer, d x , of the A 0 crystal and write the amplitudes of the harmonics at its boundaries as S , and S, dS,. The increment, dS,, of the fundamental mode is negative and proportional to the instantan~ousvalue of the amplitude S , which is determined by both the acoustic attenuation at the frequency of S , and the depletion due to the energy transferred to the higher harmonics. The increment, dS,, of the higher modes contains both negative and positive components which are due to the acoustic attenuation at the frequency of S, and the pumping of energy from the f~ndamental.This situation can be described by two coupled-wave equations: ~

+

dS1(x) -

dx

- -[a,

+ (3,(S,)]S,(X)

dS2(x) - - -a2Sa(x) dx

+ P,S?(x)

PRINCIPLES OF ACOUSTO-OPTICS

45

Diagramillustrating the generation of acousticharmonicsandthe power exchanges between the harmonics in an crystal.

where &(x), &(x), and al, are the linear strains and the attenuation coefficients of the fundamental and the second harmonic respectively,p,@,) is a factor that depends on the power level of &(x) and denotes the depletion of energy to higher harmonics, and p, is a factor that denotes the depletion of energy from S1 to S,. In Eq. we have used a square-law relationship between the positive incrementsof the second harmonic ( and the fundamental (&(x)). This square-law dependence is determined by the square-law characteristics of the acoustic nonlinearity in Eq. (85). The solutions of Eqs. and can be found by taking into account the boundary conditions Sl(0)= Sl0, S,,,(O) = 0 and the conservation of energy. The solution of Eq. has the form

which shows that the amplitude of the fundamental mode&(x) decreases as a function of distance and is determined by (1) the factor exp[ -alx] which determines the naturalpower dissipation as thewave propagates in the crystal and which is not connected with the nonlinear properties of the medium, and (2) the factor exp[-P,(S,)x] which determines the attenuation resulting from the energy transfer to the higher modes. The second factor is determined by the acoustic nonlinearity of the material and dependson theamplitude of the fundamental mode (note that pl(0) = 0). The nonlinear coefficient PI is inversely proportional to the disconti-

GOUTZOULIS AND KLUDZIN nuity length L,: P1

=

Y' Ld

where is an empirical dimensionless coefficient, and whereLd is defined as the distance at which (without attenuation al) the particle velocity becomes discontinuous, i.e., at Ld the shape of an initially harmonic wave becomes sawtoothed. Note that the numerical value of Ld can be a convenient way to express the deviation from linearity of the A 0 material. The exact value of Ld is [54]

where is a material-dependent nonlinear constant determined by the second- and third-order elastic constants. For example, for longitudinal waves along the [loo] direction in LiNbO,,

Figure 22 shows experimental data taken for the two types of energy loss mechanisms, usinga longitudinal [l111 KRSJ A 0 deflector operating at 200 MHz. The top curve is a straight line, characteristic of the process of acoustic attenuation without any nonlinearity, and it was obtained by using a very low acoustic power density (1 mW/cm2). The lower curve shows the total acoustic loss, including the nonlinear factor Pl(Sl), and was obtained by using a much higher acoustic power density (0.5 W/cm2). Note that thesecond curve changes its asymptote at thepoint x = Io, which occurs when S,(x) is attenuated to thepoint where exp[ -alx] is the dominant factor. Also note that the exact value of Io is determined by the properties of the A 0 material and the input acoustic power density. Knowing the spatial dependence of Sl(x), wecanproceedwith the solution of Eq. (88). This solution is well approximated by

where is the attenuation coefficient at the second harmonic frequency. The coefficient is

PRINCIPLES OF ACOUSTO-OPTICS

47

9

22 Example of the attentuation of the fundamental mode as a function of distance in a KRS-5 crystal for input power densities of 1 mW/cm2 and 0.5 W/cm2. Longitudinal waves were used for propagation along [l111 with an input frequency of 200 MHz. where

and is a measure of the importance of the nonlinearity relative to that of dissipation. We note that the solution given by Eq. (90) is similar to those obtained in [37, 53, and 571. Figure 23 shows an example [37]of the theoretical and experimental spatial dependence of &(x) (curve l), S&) (curve 2), and (curve 3) (it is discussed next), for a longitudinal [OOl] TeO, deflector operating at 500 MHz with an input power density of W/cm2. The data of Fig. 23 are interesting because they show the changes in the power of the harmonics for both the forward-propagating waves (0-13 mm, left half of the plot) and forthe backward-propagating waves after reflection at thecrystal end (15-28mm, right halfof the plot). Note that the secondharmonic is maximized at distance x = I, from the transducer. The exact value of is determined by equalizing the gradients of the amplitude increase and decrease of the second harmonic:

GOUTZOULIS AND KLUDZIN

48

23 Experimental data showing the spatial dependencies of the acoustic modes (Sl, and S,) for longitudinal waves along [OOl] in a TeO, deflector for f = 500 MHz and for an acoustic power density of P,(O)= 4 W/cm2. Curve 1 corresponds to Pl(x), curve 2 corresponds to P2(x), and curve 3 corresponds to P,(x). The part of the plot to the left of the dashed line inthe middle, corresponds to the forward-propagating waves, whereasthe right part corresponds to the backward propagation after reflection at the crystal end.

Equation constant then

shows that does not directly depend on the nonlinear If the medium has considerable attenuation, i.e., if >> pl,

In

=

2a,

whereas if a1=

then

1

=

G

The data of Fig. show that the second harmonic goes through a null and then it increases again. This behavior can be predicted by evaluating Eq. (89) for the forward-moving wave (over x' = 0 to x' = where is the crystal length) and for the reflected moving wave (over x' = to x' = while taking into account the change in the sign of the amplitude of S&) for the reflected wave (for a detailed treatment of this subject see From Fig. we canalso see that theslope of the fundamental (curve 1)is smaller after thereflection, and this occurs because energy isreturning to it from the higher harmonics. This shows that the assumption implied

PRINCIPLES OF ACOUSTO-OPTICS

49

in setting Eqs. (87) and (88) about the nonreciprocity of the nonlinear interaction is not always correct-in a nonlinear interaction the parameters of the high harmonics are determined by the low harmonics, and vice versa. Having described the behavior of the fundamental and the second harmonic, we can now discuss the third harmonic, S3(x). The third harmonic is mainly the result of the cross interaction between the fundamental and the second harmonic, and it can be described by

The solution of Eq. (99) has the form =

yp$S:o[Ae-a3X +

where the coefficient

- Ce-(az+al+BdX

reflects the relationship between

and

(100)

p3, and

An example of the spatial distribution of S3(x) is shown in Figs. 23 and 24. The latter shows the calculated (solid lines) and measured (dots) normalized power of (curve 2) and (curve 3) as a function of distance from the transducer for a 240-MHz longitudinal wave propagating along [loo] in a KRSS deflector and for an input power density of 1.7 W/cm2. Figure 24 shows that there is good agreement between theory and experiment and that thebehavior of S3(x) is similar to &(x); they both increase as a function of distance fromthe transducer untilattenuation losses dominate. The higher harmonics can be analyzed in a similar manner and via the following generalized equation:

We note that, as the previous procedure and Eq. (104) show, in order to find the solution for the mth harmonic we must know the solutions for all the m - 1 harmonics. In general, the form of the higher harmonics is similar to the form of the second and third harmonics, and their overall power is decreasing as the order m is increasing.

GOUTZOULIS A N D KLUDZIN 0

10

20

20

30

40

Figure 24 Theoretical and experimental data for the spatial dependencies of the acoustic harmonics for longitudinal waves propagating along a [loo] KRS-5 A 0 deflector. For this plot f = 240 MHz, P,(O) = 1.7 W/cm2, and it is assumed that p 10, k = 4, (xl = 0.25/cm, and cx(nf) = n2.26(x(f).

-

5.2 Third-Order lntermodulation Products The dynamic IMPS have been analyzed by Hecht [58],who extended the Klein and Cook [2] solution of the optical wave equation to include multiple acoustic waves at different frequencies. This has resulted in an infinite set of coupled-wave equations, which in the Bragg regime are reduced to two because of the significant phase mismatch between higher-order modes. For the case of two input acoustic signals with small amplitudes, Vl and V2, respectively, Hecht’s analytic solution of the intensity, 12,-1,of the diffracted order at 2f1 - f2 reduces to

PRINCIPLES OF ACOUSTO-OPTICS

51

where I , and I2 are the intensities of the principal diffracted modes and V j can be calculated via Eqs. (2) and (9) as

kon3pSiL 4 cos 00 For small-amplitude signals the diffraction efficiency of the principal diffracted modes is proportional to the normalized drive power (V/2)2, and thus for two equal-amplitude signals the intensity 12,- relative to the intensity of the principal diffracted modes reduces to

Equation (107) is important because it shows that the intensity of the dynamic third-order IMPs depends exclusively on the diffraction efficiency of the device, and therefore in the absence of any acoustic nonlinearities the diffraction efficiency is the limiting factor of the SFDR. The elastic IMPs are due to acoustic nonlinearities, and they can be analyzed using either (1) a procedure similar to the one described in Section 5.1 for acoustic harmonic generation, or (2) via the use of Feynman diagram techniques to analyze the various diffraction processes. A solution based on the former approach has been found by Elston and Kellman [59], whereas solutions based on the latter approach have been found by Chang [60] and by Xu [7]. Elston and Kellman solved the acoustic equation of motion (Eq. (86)) by performing the following tasks. They first expanded the strain into its spectral components up to third order, which resulted in 12 frequency components. The resulting strain expression was placed into Eq. (86) and separated into 12 coupled-wave differential equations by collecting terms at the same frequency and phase. The spatial derivatives in each of the 12 equations were then taken while the temporal derivatives were simplified by recognizing that the desired solution is the steady-state solution, which allows the time derivatives to be set equal to zero. The resulting equations were further simplified by expanding the strain at each frequency component into its real and imaginary parts, and subsequently expanding the equations into their real and imaginary parts while selecting the phases so that the IMPs grow from zero. The last step in the analysis is the inclusion of acoustic attenuation into all 12 differential equations. The form of the final 12 equations is similar, with the equation for the 2f2 - fl IMP term written as

52

KLUDZIN GOUTZOULZS AND

where S,,S1, S,, Sl-,are the amplitudes of the strains at frequencies 2f2 - fl, fl, f,, fl - f, respectively, is the acoustic attenuation at frequency 2f2 - fl, and yo is a constant that determines the rate of energy depletion and is given by yo = IcNL1/4pv3, where p is the material density and C,, is a material-dependent nonlinear coefficient. The solution of the final 12 coupled-wave partial differential equations can be performed by a simultaneous numerical solution. Elston and Kellman [59] and Pape [61] have performed such numerical solutions for the cases of [loo] LiNbO, and [OOl] TeOz respectively. Figure 25 is based on the results obtained by Pape and shows the intensity of the various harmonics and IMPs as a function of distance from the transducer. The behavior of the IMPs is similar to the behavior of the second and third harmonics described in the previous section-they increase as a function of distance from the transducer until attenuation losses dominate. Note that in contrast to the dynamic IMPs, the elastic IMPs strongly depend on the distance traveled by the acoustic wave; i.e., the level of the elastic IMPs is a function of the aperture of the A 0 device. Analytical expressions of the elastic IMP intensity were obtained by Chang [60] usingFeynman diagrams (for a detailed treatment of the IMPs via Feynman diagrams see [7]). Chang showed that the intensity of the elastic IMPs depends on the actual process that gives rise to the elastic IMPs. The two most significantprocesses involve (1)a single A 0 diffraction by the acoustically generated IMPs which are due to the second-order acoustic nonlinearity, and (2) successive A 0 diffractions by the second harmonic and the fundamental. The intensities of the resulting IMPs are given by Eqs. (109) and (110) respectively:

c!)

(Wa) n3pL

4,-1

= 1.8

4 - 1

=

n3pL

where P is given by Eq. (92), f is the frequency, T, is the time aperture of the A 0 device, p is the appropriate photoelastic coefficient, and L is the interaction length. We can now compare the relative strength of the dynamic and elastic IMPs via Eqs. (107) and (109)-(110). This comparison is facilitated by introducing [60] a critical interaction length L, defined as L, =

P'.

PRINCIPLES OF ACOUSTO-OPTICS

p p [/p ........................................

........................................................

111 m

m

...................................

...........

/

.................. :... ............. ..............................

....... ......................

...........

\

.....,. ......................

.:

.........................

........................

:

........................

(........................

......

\ 111111111111111111

54

KLUDZIN

AND GOUTZOULIS

By substituting Eq. (111) into Eqs. (109) and (110) we obtain the following relationships:

L,-I

-

(3)

A direct comparison of Eqs. (107) and (112)-(113) shows that (1) when L, is small the dynamic IMPS dominate, (2) when L,IL > 0.58 the IIelastic IMP process dominates, and (3) when LJL > 1.29 the I-elastic IMP process dominates. Figure 26 shows an example [62] of an A 0 deflector in which the elastic IMPS dominate the dynamic IMPs. The data were taken for a longitudinal [loo] Tl,AsS, A 0 deflector with a TBWP of 400. The example of Fig. 26 showsthat for an input power of 5 dBm the elastic IMPs degrade the dynamic IMP-limited SFDR by over 30 dB.

Or---

Input Power (dBm)

26 Example of an deflector in which the elastic IMPS dominate the deflector dynamic IMPs. The data were takenfor a longitudinal [loo] Tl,AsS, with a TBWP of (From

PRINCIPLES OF ACOUSTO-OPTICS

55

In order to minimize the degradation of the SFDR due to acoustic nonlinearities, the interaction length L must chosen to be greater than 1.7 X L,, or, equivalently, wemustminimize L,. Maximizing L isaccomplished by using birefringent diffraction or phased array transducers, whereas minimizing L, is accomplished by choosing materials with low acoustic nonlinear constants and by using small TBWPs. Examples [63] of materials with low L, are longitudinal [l101 GaP and longitudinal [loo] LiNbO,.

6 ACOUSTIC COLLIMATION IN ANISOTROPIC CRYSTALS When sound propagates in an acoustically anisotropic crystal, the propagation direction of the acoustic energy vector (Poynting vector), K,, does not necessarily coincide with the direction of the acoustic phase vector (wave vector) K,. The angle between K, and Kp is called the power flow angle and depends onthe shape of the acoustic wave vector surfaceK,(+,?). The acoustic wave vector surface is called the slowness surface (or the slowness curve in 2-D) and is determined by the inverse of the phase velocity as a function of the propagation direction (determined by the angles and 'U) [M]. The powerflow angle depends on the shape of K,(+,?) because K, isnormal to the tangent to the slowness surface, whereas K, is radial to the slowness surface. Examples of slowness curves are shown in Figs. 27 and 28 for TeO, in the [OOl], [loo] plane and for GaP in the [l,-1,0], [1,1,-21 plane respectively. For isotropic materials the slowness surface is a sphere, and thus the power flow angle is zero. For anisotropic materials, however, the slowness surface can take a variety of shapes, and it can be convex or concave. In general, as the curvature of the slowness surface increases, the spreading of the acoustic energy increases as well. It is therfore desirable to find certain orientations in certain crystals for which the slowness surface curvature is reduced; this will result in an acoustic beam with a significant degree of self-collimation. In these cases, the acoustic beam spread due to acoustic diffraction can be significantlyreduced. (A treatment the properties of the slowness surface and its implications can be found in [65].) For example,the slowness curve for longitudinal waves propagating along the [OOl] direction in TeO, (Fig. 27) curves outward, and this will result in some spreading of the acoustic beam. This is indeed the case, as it can be seen from the Schlieren images of a 10-channel longitudinal TeO, deflector [66] (Fig. 29), for which the acoustic beams propagate along the [OOl] direction, whereas the optical beam propagates along the [OlO] direction (i.e., k, is perpendicular in the plane of Fig. 27). These Schlieren images showthe profiles of some acoustic beams inthe plane perpendicular

+

GOUTZOULIS AND KLUDZIN

2 -

E

3 2

>

gL

-2

; -3 -5

-3

-1

3

Inverse Velocity (s/rn>

27 Slowness curves

TeO,

x10

5 "

propagation in the [OOl], [loo] plane.

to the interaction plane. On the other hand, the slowness curve for shear waves propagating along the [l,- 1,0] direction in GaP (Fig. 28) curves much less, and therefore a significant amount of acoustic focusing is possible. This is indeed thecase as can be seen from the Schlieren images of a 64-channel shear GaP deflector [66] (Fig. for which the acoustic beams propagate along the [l,- 1,0] direction, whereas the optical beam propagates along the [l111 direction (i.e., is perpendicular in the plane of Fig. 28). Figure shows that acoustic focusing has minimized the effects of acoustic diffraction, and therefore adjacent acoustic channels do not overlap, thereby eliminating acoustic crosstalk. we will see, beside the elimination of acoustic crosstalk in multichannel deflectors, acoustic focusing has significantimplications in the design of deflectors because it allows longer time apertures, T,, or higher diffraction efficiencies [67]. In order to estimate the degree of the acoustic collimation, a parameter of anisotropy, has beenused [68-711,which is defined the first coefficient in the power series representationof the slowness surface. For a given material, the anisotropy parameter b is a function the elastic coefficients and is tabulated for the pure mode axis and different crystal

PRINCIPLES OF ACOUSTO-OPTICS

57 1: 2:

[l , l

*

[ l , l ,-21

c

-

:

I

I

-2 Inverse Velocity

I

I

1

2 x10

I

I

"

28 Slowness curves for GaP for propagation in the [l,-1,0], [1,1,-21 plane.

symmetries in It can be shown that the magnitude of the slowness curve in the vicinity of a symmetry axis can be approximated by the power series

+

where is the angular deviation (in radians) of the energy vector Kp from the direction of the pure acoustic axis. In this case, the deviation of Kp causes a (1 - 26)+ deviation in the direction of the phase vector K,. The energy vector deviation affects the near-field distance, which is defined as the distance away from the transducer for which the acoustic beam is collimated (at thatdistance the 4-dB points of the acoustic profile intersect the geometric shadow of the transducer). For an acoustically isotropic medium, the near-field distance, Di, is

+

58

GOUTZOULIS AND KLUDZIN

29 Schlieren images of acoustic beams in a 10-channel longitudinal TeO, deflector: (a) adjacent channels, (b) alternatechannels. For this device the acoustic beam propagates along[OOl], whereas the optical beam propagates alongthe [OlO]. The slowness curve (Fig.27) does not allow acoustic focusing and therefore acoustic diffraction results in overlapping betweenthe acoustic beams of adjacent channels and significant crosstalk. (From

PRINCIPLES OF ACOUSTO-OPTICS 59

30 Schlieren images of a @-channel shear GaP deflector which utilizes acoustic focusing to reduce acoustic crosstalk between channels. In this device the acoustic beam propagates along [l,- 1,0], whereas the optical beam propagates along [lll].The slowness curve (Fig. along [l,- 1,OJallows a significant amount of acoustic focusing which minimizes acoustic diffraction and acoustic crosstalk. (From [67].)

where H is the transducer aperture and A is the acoustic wavelength. For an acoustically anisotropic medium it can be shown that the acoustic diffraction scales by a factor 1 - 26, and thus the near-field distance, D,, becomes

60

GOUTZOULIS AND KLUDZIN

Equation (116) implies that if the A 0 time aperture is limited by acoustic diffraction in the plane perpendicular to the A 0 interaction plane, a considerable improvement of (1 - 2b)" is possible by properly selecting the direction of sound propagation. For the GaP example of Figs. 28 and 30, 1 - 2b = 0.0264 and therefore an improvement of 380, is possible. Values of the parameterb have been computedfor various crystals, and they range from -5.23 (for longitudinal waves propagating along the c axis in Zn) [69] to -0.5 (for fast shear waves propagating along the [l101 in KRS-6)[37]. When b is negative, 1 - 26 is greater than 1, and this indicates that the near field is closer to the transducer than it is for the isotropic case ( b = 0). Examples of the values of b are shown in Table 2 for several collimating directions in crystals of high symmetries. In practice, the value of b can be estimated for any given direction via the SchaeferBergmann patterns [72], which allow the visualization of the slowness curves. The Schaefer-Bergmann pattern of the plane perpendicular to the A 0 intersection plane can be obtained by the far-field A 0 diffraction pattern. A clear pattern can be obtained by generating the largest possible number of acoustic reflections at different angles in the plane normal to theoptical wave vector. This can be achieved by using a device with a reflective rear face and in conjunction with a low acoustic frequency. Figure 31 shows a photograph of a typical Schaefer-Bergmannpattern of the [1001, [OlO] plane of a KRS-6 crystal. This crystal belongs to the cubic symmetry and has two interesting propagation directions: (1) the [1001 for a pure longitudinal mode and (2) the [l101 for a fast shear mode. For the longitudinal mode

Table

Self-CollimatedModes in Acousto-Optic Crystals

Acoustic wave direction and Optical Acoustic acoustic vector wave velocity ofCoefficient A 0 material propagation direction PbMoO, NaBi(MoO,), TeO, GaP KRS-6 KRS-5

L, 29" XY L, 26" X Y L [l101 L [l101 Fs [l101 L [io01 FS [l101 L [loo] FS l1101

M2

(X

105 cm/sec) 4.33 4.6 4.46 6.46 4. i 3 2.31 1.3 2.11 1.135 2.08

b

0.35 0.343 0.486 0.277 0.487 0.228 0.5 0.202 0.5 0.437

[X

sec'/g) 2.0 0.5 1.0 44.0 7.0 100.0

-

175.0 -

250.0

PRINCIPLES OF ACOUSTO-OPTICS

61

31 Schaefer-Bergmann diffraction pattern in the [OOl] plane of a KRS6 crystal. The [OlO] and [loo] directions are along the horizontal and the vertical coordinates respectively. (Courtesy St. Petersburg State Academy Aerospace Instrumentation.)

along [lOO], b can be written as [68, 691

the inner cruve of Fig. 31 shows, the slowness curve for longitudinal waves along [loo] is almost flat, and therefore some acoustic collimation is possible. For this case it is easily shown that D, = 1.84Di. Note that the fast shear modealong [l101 has an anisotropy coefficient b which can be adjusted by changing the direction of the optical wave vector in the plane [OOl]. Unfortunately, the exact calculations for the required angular change of the optical wave vector are very complexand lengthy, regardless of the high order of crystal symmetry involved [69]. The collimating property of the acoustic anisotropy implies reduced acoustic power requirements. Thisis because the transducer height H , and thus the height of the acoustic column, can be reduced by a factor of (1 - 2b)0.5.Since the diffraction efficiency is proportional to 1/H,the overall

-

62

KLUDZIN

AND GOUTZOULIS

power efficiency is effectively enhanced by a factor of (1 - 2b)-0.5 (in comparison with the isotropic case, all other parameters being the same). Remember, however, that for a fixed input power this will result in increased acoustic power density, which could increase the acoustic nonlinearities and thereby reduce the dynamic range of the device. Finally, the collimating properties can be used in acoustic beam folding, where the losses due to diffraction spread often limit the overall performance.

7 ACOUSTIC MODE CONVERSION The design of specialized devices may require theuse of acoustic mode converters, which convert longitudinal waves to shear waves, and vice versa. In practice, the most frequent conversion requirement is a highly pure conversion from a longitudinal wave to a shear wave. Frequencyindependent mode conversion can be easily accomplished by taking advantage of the acoustic reflections at a stress-free crystal surface [@, 73, 741. In general, in an elastically isotropic crystal, a longitudinal plane wave incident on a stress-free surface at an angle €lL to the surface normal can give rise to two reflected waves: (1) a longitudinal wave at an angle equal to that of the incident wave and (2) a shear wave at a different angle The amount of acoustic energy transferred to each of the reflected waves varies as a function of the angle of incidence. At a certain angle, the excitation of the longitudinal wavecanbecome zero, and the acoustic energy can be fully transferred to the shear wave. There are two main objectives in the design of an acoustic mode converter: (1) precise orientation of the shear acoustic wave vector along a specific direction, and (2) maximum energy transfer from the longitudinal wave to the shear wave. The first design goal can be discussed with reference to Fig. 32, which shows the geometry of a longitudinal-to-shear mode converter. For an elastically isotropic medium the boundary con-

32 Schematic

a frequency-independentacoustic mode converter

PRINCIPLES OF ACOUSTO-OPTICS dition at the surface means that the total normal component of the stress is zero. Thisimplies that atany point along the surface, the phase variation for all components of the longitudinal and shear waves must be the same. With this in mind and from the geometry of Fig. 32, we find that

K, sin 0L

=

K, sin 0,

(118)

Equation (118) is the familiar Snell's law and shows that in order to propagate a shear wave at an angle 0, the angle of the incident longitudinal wave must satisfy

Note that the angle 0, is frequency independent, and since for all solids V , < V,, the angle of the reflected shear wave is smaller than the angle of the incident longitudinal wave. The second design goal is satisfied when the reflection coefficient, rL, for the longitudinal wave is zero. In an elastically isotropic medium, rL is

[@l rL =

sin 20, sin 20, - (VL/Vs)2cos' 28, sin 20L sin 20, + (V,/V# cos2 20,

which implies that in order for rL = 0, the following equation must be satisfied:

(2) 2

sin 20, sin 20, =

cos2 20,

Equation (121) has solutions when the ratio of the shear and longitudinal wave velocities, V , and V , respectively, satisfies V,/V, > 0.565. Therefore for an elastically isotropic medium both design goals can be satisfied if the angles and 0, satisfy Eqs. (119) and (121). For example, forfused quartz the angles 0, and 0, are 42" and 25" respectively. In general, once the optimum 0L and 0, have been determined, the shear wave can be steered to thedesired direction by properly choosing the crystal cut angle 0,. Note that because of reciprocity, the mode converter also operates in the opposite direction and can convert a shear wave to a longitudinal wave. The analytical design of the mode converter for elastically an anisotropic medium is considerably more difficult. This is because the incident longitudinal wave can now give rise to onelongitudinal and two shear reflected waves [64]. The reflected waves are not always pure shear or pure longitudinal, and thus three possible polarizations can be coupled at the reflecting surface. All these must be taken into account when designing the converter, and this generally requires extensive numerical computations.

64

GO UTZO ULIS AND KL UDZIN

Acoustic mode converters have several uses, mainly in high-frequency A 0 devices. In these devices, it is generally preferable to use longitudinalwave transducers because in solids V , < V,. This implies larger half-wave transducer thickness and lower static capacitance. Furthermore, since the radiation resistance ratio, R,/R,, of the longitudinal and shear waves is determined by

where [VL/VSlfand [VL/VSlm are the velocity ratios for the piezoelectric transducer and the transforming medium respectively, a higher radiation resistance is possible. Therefore the acoustic mode conversion technique can also be used as anefficient method for wideband impedance matching between the piezoelectric transducer and the driving electronics. Mode converters may alsobe useful in increasing the tolerance of crystal orientation. For example, propagation of shear waves along the [l101 direction in TeO, without significantwalkoff requires that the crystal is oriented with extreme accuracy (e.g., This is because the high elastic anisotropy in TeO, (and similarly inthe crystals Hg2CI, and Hg2Br2) leads to a significant difference between the energy and phase velocities. Since a good x-ray from an etched surface can provide an orientation to an accuracy of -OS", the potential for a walkoff of several degrees exists if only x-ray orientation is used. When a mode converter is used, any possible misorientation of the reflecting face can be compensated by correcting the angle 0,. This may be achieved withlarger tolerances (than the direct crystal orientation) if the crystal exhibits less elastic anisotropy for longitudinal waves along the KL direction. Mode converters can also be used in collinear devices, where they may provide significant flexibility inthe overall design given the collinear propagation light and sound, and the need for optically transparent transducer structures.

ACKNOWLEDGMENTS The authors would like to thank V. Kulakov for the English translation of the work ofProfessor V. Kludzin which was written originally inRussian, and Dr. D. Pape of Photonic Systems Inc., for providing the Schlieren images of the TeO, and GaP multichannel deflectors. A. Goutzoulis would like to thank Dr. M. Gottlieb and Dr. K. Yao for helpful discussions.

P ~ I ~ C I OF P ~ACOUSTO-OPTICS ~ S

65

1. Rytov, S, M., Diffraction of light by ultrasonic waves, Trans. SUAcad. Sci. Ser. Phys., No. 2 , 222-259 (1937) (in Russian). 2. Klein, W. R., and Cook, €3. D., Unified approach to ultrasonic light diffraction, I E E E Trans., SU-14, 123-134 (1967). 3. €3alakshiy,V. J., Parygin, V. N., and Chirkov, L. E., The physical principles of acousto-optics, Radio i Sviaz, Moscow, USSR (1985) (in Russian). 4. Nelson, D. F. , and Lax, M., Theory of the photoelastic interaction, Pkys. Rev. B , 3, 2778-2794 (1971). 5. Raman, C. V. , and Nath, N. S. N. ,The diffraction of light by high frequency sound waves, Parts 1, 2,2A, 406-412, 413-420 (1935); Parts 3-5,3A7 7584, 119-126, 459-465 (1936). 6. Narasimhamurty,T. S. ,Photoelastic and Electru-optic Properties of Crystals, Plenum Press, New York, 1981. 7. Xu, J., and Stroud, R., Acousto-optic Devices: Principles, Design, and A p plications, Wi’tey, New York, 1992. 8. Kogelnik, H. ,Coupled wave theory for thick hologram gratings, Bell System Tech. J . , 48, 2909-2949 (1969). 9. Chang, I. C. , Acousto-optic devices and applications, IEEE Trans. Sonics Ultrasonics, SU-23, 2-22 (1976). 10. Phariseau, P., On the diffraction of light by progressive ultrasonic waves, Proc. Indian Acad. Sci., 44A, 165-170 (1956). 11. Smith, T. M. , and Korpel, A. , Measurement of light-sound interaction efficiency in solids, I E E E J . Quantum Electron., QE-1 , 283-284 (1965). 12. Gordon, E. I., A review of acousto-optical deflection and modulation devices, Proc. I E E E , 54, 1391-1401 (1966). 13. Gordon, E. I. , Figure of merit for acousto-optical deflection and modulation devices, IEEE J . Quantum Electron. , QE-2 , 104- 105 (1966). 14. Dixon, R. W., Photoelastic properties of selected materials and their rele-

15, 16. 17. 18. 19.

20.

vance for applications to acoustic light modulators and scanners, J . Appl. Phys., 38, 5149-5153 (1967). Harris, S. E., and Wallace, R. W., Acousto-optic tunable filter, J . Opt. SOC. Am. , 59, 744-747 (1969). Dixon, €3. W., Acoustic diffraction of light in anisotropic media, I E E E J . Quantum Electron. , QE-3, 85-93 (1967). Nieh, S. T. K. , and Harris, S. E. , Aperture-bandwidth characteristics of the acousto-optic filter, J . Opt. SOC.Am. , 62, 672-676 (1972). Chang, I. C., and Hecht, D. L., Characteristics of acousto-optic devices for signal processors, Opt. Eng. , 21 , 76-81 (1982). Hecht ,D. L. ,Variable bandshapes in birefringent acousto-optical diffraction in LiNbO,, in Annual Meeting of the Optical Society of America, Tuscon, Arizona, Oct. 1976. Abstract: J . Opt. SOC.Am., 66, 1094 (1976). Hecht, D. L., and Petrie, G. W., Angle tuned axial birefringent acoustooptic deflectorsin TeO,, in Annual Meeting of the Optical Society of America, 1980. Abstract: J . Opt. SOC.Am., 70, 1611 (1980).

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AND GOUTZOULIS

21. Chang, I. C., Designofwidebandacousto-opticBraggcells, Proc. SPIE, 352, 34 (1982). 22. Elston, G., Optically and acousticallyrotated slow shear Bragg cells in TeO,, Proc. SPIE, 936, 95-101 (1988). 23. Warner, A., White, D. L., and Bonner, W. A., Acousto-optic light deflectors using optical activity in paratellurite, J . Appl. Phys., 43, 4489-4495 (1972). 24. Hsu,H., andKavage, W., StimulatedBrillouinscatteringinanisotropic media and observation of phonons, Phys. Lett., 15, 207 (1965). 25. Bagshaw, J. M., and Willats,T. E., Aspects of the performance of broadband anisotropic Bragg cells, GEC J . Res., 3, 256-260 (1985). 26. Demidov, A. Ja., Zadorin, A. S., and Pugovkin,A. V., Wideband abnormal light diffractionby hypersound inthe crystal LiNbOS,in Acousto-optic Methods and Technology for Information Processing, LETI, Leningrad, USSR, 1980, pp. 106-111 (in Russian). 27. Uchida, N., andNiizeki,N.,Acousto-opticdeflectionmaterialsandtechniques, Proc. IEEE, 61, 1073-1092 (1973). 28. Chang, I. C., Selection of materials for acousto-optic devices, Opt. Eng., 24, 132-137 (1985). 29. Elston, G . , Amano, M.,and Lucero, J., Materialtradeoff for wideband Bragg cells, Proc. SPIE, 567, 150-158 (1985). 30. Goutzoulis, A. P., and Gottlieb, M., Characteristics and desienof mercurous halideBraggcellsforopticalsignalprocessing, Opt. Eng., 27,157-163 (1988). 31. Woodruff, T. O., and Ehrenreich, H., Absorption of sound in insulators, Phys. Rev., 123, 1553-1559 (1961). 32. Pomerantz, M., Ultrasonic attenuation by phonons in insulators, in Proceedings of the IEEE Ultrasonics Symposium, Oct. 4-7, 1972, pp. 479-485. IEEE Catalog Number: 72CH0708-8SU. 33. Bolef, D., in Physical Acoustics, (W. P. Mason, ed.), Vol. IV, Part Academic Press, New York, 1966, p. 113. 34. Spencer, E. G., Lenzo, P. V., and Ballman, A. A., Dielectric materials for electro-optic, elasto-optic, and ultrasonic device applications, Proc. IEEE, 55,2074-2108 (1967). 35. Chang, I. C., High performance wideband Bragg cells, in 1988 IEEE Ultrasonics Symposium, 1988, pp. 435-439. 36. Hecht, D. L., Spectrum analysis using acousto-optic devices,Opt. Eng., 461-466 (1977). 37. Gusev, 0. B., and Kludzin, V. V., Acousto-optic measurements, Leningrad State University, USSR, 1987 (in Russian). 38. Young, E., and Yao, S-K., Design considerationsfor acousto-optic devices, Proc. IEEE, 69,54-64 (1981). 39. Goutzoulis, A. P., Gottlieb, M., and Singh, N. B., High performance acoustooptic materials: Hg,CI, and PbBr,, presented at the SPIE Symposium on Optical Signal Processing, Vol. 1704, Paper 22, Orlando, FL, April 20-24, 1992.

PRINCIPLES OF ACOUSTO-OPTICS

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Wenkoff,M. P., and Katchky,M., An improved read-intechniquefor optical delay line correlators, Appl. Opt., 9, Gottlieb, M., Conroy, J. J., and Foster, T., Opto-acoustic processing of large time-bandwidth signals, Appl. Opt., 11, Korpel, A., Adler, R., and Desmares, P., An improved ultrasonic light deflection system, presented at the IEEE International Electron Devices Meeting, Paper Washington, DC, October Born, M., and Wolf, E., Principles of Optics, Pergamon Press, Oxford, pp. Radar Handbook, 2nd ed. (M. Skolnik, ed.), Phased array radar antennas, in Cheston, T., and Frank, J., McGraw-Hill, New York, pp. Korpel, A., Adler,R., Desmares, P., and Watson, W., A television display using acoustic deflection and modulation of coherent light, Appl. Opt., 5, Pinnow, D. A., Acousto-optic light deflection: design considerations for firstorder beam steering techniques, IEEE Trans. Sonics Ultrasonics,SU-18, Yao, S. K., and Young, E. H., Two hundred MHz bandwidth step-array acousto-optic beam deflector, Proc. SPIE, Pape, D., Vasilousky, P., and Krainak, M., A high performance apodized phased array Bragg cell, Proc. SPIE, 789, Delaney, M. J., and Yao, S. K., Widebandacousto-opticBraggcell, in Proceedings of the IEEE Ultrasonics Symposium, pp. Coquin, G. H., Griffin, J. P., and Anderson, L. K., Widebandacoustooptic deflectors using acoustic beamsteering, IEEE Trans, Sonics Ultrasonics, SU-17, Chen, T. S., and Yao, S. K., A novel phasedarray acousto-optic Bragg cell, J . Appl. Phys., Chang, 1. C., Birefringent phased array Bragg cells, in Proceedings of the IEEE Ultrasonics 1985 Symposium, pp. Shah, M. L., and Pape, D. R., Ageneralized theory of phased array Bragg interaction in a birefringent medium and its application to TeO, for intermodulation product reduction, Proc. SPIE, 1704, Richardson, B. A., Thompson, R. R., andWilkinson,C. D. W.,Finite amplitude acoustic waves in dielectric crystals, J . Acoust. Soc. Am., 44, Breazeale, M., and Ford, J., Ultrasonic studies of the nonlinear behavior of solids, J. Appl. Phys., Kludzin, V., St. Petersburg State Academy of Aerospace Instrumentation, to appear. Gedroits, A. A., and Krasilnikov, V. A., Finite amplitude elastic wavesin solids and deviations from Hook’s law, Sov. Phys. JETP, (in Russian).

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GOUTZOULIS AND KLUDZIN Torguet, R., and Bridoux, E., Etude theorique et experimentale de la generation harmonique acoustique dans le molybdate de plomb, Rev. Phys. Appl., Hecht, D. L., Multifrequency acousto-optical diffraction,IEEE Trans. Sonics Ultrasonics, SU-24, Elston, G., and Kellman,P., The effects of acoustic nonlinearities in acoustoUltrasonics Symposium, optic signal processing systems, inIEEE pp. Chang, I. C., Multifrequency acousto-opticinteraction in Bragg cells,Proc. SPIE, Pape, D. R., Acousto-optic Bragg cell intermodulation product, in IEEE Ultrasonic Symposium, pp. Goutzoulis, A. P.,Davies, D. K., and Gottlieb, M., Thallium arsenic sulfide (Tl,AsS,) Bragg cells for acousto-optic spectrum analysis, Opt. Comm., 57, Amano, M., Elston, G., and Lucero, J., Materials for large time aperture Bragg cell, Proc. SPIE, Auld, B. A., Acoustic Fields and Waves in Solids, Vols. I, 11, Wiley, New York, Rosenbaum, J. F., Bulk Acoustic Wave Theory and Devices, Artech House, Norwood, MA, Pape, D., Multi-channel Bragg cells: design, performance, and applications, Opt. Eng., Hecht, D. L., and Petrie, G. M., Acousto-optic diffraction from acoustic anisotropic shear modes in Gap, in IEEE Ultrasonic Symposium, pp. Papadakis, E. P., Diffraction of ultrasound in elastically anisotropic NaCl and in some other materials, J. Acousr. Soc. A m . , Papadakis, E. P., Diffraction of sound radiatinginto an elastically anisotropic medium, J . Acoust. Soc. A m . , Papadakis, E. P.,Ultrasonic diffractionloss and phase change in anisotropic materials, J . Acoucst. Soc. A m . , Cohen, M. G . , Optical study of ultrasonic diffraction and focusing in anisotropic media, J . Appl. Phys., Schaefer, C. L., and Bergmann, L., Uber neue Beugungserscheinungen an Schwingenden Kristallen, Naturwissenschaften, 22, Kino, G. C., Acoustic Waves: Devices, Imaging, and Analog Signal Processing, Prentice-Hall, Englewood Cliffs, NJ, Dieulesaint, E., and Royer, D., Ondes Elastiques duns les Solides, Mason et C, Paris,

2 Design of Acousto-Optic Deflectors Dennis R. Pape Photonic Systems Incorporated Melbourne, Florida

Oleg 6. Gusev, Sergei V. Kulakov, and Victor V. Molotok St. Petersburg State Academy of Aerospace Instrumentation St. Petersburg, Russia

INTRODUCTION The acousto-optic (AO) deflector deviceis one the major practical applications of the interaction of light and sound in a crystalline material. A 0 deflectors are principally used in optical scanning and information processing applications. A 0 deflectors are superior to mechanical scanners in applications where high-speed and/or nonmechanical scanning is required. In optical information processing applications an A 0 deflector can be used as a spatial light modulator (SLM) for imparting electrical information onto an optical beam. The real-time operation the A 0 deflector coupled with the high fidelity with which it transfers electrical information to the optical domain usually makes it superior to otherSLM technologies in most practical optical processing applications. It is the SLM device of choice when signal information is to be processed. An A 0 deflector device, shown in Fig. 1, consists of a piezoelectric transducer mechanically bonded to a transparent crystalline material. An R F signal input to the transducer through an RF matching network is converted to a sound wave which travels through the A 0 crystal. The traveling sound wave forms a phase grating which diffracts an optical beam incident on thedevice. An A 0 deflector is created by designing the device that themajority of the diffracted light from a collimated incident optical beam appears in a single order whose spatial position is linearly propor69

70

PAPE ET AL. Undiff racted Light

Piezoelectric

Incident Light Acousto-optic Bragg cell.

Diffracted Optical Plane Wave

Plane wave 2 Acousto-optic Bragg interaction.

tional to thefrequency of the input RF signal. In such an arrangement the deflector is said to beoperating in the Bragg regime, and the deflector is commonly referred to as a Bragg cell. In Chapter 1 the Bragg interaction is described from a theoretical viewpoint with references to the primary literature. In this chapter we describe the interaction from a geometrical viewpoint in phase space which unifies the various interaction geometries into asingle framework and aids in the practical design of a deflector. The Bragg interaction is conveniently described using a phase (or momentum) space representation as shown in Fig. 2. Conservation of momentum in the interaction requires that the momentum vector of the diffracted optical plane wave kd, be equal to the vector sum of the momentum vectors of the incident optical plane wave ki, and the acoustic

uency

h

71

DESIGN OF ACOUSTO-OPTIC DEFLECTORS plane wave, K (directed normal to the transducer):

A 0 Bragg matching is a consequence of momentum conservation, where the magnitude of the acoustic momentum vector, K , is

where the angle between the incident optical beam and the acoustic beam is the Bragg angle (inside the A 0 crystal):

-

B -

h 0

2nA

Here n is the index of refraction of the A 0 medium, h, is the free-space optical wavelength, A is the acoustic wavelength, k = k, = kt = n2n/ho, and K = 2 d A . When the A 0 deflector is illuminated at the Bragg angle, the angle €lD between the undiffracted and diffracted optical beams exiting the cell is equal to twice the Bragg angle:

where A = v/f. Thus, the diffraction angle is proportional to the input RF frequency. Using this fundamental A 0 interaction phenomena, a wide range of practical A 0 deflectors has been designed and fabricated throughout the world over the past 20 years. The typical range of characteristics of these deflectors is shown in Table 1. The primary crystalline materials for A 0 deflectors include lithium niobate (LiNbO,),galliumphosphide (Gap), tellurium dioxide (TeO,), lead molybdate (PbMoO,), and fused silica. Table 1 Acousto-opticDeflector OperatingCharacteristics Characteristic Center Bandwidth Diffraction Time aperture Number of resolvable spots resolution Frequency Optical Maximumpower FW operating

Specificatio MHz-2

MHz

kHz-80

'

40 MHz-5 GHz 10 GHz 1-80%iW 0.05-100 psec 25-5000 20 0.3-10.6 pm

1w

PAPE ET AL. The design of an A 0 deflector entails a careful balance among requirements for bandwidth, diffraction efficiency, and time aperture. The bandwidth of the deflector, which, from Eq. (4), determines the total angular deflection of the Bragg cell, is clearly a primary A 0 deflector performance parameter. Diffraction efficiency, the efficiency with which the device diffracts light, clearly can determine the practical utility of a device in a particular application. Time aperture or,in spatial terms, the width of the optical aperture, as we shall discuss, is a fundamental measure of the frequency resolution of the device and, incombination withthe bandwidth, determines the number of resolvable deflector spots. These characteristics are discussed in Section 2, where they are linked to the key system operational parameters in scanning and information processing applications. The efficiency of an A 0 deflector is a function of the strength of the A 0 interaction in the device crystalline material as well as the degree to which the acoustic wave vectors are momentum-matched to the incident optical wave vector over the operatingbandwidth of the device. In Section we show the dependence of A 0 deflector efficiency on the chief device design parameters of material andacoustic mode selection and transducer geometry length and height specification. The group of materials useful for A 0 Bragg cells is those that exhibit strong A 0 interaction, low acoustic attenuation, low acoustic velocity, and small acoustic curvature. In Section we develop an A 0 material figure of merit that relates these material parameters to the product of the time aperture and the squareof the device operating frequency. A nomogram is produced which aids in material selection. Transducer geometry design guidelines are described in Section The degree to which the acoustic wave vectors are momentum-matched to the incident optical wave vector over the operating bandwidth of the device is dependent onthe length of the transducer and thespecific interaction geometry employed in the device design. In Section 5.1 we discussthe four major classes of A 0 interaction geometries: isotropic, anisotropic, phased array, and anisotropic phased array and the determination of the optimal transducer length within each class. The transducer height determines the angular extent of the acoustic plane waves in the direction orthogonal to both the acoustic and optical propagation directions. The height is optimized that the majority of the acoustic energy remains confined to the optical illumination aperture of the device. In Section 5.2 we discuss optimization of the transducer height as well as consider nonrectangular transducer configurations. The total efficiency of an A 0 deflector is, of course, entirely dependent on the degree to which the acoustic energy launched at the transducer remains inthe optical illumination aperture. Losses inacoustic energy from

DESIGN OF ACOUSTO-OPTIC DEFLECTORS

73

acoustic diffractian and attenuation degradethe efficiency of the deflector and are discussed in Sections 6 and 7, respectively. In Section 8 we summarize the design procedure for an A 0 deflector. In Section 9 we describe specific examples of A 0 deflector designs with the aid of computer design programs which encode the design equations developed in the previous sections. The design methodology described here is one in which the design of the A 0 deflector results in the material selection, interaction geometry, and acoustic mode and orientation selection, and transducer geometry specification. The specific design of the transducer, including material selection, composition, and the electrical impedance matching network are designed separately (and discussed in Chapter In Appendix A we provide a design program from the Petersburg State Academy Aerospace Instrumentation which combines these two designs into a single program. In this way the bandshape of the electrical impedance-matching network can be modified interactively withthe A 0 bandshape to achieve a desired frequencydependent A 0 deflector diffraction efficiency response.

The main performance parameters of an A 0 deflector are shown in Table 2. The key performance parameters of an A 0 deflector for a particular optical system application usually are diffraction efficiency, bandwidth, and time aperture. These characteristics are intimately connected, and it is the goal of an A 0 deflector design to optimize one or more the characteristics given specific performance requirements and A 0 material constraints. The diffraction efficiency of a deflector is usually expressed in units of %/W and is defined as the ratio of the percentage the incident optical beam which is diffracted (Id/Zi)to the applied RF power P, (expressed in Table 2 Acousto-opticDeflectorParameters

Characteristic Center frequency Bandwidth Diffraction efficiency Time aperture Time-bandwidth product

Parameter fc

Af ~D.E.

TB = rAf

RF input power

P

Optical wavelength (free space)

x,

PAPE ET AL.

74

watts). The diffraction efficiency of an deflector is dependent on both device frequency and time aperture. The totaldiffraction efficiency can be expressed as T(D.E.(f,.)

=

(5)

sin2

where (6) where is the efficiency, which ismaterial and transducer geometry dependent, q D is the efficiency lossassociated with the diffraction of acoustic energy outside the illumination aperture of the device, is the efficiency lossassociated with acoustic attenuation in the deflector, and is the loss associated with converting electric energy into acoustic energy at the transducer. The term isapproximately equal to the total diffraction efficiency when the efficiency is small. graph versus frequency showsthe bandshape the device and provides a visual display the chief performance parameters of the deflector. The bulk of this deflector which yields a uniform chapter deals with the design of an maximized 7)D.E.(f,T) over a specific frequency range and time aperture. The diffraction efficiency is an important optical system parameter because it determines theoptical throughput power of the system. Constraints placed on the optical power at the illumination source as well as the RF power at the deflector will ultimately dictate the usefulness of a particular deflector with a given diffraction efficiency. The bandwidth and time aperture of the deflector are also primary optical system application performance parameters, bothindividually and as a product-the time-bandwidth product. For a scanning application, the key system features are number resolvable spots andresponse time. The number of resolvable spots N of an deflector is the ratio of the total optical beam deflection angle A0 to the divergence angle A+ of the optical beam exiting the deflector: q(f9.1

=

7)A07)07)a7)TRAN

7)D.E.

The total optical beam deflection angle for an input RF signal containing a range of frequencies Af is, from Eq. (4), h0 Af A0 = -

The optical beam divergence angle is

A+

A0 nD

DESIGN ACOUSTO-OPTIC OF DEFLECTORS

75

where the exact equality is dependent upon the nature of the illumination optical beam. (For example, a Gaussian optical beam has a divergence angle (4/7r)(A&D).) The number of resolvable spots is then

where = D/v is the transit time of the acoustic wave across the optical aperture D of the device. The number of resolvable spots is thus the timebandwidth product of the deflector, TB. Since optical deflection is a result of the transit of the acoustic wave across the optical beam, the speed with which the deflector can access random positions is UT. For signal processing applications, the key systemfeatures, forspectrum analysis, bandwidth and frequency resolution and, for correlation, bandwidth and number of taps. Frequency resolution is just the ratio of the total bandwidth to the number of resolvable frequencies (spots): fres

=

Af

=

1

while for correlator applications, where the A 0 deflector acts as an optically tapped delay line, the number of taps is just N, the time-bandwidth product. Given the system application, and the associated specifications for the A 0 deflector efficiency, bandwidth, and time aperture,the process of A 0 deflector device design can begin.

EFFICIENCY The efficiency with which an A 0 device deflects light, is a product of the strength of the A 0 interaction in the device crystalline material, q M , and the degree to which the acoustic wave vector is momentum-matched to the incident optical wave vector. The strength of the A 0 interaction can be found through a coupledmode analysis (see Chapter 1 and [l])in which the A 0 interaction is described by an electric field wave equation where the index of refraction includes the acoustically induced index perturbation. The strength (for an isotropic interaction) is

76

ET

PAPE

AL.

where Po is the acoustic power at the transducer, L is the path length of the optical beam in the acoustic sound field, H is the height of the acoustic sound field, and OB,= is the Bragg angle at thefrequency (nominally center) of the device where momentumis exactly matched, andM zis an figure of merit dependint only on material parameters. The degree to which the acoustic wave vector is momentum-matched to the incident optical wave vector can be determined by examining the intensity distribution of acoustic plane waves from a finite-length transducer. The intensity of the angular spectrum of acoustic plane waves exiting the transducer of length L is

Exact Bragg matching, for a fixed Bragg angle, occurs only for the one acoustic wave vector directed normal to the transducer which satisfies the momentum-matching condition expressed in Eq. (1). The distribution of acoustic plane waves resulting from the finite-length transducer, however, allows Bragg matching to occur over a range of acoustic wave vectors directed the normal to the transducer. phase-space representation of this matching is shown in Fig. 3(a) for an isotropic Bragg interaction (other typesof Bragg interactions will be discussed in Section 5 ) . Here the optical wave vectors are confined to theoptical normal surface. The range

(a)

3 Acousto-opticinteraction: (a) plane-wave distribution and(b) resulting bandshape.

DESIGN O F ACOUSTO-OPTIC DEFLECTORS

77

of the component of the acoustic plane waves normal to the center frequency wave vector K is AKz = K -h 2 where is the angular range of the acoustic plane waves. Since 26y is equal tothe angular spread of diffracted optical wave vectors, the frequency dependence the intensity I d of the diffracted optical beam is

Id

=

sin(AKzL/2) AKzL/2

(

Io

)

The resulting A 0 bandshape is shown in Fig. 3(b). 'The product of the strength of the A 0 interaction and the intensity distribution is the A 0 diffraction efficiency defined as the ratio of the intensity of the diffracted optical beam to the intensity of the undiffracted optical beam: =

k? M2PoL sin(AKzL/2) 8 cos2 O&-I( AKzL/2

)

In the next section we describe a means of selecting A 0 materials which will maximize diffraction efficiency. 4 ACOUSTO-OPTICMATERIALSELECTION In the expression for the total deflector diffraction efficiency (Eq. (5)) all of the explicit material-dependent parametershave been grouped together into the A 0 efficiency (Eq. (16)) as an A 0 figure of merit M2. For an isotropic A 0 interaction, M2 is (see Chapter 1 and [2]):

n6p2

M, = where n is the A 0 material refractive index, p is the effective photoelastic coefficient, is the density of the A 0 material, and v is the acoustic velocity. The expression for diffraction efficiency, however, also contains terms which implicitlyincorporate material-dependent parameters. Inparticular, is dependent upon the material acoustic attenuation factor, L, when optimized, is dependent on material index of refraction and acoustic velocity, and H,when optimized, is dependent on acoustic curvature aswell as acoustic velocity. In order to compare different materials for optimum

78

PAPE ET AL.

A 0 deflector performance it is useful to separate thematerial-dependent terms from L , and H and incorporate them intoa new figure of merit. The loss in efficiency associated with acoustic attenuation, qa is a result of the absorption of power in the acoustic beam as it traverses the optical aperture of the deflector. The power in the acoustic beam P&) is reduced exponentially away from the transducer (in the acoustic propagation direction x ) as P,(x) = Poe-2”

(18)

where Po is the power at the transducer and a is the material attenuation constant measured in units of neperslcm. For almost all of the common A 0 materials the attenuation constant is a function the square of the acoustic frequency. The attenuation constant can be rewritten as ff ‘=

ffof

(19)

where is the frequency-independent attenuation coefficient usually measured in units of neperslcm-G**. The average acoustic power inside a deflector of width D (= is then

The relative loss associated with acoustic attenuation is then

which contains the material-dependent attenuation constant cq,. The length of the acoustic sound field, L , determines the regime in which the A 0 interaction occurs (Raman-Nath or Bragg). This length is dependent on acoustic wavelength (and hence acoustic velocity) and material index of refraction. L can be characterized by the Klein-Cook parameter Q [l](see Chapter l) as L =

QnAz cos 27rh0

where A, is the acoustic wavelength at the center frequency of the device operating bandwidth (A, = and where Q < 0.3 forRaman-Nath diffraction and Q > 7 for Bragg diffraction. Equation (22) shows the dependence of L on n and The transducer height determines the angular extent of the acoustic plane waves exiting the transducer in the vertical direction (orthogonal to both the acoustic and optical propagation directions). Near the transducer

DESIGN OF ACOUSTO-OPTIC DEFLECTORS

79

the acoustic field remains approximately collimated. The height of the transducer is designed that the time apertureof the device is within the collimated region, thus minimizing the amount of acoustic energy outside of the optical illumination region. The intensity of the angular spectrum of acoustic plane waves exiting a rectangular transducer of height H in the vertical direction is sin(TPH/A(l - 2b) aPHIA(1 - 2b) where the acoustic curvature factor 11 - 2b( is a measure of the acoustic anisotropy of the material [4]. An isotropic material has an acoustic curvature of l and hence a b value of 0. For materials with an acoustic curvature 11 - 2bl > (<) 1, the divergence of the acoustic waves is greater (less) than in the isotropic case. The collimated acoustic field region, known as the acoustic near-field or Fresnel region, extends into the cell a distance F away from the transducer where the width the Fraunhofer region (defined as the width of the first zeros of the sinc function) corresponds to thegeometrical shadow of the transducer, asshown in Fig. 4. The angular divergence of the acoustic beam at F is

Restricting the optical aperture D to the Fresnel region (i.e., D = F = VT) yields a transducer height (where = H/F)

H is thus also dependent on v as well as the acoustic curvature 1 - 2b.

D=VT

4 Transducer height optimization.

PAPE ET A L .

80

The material-dependent portions of the diffraction efficiency can now be rewritten as (substituting Eqs. (17), (21),and (24) into Eq. (12) r)materisl dependent

=

r)AOr)= PO

1 - e-2aovlfz

=M2n$2W3v7f2

TQ

4 f l f X i f z cos OB,^

(26)

= KMKAO where we have scaled the diffraction efficiency by the input acoustic power and where we have defined a new material-dependent efficiency term

and a material-independent efficiency term

The material-dependent term canbe further reduced by usingthe acoustooptic figure of merit M3 [5]: M3 = M2nv

The material-dependent term is now

In Fig. 5 we showa nomogram usefulin the selection of an A 0 material and mode for a particular center frequencykime-bandwidth product deflector design. In this figure KM is plotted versus 7f2on a log-log plot, yielding a frequency response of the acousto-optic efficiency for a number of commonly used A 0 materials. With a specific device center frequency, bandwidth, and time aperture, as well as an acceptable loss in A 0 efficiency, a particular material and mode can be selected. An interesting feature of this plot is that KM has an approximately constant value of l/ao over a certain range of ~ f ”values. With increasing values of 7 f 2 , KM uniformly decreases by 3 dBloctave. With an acceptable A 0 efficiency loss no larger than 0.6 of the maximum, we find that the maximum allowable frequency for a time aperture is

DESIGN OF ACOUSTO-OPTIC DEFLECTORS

81

0. O'O

F"'2

(S-')

5 Frequency response

I

o'6

acousto-optic efficiency.

The quantity . pm,, as well as the primary A 0 characteristics of the materials shown in the nomogram, are given in Table 3. While this nomogram is an aid in material selection, the Bragg matching performance of each material and mode must also be known to assess the ability of the material to meet the design requirements. There are four Bragg interaction geometries than can be employed in an A 0 deflector: isotropic, anisotropic, phasedarray, and anisotropic phased array. Isotropic interactions use a single transducer element in a simple momentum-matching configuration. This interaction provides acceptable A 0 deflector performance when the bandwidth is lessthan 500 MHz. Any of the materials shown in Fig. 5 may be used in this configuration. As can be seen from Table 3, most A 0 materials have velocities in the 3-7 mm/ psec range. The limits of crystal growth as well as optical system constraints usually limit device lengths to some 50 mm, which limits time apertures to less than about 10-15 psec. Exceptions to this are the slow shear mode in TeOz (an anisotropic interaction geometry) and Hg,Cl,. These materials have an order-of-magnitude slower velocity than the other materials in Table. 3 and thus device time apertures as long as 100 psec are possible.

82

PAPE ET AL.

a m 4 w n w b m

$I

m

DESIGN OF ACOUSTO-OPTIC DEFLECTORS

83

For bandwidths greater than 500 MHz, one of the other interaction configurations must be used. The anisotropic interaction involves Bragg matching betweenoptical wave vectors of two different polarization states. The center acoustic frequency involved in the Bragg matchingis determined by the birefringence of the material. Thus this interaction has a device center frequency constraint. The two most commonly used modesfor this interaction are the slow shear TeOz mode, where the center frequencies Y mode in are constrained to be less than 100 MHz, and the shear LiNbO,, where the center frequency is about GHz. The phased array interaction geometry uses a segmented transducer which spatially steers the acoustic beam in the device to achieve Bragg matching over a wide bandwidth. The advantage of this approach over the anisotropic approach is that the center frequency is not constrained by material parameters. Any of the materials shown in Fig. 5 may be used in thisconfiguration. The phased array geometrycanalsobeapplied to an anisotropic materialto allow some freedom the in choice of center frequency. The design of the transducer for each of these interactiongeometries is discussed in detail in the next section.

5 TRANSDUCERGEOMETRY DESIGN The efficiency (Eq. (16)) is dependent on both the acoustic beam length and the acoustic beam height. To theextent that the acoustic beam remains collimated in the device, the acoustic beam length is determined by the transducer length L , and the acoustic beam height is determined by the transducer height H . In this section we discuss the optimal design efficiency. of L and H as well as the illumination angle which maximize

5.1 TransducerLength We have already discussed three important criteria which influence the design of the transducer length. The first is that the strength of the A 0 interaction is directly proportional to the transducer length (Eq. In order to maximize the A 0 deflector efficiency we thus seek to maximize the value of L . Secondly, the sound field must be long enough to ensure that the A 0 deflector operates in the Bragg regime. This constraint (Eq. sets a minimum value for the transducer length:

The third consideration is that the divergence of the angular spectrum of acoustic plane waves in the length direction, and hence the bandwidth

PAPE ET AL.

84

of the device, is inversely proportional to L (Eq. (13)). This constraint places a minimum value of L consistent with bandwidth requirements. An L is usuallychosen that simultaneously optimizes both efficiency and bandwidth. Isotropic Interaction The Bragg interaction in an isotropic optical medium was historically the first A 0 interaction studied and utilized. It remains the most common interaction geometry used in deflector devices. A phase-space representation the isotropic Bragg interaction in an isotropic medium is shown in Fig.6, where thecircle is the optical normal surface whose radius is k. The range acoustic wave vectors present in a device is (found through the geometrical construction shown in Fig. 6) 2k8y AK

COS

=

4n AKJC COS h[l - (Af/2)*]

where the angular range of the acoustic plane waves, is equal to the sum of the angular spread at thelower band-edge frequency (ayL) and the upper band-edge frequency cos OB,c is the Bragg angle at the center frequency of the bandwidth Af of the deflector, and AKz, the range the component of the acoustic plane waves normal to both the lower bandedge frequency wave vector KL ( =272fLlv)and the upper band-edge fre-

6 Isotropicacousto-opticinteraction.

quency wave vector

AKz KLSyL = K&yu (34) where we used the facts that Af = fu - f L and fc = v;/ + is a measure of the momentum mismatch in the A 0 at the lower (upper) band edge frequency. Usually, a deflector is required to have a specified E dB bandwi~th;i.e. , the intensity of the diffracted light at the two extremes of the deflector bandwidth is required to be E dB below the intensity at the center frequency. The angular spread of the acoustic plane waves (Eq. (13)) is then designed so that I(SyL) = I(Syu) = lolO-E'lo.For the commonly specified 3-dB bandwidth deflector: =L:

or 0.971"

L,=-

In general, L,=C-

71"

(37)

where C == 1.0,0.9, 0.74,0.64,0.5 for 4-, 3-, 2-, 1.5,and 1-dB bandwidth specifications, respectively. In the case of a 3-dB bandwidth specification, substituting Eq. (33) into Eq. (36) yields the optimal transducer length for a 3-d deflector:

Likewise the expression for the transducer length for an E-dB bandwidth deflector, substituting Eq. (33) into Eq. (37), is

where C is as defined previously. Equation (39) specifies an optimum value of I, for a specific fractional bandwidth (Aflfc) and E-dB bandwidth specification. The value of I, should

86

ET

PAPE

AL.

not become smaller, however, than thevalue which ensures thatthe device is operating in the Bragg regime (Eq. (32)). The illumination angle is optimized to create a bandshape with equal intensities at the band edges. The optimized illumination angle is larger than theBragg angle at thedeflector center frequency because the angular range of acoustic plane waves in the upper half of the band is smaller than the angular range in the lower half of the band. The optimized incident illumination angle, is the sum of the Bragg angle at the center frequency and the angle (measured with respect to the normal to the transducer) of the acoustic wave vector which bisects the total angular spread of acoustic wave vectors over the bandwidth of the deflector (using Eq. (34)):

Anisotropic Interaction In theisotropic Bragg interaction exact A 0 Bragg matching occurs at one frequency. Bandwidth is achievedby momentum-matching the distribution of acoustic plane waves generated by the finite-length transducer. Wider bandwidth is achieved by reducing the length of the transducer to create a larger distribution of acoustic wave vectors. The utility of this design technique is limited because the efficiency of the deflector is proportional to the transducer length. In an anisotropic or birefringent interaction an acoustic mode is used which couples an extraordinary optical mode to an ordinary optical mode. With this technique A 0 Bragg matching over a large bandwidth is possible without resorting to unacceptable small transducer lengths (and hence efficiencies) The standard phase-space representation of the anisotropic Bragg interaction is shown in Fig.7 for a positive uniaxial crystal. The index ellipsoid consists of two surfaces; i.e., two independent linearly polarized optical plane-wave states are. allowed in the birefringement material. One state, the “ordinary” wave, is characterized by i directionally invariant index of refraction no. The other state, the“extraordinary” wave, is characterized by a directionally variant index ne. The optical normal surface of the crystal consists of a sphere of radius 21rnJX and an ellipsoid of revolution. In the standard arrangement the acoustic wave vector, K,is arranged to lie tangential to one of the optical normal surfaces of the birefringent crystal. Hence this interaction geometry is sometimes referred to as “tangential phase matching.” With this arrangement Bragg matching occurs over a larger range of frequencies than that available from the isotropic interaction (where the

DESIGN OF ACOUSTO-OPTIC DEFLECTORS

Figure

Anisotropic acousto-optic interaction.

Figure 8 Anisotropic acousto-optic interaction-wide bandwidth arrangement.

acoustic wave vector bisects the optical normal surface). Additional bandwidth is available by moving the acoustic wave vector horizontally away from the tangential condition that itlies on a line (the “Bragg matching” line) constructed parallel to the tangent. In this new arrangement two acoustic wave vectors intersect the optical normal surface, K, and K*, as shown in Fig. 8. Hence, exact Bragg matchingis achieved at two frequencies

PAPE ET

instead one. This results in a symmetric bandshape, peaked at two frequencies nominally equidistant from thecenter tangential matching frequency. To achieve an equal-ripple bandshape over a bandwidth Af, the Bragg matching line is placed a distance AK, away from the tangential line that it bisects the angular spread of acoustic wave vectors, 2 AK,. Using geometrical arguments, the range of acoustic wave vectors within the bandwidth of the deflector, AK = 2 ~ A f l vcan , be written as

(where the A C term is dropped as it is some three orders of magnitude smaller than kd). From considerations of the isotropic case we found that (Q. AKz = C -

L

where C, as before, determines the ripple in the bandwidth. Solving for the optimum anisotropic transducer length, L,, we obtain

In comparison to the isotropic design (Eq. (39)) the anisotropic transducer is approximately six times longer. (We note, parenthetically, that this length is twicethe length of the transducer required to achieve the same bandwidth when the tangential matching condition is used.) The optimum illumination angle for this configuration can be calculated by involving the conservation of momentum relationship (see Chapter 1). The conservation of momentum may be written both parallel and perpendicular to the acoustic wave vector: kd sin e d

+ k, sin

=

K

(44)

and (45)

kd sin e d = k, sin 8,

where Oi(Od) is the angle between the incident (diffracted) optical wave vector and thenormal to theacoustic wave vector. Solving these equations simultaneously leads to A nd sin 8d = n, sin 8, = fV

DESIGN OF ACOUSTO-OPTIC DEFLECTORS and

The illumination angle for tangential matching is determined by setting the frequency in Eq. (47) to the tangential matching frequency. From Fig. 7 we find that the length of the tangentially phased matched acoustic wave vector, K,, is

and hence the frequency at which tangential phase matching occurs, fi, is

fi = ; d v d

(49)

The tangential matching illumination angle is then

The optimum illumination anglefor the wide-bandwidth arrangement shown in Fig. 8 is slightly larger than the tangential matching illumination angle. The figure of merit M 2is slightlydifferent for theanisotropic interaction. It is defined as (see Chapter 1)

Anisotropic Interaction in Optically Active Materials Optically active materials are those in which the plane of polarization of a linearly polarized incident light beam is rotated upon passage through the material. Optical activity in birefringent materials results in a slight perturbation inthe optical normal surfaces. This perturbation breaks the degeneracy along the optic axes. The illumination angle for ananisotropic interaction (Eq. (47)) must therefore be modified for optically active materials [7]. Optical activity results from a difference in the velocity of optical propagation in the material for right and left circularly polarized light. The amount of rotation R (per’unit length) is

R=--6

h

PAPE ET AL.

90

where 6, the optical activity, is

a = - n, - n, 2no Near the optic axis the optical normal surfaces can be written as

n,(e) cos2 n; (1 - 6’) nf(0) COS’ n; (1 + ti2)

+ $(e) nasin2 +

= l

sin2 e = l n3

Equation (47) can then be rewritten for optically active materials as

Phased Array Interaction The phased array Bragg interaction utilizes a phased array transducerwhich behaves like a phased array antenna.As the frequency input to the deflector changes, the acoustic beam is steered spatially. Much like the anisotropic interaction, this effect canbeused to provide a more optimum Brzgg matching condition over a wide bandwidth and increase the efficiency of a deflector as much as six times over thatprovided by a conventional singleelement transducer [ 8 ] . Unlike the anisotropic interaction, however, the phased array geometry does not constrain the design of an A 0 deflector to a material-dependent device center frequency. The function and acoustic radiation pattern of a phased array transducer is shown in Fig. 9. The transducer is composed of N individual elements, each of length W on centers D.The total length of the transducer array is L (= ( N - l)D + W). Each element of the transducer is phase shifted by IT degrees with respect to the neighboring element. As a result of constructive interference, the resulting acoustic wave is steered off the boresight by an angle p given by (for small angles)

As the frequency is varied, the acoustic wave vector tracks along a line a fixed distance nlD away from the normal to the transducer array. The phase-space representation of the phased array Bragg interaction is shown in Fig. 10. The tracking line of the acoustic wave vector (which

DESIGN OF ACOUSTO-OPTIC DEFLECTORS Acousto-Optic Material

/

L " /

/

/

/

17/

/

/

/

/

/

/

/

/

"

I

-

/

/

Constructive Interference

/

N Element Phased Array Transducer

Phase

-L-

9 Phased array transducer.

10 Phased array acousto-optic interaction.

91

PAPE ET AL.

92

is normal to the transducer array) is designed to bisect the index ellipsoid at two points. Here, as in Fig. 8, the tracking line is a distance ITTTIDaway from the normal to the transducer. Exact A 0 Bragg matching is then obtained at two frequencies, similar to that achieved in an anisotropic design (Fig. 8). This results in, like the anisotropic design, a deflector with a broader bandwidth and higher efficiency than that obtained from the single frequency-matching condition of the simple transducer. The goal of a phased array A 0 Bragg cell deflector design is to provide a symmetric minimum-ripple bandshape with maximum efficiency for a specified bandwidth. This requires the optimum placement of the acoustic wave vector tracking line. The optimum position of the acoustic wave vector tracking line is found using geometric arguments with the aid of Fig. 10. To achieve a symmetric bandshape, the tracking line is established so the center frequency of the deflector is midwaybetween the two Bragg matched frequencies. For small angles, the center frequency acoustic wave vector intersects the tracking line at the midpoint between the two Bragg matched points. To achieve an equal-ripple bandshape, thetracking line is placed that it bisects the angular spread of acoustic wave vectors (similar to the anisotropic construction). The resulting optimum phased array transducer length Lpa,is 8nv2 (Afl’A the same as in the anisotropic case. similar geometric construction can be used to find the array centerto-center spacing D . Conservation of momentum requires that L,, =

-

Solving for D we find

The optimum number of phased array transducer elements N is then just

N =L D = C[8($)’

- 11

The optimum length W of an individual phased array element is found by considering the angular distribution of plane waves produced by the array [ g ] . This distribution of plane waves or the Fouriertransform of the

DESIGN OF ACOUSTO-OPTIC DEFLECTORS

93

array, by the convolution theorem, is composed of the product of the transform of an individual element and the transform of an N-element, alternating-sign, delta function array. The horizontal transform of an individual element, a broad sinc function with zeros at 1/W, scales the transform of the N-element delta function array, a series of sinc functions located at n/2D (n odd), each with zeros at 1/L. The main acoustic lobe is maximized by maximizing the broad sinc function, sin(vWp)/vp, at = 1/20, the location of the main lobe. The optimized ratio of the length of an individual element to thearray center-to-center spacing is found to beWID = 0.742. The optimum illumination angle for the phased array geometry is approximately the Bragg angle at the center frequency; i.e.,

Ad OB,= = sin" 2 2nv The A 0 efficiency for a single-element transducer (Eq. (16)) must be modified for the phased array transducer. The angular distributionof acoustic plane waves from a v-phased array transducer is similar to the angular distribution of optical plane waves from a diffraction grating [9]: I(y) =

(i)2ry)2(-) N sinsin Naa

where KD =

kW -sin 2

For Bragg matching to occur, = OB,i - OB,= Phased Array Anisotropic Interaction The tangential phase-matching frequency (and hence deflector center frequency) in an anisotropic interaction is fixed by the birefringence of the material. Using the phased array design technique (where the spacing of the individual transducer elements determines the deflector center frequency) in an anisotropic interaction removes this center frequency constraint. Using a phased array transducer in the anisotropic material thus provides additional design flexibility (as well as a much larger transducer area which reduces the acoustic power density and can, in some cases, reduce A 0 nonlinearities [ l o ] ) .

PAPE ET AL.

The phase-space representation of the phased array anisotropic Bragg interaction is shown in Fig. 11. The tracking line of the acoustic wave vector is designed to bisect the inner index ellipsoid at two points, similar to the isotropic phased array design (Fig. 10). As in both the anisotropic (Eq. and the phased array (Eq. (57)) interaction geometries, the optimum transducer length for the phased array anisotropic interaction is

A similar geometric construction to that used to find D in the isotropic phased array case can also be used to find the value of D for the anisotropic case. Conservation of momentum requires that

Solving for D we find D =

Ao(nr(03 - hoc (n,(€I,) - AoC ITIL)~ + (hof,/v)’

- n;(Oi)

(67)

The optimum number of phased array transducer elements N can be calculated as before from N = L / D , and, by the same arguments as before,

11 Anisotropic phased array acousto-optic interaction.

DESIGN OF ACOUSTO-OPTIC DEFLECTORS

95

the optimized ratio of the length of an individual element to the array center-to-center spacing is WID = 0.742.

5.2 Transducer Height The transducer height determines the angular extent of the acoustic plane waves exiting the transducer in the vertical direction. Near the transducer the acoustic field remains approximately collimated. In order tomaximize the acousto-optic interaction efficiency, the height of the optical beam illuminating the deflector is set equal to the transducer height, and the width of the optical beam is set equalto thetime apertureof the deflector, as shown in Fig. 4. The height of the transducer is designed that the time aperture of the device is withinthe collimated region, thus minimizing the amount of acoustic energy outside of the optical illumination region. As discussed in Section 4, the optimum transducer height is

Transducer Height Apodization The near or Fresnel region of the sound field is highly nonuniform in intensity [ll].This is a result of interference between the acoustic plane waves generated by the finite length and height transducer. This interference manifests itself as side lobes in the far or Fraunhofer region of the sound field. This nonuniformity in the near field and side lobes in the far field can be deleterious. In an A 0 system where the Bragg cell is imaged, the nonuniformity in the sound filed will result in a nonuniform optical diffraction pattern. If the optical beam extends beyond the shadow of the transducer, optical coupling to acoustic side lobes can occur, leading to unwanted diffraction. In an A 0 system where the optical beam does not fill the entirevertical height of the sound field, local variations in the sound intensity may severely impact the diffraction efficiency. The nonuniformity in the acoustic near field (and hence the side lobes in the acoustic far field) can be greatly reduced by shaping or apodizing the transducer. The effect and utility of apodizing the transducer in the height direction in the farfield is similar to windowing in harmonic analysis [12].Windows or shapes such as diamond (triangle), Gaussian, Hanning, Hamming, etc., can be applied in the transducer height direction [13].An example of a photomask for three different phased array transducer windows is shown in Fig. 12 [14].These apodization patterns, while resulting in a more uniform and lower-side-lobe beam, result in a larger acoustic divergence than the rectangular shape. To compensate, the transducer

AL.96

ET

PAPE

Figure 12 Phased arraytransducerapodizationpatterns.

height must be increased. Typically the height is made about 40% higher than for the rectangular case. With apodization, the acoustic side lobes can be reduced from the - 13-dB level for a rectangular shaped transducer to some - 30 dB.

5.3 CylindricalTransducer We have shown that the angular width of the acoustic plane waves exiting the transducer in both the acoustic sound field length and height direction is inversely proportional to the transducer length and height dimensions, respectively. Since the angular width of the acoustic plane waves in the length direction is directly proportional to bandwidth, decreasing the transducer length results in a larger-bandwidth device. Another technique which can be used to increase the bandwidth without decreasing the transducer length is to use a cylindrical focusingtransducer, as shown in Fig.13 (Such a transducer is formed using a piezoelectric thin-film material (see Chapter 6) deposited on the end of a cylindrically shaped A 0 substrate) [15-171.

DESIGN OF ACOUSTO-OPTIC DEFLECTORS

,

\

13 Cylindricaltransducer (top view). The angular spread acoustic plane waves exiting a cylindrical transducer of length L, is (from Fig. 13) LC 2R where R is the radius (focal length) of the cylindrical transducer. The spread of the acoustic beam is thus no longer inversely proportional to the transducer length, but, by changing R , can be adjusted independently of LC. This approach provides the freedom to increase the transducer length to reduce the power density in the device. The A 0 efficiency in this configuration is reduced from that of the flat transducer configuration, however, by an amount proportional to the increase in the width the angular spectrum. For a cylindrical transducer length equal to the flat transducer length L , the increase in the angular spectrum width, and hence decrease in efficiency, qc, is Tc

=

L2

2RA

This design strategy thus also has the disadvantage of,the conventional flat isotropic transducer design in that the diffraction efficiency decreases with increasing bandwidth. Also, as discussed in Chapter 6, the inherent efficiency the thin-film piezoelectric material required for thecylindrical transducer is less than that of the platelet material used to fabricate a flat transducer. 5.4

Multichannel Transducer

A multichannel transducer, unlike the phased array transducer, consists of individually addressable electrodes on the same transducer substrate. This structure is used to create a multichannel A 0 deflector, as shown in Fig. [M].The design of a multichannel deflector, with the placement

PAPE ETAL. I

,

Multichannel Bragg cell.

of multiple electrodes in close proximity on a common acoustic substrate, is constrained by crosstalk and thermal requirements not found in the design of a single-channel device. The design of a single-channel transducer of a multichannel Bragg cell follows the design procedures discussed in this section. As discussed in Section 5.1, the length of an individual transducer electrode is optimized for the bandwidth the device and the height of an individual electrode is optimizedto minimize acoustic diffraction in the device (see Section 5.2). The separation of the multiple transducer electrodes in a multichannel Bragg cell deflector is chosen to minimize acoustic crosstalk for a given time aperture. Acoustic crosstalk arises from diffraction spreading the acoustic wave in the transducer height dimension into adjacent channels. A coarse estimate of the crosstalk in a multichannel transducer can be found using the simple model shown in Fig. 15. From Eq. (23), the angle at which the acoustic beam has its first null, Po, is Po =

All - 2bl H

One simple way to calculate the acoustical crosstalk is to assume that all the acoustic energy between P = 0 and = Po intersects the adjacent channel beyond the optical aperture and thus does not contribute to adjacent channel crosstalk. The remaining acoustic energy between = Po and = d 2 does intersect the adjacent channel and thus contributes to

DESIGN OF ACOUSTO-OPTIC DEFLECTORS

99

Optical Aperture D

Region Crosstalk

15 Multichannel-transduceradjacentcrosstalkmodel.

adjacent channel crosstalk. Here Po is just

Po = tan-1[

]

S -DH/2

where S is the center-to-center spacing of the electrodes. Adjacent channel crosstalk IAcc, measured in dB, is then defined as 10 times the log of the ratio of the intensity of the acoustic energy intersecting a channel to the intensity the ambient acoustic energy in the channel when the adjacent is off

I&--

sin(.rrpH/A(l - 2b)) ~PHlh(1- 2b) = 10 log

sin(.rrpH/A(l - 26) rPHIh(1 - 26))

(73)

Conventional multichannel-transducer design methodology has been to that crosstalk within space the multiple transducers far enough apart the required time aperture is maintained below a given value. The disadvantage of this technique is that the throughput diffraction efficiency (defined as the product of the acousto-optic diffraction efficiency within each acoustic channel and the spatial duty cycle of the transducer array) is low. The size of such a device becomes exceedingly large for large numbers of channels. Also such devices can only be effectively used with multiple optical beam illumination.

l00

PAPE ET AL.

One way to increase the spatial duty cycle without increasing crosstalk is to apodize the transducer electrode [13,14]. By apodizing the electrode, the side lobes in the radiated acoustic energy beam can be reduced. Apodization, however, results in an increase in the width of the main beam which increases acoustic crosstalk and thus reduces the effective time aperture of the device. The increase in main beamwidth can be compensated by increasing the height of the transducer. Increasing the transducer height, however, leads to a reduction in diffraction efficiency. The most effective way of minimizing acoustic crosstalk in multichannel Bragg cells is through the use of acoustic anisotropy (see Chapter 1 and [18]). The acoustic beams in acousticallyanisotropic materials with acoustic curvature 1 - 2b near 0 remain approximately collimated and do not appreciably diffract into the adjacent channel. These “self-collimating” modes provide the means to simultaneously minimize transducer electrode spacing and adjacent channel acoustic crosstalk. This simple crosstalk model (Eq. (73)) shows the impact of the acoustic curvature 1 - 26 in adjacent channel crosstalk. For example, for H = 100 pm, S = 300 and D = 4.2 mm, the adjacent channel crosstalk in longitudinal mode TeOz (where l - 2b = 0.6) at an RF frequency of 300 MHz is - 16 dB, while for the collimated shear mode in GaP [l91 (where 1 - 2b = 0.026) it is dB. This simple model overestimates acoustic crosstalk because it does not consider the interaction of light with the acoustical beam. First, the leaking acoustic beam is diminished in energy from the main beam, leading to less light diffraction from the leaking beam, and secondly, the leaking acoustic beam is not as optimally Bragg matched as is the main beam to the incident light, also leading to less lightdiffraction. Experimental observation confirms a more rigorous integrated A 0 diffraction analysis, which shows that the adjacentchannel crosstalk in TeO, is about - 20 dB, while for GaP it is - dB [20]. A second consideration in multichannel transducer design is thermal dissipation. A large number of transducer electrodes confined to a relatively small volume can, when driven with sufficient RF power, lead to an excessive amount of heat dissipation at the transducer. While transducer degradation or failure must be considered, of more importantconcern are the thermal gradients that will form between the transducer and the edge the device. Thermal gradients will cause acoustic velocity and spatial refractive index gradients that can result in Bragg angle changes and unwanted optical beam deflection [21]. Materials with high thermal conductivity along with judicious use of heat sinking are required to minimize thermal gradients. GaP is also an attractive material from a thermal performance consideration since its thermal conductivity (0.545 Wkm-”C) is

DESIGN OF ACOUSTO-OPTIC DEFLECTORS

101

an order magnitude larger than that of the othercommon multichannel A 0 materials, TeO, and. LiNb03.

6 ACOUSTICDIFFRACTION LOSS Acoustic diffraction loss is the result the acoustic beam diverging from the transducer (in the vertical direction) outside the optical illumination region. An A 0 deflector is usually designedto avoid this loss by optimizing the transducer height that thecollimated (Fresnel) region of the acoustic beam coincides with the time aperture the device (see Sections and 5 ) . Other constraints (e.g., electric impedance matching; see Chapter however, manyresult in a transducer height smaller than optimum. In such a design the acoustic Fraunhofer diffraction region (where acoustic energy extends beyond the optical illumination region) extends into the time aperture, resulting in unused acoustic energy. The loss associated with acoustic diffraction can be calculated by comparing the area the optical illumination region to the area the acoustic beam, as shown in Fig. 16. We assume that the intensity of the optical beam is uniforminside the region shadowed by the transducerof area HD, where D is the time-aperture distance of the device. We also assume that the intensity of the acoustic beam is uniform over the collimated region HFplus the Fraunhofer region of area ( ( D - F)H + ( D - F)(H' - H)), where F is the collimated region distance and H = HD/F. The acoustic diffraction loss q D is then the ratio of these two areas: qD

= HF

+

HD H(D - F ) + (HD/F - H)(D - F )

-

Diffraction loss.

102

PAPE ET AL.

7 ACOUSTIC AlTENUATlON LOSS Acoustic attenuation loss is the result of the reduction in the intensity of the acoustic beam away from the transducer due to the absorption of acoustic energy by the A 0 material and theconversion of acoustic energy into heat energy. As discussed in Section the intensity in the acoustic beam is reduced exponentially away from the transducer as Z(x) = Zoe-2px

where Zo is the intensity at the transducer, x is the distance from the transducer along the optical aperture, and a is the material attenuation constant in nepers/cm. The attenuation constant can be rewritten as (see Chapter 1) a =

:'

(76) where a. is the frequency-independent attenuation coefficient, usually in nepers/cm-GHz*. It is sometimes more convenient to write the attenuation in terms of common logarithms: a =

aof

20 log,, e

where now a, is now measured in dB/cm-GHz2 can also be expressed in dB/psec-GHz2by multiplying by the velocity). The acoustic atteniation loss over the optical aperture D is

which, using D =

VT, can

also be written as

where now a, is now measured in dB/p,sec-GHz*.

DESIGN OF ACOUSTO-OPTIC DEFLECTORS

8 SUMMARY OF A 0 DEFLECTOR EFFICIENCY AND DESIGN PROCEDURE The total diffraction efficiency of an A 0 deflector, Eq. written (using Eqs. (6), (16), (74), and (79)) as l)D.E.

=

sin2hA0

1)D

can now be (80)

The procedure fordesigning an A 0 deflector that maximizes diffraction efficiency for a specified deflector bandwidth and time aperture is then Select an A 0 material and mode with considerations for large figure of merit K,,,, (Section 4). Select an A 0 interaction geometry (isotropic, anisotropic, phased array, or anisotropic phased array) (Section 5). Maximize the transducer length L consistent with bandwidth requirements (Section 5). Minimize transducer length H consistent with diffraction loss requirements (Sections 4 and 6). Calculate frequency and time-aperture-dependent deflector efficiency using Eq. (75) (with the loss from power conversionat the transducer calculatedusing the design procedures outlined in Chapter 5).

9 A 0 DEFLECTOR DESIGNS Following the design principals established in this chapter, we examine the design of five representative A 0 deflectors, each utilizing a different interaction geometry. For each interaction geometry design a computer program has been written in Microsoft Quick Basic. Each program follows the design methodology presented in this chapter. The user inputs the basic material parameters of the material andacoustic mode used in the deflector free space optical wavelength (LAM), index of refraction (INDEX), acoustic velocity (VEL), figure of merit M2 acoustic attenuation constant q,(ALPHAL), acoustic curvature parameter b (B), RF power (P), and bandwidth ripple specification C (C). The user also inputs the desired bandwidth (BW) and time aperture (TAU), and,when not constrained by an anisotropic interaction, the desired center frequency (FCENTER). Eachprogram first calculates the Bragg angle at thedesired cerlter frequency (BRAGGC). Then the optimal transducer length TRANL and the optimal transducer height

104

PAPE ET AL.

TRANH arecalculated. Each program then begins a loop where the values of AK, (DELKZ) for a number of frequencies within the bandwidth of the deflector are calculated. Within the same loop the A 0 efficiency (ETAAO) and the loss associated with acoustic attenuation (ETAALPH) are calculated. Finally the diffraction efficiency (ITEN) is calculated using Eq. (75). We assume in these designs that the transducer height is optimal and thus there is no diffraction loss (i.e., = 1). We also assume there is no conversion loss at the transducer (q= 1). Each program generates efficiency data in tabular form. These programs provide nominal values for L , H,and the illumination angle at the device center frequency. Once the program has calculated these values, the designer should vary these parameters by some 10% or to understand the trade-offs involved in changing L (and, in the case of a phased array transducer, W, D,and H , and the illumination angle to achieve an optimum bandshape. For this purpose it is convenient to link the program to a display routine that the.bandshape may be viewed in real time as the designer alters parameters.

9.1 500-MHz Isotropic Gallium Phosphide Longitudinal Mode Deflector A computer program which calculates the bandshape of an isotropic 500MHz bandwidth, l-psec time-aperture GaP longitudinal mode deflector is shown in Fig. 17. The longitudinal mode in GaP is particularly attractive for wider-bandwidth A 0 deflector devices because of its relatively high figure of merit and acceptable acoustic attenuation. The specific material properties for the L[110] GaP mode are n = 3.31, v = 6320 m/sec, = 8.0 dB/pec/GHz2, and M2 = 44.6 m2-sec/kg. The program calculates the Bragg angle at the desired center frequency (BRAGGC) using Eq. (3) and the nominal transducer length L (TRANL) using Eq. (39). The program then finds the optimum transducer height H (TRANH) using Eq. (25). The program then calculates the value of (DELKZ) using Eq. (37). Within the same program loop the A 0 efficiency (ETAAO) is calculated using Eq. (16), and the loss associated with acoustic.attenuation (ETAALPH) is calculated using Eq. (79). Finallythe diffraction efficiency ITEN is calculated using Eq. (80). We assume in this design that the transducer height is optimal and thus there is no diffraction loss (i.e., q D = 1). We also assume there is no conversion loss at the transducer (q= 1). Figure 18 shows a plot of the bandshape for this deflector as calculated by the program in Fig. 17. A center frequency of 770 MHz is selected, and a 3-dB bandwidth is specified. The transducer geometry parameters cal-

DESIGN OF ACOUSTO-OPTIC DEFLECTORS REM REM OPEN

#l

FOR OUTPUT

= = 5E+08

XC=(lAM'FCENTER/(2'VEL'INDEX)) BRAGGC=(ATN((XC)/SaR(1-XCA2)))'(1+(BW/(2'FCENTER))A2) TRANL=(2'C'INDEX'(VEL"2)^COS(BRAGGC)/(LAM'FCENTER'BW))

Is',

PRINT PRINT PRINT

IS', IS',

FOR

IF

TO

THEN

WRITE # l , NEXT END

17 IsotropicBragg cell design program-GaP example.

105

19 Isotropic GaP deflector bandshape: L = 14.0 mrad,

= 1 psec.

=

1.0 mm, H = 234.5 pm,

DESIGN OF ACOUSTO-OPTIC DEFLECTORS

107

culated by the program are L = 1.09 mm, H = 234.5 km, and Oi = 12.9 mrad. The calculated bandshape shows that the device does not achieve the 500-MHz 3-dB bandwidth as desired. The value of L is lowered to 1.0 mm (increasing bandwidth), and the illumination angle is increased to 14.0 mrad. Figure 19 shows a plot of the bandshape using these parameters. The bandshape shows a peak efficiency of 135%/W offset from the center frequency at about 800 MHz with a 500-MHz 3-dB bandwidth centered at about 750 MHz. An example of an isotropic GaP deflector is shown in Fig. 20.

9.2 1-GHz Anisotropic Lithium Niobate Shear Mode Deflector A computer program which calculates the bandshape of an anisotropic 1-GHz bandwidth, 300-nsec time-aperture LiNbO, shear mode deflector is shown in Fig. 21. This nominally tangentially phase-matched shear mode in LiNbO, is particularly attractive forwider-bandwidth A 0 deflector devicesbecause its highmatchingfrequency (2.5 GHz) and low acoustic attenuation (1 dB/ksec/GHz*) provide the possibility of achieving deflec-

Figure 20 Isotropic GaP deflector: center frequency 1.0 GHz, bandwidth MHz, time aperture 0.5 psec, and minimum diffractionefficiency 5O%/W at 632.8 nm. (Photo courtesy Crystal Technology.)

PAPE ET AL.

108 REM

FOR FOR =

= =

I

FCENTER=(VEUlAM)'SQR(INDEXl"2-INDEXD"2)

IS' XC=(LAM'FCENTEW(2'VEL'INDEXI)) BRAGGC=(ATN((XC)/SQR(1-XCA2))) TRANH=VEL'SQR((TAU*ABS(ld'B))/FCENTER) IF <=.00005

IS' IS' IS'

FOR

*(l+(((VEL/(FgLAM))"2)'(INDEXlA2-lNDEXD"2))) BRAGGF=ATN((XF)/SQR(1-XFA2))

IF

#l,

CLOSE

21 Anisotropic Bragg cell design program"liNb0,

example.

DESIGN OF ACOUSTO-OPTIC DEFLECTORS

109

tors with bandwidthsin excess of 1GHz. This mode is tangentially matched at anangle of 35"with respect to theY axis. The specificmaterial properties for the S[100] 35" Y LiNb03 mode are (at A = 815 nm) ni = 2.2556, nd = 2.1732, v = 3465&sec, % = 1.0 dB/psec/GHz2, and M2 = 17.9 m2-sec/kg. The program calculates the Bragg angle at thetangential matching frequency(BRAGGC) using Eq. (49) and thenominal transducer length L (TRANL) using Eq. (43). The program then finds the optimum transducer height H (TRANH) using Eq. (25). If the calculated height is smaller than 50 pm, the height is set at 50 pm for wire-bonding considerations. The program then calculates the value of (DELKZ) using Eq. (42). Within the same program loop the A 0 efficiency (ETAAO) is calculated using Eq. (16), and the loss associated with acoustic attenuation (ETAALPH) is calculated using Eq. (79). Finally the diffraction efficiency ITEN is calculated using Eq. (80). In this design the transducer height is taller than optimal, and thus there is no diffraction loss (i.e., q D = 1). We also assume there is no conversion loss at the transducer (q= 1). Figure 22 shows a plot of the bandshape forthis deflector as calculated by the program in Fig. 21. A center frequency of about 2.575 GHz is predicted, and a 3-dB bandwidth is specified. The transducer geometry parameters calculated by the program are L = 230 pm, H = 50 pm, and Oi = 271 mrad. The calculated bandshape shows the device operated at the tangential phase-matching condition with a 3-dB bandwidth of about 700 MHz. In order to achieve greater bandwidth, the illumination angle is increased slightly (by 3 mrad), and the transducer length is lowered to 200 pm (also increasing bandwidth). Figure 23 shows a plot of the bandshape using these parameters. The bandshape shows the characteristic double-peak efficiency. The device has a peak efficiency of 40%/W and a 3-dB bandwidth of about 1 GHz. The right-hand peak is lower than the left due to acoustic attenuation. Figure 24 shows an example of an anisotropic LiNbO, shear mode deflector.

9.3 32-MHz Optically Active Anisotropic Tellurium Dioxide Slow Shear Mode Deflector A computer program whichcalculates the bandshape of an optically active anisotropic 32-MHz bandwidth, 50-psec time-aperture TeO, shear mode deflector is shownin Fig. 25. The slow shear [l101 mode in Te02is unique in that it has a very high figure of merit (almost two orders of magnitude larger than other A 0 materials) and a very low acoustic velocity (about an order of magnitude lower than other A 0 materials). This makes the material particularly attractive for long time-aperture deflectors.

PAPE ET AL.

110

22 Anisotropic LiNbO, deflector bandshape:L Oi = 271 m a d , = 300 nsec.

=

pm,H = 50 Km,

The interaction geometry for this mode is shown in Fig. 26 [7].The degeneracy of the optical index surfaces is lifted by optical activity at the optic axis where a tangential phase-matching arrangement is used. The tangential matching frequency at A = 632.8 nm is 37.5 MHz. The specific material properties for the S[llO] TeO,, mode are (at A = 632.8 nm) no = 2.26, ne = 2.41, v = 616 &sec, = 17.9 dB/psec/GHz*, and M2 = 7.3 m2-sec/kg. The program uses a user-input center frequency near the tangential matchingfrequency as (FCENTER). The program calculates the Bragg angle at this frequency (BRAGGC) using Eq. (56) and the nominal transducer length L (TRANL) using Eq. (43). The program then finds the optimum transducer height H (TRANH) using Eq. (25). The program then calculates the value of (DELKZ) using Eq. (42). Within the same program loop theA 0 efficiency (ETAAO) is calculated using Eq. (16) and the loss associated with acousticattenuation (ETAALPH) is calculated using Eq. (79). Finally the diffraction efficiency ITEN is calculated using Eq. (80). In this design we assume no diffraction loss (i.e.,

DESIGN OF ACOUSTO-OPTIC DEFLECTORS

8, =

111

23 Anisotropic LiNbO, deflector bandshape: L = 200 pm,H = 50 pm, mrad, T = 300 nsec.

qD = 1). We also assume there is no conversion loss at the transducer = 1). Figure shows a plot of the bandshape forthis deflector as calculated by the program in Fig. 25. The program initially calculates a transducer length of 16 mm, resulting in a smaller-than-desired bandwidth and a transducer area which makes the device difficult to impedance-match. By decreasing the transducer length to 2 mm, a broader bandwidth is obtained (about a 2-dB bandwidth of 32 MHz) at a center frequency of about 48 MHz with a peak efficiency of about The transducer geometry parameters calculated by the program are L = 2 mm, H = 4.8 mm, and Oi = 23 mrad. An example of a slow shear TeO, deflector is shown in Chapter 1 in Fig. 1. Because the tangential matching frequencyfor this device is low, a large bandwidth is not obtainablewith this orientation. Also,circularly polarized light must be used to obtain the maximum diffraction efficiency. Alternative orientations have been investigated where either the direction of

(%-RAN

112

PAPE ET AL.

24 Anisotropic LiNb03 deflector: bandwidth GHz, center frequency 2.25 GHz, time aperture ns, and minimum diffraction efficiency of at 632.8 nm. (Photo courtesy of Westinghouse Electric Corporation.)

acoustic propagation is rotated away from the [l101 direction (“acoustically rotated”) or the optical illumination is rotated away from the plane containing the [l101 and [Ool] axis (“optically rotated”) While the first approach can yield a higher center frequency, the anisotropy of TeOz is so large that propagation away from the [l101 axis will lead to significant energy “walkoff.” The second approach also leads to higher-centerrequency devices, but the orientation allows Bragg matching to occur between the diffracted beam and theacoustic beam, resulting in a degeneracy at the midband. Design strategies for these two approaches are described by Xu and Stroud

9.4 500-MHz Phased Array Lithium Niobate Longitudinal Mode Deflector computer program which calculates the bandshape of a phased array 500-MHz bandwidth, 2-psec time-aperture LiNb03 longitudinal mode deflector is shownin Fig. 28. The longitudinal mode in LiNb03is particularly attractive for wideband large-time-bandwidth-product deflector de-

DESIGN OF ACOUSTO-OPTIC DEFLECTORS

II3

REM REM FOR

= = =

=

IS'

PRINT

XC=(LAM'FCENTER/(2~VEL*lNDEXD))'(1+((4'lNDEXDn2*((VEU(FCENTER*~M)~2))

BRAGGC=ATN((XC]/SQR(l-X0'2)) TRANH=VEL.SQR((TAU'ABS(1-2'B))/FCENT€R) IS'.

IS', Is'. FSTOP=FCENTER+(3'BW/4)+2'BW FOR

BRAGGB=ATN((XB)/SQR(1-~2))

+(((VEU(F'LAM)~2~((SlN(BRAGGB)'INDEXUlNDEXD)~2)~(lNDEXl~2-lNDEXDn2)))

IF

THEN

*(SlN(DELKZ*TRANL/2)/(DELKZ*TRANU2))A2

WRITE

25 OpticallyactiveanisotropicBragg ample.

cell designprogram-TeO,

ex-

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PAPE ET AL.

26 Slow shear TeO, anisotropic acousto-opticinteraction.

H

=

27 Optically active anisotropic TeO, deflector bandshape: L 4.8 mm, = 23 mrad, = 50 Fsec.

=

2 mm,

115

DESIGN OF ACOUSTO-OPTIC DEFLECTORS REM

=

=

B=-.

= XC=(LAM'FCENTEW(VEL*INDEX)) BRAGGC=ATN((XC)/SQR(1-XCA2)) D=INDEX'(VELAZ)/(LAM'(FCE~ERA2~(l-(((BW/FCENTER)A2)/8)))

-

.5

-

.5

TRANH=VEL'SQR((TAUgABS(l-2'B))/FCENTER) Is'. IS', IS', Is'.

IS',

STEP BRAGGF=ATN((XF)/SQR(l-XF"2))

ALPHA=(K*D/2)*(SlN(GAM)-SIN(Pl/(K'D)))

/(8'TRANH'(COS(BRAGGC))"2))'(1/N"2)'((2/P1)A2)

28 Phased array Bragg cell design program-LiNbO,

example.

PAPE ET AL.

116

vices because of its low acoustic attenuation (1 dB/psec/GHz2). The low figure of merit for this mode (7 X sec2/kg) makes it attractivefor the application of a phased array transducer. The specific material properties for the L[lOO] LiNb0, mode are (at A = 632.8 nm) n = 2.2, v = 6570 ndsec, a. = 1.0 dB/psec/GHz2,and M , = 7 X sec3/kg. The program calculates the Bragg angle at a 750-MHz device center frequency (BRAGGC) using Eq. (61), the nominal transducer length L (TRANL) using Eq. (57), and thenominal transducer center-to-center spacing D (D) using Eq. (59). The length of each individual element W (W) is found using WID = 0.742 (see the subsection “Phased Array Interaction”). The total number of phased array elementsN (N) is then calculated using Eq. (60). The program then finds the optimum transducer height H (TRANH) using Eq. (25). The program then calculates the value of (DELKZ) using Eq. (42). Within the same program loop the A 0 efficiency (ETAAO) is calculated using Eq. (16), where the sinc term is modified using Eq. (62) and the loss associated with acoustic attenuation (ETAALPH)is calculated using Eq. (79). Finally the diffraction efficiency ITEN is calculated using there isno diffraction loss (i.e., Eq. (80). In this designweassume q D = 1). We also assume there is no conversion loss at the transducer (TTRAN

= 1).

Figure 29 shows a plot of the bandshape forthis deflector as calculated by the program in Fig. 28. The transducer geometry parameters calculated by the program are L = 4.52 mm, N = 16 elements, D = 282.5 pm, W = 209.6 pm, H = 386.8 pm, €li = 32.8 mrad. The bandshape shows the characteristic double-peak efficiency. The device has a peak efficiency of 23%/W and a 3-dB bandwidth of about MHz. Figure 30 shows the experimentally measured bandshapeof a truncated Gaussian apodized phased array (bottom pattern in photomask shown in Fig. 12) LiNbO, deflector fabricated with these design parameters [14].

9.5 60-MHz Anisotropic Phased Array Tellurium Dioxide Slow Shear Mode Deflector A computer program which calculates the bandshape of an anisotropic phased 60-MHz bandwidth, 50-psec time-aperture Te02slow shear mode phased array deflector is shown in Fig. 31. -This design provides a wider bandwidth deflector than the conventional anisotropic approach without the use of rotating either the acoustic or optical wave vectors. The specific material properties for the S[110] TeO, mode are (at A = 810 nm), = 2.26, nd = 2.26, v = 616 m/sec, ce, = 17.9 dB/p,sec/GHz2, and M , = 7.3 X m2-sec/kg. The user inputs the desired center frequency (FCENTER), and the program calculates the Bragg angle at

DESIGN OF ACOUSTO-OPTIC DEFLECTORS

l17

.

I 500 MHz

I 750 MHz

I 1000 MHz

30 Phased array LiNbO, deflector experimentally measured bandshape

PAPE ET AL.

118

ANISOTROPIC PHASEDARRAY BRAGG CELL DESIGN PROGRAM REM PARAME3ERS ARE FOR SLOW SHEAR MODE TE02 OPEN "DATA" FOR OUTPUT AS #I Pl=3.14159 LAM = 8.1E-07 Kl=Z~PI~LAM BW = 5E+07 TAU=.00005 INDEXI=2.26 INDEXD=2.26 VEL=616 M2=?.3E-13 ALPHAO= 17.9 ALPHAL=ALPHAO"LOG(10)/10 B=-26.4 P=.l c=.53 FCENTER = 9E+07 XC=(LAM"FCENTE~(VE~INDEXI)) BRAGGC=ATN((XC)/SQR(1-XC"2)) TRANL=Cg8*lNDEXl'VEL"2/(BWA2~LAM) D=LAM"(INDEXI-(LAM'CTTRANL))I(((INDEXl~~LAM*C~RANL))"2) +((LAM* FCENTEW E L)"2)- 1NDEXD"2) W=.742"D IF (TRANUD)/2 lNT((TRANUD)/2) >= .5 THEN N=lNT(TRANUD)+l ELSEIF (TRANUD)/2 lNT((TRANUD)/2) < .5 THEN N=IN~(TRANUD) END I F TRANL=D*N ~ R A N H = V E ~ S Q R ( ( T A ~ * A S-2"B))IFCENTER) S(1 PRINT "TRANSDUCER LENGTH IS', TRANL PRINT "TRANSDUCER ELEMENT LENGTH IS",W PRINT "TRANSDUCER CENTER-TO-CENTERSPACING Is", D PRINT "NUMBER OF TRANSDUCER ELEMENTS Is",N PRINT "TRANSDUCER HEIGHT IS", TRANH PRINT "ILLUMINATIONANGLE IS", BRAGGC BRAGGC=.0516 FSTART=FCENTER-(3"BW/4) FSTOP=FCENTER+(~BW~4) FRES=BW/30 FOR F=FSTART TO FSTOP STEP FRES XF=LAMgF/(2'VEL*INDEXl) BRAGGF=AlN((XF)/SQR(1-XFA2)) GAM=BRAGGF-BFWGGC IF GAM=O THEN GAMslE-32 K=2"P I"F/VEL BETA=(K"W/2)*SIN(GAM) ALP HA=(K" 012)" (SIN(GAM)-SIN( P I/(K"D))) IF ALPHA=O THEN ALPHA=IE-32 ETAAO=((K1"2"P"M2"TRANL)/(8"TRANH"(COS(BRAGGC~)"2)~~( 1/NA2)*((2/P1)"2) "((SIN(BETA)/BETA)"2)"( (SIN( N*ALPHA)/SIN(ALPHA))"2) ETAALPH=( 1*EXP(-ALPHAL*((((F)/l E+09))"2)*TAU*lOOOOOO~)) /(ALPHAL"( ((( F)/1E+09))"2)*TAU* 1OOOOOOi) ETA=ETAAO"ETAALPH lTEN=SlN(SQR(ETA))A2 RITE # l , F/lOOOOOO&,lTEN*lOOO NEXT CLOSE #1 END

-

-

Anisotropic phased array Bragg cell design program-TeO,

example.

DESIGN OF ACOUSTO-OPTIC DEFLECTORS

119

the tangential matchingfrequency (BRAGGC)using Eq. (61), the nominal transducer length L (TRANL) using Eq. (65), and the nominal transducer center-to-center spacing D (D) using Eq. (66). The length of each element “(W)isfoundusing WID = 0.742 (see the subsection “Phased Array Interaction”). The total number of phased array elements N (N) is then calculated using Eq. (60). The program then finds the optimum transducer height H (TRANH) using Eq. (25). The program then calculates the value of (DELKZ) using Eq. (42). Within the same program loop the A 0 efficiency (ETAAO) is calculated using Eq. (16), where the sinc term is modified using Eq. (62), and the loss associated with acoustic attenuation (ETAALPH) is calculated using Eq. (79). Finally the diffraction efficiency ITEN is calculated using Eq. (80). In this design we assume there is no diffraction loss (i.e., q D = 1) and no conversion loss at the transducer (%RAN

=

Figure 32 shows a plot of the bandshape for this deflector calculated by the program in Fig. 31. A center frequency of about 85 MHz is predicted,

120

PAPE ET AL.

Phased array TeOz deflector. (Photo courtesy Incorporated.)

Photonic Systems

and a 3-dB bandwidth of about 57 MHz is predicted. The high acoustic attenuation in this material is responsible for the low right-diffractionefficiency peak. The transducer geometry parameters calculated by the program are L = 1.7 mm, N = elements, D = pm, W = pm, H = 3.37 pm, Oi = mrad. The illumination angle was lowered to mrad to achieve a more symmetrical 3-dB bandshape. The device has a peak efficiency of 44%/W. Figure 33 shows an example of a phased array TeO, deflector designed using these parameters which achieved a peak diffraction efficiency of 30%/W.

ACKNOWLEDGMENTS The authors would like to thank V. S. Kulakov for the English translation of the work of Gusev, Kulakov, and Molotok, which waswritten originally in Russian. D. R. Pape wishes to acknowledge stimulating conversations with A. Bardos and B. Beaudet of Harris Corporation and M. Shah of M W Electronics, Inc. concerning the design of A 0 deflector devices.

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121

1. Klein, W. R., and Cook, B. D., Unified approach to ultrasonic light diffraction, IEEE Trans. Sonics Ultrasonics, SU-14, 123-134 (1967). 2. Smith, T. M., and Korpel, A., Measurement of light-sound interactions efficiency in solids, IEEE J . Quantum Electron., QE-I , 283-284 (1965). 3. Auld, B., Acoustic Fields and Waves in Solids, Krieger, Malabar, F L Y 1990, Chap. 3. 4. Papadakis, E., Diffraction of ultrasound radiating into an elastically anisotropic medium, J. Acoust. Soc. Am. , 36,414-422 (1964). 5. Dixon R. W., Photoelasticproperties of selected materialsand their relevance for applications to acoustic light modulators and scanners, J . Appl. Phys., 38, 5149-5153 (1967). 6. Dixon, R. W., Acoustic diffraction of light in anisotropic media, IEEE J . Quantum Electron., QE-3, 85-93 (1967). 7. Warner, A. W., White,D. L., and Bonner, W. A., Acousto-opticlight deflectors using optical activity in paratellurite, J . Appl. Phys., 43,44894494 (1972). 8. Gordon, E.I., A review of acoustooptical deflection and modulation devices, Proc. IEEE, 54, 1391-1400 (1966). 9. Hecht, E.,Optics, Addison Wesley, Reading, MA, 1987, Chap. 10. 10. Shah, M. L., and Pape, D. R., A generalized theory of phased array Bragg interaction in a birefringent medium and its application to TeO, for intermodulation product reduction, Proc. SPIE, Advancesin Optical Information Processing V,1704, 210-220 (1992). 11. Cook, B. D., Cavanagh, E., and Darby, H. D., A numerical procedure for calculating the integrated acoustooptic effect, IEEE Trans. Sonics Ultrasonics, SU-27, 202-2206 (1980). 12. Hams, F. J., On the use of windows for harmonic analysis with the discrete Fourier transform, Proc. IEEE, 66, 51-83 (1978). Opt. Eng. ,25,30313. Bademian, L., Parallel channel acousto-optic modulation, 308 (1966). 14. Pape, D. R.,Wasilousky, P. A., and Krainak, M., A high performance phased array Bragg cell, Proc. SPIE, 789, Optical Technology for Microwave Applications 111, 116-126 (1987). 15. Cohen, M. G., Optical study of ultrasonic diffraction and focusing in anisotropic media, J. Appl. Phys., 38, 3821-3828 (1967). 16. Maydan, D., Acoustooptical pulse modulators, IEEE Trans., VQ-6, 15-24 (1970). 17. Zadorin, A. and Sharangovich, S. N., The calculation of the frequency band of an acousto-optic modulator with a cylindrical piezotransducer, Izv. SSSR, Radioelektron., 28, 76-78 (1985). (Russian) 18. Pape, D. R., Multichannel Bragg cells: Design, performance, and applications. ODt. Ena.. 31. 2148-2158 (1992).

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Hecht, D. L.,and Petrie, G. W., Acousto-optic diffractionfromacoustic anisotropic modes in gallium phosphide, Proceedings of the I980 IEEE Ultrasonics Symposium, pp. Beaudet, W. R.,Popek, M., and Pape, D. R., Advances inmultichannel Bragg cell technology, Proc.SPIE,Advances in Optical Information Processing IZ, 639, Fox, A. J., Thermal design for germanium acoustooptic modulators, Appl. Opt., 26, 22. Elston, G., Optically and acoustically rotated slow shear Bragg cells in TeO,, Proc. SPIE 936, Advances in Optical Information Processing, Xu, J., and Stroud, R.,Acousto-OpticDevices, Wiley, New York, Chap. 6.

Design of Acousto-Optic Modulators Richard V. Johnson Crystal Technology, Inc. Palo Alto, California

INTRODUCTION 1.1 BriefHistoryand Scope Acousto-optic component technologies have evolved naturally out of fundamental scientific research into ultrasonics. Among the most powerful tools for studying ultrasonic propagation, absorption, scattering, and reflection phenomena are optimal imaging techniques, especially schlieren imaging. The schlieren images have suggested the concept of an optical modulator in which light intensity can be controlled by an electronic drive signal. Some of the earliest efforts at fabricating acousto-optic modulators were initiated over 50 years ago, long before the invention of the laser. Interested readers are directed to thebook by Bergmann for a more complete description.of this early work [l]. One of the earliest uses of an acousto-optic modulator in an electrooptic system was for large screen projection of television images in theaters, developed in thelate by the Scophony Laboratory in London [l-41. Even by today’s standards, this scanner stands as one of the most subtle and sophisticated electro-optic systems ever developed. The Scophony scanner is one of the few systems to take full advantage of the acousto-optic modulator’s scrolling spatial light modulation behavior. The Scophony scanner architecture was a key enabling concept to maximize

JOHNSON light energythroughput to theimage plane, asthe original light source was a spatially incoherent arc lamp. we shall see in Section 4, an acoustooptic Bragg cell performs by far the best as a temporal “point” modulator when an incident light beam has the highest possible spatial coherence. Hence, significant market applications for acousto-optic technology had to wait until the invention of the laser in the early By the time lasers wereinvented, key manufacturing processes for acoustooptic components had already been refined to a very high level. The reason was a fortuitous synergy between acousto-optic component manufacturing processes and ultrasonic delay line manufacturing processes. Ultrasonic delay lines were a major market during this period some years ago. Both component categories require piezoelectric transducer plates to be bonded to a polished flat surface,under high pressure in a vacuum chamber. (See discussionin Chapter Bothcomponent categories require the transducer to be ground and polished to final thickness, thereby defining the centerfrequency of the transducer response bandwidth.Both categories require electronic impedance matching circuits to couple RF energy efficiently from 50-ohm instrumentation to a generally non-50 ohm, reactive, dispersive transducer element. Indeed, the onlymanufacturing process required for acousto-optic components which hadnot already been realized with ultrasonic delay lines is a high-quality antireflection coating on the two optical windows. This coating technology already existed from other sources. Acousto-optic modulators can be batch-processed for significant reduction of manufacturing costs (Fig. a result, acousto-optic component technology and markets have evolved dramatically over the past years, as witnessed by the subjects contained within this book The scope of this chapter is to elucidate design principles for acoustooptic modulators Section reviews major markets for the modulator to determinewhich performance measuresare most critical for practical applications. The fundamental operatingconcepts of a modulator are detailed in Section 2, devoid of mathematical complexities, in preparation for detailed analyses contained in Sections The RF drive power and materials requirements for an intensity modulator are studied in Section Requirements of the incident light source for best modulator operation are reviewed inSection 4, and static contrast ratio is calculated for a lowestorder TE% Gaussian profile laser beam. simple model of modulator temporal response is given in Section 5, a single parameter measure of modulator performance isdefined with respect to risetime, and a numerical algorithm is detailed for calculating modulator response to any arbitrary video signal V(t). The finite thickness the sound field, defined by the transducer length L, affects a number of modulator performance parameters, including light diffraction efficiency, optical beam profile distortion,

DESIGN OF ACOUSTO-OPTIC MODULATORS

125

Photograph of typical acousto-optic modulators.These modulators can be batch processed for low manufacturing costs.

JOHNSON

126

and in extreme cases, a degradation in temporal response, as described in Section 6 . Identifying an optimum modulator design involves arbitrating between conflicting performance requirements. A candidate modulator design strategy is listed in Section 7. This design strategy embodies conventional modulator design wisdom, but clever system designers have invented a number of techniques for obtaining even more performance from a modulator. In Section 8, we review four different approaches for maximizing the performance of a laser scanning system using an acousto-optic modulator. Section 9 concludes this chapter.

1.2 Current Modulator Markets partial list of today’s markets for intensity modulators is given in Table 1. By far the largest market share is for laser scanning systems for applications as diverse as reprographics, medical imaging, or VLSI mask generation. A second major market share is for Q-switching of lasers for machining, materials processing, and medical and dental procedures. A market segment primarily for metrology and LIDAR employs intensity modulators for their ability to Doppler-shift the temporal frequency of a laser beam. Finally, a small but rapidly growing market is developing for Table

Acousto-opticModulatorMarkets

Laser scanning: 2D Imaging Reprographics Nonimpact printing Color separation Laser typesetters Medical x-ray digitizing and reconstruction Large screen television displays Laser plotters Laser-based VLSI mask maker Ablation imaging Laser scanning, other categories Printed circuit board inspection Laser optical disk mastering systems Measuring dopant levels of silicon wafers AOQS for pulse laser operation Laser machining and material processing Medical surgery procedures Dental procedures Laser heterodynemetrology OTDR switching

DESIGN OF ACOUSTO-OPTIC MODULATORS

127

optical time-domain reflectometry (OTDR) instruments for diagnostic inspection of installed fiberoptic networks. We will explore representative examples of each of these market categories in turn. Laser Scanning Systems typical laser scanner system is shown in Fig. 2 [17-201. It consists of a high-radiance laser light source, an intensity modulator, a scanning means for sweeping the laser light across a photoreceptor surface (such as the rotating polygon mirror shown in the figure), and suitable lenses and mirrors forfocusing and directing the laser light. drum or a belt, notshown in this figure, provides motion along the orthogonal image direction that subsequent scan lines are properly registered in sequence to form an image. A key design parameter is the smallest image area which can be formed by a scanner (a picture element, or pixel), whichgoverns the resolution required of the optics and the data rate required of the intensity modulator. match the visual acuity of most human observers, ascanner resolution suitable for most text-based business documents is 300 pixels

,

I"d

2 Schematic diagram key optical components.

a flying spot laser scanning system, showing the

JOHNSON

128

per inch, whereas graphics or half-tone images require higher resolutions for best image quality. Let us calculate typical modulation bandwidth requirements of the modulator in a laser scanning application. The modulation bandwidth is governed by the scanner resolution, the scan rate in terms of how many copies per second, the area of the copy being scanned, and an efficiency factor which considers scanner retrace and electronic housekeeping requirements. Consider first a comparatively low performance scanner. Assuming a resolution of 300 pixels per inch, an 8.5-by-11-inch document, a scan rate of a document a second, and an active scan time to total scan time efficiency of this implies a video data rate (8.5"

X

ll")/document X

X

(300pixels/inch)2

1 document/sec = 10.5 megapixeldsec 80%

This can be converted into a maximum bandwidth requirement fm for the intensity modulator using the expression 1Hz =

(2)

pixels/sec

which for the example considered above corresponds to a modulation bandwidth of MHz. This is a very modest performance requirement for an acousto-optic modulator. Let us bracket typical scanner requirementsby considering a much higher performance system, a scanner with 600 pixels/inchresolution, copies/ sec throughput rate, and again an 80% active scan duty cycle. The modulator data rate for this application is fM =

=

(8.5"

X

ll")/document

X

(600 pixels/inch)2

X

(1 W 2 pixeldsec) MHz

X

document/sec 80% (3)

This approaches the upperlimit of bandwidth which an acoustooptic modulator can comfortably deliver with high light diffraction efficiency. Another critical performance parameter needed to specify the modulator is the risetime, which determines fidelity of the temporal modulation, as discussed in Section 5. A fast risetime enables modulator output which closely tracks the input video signal; conversely, a slow risetime causes considerable blurring of the output signal. In a laser scanning system, the

DESIGN O F ACOUSTO-OPTIC MODULATORS

129

finite dimension of the scan spot also serves to blur the final exposure record, and indeedis usuallythe dominantblurring mechanism. One measure of modulator and scanner fidelity is the dynamic contrast ratio in response to a square pulse video signal train. A powerfulmethod foranalyzingscanner performance isthe modulation transfer function (MTF), i.e., the contrast ratio response (in terms of modulation depth) to a sinusoidal video signal. This analysis easily combines response degradation effects due to the finite scan spot dimension and the finite modulator response time. All scanner architectures exhibit a fundamental cutoff frequency Alp/#

fcutoff

=

V-n

due to thewave nature of light, in which F/# is the flnumber of the scan beam incident upon the final image plane, andV,, is the speed with which the scan spot sweeps across this image plane. For a flying spot scanner, the MTF contribution due to the finite sizeof the scan spot alone, independent of the modulator temporal response contribution, results in a steady monotonic response falloff, froma peak response at the lowest spatial frequencies to response cutoff at fmtOft. According to conventional flying spot scanner design, any modulator frequency response rolloff exacerbatesthe total scanner MTF rolloff. Hence conventional scanner design philosophy is to choose a modulator risetime as short possible, within cost constraints. In Section 8 we consider an alternativescanner architecture, the Scophony scanner, which exhibitsoutstanding MTF by exploitingthescrollingspatialmodulation characteristic of the acousto-optic modulator. Q-Switched Lasers A number of applications, such as laser machining, medical and dental surgery processes, and certain scientific research experiments benefit from a laser which emits short discrete pulses of very high peak power, rather than a cw laser of much lower power. A standard approach forachieving high pulse powers is Q-switching A number of alternative techniques exist for Q-switching. For example, electro-optic Pockels cell Q-switches (EOQS) are most useful for very high gain lasers and very short pulse modulation requirements (e.g., laser target designators) which cantolerate higher levels of optical loss. Acousto-optic modulators are most suitable for low-gain cw-pumpedor repetitively pumped lasers which demand lowest possible cavity losses to achieve peak power. These components are referred to as acousto-optic Q-switches (AOQS); see Fig. for a typical laser cavity configuration and Fig. for a photograph of a typical Q-switch. increase the laser cavity loss, an RF signal is applied to the AOQS.

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JOHNSON

%-1” a

E

LASER CAV TY M RROR

DEFLECTED LIGHT

-/ DEFLECTED L

LASER CAV I TY ACOUSTO-OPTIC MIRROR 0-SW ITCH

Schematic diagram of a laser cavity with an acousto-optic Q-switch for generating short laser pulseswith high peak powers.

Photograph of a typical acousto-optic Q-switch. This unit requires 70 W of RF drive power and requires water cooling.

This allows the internal optical power to build up tovery high levels. The RF is then turned for a short period of time, which suddenly lowers the cavity loss, and allows a very large laser pulse to build up in the cavity. After this pulse has built up and left the laser cavity, the RF can be turned on again and the process repeated at pulse rates as high as 1 kHz.

DESIGN OF ACOUSTO-OPTIC MODULATORS

131

Compared with EOQS, AOQS exhibit very low optical insertion loss (
132

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combined with a portion of the incident laser beam at an optical detector. The two laser beams beat at the RF carrier frequency. The phase of the beat signal, measured with respect to the original RF drive signal for the modulator, is directly related to the time of flight of the diffracted light, hence to thedistance of the object to be measured. The heterodyne optical detection scheme allows for significant improvement of the signal-to-noise performance. This is just oneexample of a growing number of instruments which exploits the Doppler frequency shift characteristic of an acoustooptic Bragg cell. Optical Time-Domain Reflectometry Another small but growing market exists for acousto-optic modulators for optical time-domain reflectometry, a method for diagnosing the optical transmission performance of fiberoptic networks In an OTDR, a short laser pulse is launched into the fiber to be measured, andany back reflections are measured by an optical detector and recorded asa function of the time interval from the original laser pulse. Intense back reflections appear, forexample, whenever a bad fiber splice exists. The time interval between the original pulse and the return pulse gives information about the distance of the bad splice from the end of the fiber. At much lower intensity levels, a continuous return signal consisting of Brillouin scattering occurs for all fibers, and can be used to monitor the local transmission characteristics of the fiber. An OTDRcan be assimple and economical as a fiber coupler. However, more sophisticated instruments use an acousto-optic shutter to blank the optical detector during the initial laser pulse launch, during which intense back reflections could otherwise saturate the detector and cause it to be blind to a short section of fiber. An interesting OTDR configuration is shown in Fig. 5 which employsan acousto-optic modulator both as a shutter to protect the optical detector and also to allow heterodyne detection of the reflected light [22]. 1.3 Modulator PerformanceRequirements

From the above discussion of application requirements, we can identify some of the morecommon performance specifications of an acousto-optic modulator, listed in Table 2. These requirements fall broadly into categories of temporal response, light throughput efficiency, and interface characteristics, including optical, electrical, and mechanical. Most of the challenge in designing a modulator is to strike an optimum balance between conflicting requirements for high light throughput and fast temporal response, as detailed in Section 7.

DESIGN OF ACOUSTO-OPTIC MODULATORS BEAM SPLITTER

-

,0

LO LASER

0

BRAGG CELL SWITCH

BACKSCATTER DETECTOR

W Figure 5 Schematic diagram of an optical time-domain reflectometer using an acousto-optic modulator for heterodyne signal detection.

2 BASICMODULATORCONCEPTS Having introduced a number of applications for acousto-optic modulators, wenowreview the basic operating principles at the simplest and most intuitive level, devoid of mathematical complexity. We start with a discussion of the acoustic generation, propagation, and termination in the modulator head. Next, the RF drive electronics needed to convert an electronic video signal V ( t ) into a suitable modulator drive signal are reviewed. We discussoptical diffraction characteristics of the modulator, and review alternative schemes for converting the modulator’s optical diffraction pattern into an intensity modulation. Each scheme has distinct modulation characteristics. Finally, we briefly discuss temporal response concepts and the sensitivity of modulator performance on critical angular alignment with respect to the incident light beam.

2.1 The Modulator Head A typical block diagram for an acousto-optic modulator is shown in Fig. 6. See Fig. 1 for a corresponding photograph. The modulator consists of

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Table 2 Typical Modulator Performance Requirements Temporal response Risetime/falltime Frequency Bandwidth to 3-dB rolloff Dynamic contrast ratio Spurious modulation suppression Light throughput efficiency Passive.throughput Active modulation efficiency Optical system interface Incident laser wavelength (range) Incident laser polarization state Incident laser fluence Optical aperture dimensions Static contrast ratio Mechanical package interface Bragg angle adjustment sensitivity Beam height placement accuracy RF drive electronics interface Drive power needed maximum diffraction efficiency Drive power limitations Camer frequency Connector type Impedance matching VSWR

a transparent medium shaped and polished with two optical windows and a flat surface onto which a piezoelectric transducer is attached. The transducer is typically a single crystal of a piezoelectric material such as lithium niobate. It is attached to themodulator head by one ormore metallayers, which also serve as electrical contact for an drive signal. A top metal electrode completes the electrical contact, such that anoscillating RF drive signal applied to these electrodeswill cause the transducer to vibrate at an ultrasonic frequency, typically in the range 40-500 MHz.The dimensions of this top electrode, height H (orthogonal to light propagation direction) and length L (parallel to light propagation direction), along with the RF carrier frequency f, help definethe modulator performance. An electronic impedance-matching network is usuallyinterposed between the drive electronics and the transducer to minimize reflection of FW power from the transducer back into the drive circuitry, which might otherwise damage the electronics. By careful design of the acoustic properties of the metal bonding layers, a portion the transducer’s ultrasonic energy is coupled F

W

,

DESIGN OF ACOUSTO-OPTIC MODULATORS

135

'

-R

6 Diagram of an acousto-optic modulatorhead showing the cell, piezoelectric transducer and associated metal bonding and electrode layers, and electronic impedance-matching network. See also Fig. 1 for a photograph of a typical modulator head.

into the acousto-optic cell as a traveling sound wave. This acoustic beam travels with sound speed V , past an incident light beam to theback of the modulator cell. The sound field must be properly terminated at the back of the cell to prevent it from being reflected back into the laser light beam, which would otherwise cause spurious time-delayed optical modulation. This acoustic termination is typically achieved bygrinding the back surface at an angle such that any reflected sound energy no longer has optimum propagation direction for maximum light modulation. The back surface is also often loaded with an acoustically absorbing material. Any reflected sound energy iseventually absorbed by the modulator medium. Most modulator applications are not sensitive to back acoustic reflections, but for signal processing or for very high dynamic range laser recording, this can be a significant design issue. A schlieren photograph of a modulated sound field propagating through a typical modulator is shown in Fig. 7. The transducer which generates this sound field is located to the left. Note from this photograph a slight diffractive broadening of the sound field as 'it propagates to theright. The angle termination of the back face is quite visible in this photograph, as is a small amount of reflected sound energy.

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Figure 7 Schlieren photograph of the soundfieldinside a typical modulator. The transducer on the left, and the angled back face ison the right. Note a slight diffractive broadening of the sound field as it propagates from left to right. Note also some evidence of sound reflection of the angled backface.

R FC A R R I E R OSCILLATOR

ELECTRONIC

MATCH I NG

VIDEO I N P U T

RMFI X E R

WI POWERAMP

Block diagram of RF drive electronics required by an acousto-optic modulator. Theelectronics consistof an RF camer frequency oscillator,a balanced diode RF mixer for impressing an electronic video signal onto the camer, and a wideband power amplifier to drive the modulator at peak diffraction efficiency.

2.2

Drive Electronics

The electronics needed to convert an incident electronic video signal V(t) into an appropriate RF drive signal are shown in Fig. 8. The video signal is amplitude modulated onto a periodic (typically sinusoidal) carrier signal with frequency f,, such that the resulting rf drive signal has the form V(r)

DESIGN OF ACOUSTO-OPTIC MODULATORS

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c0s(27rfct). The carrier signal is generated by an oscillator. The video is introduced by an RF mixer, typically a balanced diode ring. The resulting drive signal is amplified that it has sufficient power (typically 0.25-5 W, depending upon the modulator medium and performance regime) to drive the modulator. typical drive signal sequence fordigital modulation is shown in Fig. 9, and a comparable drive signal sequence for analog modulation is shown in Fig. 10. The toptrace in these two figures represents the output the carrier oscillator, the middle trace represents theincident

RF CARRIEROSCILLATIONS

INPUTVIDEOSIGNAL

Ti MODULATED

D R I V ES I G N A L

Typical RF drive signal sequence for a binary digital video signal.

R F CARRIEROSCILLATIONS

INPUTVIDEOSIGNAL

MODULATED

D R I V ES I G N A L

Typical RF drive signal sequence for an anaIog video signal.

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video signal, and the bottom trace represents theresulting RF drive signal which is applied to the modulator head.

2.3 OpticalDiffractionCharacteristics The propagating soundfield inside the modulator flows throughan incident laser beam, interacting with the light energy by means of the elusto-optic effect, i.e., a local perturbation in the index of refraction induced by a stress field associated with the sound wave. Because the sound wave is periodic in space, the photoelastic perturbation the index has the form of a volume phase grating which moves through the cell with the speed of sound. An incident and generally collimated laser beam, propagating through the volume phase grating, is diffracted into a series of discrete diffraction orders, asdiagrammed in Fig. 11. Each orderis separated fromits nearest neighbor by angle.

in which X. is the wavelength of the incident laser light, fc is the acoustic carrier frequency, and Vs is the speed of sound in the modulator medium. Let us calculate a typical diffraction angle: a typical carrier frequency is 100 MHz, a typical speed sound is of order 4 m d p s e c so for a 633-nm helium neon laser beam, a typical diffraction angle is 16 mrad (almost a degree). Thusthe angular separation is fairly small. Nevertheless, by using spatially coherent laser light, these orders can be cleanly separated. Because the modulator response is strongly dependent upon the wavelength

2ND D I FFRACT I ON ORDER * I S TD I F F R A C T I O N

I NC I DENT LASER

ORDER

OTH D I F F R A C T I O N ORDER

dI ST

D I FFRACT I ON ORDER

11 The acousto-optic modulator splits anincident focused laser beam into several discrete diffraction orders. These orders are identified by an integer index, e.g., zeroth order, positive first order, etc. Each order is separated from its neighbors by a shift in ,its propagation angle OShin. The shift angle is governed by the RF camer frequency; the, distribution of energy among the several diffraction orders is governed by the RF drive power.

DESIGN OF ACOUSTO-OPTIC MODULATORS

139

of the incident light, we shall for simplicity assume a monochromatic light source hereinafter. The various discrete diffraction orders are identified by an integer index. The zeroth order refers to the output light beam which propagates collinearly with the incident light (Fig. 11). If RF power is removed fromthe modulator, thenonly the zeroth-order light would exist. Higher diffraction orders are numbered consecutively from this zeroth order, with positive integers on one side of the incident light, and negative integers on the opposite side. A Doppler frequency shift has been observed in the diffraction orders, caused by diffraction from a moving phasegrating. The amount of Doppler frequency shift corresponds to theindex of the diffraction order. Thus the zeroth diffraction order has no frequency shift with respect to theincident light beam, whereas the mth diffraction order has a frequency shift of m times the carrier frequency fc. This frequency shift can be used to distinguish clearly between positive and negative diffraction orders. The Doppler shift is critical for a few applications, such as heterodyne detection of vibrating surfaces, in which more than one diffraction order are combined at an optical detector. For most applications, only one diffraction order is directed into an optical detector, so existence of the Doppler shift is not observable. We will neglect this effect in the remaining discussion, and instead identify the positive first diffraction order as that orderexhibiting the greatest coupling efficiency to theincident light power by virtue the modulator’s angular alignment. Unless otherwise required for clarity, we will simply refer to this as the first order beam. The choice of transducer length L deteimines whether the modulator exhibits Raman-Nath, Bragg regime, or intermediate diffraction characteristics. (See discussion in Section for moredetails). Most modulators are designed to operate near the Brugg regime, in which only one higher diffraction order dominates the diffraction process, and only whenstringent angular alignment betweenthe sound field and the incident light is imposed. Best modulation efficiencyoccurs when the incident light enters thesound field at a small angle. %rags

=

‘OfC eshiyi 2v, -

called the Bragg angle. We shall assume hereinafter, unless stated explicitly otherwise, that theincident light is aligned at precisely the optimum Bragg angle. Best modulator operation occurs just outside of this Bragg regime, such that the negative first and positive second diffraction orders receive a small but noticeable amount of the incident light power. These higher orders introduce a small but important amount of parasitic coupling loss,

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degrading the light throughput efficiency at saturation into the positive first diffraction order (Fig. 11).

desired

2.4 Intensity Modulation andTransferFunction A phasegrating, such as an acoustooptic modulator, conserves light power. The sum of the light intensities in the various diffraction orders is equal to the incident light intensity. convert the phase modulation into an intensity modulation, we need to filter the diffraction orders, i.e., to pass one ormore orderswhile blocking the remaining orders. Several alternative filtering schemes are common with acousto-optic modulators. By far the most popular configuration is to pass the first diffraction order (with modulator angular alignment optimizedfor maximum diffraction efficiency into this order), with all other orders blocked. The modulator transfer curve for this configuration can be approximated by the analytic expression q=-=

in which q is the diffraction efficiency, defined as the ratioof power in the 1st order to the incident light power, P, is the acoustic beam power, and PPakis the power needed for peakdiffraction efficiency, discussed in more detail in Section This configuration of passing the first diffraction order offers the best .static contrast ratio, which is the ratio of the output light power for a full on video state to the outputlight power for a full off video state. This configuration offers less than 100% diffraction efficiency in practical temporal modulation applications because of angular sensitivity effects discussed in Section In practice, modulator performance involves a tradeoff between fast response and high diffraction efficiency. Diffraction efficiencies of order of 70% are common. An alternative spatial filtering configuration is to pass the zeroth-order light and block all higher orders. The modulator transfer curve for this configuration can be approximated by the complement of the abovetransfer curve, i.e.,

This configuration offers almost 100% light throughput, the highest of any modulator configuration. However, the contrast ratio even for lowest video frequencies is at best modest. The off state is rarely ever truly off. Yet another scheme for, deriving optical intensity modulation does not involve spatial filtering, but rather separation of the diffraction order by optical polarization. This is effective when the acousto-optic modulation

DESIGN OF ACOUSTO-OPTIC MODULATORS

141

diffracts the incident laser light into an orthogonal optical polarization state. This can be most useful for particular applications requiring exceptionally high contrast ratio performance.

2.5TemporalResponse A major performance consideration for an acousto-optic modulator is the temporal response. The response time is governed by the acoustic transit time defined as the time required by an acoustic wavefront to flow past the light beam. If the incident laser beam has diameter Din,then the transit time is

For example, consider a laser beam with a diameter of 1 mm. Assume a speed sound in the modulator of order mm/psec. Then the acoustic transit time is 250 nsec. This time can be reduced by employing an alternative modulator medium with a higher sound speed, or more usually, by focusing the incident light beam to a smaller beam diameter. A l o x reduction in beam diameter to 100 pm causes the transit time to reduce to 25 nsec, which is well within the capability of most acousto-optic modulators. A further 10 X beam diameter reduction, however, causes severe performance loss in most modulators because of diffraction effects, discussed next.

2.6 Limits to Focusing The Incident Light Because of the wave nature of light, if a laser beam is strongly focused so that it converges to a small diameter, this beam is no longer well collimated; it spans a range propagation angles, as sketched in Figs. 11and 12. The propagation angle distribution, such as thatshown in Fig.12, is mostclearly resolved after the light has propagated some large distance from the modulator. (See standard optics texts, e.g., [21] for a discussion of Fraunhofer and Fresnel diffraction theory.) One practical limit to the focusing of the incident lightbeamis the need for clean separation of the zeroth and positive first diffraction orders (Fig. 12). Also, the modulator does not respond equally to a wide range propagation directions, but rather is strongly angle dependent. This leads to a reduction in diffraction efficiency, possibie distortion of the light beam profile, and in extreme cases, a degradation of a modulator’s temporal response. In this section, we have outlined the key physical mechanisms responsible for modulator operation, presentedwith minimal mathematical complexity. We have reviewed the generation, propagation, and termination

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I

ANGLE

12 This diagram shows the optical intensity profile of the zeroth and positive first diffraction orders as a function of the propagation direction of the beams (i.e., far-field regime). The shift angle shown inFigure 11 allows these beams to be separated. If the carrier frequency is not high enough, then these beams will overlap, and some zeroth order light will leak into the positive firstorder beam, degrading the modulator's static contrast ratio.

of the sound field in the modulator head, theRF drive electronics needed for amplitude modulation of an oscillating carrier signal, the light diffraction properties of a phase grating, and means for converting the phase modulation into intensity modulation. The temporal response limits of an acousto-optic modulator have been expressed in termsof the acoustic transit time needed for a sound wave front to travel through the incident laser beam, and various mechanisms which practically limit the degree of focus of the incident light have been listed.

3 DRIVEPOWER AND MATERIALSSELECTION We derive expressions in this section for calculating the RFpower requirements of a modulator, and comparefigures of merit for various modulator media We start with a brief derivation of the modulator's transfer function, devoid of tensor complexities and highlightingthe key conceptual steps. From this derivation, we obtain an expression relating the acoustic power P, to themodulator's diffraction efficiency. All material parameters in this expression can be combined to define a figure of merit M*,which is most useful for modulator design once a particular modulator medium has been selected. However, alternative figures of merit are more appropriate for comparing alternative media because of scaling rules for optimally selecting the transducer dimensions L and H , rules which we will derive in later sections. Finally, we reviewa partial list of modulator media.

DESIGN OF ACOUSTO-OPTIC MODULATORS

143

We start our derivation of the modulator transfer function with phasegrating diffraction theory [35-371. Klein and Cook, among others, have shown that diffraction efficiency of a volume phase grating is expressed by

in which Zin is the incident light intensity, Zl is the light intensity diffracted into the 1 diffraction order, and V is a measure of the grating strength. For now, we assume no angular misalignment; the effects of such misalignment will be considered in detail in Section 6. The grating strength V is defined as the peak optical phase modulation induced in a light beam by a photoelastically induced shift Sn in the local index refraction,

in which L is the transducer length and X. is the light wavelength. From photoelastic theory, we can relate the shift in index of refraction Sn to a strain field S associated with the acoustic wave by

( 3 =ps in whichp is the photoelastic coupling factor (a fourth-rank tensor). Finally, we can relate the acoustic strain S to the acoustic power P, by

in which is the mass density of the acousto-optic medium and V, is the speed of sound. These equations can be combined to yield

As explained in the beginning of this section, we have purposefully suppressed tensor considerations. The reader is referred to the work of Chang for a more complete tensor analysis [12]. Tensor analysis is necessary to account for different figure of merit for longitudinal mode sound propagation versus shear mode propagation and for different response for the two orthogonal input light beam polarization states. For purposes of this discussion (Table 3), we will confine our attention to longitudinal mode propagation interactions, which exhibit the highest sound speeds, hence

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Table 3 PartialList of Acousto-optic Media Medium Fused silica Water Polymethylmethacrylate 3.0 SF-8 4.0 Lead molybdate Tellurium dioxide

Index of sound refraction

Speed of

1.46 1.333 1.492 2.0 1.685 2.39 2.26

5.96 1.50 2.77 3.89 3.63 4.2

M, 1.0

6.1 1.7 14.6 17.6

M2 1.0

106 26 23.9 22.9

M3

1.0

24 6.7 24 25

the highest risetime response rates, albeit often with lower figure of merit compared with shear mode interaction in the same medium. For peak diffraction efficiency, an acoustic power P, of

A:(H/L) P, = is required. In this last expression, we have grouped all of the materialsrelated parameters into a figure of merit M,, defined to be

This is the most useful figure of merit for component design once a modulator medium has been chosen. It is not the appropriate figure of merit, however, for selecting the most efficiency modulator medium from alternative candidates because additional material parameters occur in scaling the transducer dimensions L and H in Eq. (15). For example, we will show in Section 7 that a good design strategy is to scale the transducer length L such that a dimensionless parameter N , defined by

is held constant. From this scaling equation, we can derive an alternative figure of merit

Similarly, the transducer height H is generally scaled to the incident light diameter D,. From risetime Eq. we will see thatthis diameter scales

with the modulator's speed of sound Vs, assuming a fixed risetime specification. Hence another useful figure of merit is

The figures of merit for several alternative modulator media are listed in Table 3. This brief review of representative media is not intended to be comprehensive, but more an anecdotal commentary on the interesting history of acousto-optic modulators. The first entry is quartz, which is not the most efficient modulator medium, but has excellent acoustic and optical propagation properties. Quartz is often selected for modulation of ultraviolet light or whenever very low scattering losses are desired, despite its need for very high RF drive powers. Quartz has often been used as the benchmark medium for scaling the figures of merit of alternative modulator media. The next entry is water, a rather unusual candidate for a modulator medium today. Liquids in general, and water in particular, have very high figures of merit and have played a major role in early acousto-optic modulators, especially for lower carrier frequencies. As carrier frequencies increased, liquids become more and more prone to cavitation (spontaneous generation of the gas phase in response to ultrasonic agitation). Such cavitation catastrophically scatters the laser beam, and hence renders the medium unacceptable. The next entry is polymethyl methacrylate ( P ~ ~ Aa ) plastic. , searchers at Xerox and independently at Kodak have discovered that various plastics exhibit quite attractive figures of merit, comparable to more traditional single-crystallinematerials. This offered the tantalizing prospect of very low cost injection-molded modulators. Unfortunately, plastics often suffer from excessive acoustic absorption, rendering most devices studied to date unacceptable because the sound fields induce severe thermal distortion of the laser beam. SF-8, a dense flint glass, is the next medium listed in Table 3. the largest fraction of modulators manufactured today are made of glass [30]. These modulators are rugged, comparatively inexpensive, excellent performance for carrier frequencies up to about 100 M modulator Performance becomes marginal for carrier frequencies of approximately 150 MHz, at least for traditional design approaches, because the scaling laws require rapidly increasing RF power densities, leading to severe stress and thermal loads in the transducer region. For higher carrier frequency operation, single crystals of select media are preferred. The two most popular choices in the market today for visible light applications are lead molybdate (PbMoO,) [33] and tellurium dioxide

JOHNSON (TeO,) The latter is especially interesting for deflector and tunable filter applications because of an unusually low slow shear mode velocity. For far more detailed surveys of figures of merit for alternative media, the interested reader is directed to any of several excellent review articles (e.g. , Pinnow Uchida and Niizeki Eschler and Weidinger

4 LIGHT SOURCE REQUIREMENTS AND STATIC CONTRAST RATIO The properties of the incident laser light source have a significant impact upon modulator performance, both in temporal response and in ability to separate the various discrete diffraction orders, asmeasured by static contrast ratio. One light source profile excels over all others in giving the best modulator performance: a TEIM, lowest-order laser mode, i.e., one with a Gaussian profile. In this section, we detail the relation between the spatial profile inside the modulator,which governs the response time performance, and the propagation angle profile (also known as thefar-field profile) which governs the static contrast ratio. We calculate the static contrast ratio for a TEM, mode beam, thereby deriving design rules for minimum acoustic carrier frequencies fc needed for acceptable contrast ratio. Consider a monochromatic light source with wavelength X. and spatial amplitude profile of Ein(x)inside the modulator, in which x is the direction of sound field propagation. The temporal response of a modulator is governed by the acoustic transit time, i.e., the time required by a sound wave front to pass through the incident laser beam. keep the response time as short as possible, the incident laser is typically focused to a small spot diameter. Because of the wave nature of light, the process of focusing to a small spot causes the angular (far-field) distribution to broaden. This places a practical limit on the amount of focus which can be accomplished while still obtaining reasonable separation of the diffraction orders. From physical optics, we learn that the angular distribution Ein(0)can be derived from the near-field distribution Ein(x)by a Fourier transform:

This is the angular profile of the beam as it propagates through air, outside of the modulator. Our focus in the next sections, however, will be the interaction of the optical angle profile with the sound field's angle profile inside the modulator medium. Therefore, we will hereinafter replace the wavelength in air, ho, with the wavelength in the modulator medium, hdno, in which no is the index of refraction of the modulator medium.

DESIGN OF ACOUSTO-OPTIC MODULATORS

147

Only a light source with the highest possible degree of spatial coherence can simultaneously exhibit a compact spatial and angle space profile. The highest coherence is associated with a TEM, Gaussian profile laser beam of the form

) : ; (-

Ein(x) = exp

in which D , is the diameter of the light beam at focus, measured to the l/$ intensity point (i.e., 13.5% of peak intensity). From Eq. (20), we find that the associated propagation angle amplitude profile is a Gaussian,

as is the intensity profile f i n ( € ) )

in which the angular divergence diameter

is defined by

Note that the angular spread is inversely proportional to the diameter of the incident laser beam at focus. The more we focus the incident beam, the more the angular profile expands. The expanding angular profile becomes a problem when we attempt to separate the various diffraction orders. Consider Fig. 12, which shows the angular distribution for an incident TEM, laser mode (on the left) and the corresponding angle-shifted first diffraction order (on the right). In this figure, we assume that the incident light is directed along propagation angle - OBrag&,with respect to the transducer, diffracting a first-order beam which propagates along angle +eBragg.The first-order beam is typically separated from the incident laser beam by placing a beam block in the farfield distribution such that angles up to 0 are blocked, but angles from 0 to 20Bragg (= eshift)are passed. beam block at 2eBragg is good practice to suppress vestigial light scattered into thepositive second diffraction order from mixing with the desired modulated laser beam.) portion of the incident laser beam has propagation angle components which extend beyond 0.50shiftand hence are passed on with the desired modulated light beam. This occurs even when the modulator is turned completely off, and hence defines one limit to the modulator’s static contrast ratio, defined as

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the ratio of modulated light intensity for a full on modulator state to that for a full off modulator state. Thus we find static contrast ratio

For a Gaussian profile, the integral in the denominator of Eq. (25) evaluates to a well-defined constant, and theintegral in the numeratorcan be expressed in terms of the complementary error function erfc(x), defined by erfc(x) = 1 - erf(x) (26) with

Tables of error function values and numerical approximations can be found in Stegun and Abramowitz Using this function, we find for a TEM, mode &

static contrast ratio = erfc

[(L) (a)]

in which A is the acoustic carrier wavelength, A = Vslfc. A plot of the dependence of static contrast ratio on the dimensionless ratiopDin/A fora TEM, laser mode is shown in Fig. 13. Static contrast ratios in excess of 103-104 are difficult to obtain because of scattering in the modular volume and on the optical windows. Also, static contrast ratios in excess of this are not recommended because they imply increased acoustic carrier frequencies fc, which we will see in Section 6 cause difficulties with light throughput efficiency, beam profile distortion, and temporal response. Thus we find from Fig. 13 that a fairly constrained range dimensionless parameter Din/Agives acceptable performance. Lucero et al. have compared the staticcontrast ratio associated with the next higher TEIvbl. laser mode, scaled to provide the same risetime a comparable TEM, laser mode Higher-order modes exhibit even more extreme degradation of contrast. Thus we will assume TEM, Gaussian profile incident laser beams hereinafter for “point” temporal modulation requirements.

DESIGN OF ACOUSTO-OPTIC MODULATORS I0 4

l-

<

I

[r

102: Z

0

101:

<

l-

100:

0

2

3

INCIDENT

13 The static contrast ratio is a sensitive function the incident light beam diameter Dinscaled to the acoustic carrier wavelength A (= VJf,-, in which V , is the speed soundin the modulator medium, and f c is the RF carrier frequency).

5 TEMPORALRESPONSEMODEL An acousto-optic modulator’s temporal response can best be understood from a very simple conceptual model. In this section, we will detail key assumptions of this model and present aresponse equation in the form of a convolution integral. Bymeansof this convolution integral, a singleparameter measure of modulator temporal response in terms of risetime can be derived which adequately summarizes the modulator’s temporal performance. However, for a complete model of temporal response, we need more than asingle-parameter specification; we need analgorithm for calculating the modulated light profile in response to any arbitrary input video signal. Because the fundamental model equation is a convolution integral, powerful tools linear systems analysis can be applied. In particular, the temporal response an acousto-optic modulator can be completely described by its frequency response, expressed as a modulation transfer function or M T F . For the final topic in this section, we apply the MTF formalism to a particular video signal category consisting of a binary digital pulse sequence, exploring in particular the dynamic contrast ratio of the modulator and how it degrades with increasing video pulse repetition rates.

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5.1 Convolution Integral Response Model Several assumptions define this model. The first key assumption isthat an acoustic field with finite length L can be approximated by an equivalent modulation field, of comparable phase grating strength V (as defined by Eq. (U),but with infinitesimal depth L + 0. This assumption eliminates dependence onlight propagation angles, a critical topic which will be studied in detail in the next section. The second simplifying assumption is that the intricate configuration of diffraction order blocks, whereby the sound field’s phase modulation is converted into an intensity modulation, can be expressed simply by a transfer function of the form of Eq. (10) which relates the modulated light intensity I , to the incident light intensity Io. We repeat two key equations for convenience of the reader:

with grating strength V related to the acoustic drive power P, by

Let us define a coordinate system to aid in the following discussion. Spatial coordinate x refers to the direction of sound propagation in the modulator; spatial coordinate refers to the normal direction of light propagation (actual light propagation will be at a slight angle with respect to this axis); t denotes time. The intensity profile of the incident laser beam inside the modulator cell is Zin(x);we assume a steady-state beam. For purposes of this analysis, we willexpress the input video signalas a temporal modulation of the RF drive power P,@, which maps into an equivalent light intensity modulation q ( t ) by means of Eqs. (29) and key attribute of an acousto-optic modulator is that this modulation is derived from a propagating acoustic field with speed V,, and hence is representative of the class of scrolling spatial light modulators. Thus the intensity profile of the modulated light beam emerging from an acoustooptic cell C) is given by a sliding overlap of the incident light profile Zin(x)and the traveling modulation q(t -

scrolling spatial light modulator should be distinguished from a more typical temporal modulator with ideal response

Zl(x, C) = Zin(x)q(t)

temporal pure

modulation

(32)

DESIGN OF ACOUSTO-OPTIC MODULATORS

151

modification of the spatial profile of the laser light occurs in a simple temporal modulator. An electro-optic Pockels cell modulator is a good approximation of a purely temporal modulator. An acousto-optic modulator inevitably alters the laser spatial profile Il(x, t ) as part of the modulation process. The final step in temporal response modeling is to specify howthe system under consideration responds to this spatial modulation. Different systems have different responses, requiring different response models. For example, laser scanners can be quitesensitive to thespatial modulation process. One architecturein particular, the Scophony scanner, exhibits outstanding resolution performance by explicitly capitalizing on this scrolling spatial light modulator process, as discussed in Section 8. Conversely, traditional sqanners such as a flying spot’scanner which are not designed with regard to thescrollingspatial modulation of the acousto-optic modulator can suffer serious resolution performance degradation, depending upon the orientation of the modulator within the scanner system. For purposes of the present analysis, let us consider the output of a broad-area photodetector which integrates overall spatial profile details of the output light beam. This leads to an integral formulation of modulator response in which the detector output signal P(t) is given by

An appropriate scaling parameter has been suppressed in this last equation for simplicity of discussion.

5.2 Modulator Risetime Let us apply this response integral model to a particular video signal consisting of a step pulse U(t), defined by U(t) =

1

0

fort > 0 fort < 0

When the incident light profile is a Gaussian of form

I&)

= exp

(2;)

as discussed in Section and the video profile is a step pulse, then the modulated light profile P(t) has an analytical expression in terms of an

152

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error function:

[

P(t) = 0.5 1 + e r f ( F ) ]

(The error function was defined by Eq. (27) in the previous section.) The shape of this pulse edge response is shown in Fig. 14. Modulator performance can simply be characterized by risetime, defined as thetime interval needed for the output light to grow from 10% to 90% of its quiescent (i.e., steady) state (Fig. 14.) From tables .of the error function, one can calculate the modular risetime to be 0.64Di,

T R = - =

VS

0.647

(37)

in which T is the acoustic transit time introduced in Section 2. For example, a laser beam with 1000-pm diameter in a modulator with speed of sound of order 4 mm/sec would have a risetime of 160 nsec. Faster response can be obtained by using a modulator medium with faster speed of sound, or more typically by focusing the laser beam. A beam with 100-pm diameter in the same medium wouldhave 16-nsec risetime. We will show in the next section that focusing the laser beam to improve risetime degrades the modulator's light throughput efficiency; a classic design compromise for

z !

Z

I

2

-I

14 A useful measure of modulator temporal response is the risetime in response to a step-pulse video signal. The risetime is defined as the time needed by the modulator for its output to grow from 10% to 90% of the final quiescent light level. This gives a temporal response measure in terms of a single number.

DESIGN OF ACOUSTO-OPTIC MODULATORS

153

acousto-opticmodulators exists between fast response and highlight throughput efficiency. 5.3

Modulation TransferFunction (MTF)

Risetime offers a convenient characterization of modulator response in terms of a single parameter, but a more comprehensive statement of temporal response is needed. For example, consider a video signalwhich consists of a square pulse train. What precisely is the modulator output profile, and how can we best calculate it? This questionwill be important in discussing the next topic, dynamic contrast ratio. Because modulator response Eq. (33) is a linear convolution integral, the powerful tools of linear analysis can be applied. In particular, we find that Fourier transforming the response Eq.(33) yields anespecially simple expression of the form

m = "Wf)V(f)

(38)

in which P ( f ) is the Fourier transform of the broad-area detector output signal P(t), defined by

V ( f )is similarly the Fourier transform of the modulation signal q ( t ) , and MTF(f) is defined by r+-I

The MTF of an acousto-optic modulatorin response to a Gaussian input light profile thus is

in which fo is the frequency to the l/$ response rolloff, given by @vs

fo =

.rrD,

more common measure of frequency response rolloff is f3dB, the rolloff to the 50% reduction point, which is related to fo by

I54

JOHNSON

Let us incorporate Eq. which defines the modulator risetime T R to give an alternative expression for scaling frequency f3dB as 128V-2 f3dBTR

=

IT

= 0.48

(sinusoidal video)

(44)

Let us detail one possible algorithm for analyzingthe temporal response to an arbitrary videosignal usinga fast Fourier transform (FR). Assume that the video signal q ( t ) to be analyzed is defined over a time interval T , sampled at discrete times. A FlT of this signal will produce a spectral distribution sampled in frequency intervals of Af = UT. Let the frequency samples be indexed by integer m, such that the mthsample has frequency mlT. This frequency component should be factoredby the modulator MTF: MTF at interval m = exp

(

After factoring by this MTF response, the resulting spectral distribution should be inverse-Fwd to yield the predicted modulator response. We will consider next a specific case of this analysis, in which the video signal is a square pulse video train. 5.4 DynamicContrastRatio The modulator design strategy which we willelucidate in Section 7 requires as one principle input the modulatorrisetime T R , from which the requisite incident light diameter can readily be derived. Often, however, a system designer does not start with a clear definition of risetime, but rather of maximum modulationrate fM. A particular risetime value must be selected with respect to the fidelity of reproduction of the incident video signal needed for particular application. Consider for example a typical laser scanning system as discussed in Section 1. The maximum modulation frequency fM can easily be identified for a particular system specification, but the requisite modulator risetime is less obviously selected. In practice, the principal degradation attributed to the finite response time of an acoustooptic modulator in a laser scanning application is a reduced contrast ratio of ON light intensity to OFF light intensity. By identifying a dynamic contrast ratio target, the necessary risetime can be inferred. Assuming a Gaussian input light profile, one can calculate dynamic contrast ratios as a function of video pulse repetition rate, with results as shown in Figs. 15 and Figure 15 shows increasing levels of blurred modulationwhich occur for increasingly higher values of modulator risetime T~ when the incident video signal is a square pulse train. The lowest video bandwidth-

DESIGN OF ACOUSTO-OPTIC MODULATORS

>-

155

t

z z

W

-

I

c3

-I

L

TIME

Figure 15 finite modulator risetime is associated with a degradation in fidelity of modulator output. Consider for example a square pulse video signal. Typical modulator outputs are as shown in this figure, with best fidelity for lowest video bandwidth-modulator risetime product.

I000 : I t

I

0

300: IT

100: (r

t-

Z

0

30:

U

10: E

< 0

1:

0.0 0.2 0.4 0.6 0.8 1.0 RISETIME-MODULATION FREOUENCY PRODUCT

Figure One measure of modulatorfidelityis the dynamiccontrast ratio between on levels and off levels in responseto a square pulse videotrain, as shown in Figure 15. This contrast ratio degrades rapidly for higher and higher risetimes.

156

JOHNSON

modulator risetime product of 0.1 gives best fidelity of modulation, with excellent dynamic contrast ratio. The highest bandwidth-risetime product of 1.0 shows excessive blur, such that very little evidence of modulation remains in the broad-area photodetector output.Figure 16 showsthe degradation in contrast ratio forincreasing levels of bandwidth-risetime product (assuming a TEM, laser profile and a square pulse video train). Consider a specific numerical example of a laser scanning system with a maximum video bandwidth fM of24 MHz, a dynamic contrast ratio requirement of no worse that 30:1, and let us assume an SF-8 dense flint glass modulator with a speed of sound V , of 3.89 km/sec (Table From Fig. 16, we find that we need a bandwidth-risetime product of 0.43, from which we can calculate that we need a modulator risetime of 19 nsec. This implies an incident light beam diameter Dinof 115 km. This concludes our discussion of temporal response. In this section, we have identified a simple conceptual model for predicting the temporal response of an acousto-optic modulator. A single-parameter characterization of modulator response in terms of step pulse risetime has been defined and calculated. numerical procedure for calculating modulator response to any arbitrary inputvideo signal has been detailed, anda specific case of dynamic contrast ratio degradation for a square pulse video train has been calculated. One principal assumption of these numerical studies is that we are modeling the response of a broad-area photodetector. An alternative configuration, a laser scanning system in a Scophony configuration, will be reviewed in Section 8. A second key assumption of this model is that the sound field is replaced by an equivalent field of zero depth L 0. This assumption avoids light propagation angle dependence, which is the topic of the next section.

-

6 LIGHT THROUGHPUT EFFICIENCY AND THICK SOUND FIELD EFFECTS The principal focus of this section is on modulator light throughput efficiency, with special’attention on two important mechanisms by which efficiency is degraded. Both mechanisms derive from the finite sound field depth, given bythe transducer length L. Secondary topics will be distortion of the light beam profile due to propagation angle sensitivity, and a degradation in temporal response with large sound field depths L. Let us define light throughput efficiency q as the ratio of the modulated light intensity IIto theincident light intensity Iin.To a good approximation, this can be decomposed into three -separate terms,

DESIGN OF ACOUSTO-OPTIC MODULATORS

157

inwhich qpassive refers to the transmission efficiency of the modulator considered as a passive optical window, including antireflection coating performance and bulk scattering and absorption losses. The second factor, qwindow(A), embodies diffraction efficiency losses due topropagation angle misalignment between the light and sound fields, and is defined and analyzed in Section 6.1. A dimensionless scaling parameter A , introduced in Section 6.2, governs the efficiency loss and a distortion of the diffracted light beam profile compared withthe incident light profile. This parameter also impacts the modulator risetime, as discussed in Section 6.3. The third factor, qparasitic(N), expresses the efficiency loss of coupling light from the incident beam into the positive first diffraction order in the presence parasitic coupling to higher diffraction orders, and is studied in Section 6.4. This efficiency is governed by a dimensionless scaling parameter N , also introduced therein.Most results presented in the literature andin this section are derived from simplified analyses most applicable in the limit of low diffraction efficiency. Accurate analysis at higher diffraction efficiencies requires numerical methods. Numerical analysis methods are reviewed in Section 6.5. Both dimensionless design parameters A and N depend upon the modulator transducer length L . Efficiency lossdue towindow effects embodied by A is minimized by a short L ; efficiency loss due to diffraction order parasitic effects as measured by N is minimized by a long L. The optimum balance between these two conflicting requirements is the topic of Section 7. First, let us introduce the concept of the modulator’s angular acceptance window.

6.1 Modulator Angular Acceptance Window The modulator’s angular acceptance window can be defined and measured by a simple experiment, as diagramed in Fig. 17. The modulator is mounted on a motor-driven rotary stage with rotation axis mutually orthogonal to the light propagation and sound propagation directions, and preferably passing through the intersection of the light and sound beams. A constant RF drive signal is applied to the modulator while it is rotating. The modulator is illuminated by a well-collimatedlaser beam (confined in the transducer H direction to minimize aperturing effects). This incident laser beam, after passing through the modulator sound field, divides into several discrete diffraction orders, as shown in Fig. 17. These diffraction orders remain essentially fixed with respect to the optical bench top (at least for small rotation angles about optimum Bragg alignment). Hence several discrete photodetectors can be arrayedto monitor the diffraction efficiency, one detector for each diffraction order.

158

JOHNSON

*2M

An important aspect of acousto-optic modulator response is the concept of an angular admittance window. This admittance window can be measured in the laboratory by a setup as shown in this figure. The modulator is placed ona motorizedrotationstage,andtheoutput of oneormorediffractionordersis monitored by an optical detector while the modulator is rotating. Typical results of this experiment are shown in Figure18.

A computer simulation of typical results expected from such an experiment is shown in Fig. 18. Five curves are shown in this figure. The top curve represents the outputof the photodetector intercepting the positive second diffraction order beam (multiplied by for convenience in plotting); the next curve down represents the positive first order optical power, etc. The abscissa is the angle of the Bragg cell measured with respect to the nominal propagation direction of the incident light beam. A zero angle implies that theincident light propagates parallel to thetransducer. Angles are given in dimensionless units, scaled tothe Bragg angle defined previously by Eq. (6) in Section 2. The ordinate axis isscaled to theincident light power for each of these five curves; the top tic mark in each case represents 100% diffraction efficiency, i.e., 100% of the incident light power. The title N = 1.0 refers to a dimensionless design parameter which will be discussed shortly. All curves shown assume peak diffraction efficiency at a grating strength V = radians. Let us consider in detail the diffraction into the positive first order (second curve from the top in Fig. 18). Almost all of the incident light power (97%) is coupled into the positive first order, but only when the incident light passes through the modulator sound field at precisely the Bragg angle OBragg. Small deviations from this optimum angle cause significant degradation the diffraction efficiency. This behavior defines an

DESIGN OF ACOUSTO-OPTIC MODULATORS

159

+2ND ORDER I NTENS I TY

+lST ORDER -4 -3 -2 - 1

0 + l + 2 +3

+l

-1

- 1ST -4 -3 -2 - 1

-2

-1

0 +l

0

+l

+z ORDER +2

+2

18 Associated with each diffractionorder is its own distinctangular admittance window. Generally, best diffraction efficiency into that diffraction order occurs only within a narrow angular alignment bandof the modulator with respect to the incident laser beam.

angular acceptance window, and has major implications for modulator performance. The shape of the first order’s angular admittance window has the general appearance of a sinc2 function. Indeed, Gordon [l31 has shown that in the limit of low sound grating strength V (as defined by Eq. (ll)),the angular windowis directly related to lS(0)12, in which S(0) is the soundfield’s propagation angle distribution. This angle distribution is related to the stress distribution S(z) by a Fourier transform of the form

160

JOHNSON

A typical stress distribution S(z) is a rect function of length L ,

s(z> = rect(:)

=

{

1

0

L

for1 . 1 2 otherwise

The corresponding angle distribution then is a sinc function of the form

in which sin(.rrx) sinc(x) = the window's scaling angle =

A L

is defined by (51)

.and A is the acoustic carrier wavelength (= VJfc). The analytical tools of Gordon and Maydan have provided seminal insight into modulator operation, but these tools are most accurate only in the limit of very low diffraction efficiencies. However, the concept of a modulator angular acceptance window is not so limited. A more accurate expression for the angular acceptance window,suitable for high diffraction efficiencies as well as low, can be derived from the Raman-Nath coupledwave equations in the Bragg regime limit for which only the zeroth and positive first diffraction orders are significant. See, for example, discussion by Klein and Cook [36, An analytical expression for the acceptancewindow can be derived in the form

in which

We find that thewindow shape changes minimally for grating strengths V up to saturation V = m. Beyond saturation, significant distortion of the window shape can be observed, but this is not a standard modulator operating regime. Having introduced the concept of an angular acceptance window, let us next explore its impact on a typical focused laser beam..

DESIGN OF ACOUSTO-OPTIC MODULATORS

161

6.2 Modulated Light Beam Profile Distortion Consider another experiment: let the incident laser beam be strongly focused to a very small spot profile for fastest possible risetime. Let the incident laser beam have a round spot profile, and let the angular alignment between the incident light and the modulator be adjusted to maximize the light diffraction efficiency into thefirst order. Now look at the beam profiles the zeroth and first diffraction orders in the far-fieldlimit at some distance downstream of the modulator. typical pair of profiles is shown in Fig. 19 in contour and isometric plots. Note from this figure that the

ZEROTH CRIER

FIRST

n

W The small angular acceptance windowof a typical acousto-optic modulator implies important limitations on modulator performance. In this figure, we show the far-field propagation angle distribution of the zeroth and positive first diffraction orders when the incident light beam has been tightly focused into the modulator to reduce modulator risetime. Focusing spreads the distribution of incident light propagation angles. Not all angle components pass through the modulator's angular acceptance window.

JOHNSON

162

first order beam is not round but elliptical, even though the incident laser beam was round. Also observe the distinctive structure of the zeroth-order beam which emerges from the modulator. A central dark band appears in this profile, corresponding to the light which has been diffracted into the first order, but on either side of this dark band are bright areas corresponding to light which has not coupled efficiently. (This dark band in the zeroth order can be used to optimize the alignment of the modulator with respect to the incident laser beam.) The profile distortion and diffraction efficiency degradation evident in the first diffraction order can best be understood with respect to the modulator’s angular acceptance window. Let us overlay the incident light angular intensity profile (a Gaussian) on top of the modulator’s angular acceptance window, as shown in Fig. 20. Three separate plots are shown in Fig. 20. All three assume fixed transducer length L and fixed acoustic carrier frequency fc, hence all three have identical angular acceptance window span The three differ in amount of focus of the incident laser beam. The top view shows the far-field profile associated with a comparatively large incident beam (hence comparatively slow modulator response

W

mow I

20 One important dimensionless scaling parameter which characterizes acousto-optic modulator performance is the ratio A of the incident light beam’s propagation angle spread to the modulator’s angular acceptance windowspread.

DESIGN OF ACOUSTO-OPTIC MODULATORS

163

time). A large beam tends to stay well-collimated, it fits easily within the modulator’s angular acceptance window.Contrast this with the bottom figure, which shows the far-field profile associated with a strongly focused incident laser beam. A significant fraction of this incident light beam falls outside of the acceptance window, hence the resulting first-order beam exhibits strong profile distortion and severe loss of diffraction efficiency. The relevant parameter which governs this degradation is a dimensionless scaling of the optical beam divergence to the modulator window spread

as introduced by Maydan the inverse parameter,

Young and Yao [15, 161 have introduced

We will use the A parameter. A small value of A corresponds to wellcollimated laser light (slow risetime) and minimal angular window degradation. A large value of A corresponds to fastest modulator response, but with severe window-induced distortion of the modulated laser beam and with significant light throughput loss. The light throughput loss can be readily calculated by a numerical integration of the incident light’s Gaussian intensity profile with the modulator’s angular window, with results as shown in Fig. 21. Two alternative acceptance window scalingfactors have been shown in Fig.21. The scaling most frequently used in this chapter assumes constant grating strength V , for constant diffraction efficiency (usually at peak diffraction efficiency, V = IT) at optimum Bragg angle alignment. Hence, as varying transducer lengths L are considered, the RF drive power P, must be adjustedin inverse proportion to the length, per Eq. in Section 2. An excellent approximation to this curve, useful for modulator design work, is qwindow(A) = 1 - 0.210773A2+ 0.026156A4

for 0 A

2

(56)

(This approximation applies particularly for high grating efficiencies, V = IT.) An alternative scaling, useful for direct comparison with the work of Maydan assumes fixed RF drive power P,, hence a grating strength V which is directly proportional to thetransducer length L . Let us next consider the distortion of the near-field profile of the first diffraction order beam compared withthe incident laser beam, assuggested by Fig. 22. An excellent approximation to the first-order profile can be derived in the limit of small diffraction efficiency(i.e., small grating strength

JOHNSON I00X >.

I

I

I

I

l

I

I

I

z

-

W

I -

l-

3

FIXE0 GRATING STRENGTH V

OPTICAL / ACOUSTIC DIVERGENCEANGLE

-

RATIO A

21 The modulator's angular acceptance window blocks some the incident light energy, resulting in a reduced light throughputefficiency. The amount this light throughput reduction is dependent upon how the angular acceptance window scales with different transducerlengths L. alternative scaling choices are shown in this figure.

V). In this limit, the first-order profile is given by a convolution of the incident light profile Ein(x)and the sound field profile S@), scaled by an obliquity factor x = z&,ifi: Defining the first-order beam diameter at the ll8 intensity points, and assuming the Ein(x) and S(z) profiles given previously by Eqs. (21) and we find to an excellent approximation

+ (Leshift)211R which can be rewritten =

Dl = Din[1 +

@Y]ln

DESIGN OF ACOUSTO-OPTIC MODULATORS

165

1

\

22 Acousto-opticmodulationcan broaden the dimension of the diffracted beam with respect to the incident beam because of the finite sound field depth L and the oblique propagation angle needed for maximum diffraction inthe Bragg regime.

This relation is plotted in Fig. 23. We find minimal beam diameter growth for values of dimensionless design parameter A up to 1 and significant growth for larger values. This analysis assumes a small diffraction efficiency. For larger values of grating strength V , numerical methods can be used to determinethe first-order profile. We find that forgrating strengths up to V = IT (peak diffraction efficiency), the diameter growth iswell approximated by Eq. and Fig. 23. Significant profile distortion occurs for higher grating strengths (overdriven modulator), butthis is not a typical operating regime. 6.3

Risetirne Dependence upon Transducer Length

The temporal response model presented in the previous section apples in the limit cf a very thin transducer length L. Maydan [l41 has analyzed the impact of a finite sound field length L upon the temporal response of a modulator, and has shown that the risetime expression given by Eq. (37) must beadjusted upward whenthe transducerlength L is significant. Chang [l21 has performed a similar analysis in terms of modulator frequency response, showing the bandwidth degradation as the transducer length L increases. We will show in the next section that, foran optimal modulator design, this temporal response degradation should be minimal. Our purpose in this section is not to present a detailed or rigorous analysis, but to

JOHNSON 4

"

h- 5 2 2 1

z

/

DIVERGENCE

23 Growth of the positive first-diffraction-order beamdiameter D , scaled a function of the transducer length L, as scaled by the dimensionless divergence angle ratio A .

to the incident light beam diameter Din

give a rough order-of-magnitude estimate of this effect, highlighting the physical mechanism involved. Consider Fig. 22, which demonstrates the effect of the oblique propagation angle of the incident light beam. The effective light beam profile encountered by a sound wave front is not the incident profile Ei,(x), but rather a convolution Ein(x)with the sound field profile s(x/8B,,gg). Note that the appropriateobliquity factor forrisetime analysis isthe Bragg angle OBragg, not the interorder shift angle eshift.This can best be appreciated from Fig. 22 in the limit of infinitesimal incident light diameter D,. In this limiting case, the acoustic transit time T is given by L8Bragg/V,; we shall estimate the risetime T~ to be of order TR

=

o-8L0Bragg

VS

DESIGN OF ACOUSTO-OPTIC MODULATORS

167

For intermediate cases, let us approximate the appropriate risetime by a root-mean-square analysis; i.e.,

which leads to typical results as shown in Fig. 24. The parameter N listed in the figure is the dimensionless parameter scaling the transducer length L discussed more fully next. As we have stated, the impact of the transducer length L on risetime and bandwidth should be negligible for a proper modulator design. However, in situations for which this effect is significant, a numerical analysis of the response time is strongly recommended rather than a small signal analysis. When a modulator is operated at high diffraction efficiency, the oblique light propagation angle introduces an asymmetry in the risetime and falltime, as reported by Magdin and Molchanov [40]. This effect is readily described by numerical methods [41]; see the discussion at theend of this section on numerical analysis. Angular window-induced diffraction efficiency degradation is critical to modulator performance, but constitutes only the first of two major efficiency loss mechanisms.Let us next reviewthe other major loss mechanism.

24 The same mechanism which causes a growth in diffracted light beam diameter D , also causes a growth in the temporal response of the modulator. An acoustic wave front takes a longer time to travel through the incident light beam than just the transit time based on the input diameter Din.

168

JOHNSON

6.4 ParasiticDiffraction Loss Most analyses of modulator performance for mathematical simplicity neglect the existence of higher diffraction orders shown in Fig. 11. However, these orders can clearly be seen in the laboratory, and their existence has a critical impact on the overall light throughput efficiency. The best approach to evaluating their significanceis to model the modulator as a pure sinusoidal phase grating [35-371. Such a model leads to thefamous RamanNath coupled-wave equations. Excellent studies of numerical solutions to these equations havebeen published by Klein and Cook [36, 371. We summarize the most relevant results herein. Klein and Cook define three dimensionless parameters which characterize a particular grating diffraction problem. The first parameter is the grating strength V (Eq. (11)). The second parameter measures Bragg alignment angle mismatch. The third is a dimensionless parameter which scales the transducer length L. Klein and Cook use the parameter Q, defined by

as do Young and Yao [15]. Maydan [l41 uses a very similar parameters N , defined by Eq. (17) such that = 47rN. We will use the N parameter hereinafter. Inangle space, the N parameter scales the separation between diffraction orders eshifi to the modulator window spread

An alternative interpretation expresses the N parameter as the “wave intercept number,” seeFig. 25. In this figure, we follow a light ray traveling through the sound field at theoptimum angle €lBragg = &ifi/2 for maximum light diffraction into thefirst order. We count the number of acoustic carrier wave fronts which are crossed by this light ray; this number is our parameter N. The significance of parameter N on selectivity of coupling to particular diffraction orders can best be understood with respect to Figs. 26 and 27. These figures show the results of the rotating modulator response experiment sketched in Fig. 17; they differ from Fig. 18 only in the value of the dimensionless length scaling parameter N . In Fig. 26, we consider a small value of N = 0.1, for which the individual diffraction-order angle window spreads are large with respect to thediffraction order shift angle eshift. This means that, forany given angular alignment, several diffraction orders can extract energy out of the incident light beam. No one order dominates the coupling, hence no one orderreceives a majorfraction of the incident light

DESIGN OF ACOUSTO-OPTIC MODULATORS

INCIDENT LIGHT BEAM

25 An important dimensionless parameter for modulator design is the wave intercept number N . One interpretation of this parameter is the numberof acoustic carrierwave fronts crossed the incident light beam asit travels through the sound field of length L with oblique angle OBragg.

power. We can also see that theangular alignment sensitivity for this class of device is quite low. These characteristics define a Raman-Nath modulator. Compare this with Fig. 27, which shows the angular sensitivity for a modulator with larger N = 10. Any given diffraction order in Fig. 27 has a quite narrow angular acceptance window compared withOshift. Hence very selective coupling into just one higher diffraction order can be achieved by proper angular alignment. That diffraction order can then receive the majority of the incident light power. These characteristics define Braggregime diffraction. Figure 28 shows the results of a numerical study of coupling efficiency into thefirst diffraction order as a function of the dimensionless parameter N , showing clearly the increasingly effectivecoupling selectivity for higher and higher values of N . (This figure assumes perfect Bragg alignment for coupling into the +first diffraction order, and constant grating strength V = IT.) The Raman-Nath diffraction regime is traditionally associated with N < 0.1, Bragg with N 2 1.0, and 0.1 N < 1.0 defines a transition regime with diffraction characteristics intermediate between Raman-Nath and Bragg behavior. In thenext section, we show that optimum modulator performance occurs in the transition regime. In this section, we have studied two major mechanisms by which light diffraction efficiency is degraded. One is a window effect, associated with an angle mismatch between the sound field and the incident light field. The second is parasitic coupling to higher diffraction orders. Efficiency

I70

JOHNSON

IN +2ND ORDER I NTENS I TY

=

f

c__ __ -4 -3 -2 0 + l +2 +4

-4

-3

-2

-1

0

+l

+2

0

+l

+2

+4

0TH ORDER /

-4

-3

-1

-4

-3 -2 - 1

I

0

.

+l

+4

ST ORDER .

.

,

+ 2 +3 + 4

-2ND ORDER -4

-3

-2 - 1

0

+l

+2

+4

26 Another interpretation of the wave intercept number N is a dimensionless ratio of the Bragg angle to the angular admittance window spread. This figure showsthe results of the angular admittance window measurement (i.e., Fig. 17) for small N , i.e., large acceptance windows compared with the Bragg angle. Compare this with the next figure showing angular admittance measurements for large wave intercept number N . The broad acceptance windows mean that several diffraction orders can couplethe incident light energy, implying that no onehigher order can dominate the coupling. This is characteristic of Raman-Nath regime diffraction.

degradation due to window effects can be minimized by a very wide modulator window, whichoccurs for very short transducerlength L ; efficiency degradation due toparasitic coupling can be minimized by very longtransducer length L , with associated narrow angular admittance window. In the next section, we propose a modulator design strategy which optimizes these two conflicting constraints.

DESIGN OF ACOUSTO-OPTIC MODULATORS

IN

=

+2NO ORDER I NTENS I TY -3

-4

+

-2

171

-I

1

0

+l

+2

+4

1 ST ORDER

-4

-3 - 2 - 1

0

+I

+2

+4

-4

- 3 -2

0

*I

+2

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- l S T ORDER -4

-3 -2 - 1

0

+l

+2

+4

-4

-3 - 2

0

+I

+2

+4

-1

27 This figure shows the results of the angular admittance window measurement for large N , i.e., small acceptance windows compared with the Bragg angle. This implies a high degree of angular selectivity in the acousto-optic diffraction process for coupling into just one higher diffraction order. This is characteristic of Bragg regime diffraction.

6.5 Numerical Modeling Techniques The analyses given in the literature andin this section on thick sound field effects typically assume low diffraction efficiencies for simplicity. This allows a Born scattering integral approximation, as detailed by Gordon often with analytical solutions. For higher diffraction efficiencies, numerical methods are strongly recommended. Consider first a sinusoidal carrier with no video modulation. The differential equationdescribing light propagation leads naturally to a coupled set of differential equations, each describing the evolution of a particular diffraction order This set is the Raman-Nath equations, and these

172

JOHNSON

-

-

-

N 28 The wave intercept number N governs the saturation diffraction efficiency into the positive first diffraction order. This figure assumes ideal Bragg angle alignment for positive first-order coupling, and a constant grating strength V of radians which gives peak diffraction efficiency in the Bragg regime. The saturation diffraction efficiency is low for small values of N because of parasitic coupling into higherdiffraction orders, whereas the peak diffractionefficiency approaches 100% for high values of N .

equations can be solved by direct numerical integration. Alternatively, they canbe solved by eigenstate analysis The existence video modulation considerably complicates the analysis. In the special case of a periodic video signal, with a modulation overtone identical to an overtone the carrier frequency,a coupled set of differential equations can still be derived, as shown by Klein and Cook and by the author [41]. This can be a powerful tool for analyzing modulator performance in the highdiffraction-efficiencyregime. An alternative approach has been taken by Korpel and Poon [42-441. They derive their analysis from a scattering integral formulation of the modulation process. This scattering integral can be expanded in a perturbation series in powers the grating strength V . The first-order term in this series is the Born approximation, considered by Gordon Higherorder termsexhibit considerable physical content (e.g., momentum matching constraints), and hence this approach serves as a powerful research and teaching tool. However, in the author’s experience, this perturbation series approach does not lenditself gracefully to engineering analysis. The

DESIGN OF ACOUSTO-OPTIC MODULATORS

173

proliferation of temporal/spatial harmonics with successive perturbation orders rapidly makes this method unduly cumbersome. A numerical approach which allows a design engineer to concentrate most directly on the physics of the problem, with least overhead of numerical algorithmic issues, is the optical beam propagation method (BPM) [45-491. The primarynumerical tool neededin this approach is a fast Fourier transform. Unlike eigenstate analysis, intermediate mathematical steps in the solution have direct intuitive interpretations. BPM has been applied to a broad variety of problems, ranging from acoustic-optic modulator response to channelwaveguide structure analysis to fiber mode propagation studies. The author strongly recommends the interested reader to explore this analytical method.

7 MODULATOR DESIGN STRATEGY We introduce a modulator design strategy in Table 4, suitable for most design applications. An optimum modulator design is defined by a limited range of dimensionless scaling parameters, as listed in Tables 5 and 6. Design recommendations of Maydan [l41 and Young and Yao [15,16] are compared with the recommendations presented in this chapter (Figs. 2932). We will find that recommendations are very similar, but notidentical, and that a review of the differences proves to be quite instructive. The modulatorperformance analyses developed to datewith associated dimensionless design parameters are summarized in Table 5. The choice of optimum modulator design involves a trade-off of conflicting requirements. For example, static contrast ratio can be made arbitrarily high (within constraints of volume scattering and surface quality) by setting a high acoustic carrier frequency fc. However, this will significantly increase the RF drive power P, required for peak diffraction efficiency. We need a design strategy to arbitratebetween these conflicting demands. The identification of one strategy for all possible design constraints is probably too ambitious a goal; however, a useful candidate strategy is outline in Table 4, and is the topic of this section. The first step in modulator design is a statement of system requirements: optical wavelength ho, modulation bandwidth fM, and minimum requirements on static contrast ratio and dynamic contrast ratio (or equivalent measure of temporal modulation fidelity). A candidate modulatormedium with specified interaction orientation is next identified, typically a dense flint glass or a crystal such as lead molybdate or tellurium dioxide. The choice of crystal and interaction orientation defines the index of refraction no,the speed of sound Vs, and the figure of merit M2. From the specification

174 Candidate Modulator Design Strategy 1. Set system specifications optical wavelength h, modulation bandwidth fM minimum static contrast ratio minimum dynamic contrast ratio 2. Identify candidate A 0 modulator medium Index of refraction no Sound speed r/, Figure of merit M z 3. ~dentifyrisetime requirement Implies light beam diameter Din dentify minimurn static contrast ratio Implies acoustic carrier frequency f c 5. Identify optimum scaling parameter N Implies transducer length L 6. ~ a l c u l a t eRF drive power P, and power density 7. Are power and power density acceptable? Yes -+ complete design No -+ revise specifications choose alternative medium choose anisotropic interaction choose phased array electrode configuration

S u m ~ a r yof Modulator Performance Analyses ~erformancemeasure

F drive power P,, power density Static contrast ratio Dynamic contrast ratio

Dimensionless design parameter

Section 3 4

5 6

Saturation

on modulation fidelity, a risetime requirement T~ is identifi~d,which in turn implies a specific incident light beam diameter Din.The requirement on static contrast ratio then can imply a minimum acceptable acoustic carrier frequency fc. We will show in this section that best modulator performance occurs for a limited range of the dimensionless parameter N.

DESIGN OF ACOUSTO-OPTIC MODULATORS Table Parameter

175

Alternative Modulator Design Targets YoungMaydan

and Yao

Johnson

A N

DJA

Not mentioned, implied

1 INTERCEPT NUMBER N

29 The modulator’s total light throughput efficiency shown here results from two factors, the angular admittance window and the saturation diffraction efficiency. The modulator response peaks for wave intercept number N = 0.5. The light throughput efficiency degrades for smaller N because of degraded saturation diffraction efficiency (Fig. 28). The efficiency degradesfor larger N because the modulator’s angular acceptance window collapses as N grows larger (Fig.

Given a target N and an acoustic carrier frequency fC, we can calculate an associated transducer length L. Finally, we calculate the required RF drive power P, and power density, and compare thesewith reasonable limits for the particular modulator medium under consideration. If the power and power density fall within acceptable bounds, we haveour modulatordesign. If the power and/or power density are unacceptably high, then we have four options, as shown at thebottom of Table 4. The first option, of course, is to relax on one more of the system requirements. The second option is to consider an alternative and more efficient .modulator medium. If we

JOHNSON

176 1

>

U

z

W

l” U

<

E 0

CARRIER FREOUENCYR SET ME 30 Fast risetime any given acousto-opticmodulator is obtained only at the expense degraded light throughput efficiency.

had chosen a dense flint glass, we could next try tellurium dioxide. The final two options seek to break the design deadlock bymodifying the modulator’s angular window performance. One is to use anisotropic Bragg diffraction and a second option is to break the transducer into several discrete segments and use phased array techniques to manipulate the sound pattern. Both techniques are critical to the success of acoustooptic deflector design, and are described in detail in the previous chapter. Major modulator performance analyses and parameter recommendations have been published by Maydan [l41 and Young and Yao 161; these recommendations are summarized in Table 6 in terms of three dimensionless design parameters: N , A , and Din/A. Please be careful in reviewing the published parameter recommendations. These three parameters are not mutually independent, but rather are related by

N =

(z)

A

e)

Not all published parameter combinations satisfy this self-consistency requirement.

177

1

TICAL

2

3

EAM

DIAMETER ElIR/ A

4

Modulator light throughput efficiency degrades as the incident light beam is focused to a smaller spot for faster risetime because of angular admittance window effects.

The parametric recommendations listed in Table 6 are similar, but not identical. For example, Maydan recommends N 2 1.0. His intent is to (minimize parasitic diffraction losses) by operating in the maximize qparasitic Bragg regime. By convention, the Bragg regime operation is identified by N 2 1.0 [36]. Maydan’s analysis focused on modulator window effects and did not explicitly factor qparasitic effects. Young and Yao analyzed more closely the competition between optimizing qwindow and qparasitic, and found that a much smaller value of N = 0.5 gave acceptable (and as we shall show, superior) performance. The loss in qparasitic is a mere 4% when reducing N from 1.0 to 0.5, but the angular acceptance window doubles. This interplay is best shown by Fig. 29, which shows the peak d~ractionefficiency at saturation (i.e., for a grating strength V = T) for a focused laser beam, plotted as a function of the transducer length 1; scaled by the dimensionless parameter N . Peak diffraction efficiency is derived by multiplying the window efficiency rolloff behavior (shown in Fig. 21) with the parasitic diffraction loss behavior (shown in

JOHNSON

1

WAVE INTERCEPT NUMBER

32 Animportantaspect of modulatordesignisthe RF drivepower needed to achieve peak diffraction efficiency. This figure shows the diffraction efficiency scaled to the RF drive power needed to read peak diffraction.

Fig. subject to theconstraint of Eq. (This figure has never before been published in the literature.)As we see from this figure, the diffraction efficiency peaks at about N = 0.5, and degrades gradually thereafter because of collapsing angular acceptance window constraints. Figure 29 summarizes the design constraints on the modulator component manufacturer, who has direct control over the acoustic carrier frequency fc and on the dimensionless parameter N , but not on the incident light beam diameter D,. A companionFigure 30 summarizes the modulator performance from the perspective of the modulator user, who has direct control over the incident light diameter Din but not the modulator’s dimensionless design parameter N . This figure shows the degradation in peak diffraction efficiency as a function of risetime, and combines the information in Figs. (risetime dependence on beam diameter Din)and Fig. 31 (diffraction efficiency dependence on beam diameter Din). Another majordiscrepancy in recommendations of optimum design parameter range is Maydan’s choice of of 1.5-2.0, which is significantly higher than the Young and Yao or this author’s recommendations. The reason for Maydan’s choice is that he studied diffraction efficiency per unit

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drive power P, rather than diffraction efficiency per unit grating strength V . In the absence of factoring qparasitic effects, Maydan’s analysis would have shown that modulator acceptance window effects disappear as the transducer length L collapses to zero. This is not a realistic design option, however, as the drive power P, must increase to unacceptably high levels to maintain reasonable diffraction efficiencies. To give a more realistic design analysis, Maydan chose to present diffraction efficiency per unit drive power. In our analysis, if the performance is presented in terms of diffraction efficiency per unit drive power, asshown in Fig. 32, then longer transducer lengths and larger values of dimensionless parameter N would clearly be favored. Thus we can formulate the following design rule. If the RF drive power and power density derived from the design algorithm shown in Table are at acceptable levels, then best modulator performance (in the sense of maximum peak diffraction efficiency) occurs for N of approximately 0.5. However, if the power and/or power density are excessive, then increasing N to 1.0 is advised. The peak diffraction efficiency will degrade somewhat, but a doubling of the transducer length will halve the drive power and reduce the power density by a factor of 4. For higher performance devices, this can significantly reduce thermal and reliability issues. In practice, for any given modulator medium, a well-defined family of modulator products covering a range of performance/price options can be designed. A typical product group offering from one representative vendor, Crystal Technology, is summarized inTable 7 and Figs. 33-36. Note from these figures the general trend that highest performance (fastest risetime) is associated with the highest carrier frequency devices, with the highest RF drive powers and the smallest incident light beam diameters. In this product offering, an RF drive power limit of 1 W is recommended by the manufacturer. Hence the highest-performance device, a 500-MHz carrier Table Crystal Technology Acousto-optic Modulator Performance Specifications

Carrier frequency Model

(MHz)

Optical wavelength (nm)

Maximum data rate (MHz)

Active aperture (mm)

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Figure The acousto-optic modulator design rules discussed in Section.7 lead naturally to a series of distinct products, distinguished primarily by the choice of acoustic carrier frequency, and with all other performance attributes scaled accordingly. Shown here is the tellurium dioxide modulator productline for Crystal Technology, Inc., which has 80-MHz,llO-MHz, 200-MH2, and 500-MHz versions.

frequency modulator, exhibits significantly lower diffraction efficiency because the power needed to reach peak diffraction exceeds the l-W safety limit (Fig. 36). This concludes our discussion of design strategy issues.

8 SCANNER SYSTEMINTEGRATIONISSUES We have reviewed the performance of an acousto-optic Bragg cell as a conventional “point” temporal modulator.However, system performance can often be enhanced, sometimes dramatically, by exploiting unique characteristics and capabilities of an acousto-optic modulator. In this section, we sketch four examples in the context of laser scanning systems. The following discussion isintended to suggestive of modulator capabilities, not an exhaustive discourse of technical details; references to literature are given for morecomprehensive treatment. The four techniques discussed

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36 The diffraction efficiency as a function of RF drive power is shown for Crystal Technology’s tellurium dioxide modulator family. Peak diffraction efficiency is achieved at drive powers up to 1W for the80-MHz, 110-MHz, and 200MHz units. The 500-MHz unit requires more than 1 W to reach peak diffraction efficiency. However, the manufacturer recommends that no more than 1 W be applied to keep thermal stress within tolerable limits. Hence this device must be operated at less than peak diffraction efficiency.

herein include polygon scanner facet tracking for improved light throughput and reducedpolygon size, two alternative methods forgenerating multiple independently modulated output beams, and the Scophony scanner architecture for achieving maximumdynamic contrast ratio performance by exploiting the scrollingspatial modulation feature of an acousto-optic Bragg cell.

8.1 Acousto-opticFacetTracking One of the most challenging aspects laser scanner design is the rotating polygon mirror. The mirror must satisfy a number of constraints. The first constraint is that the facet must be at least a certain minimum size to achieve the resolution performance required of the scanner (e.g., Eq. (4) which identified a scanner cutoff frequency). For purposes of the following discussion, let us label this minimum aperture size W . The second constraint

DESIGN OF ACOUSTO-OPTIC MODULATORS is that the facet must direct laser light to thescanner image plane with as high a throughput efficiency as possible. This second constraint is made all the more challenging because the polygon facet translates as well as rotates during the scanning sequence (Fig. causing a decentration of the incident laser illumination with respect to the facet. If the facet size is just large enough to achieve the resolution requirements, andif the incident illumination just fills the facet, thenthis decentration will severely degrade both the scan spot power and the scan spot dimensions over most of the scan sequence. As an extreme example, consider the bottom illustration in Fig. 37, in which the illumination profile is midway between the facet which is just finishing its scan sequence and the next adjacent facetwhich is just starting its scan sequence. Only half of the light power falls in the first facet, and hence the scan image spot only has half the peak light power. Furthermore, because of diffraction effects, this scan spot is spread at least 2 compared with its center-of-scan profile.

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37 A fundamental design problem for a laser scanning system utilizing a rotating polygon mirror that the mirror translates as well as rotates during the scan cycle. The incident light beam canbe properly centered within the scan facet only at one instant during the scan sequence. all other times, the light beam is decentered.

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Two alternative approaches havebeen developed to control this problem. In one approach, the polygonis made much larger than width W normally required by resolution considerations, while the incident light has width W (top illustration in Fig. 38). This means that essentially allpf the incident illumination falls within the clear aperture of the polygon over most of the scan sequence. This approach is named the underfilled facet condition. It has the advantage of excellent light throughput efficiency, but at the cost of a painfully large polygon. At high scan speeds, this large polygon represents a difficult mechanical engineering design challenge. The second approach is to scale the polygon facet width to theminimum required W needed for scan spot resolution, and to spread the incident laser illumination over several facets (bottom illustration in Fig. The facet of interest capturesonly a fraction of the incident light power, typically of order so this approach has significantly lower light throughput efficiency, hence requires a much more powerful (and often much more expensive) laser. However, the polygon is the smallest that it can be from optical resolution considerations. The relative performance of these alternative design options are compared in Fig. 39. (In this figure, SOS stands for start of scan, COS for center of scan, and EOS for end of scan.) When the scanner modulatoris an acousto-optic Bragg cell, then a third alternative exists for polygon facet illumination: acousto-optic facet tracking. The essential conceptissketchedinFigs. and By steadily

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38 Several design approaches have been developed to cope with the facet decentration problem in the lastfigure. One approach scales the incident light beam much smaller than thepolygon facet; this is called underfilled polygon illumination. A second approachspreads the incident light beam over several facets; this is called overfilled polygon illumination.

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This sequence shows the acousto-optic facet tracking concept in action. The modulator’s carrier frequency is constantly shifted that the output light remains centered on the polygon facet throughoutthe scan sequence. At the end of the scan sequence, the carrier frequency is reset to begin the next scan cycle, causing the light beam to jump to the next adjacent facet, changing the RF carrier frequency fc, rather than keeping it fixed, which would be normal modulator practice, the diffracted light beam emerging from the modulator will sweep through a range of propagation directions. By careful system design, this beam cantrack the translation of the polygon facet. The resulting scan sequence is shown in the next figure, Fig. 41. In this approach, the polygon facet can take its smallest size W , and the incident laser illumination is scaled to just fill the polygon facet. A linear frequency chirp from the RF carrier oscillator causes the light to remain centered within the facet aperture. At the end the scan sequence, the RF frequency is rapidly reset to begin the next chirp, causing the laser

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beam to shift rapidly to the next adjacent facet. The modulator should blank the light beam during this short retrace period to prevent spurious recording. The requirement that an acousto-optic modulator performfacet tracking as well as temporal modulation increases the performance requirements on the modulator. These requirements must be carefully specified and considered when selecting a suitable modulator.

8.2 Multiple-Beam Scanning For very high performance scan systems, even when using facet tracking, a polygon mirror canbeexcessively large and spin at excessivelyhigh rotation rates. The most effective technique to reduce the rotation rate is to scan multiple independently modulated beams at the same time. One approach for achieving multiple output beams from a single acousto-optic modulator with a single transducer is sketched in Fig. 42. This approach works bests when the temporal modulation requirements per channel are modest. Also, the output intensity of any one channel is influenced by the video signal in adjacent channels, since all output channels derive their

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42 One of the most demanding design constraints in a laser scanner is the rotation speed of the polygon mirror. This rotation canbe significantly reduced by scanningmore than one output light beamat a time.An acousto-optic modulator can generate several essentially independent beamsfrom one common input beam by summing several discrete RF carrier frequencies.

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optical powerfrom the same input pump beam. This crosstalk can be reduced by operating at reduced diffraction efficiency, and electronic or computer-defined video predistortion can further compensate for the crosstalk. For higher temporal modulation performance systems, the preferred implementation of a multiple-output-beam modulator is shown on theright in Fig. 43. For comparison, a standard single-channel acousto-optic modulator is shown on the left. The multiple-channel modulator consists of a single acousto-optic cell with a single large transducer bonded to it. Individual independent channels are derived by photolithographically patterning separate top electrodes. Electronic and acoustic isolation are often enhanced in some designs by cutting a shallow trench between adjacent channels with a dicing saw. The optimum modulator design for any given channel is identical with the analysis given in the previous sections. The additional design challenges from such a multiple-channel modulator are to keep the electronic and acoustic crosstalk to a minimum 521. One example a multiple-channel Braggcell is shown in Fig. 44, showing a 32-channel longitudinal mode tellurium dioxide device with MHz carrier frequency, developed by Crystal Technology of Palo Alto, CA [53]. The package dimensions are 2 inches (optical path length) X inches 3 inches. The RF drive signals are applied by stripline PC board,

alternative approach to multiple-beam modulation is to pattern multiple discrete transducer electrodes on top of a common transducer. This figure compares a standardsingle-channelmodulator on the leftwith a four-channel modulator on the right. (The circles on the endface represent the incident laser beam profile.)

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Photograph of a 32-channel modulatortdeflector developed by Crystal Technology. The carrier frequency is 400 MHz, andthemodulatormediumis tellurium dioxide.

with 40 dB of electrical channel isolation and & 1" maximum phase error. Each electrode's impedance-matching circuit is housed in a separate mechanical compartment to suppress electrical crosstalk. The transducer electrode shapes are apodized to minimize acoustic diffraction-induced crosstalk. Miniature RF connectors are used that all channel inputs could be conveniently located on one mounting surface. For 632.8-nm laser light, the diffraction efficiency is40% per watt of RF drive power, with typically

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dB of optical channel-to-channel isolation. In general, performance of this device is primarily limited by electrical, rather than acoustic, crosstalk.

8.3 ScophonyScannerArchitecture The final topic in our discussion of scanner system integration issues is a brief introduction to the Scophony scanner, an alternative to the more traditional flying spot scanner[ The essence of flying spot scanner design strategy is to image as small a scan spot as possible and to use a very fast temporal modulator to impress the video signal. The Scophony scanner uses essentially the same scanning components as flying spot scanner (Fig. 2), but takes a radically different design strategy for using these components. The essential concept of the Scophony scanner is that the video image to bescanned exists as a traveling sound field inside the modulator(Fig. 7). The scanner, then, is an imaging system projecting this acoustic image onto the final scanner image plane. Consider Fig. 45 which showsthe essential features of the Scophony scanner. Three separate time snapshots are shown: the top set of figures shows an early time in which two video pulses are just leaving the transducer, the middle set of figures shows a later time snapshot in which the two video pulses have propagated to the center of the laser illumination, and the bottom set of figures shows a still later time in which the pulses have propagated to the

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far edge of the laser illumination. Unlike a typical temporal modulator, the laser illumination for Scophony scanning is spread overa considerable portion of the acoustic propagation path. Contrary to popular misconception, however, the laser illumination does not have to image a full video scan line at any one instant. The middle columnof three figures in Fig. shows the schlieren image of these acoustic pulses which is projected onto the image plane by the scanner optics, in the absence of any scanning motion. The scanner optics project the image with optical magnification M , that the pulse images move across the image plane with speedMVsound. In theabsence of scanning motion, these moving pulse images create a blurred exposure, and no effective recording takes place. The Scophony concept is to introduce a scanning motion with speed V,,, whichis opposite in direction to the acoustic image motion andequal in magnitudeto theacoustic image speed. This causes the acoustic images to be “frozen” in place, allowing for an excellent exposure profile to be generated, as shown in the right-hand column in Fig. The scan spot consists of a window which travels with speed V,,,, which extends over several pixels of distance, and which is segmented by the video image to be painted. The Scophony scanner directly exploits the scrolling spatial modulation characteristic of an acousto-optic Bragg cell and circumvents the temporal response degradation whichwas detailed in Section 5 for a broad-area detector. The dynamic contrast ratio of the exposure profile imaged by a Scophony scanner is superior to that of a flying spot scanner, as seen in Fig. up to the cutoff frequency associated with the Scophony scanner. Several techniques have been identified and published for electronically processing the video signal to extend the resolution performance of a Scophony scanner, as shown in Fig. 9 CONCLUSION

Acousto-opiic modulators have had a fascinating history spanning more than five decades. These highly reliable components are robust and can be manufactured by batch processes for low unit cost. The acousto-optic modulator has spawned a number of related useful component technologies, including deflectors and tunable filters. The analysis, both numerical and closed form, of acousto-optic interactions is a large and active research field. We havereviewedbasic operating principles of an acousto-optic modulator and have presented several simple analyses of modulator performance, with special emphasis on its performance as a “point” temporal modulator. Several examples of scanner system implementationsof acoustooptic modulators have been reviewed. We find that best system perform-

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SCOPHONY SCANNER WITH ELECTRONIC PROCESSING

VIDEO SIGNAL FREQUENCY SCANNER

CUTOFF FREQUENCY

The exposure fidelity of a flying spot scanner can be compared with that of a Scophony scanner by means of its modulation transfer function ("IF). All scanners exhibit a common cutoff frequency defined by the flnumber of the scanner optics and the wavelength of the light source. Superior dynamic contrast ratio is shown by the Scophony scanner compared with the flying spot scanner for frequencies up to half of this cutoff. Various video signal processing techniques have been identified to extend the Scophony resolution performance upto the full cutoff frequency.

ance often occurs whenever a system canexploit the uniquescrollingspatial modulation characteristic of an acousto-optic cell; an excellent example of one such system is the Scophony scanner.

ACKNOWLEDGMENTS The author would like to thank John Reilly for assistance with marketing information and for obtaining several photographs used in this chapter; Crystal Technology, Inc., for photographs 1, and Xerox Corporation for photograph 7 and Figs. 2 and David Hecht and David Yevick for anintroduction to BPM;Armand R.Tanguay, Jr., fornumerous

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stimulating technical discussions; and my wife Claudia M. Frank for her patient support during a lengthy manuscript preparation process.

REFERENCES Bergmann, L., Ultrasonics, Wiley, New York, pp. Okolicsanyi, F., The wave-slot, an optical television system, Wireless Eng., 14, Robinson, D.M., The supersonic lightcontrol and its application to television with special reference to the Scophony television receiver, Proc. IRE, 27, Lee, H. W., The Scophony television receiver, Nature, Adler, R., Interaction between light and sound, IEEE Spectrum, 4 , Damon, R. W., Maloney, W. T., and McMahon, D. H., Interaction of light with ultrasound: phenomena and applications, in Physical Acoustics, Vol. (W. P.Mason and R. N. Thurston, eds.), Academic Press, New York, pp. Gottlieb, M., Ireland, C. L. M., and Ley, J. M., Electro-optic and Acoustooptic Scanning and Deflection, Marcel Dekker, New York, Korpel, Adrianus, Acousto-optics-a review of fundamentals, Proc. IEEE, Special Issue on Acousto-optic Signal Processing, Korpel, A.,Acousto-optics, in Applied Solid State Science, Vol. I1 (R. Wolfe, ed.), Academic Press, New York, Korpel, *A.,Acousto-Optics, Marcel Dekker, New York, Sapriel, J., Acousto-Optics, Wiley, New York, Chang, I. C., Acoustooptic devices and applications, IEEE Trans. Sonics Ultrason., SU-23, Gordon, E.I., A review of acoustooptical deflection and modulation devices, Proc. ZEEE, 54, Maydan, Dan, Acoustooptical pulse modulators, IEEE J. Quant. Electron., QE-6, Young, E. H., Jr., and Yao, Shi-Kay, Design considerations for acoustooptic devices, Proc. IEEE, Special Issue on Acousto-optic Signal Processing Hams Corporation, Bulk acousto-optic device technology, inAcousto-Optic Signal Processing (Norman J. Berg and John N. Lee, eds.), Marcel Dekker, New York, Beiser, L., Laser scanning systems,in Laser Applications, Vol. (M. Ross, ed.), Academic Press, New York, pp. Urbach, J. C., Fisli, T. and Starkweather, G. K., Laser scanning for electronic printing, Proc. ZEEE, 70, Johnson, Richard V., Optical scanning architectures for electronic printing applications,” Proc. SPIE, 753,

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20. Hecht, D. L., Multibeam acoustooptic and electrooptic modulators, Proc. SPIE, 396, S-9 (1983). 21. Siegman, Anthony E., Lasers, University Science Books, Mill Valley, CA, 1986, pp. 1004-1040. 22. Tateda,M., andHoriguchi, T., Advancesinopticaltime-domainreflectometry, J . Lightwave Technol., 1217-1224 (1989). 23. King, J. P. et al., Developmentof a coherent OTDRinstrument, J . Lightwave Technol., Lt-5, 616-624 (1987). 24. Pinnow, D. Guidelines for the selection of acoustooptic materials, IEEE J. Quantum Electron., QE-6, 223-238 (1970). 25. Pinnow, D. A., Elasto-optical materials, in CRC Handbook of Lasers (R. J. Pressley, ed.), Chemical Rubber Co., Cleveland, OH, 1971. 26. Uchida, N., and Niizeki, N., Acousto-optic deflection materials and techniques, Proc. IEEE, 61, 1073-1092 (1973). 27. Biegelsen, David K.,An ultrasonic technique for measuring the absolute signs of photoelastic coefficients and its application to fused silica and cadmium molybdate, Appl. Phys. Lett., 22, 221-223 (1973). 28. Dixon, R. W., Photoelastic properties of selected materials and their relevance for applications to acoustic light modulators and scanners, J . Appl. P h y ~ . , 5149-5153 (1967). 29. Dixon, R. W.,and Cohen, M. G., Anew technique for measuring magnitudes of photoelastic tensors and its application to lithium niobate, Appl. Phys. Lett., 205-207 (1966). 30. Eschler, H., and Weidinger, F., Acousto-optic propertiesof dense flint glasses, J. Appl. Phys., 65-70 (1975). 31. Gottlieb, M., and Roland, G, W., Infrared acousto-optic materials: Applications, requirements, and crystal development,Proc. SPIE, 214,88-95 (1979). 32. Gottlieb, M., Isaacs, T. Feichtner, J. D., and Roland, G. W., Acoustooptic properties of some chalcogenide crystals,J. Appl. Phys.,45,5145-5151 (1974). 33. Pinnow, D. A., Von Uitert, L. G., Warner, A. W., and Bonner, W. A., Lead molybdate: a melt-grown crystal witha high figure of merit for acoustooptic device applications, Appl. Phys. Lett., 15, 83-86 (1969). 34. Uchida, N., and Ohmachi, Y., Elastic and photoelastic properties of TeO, single crystal, J . Appl. Phys., 40, 4692-4695 (1969). 35. Gaylord, T. K., and Moharam, M. G., Analysis and applications of optical diffraction by gratings, Proc. IEEE, 894-937 (1985). 36. Klein, W. R., and Cook, Bill D., Unified approach to ultrasonic light diffraction, Trans. Sonics Ultrason., SU-14, 123-134 (1967). 37. Klein, W. R., Cook, B. D., and Mayer,W. G., Light diffractionby ultrasonic gratings, Acoustica, 15, 67-74 (1965). 38. Abramowitz, Milton, andStegun, Irene A., Handbook of Mathematical Functions, with Formulas, Graphs, and Mathematical Tables, Dover, New York, 1972, Chap. 7.

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and Johnson, R. V., The effect of laser beam 39. Lucero, J. A., Duardo, J. transverse mode and polarization properties on A - 0 modulator performance, Proc. SPZE, 30, 32-39 (1976). 40. Magdin, L. N., and Molchanov,V. Ya., Nonreciprocal phenomena in acoustooptic modulators, Phys. Tech. Phys., 22, 637-639 (1977). 41. Johnson, Richard V., Temporal response of the acoustooptic modulator in the high scattering efficiency regime, Appl. Opt., 903-907 (1979). 42. Korpel, A., Two-dimensional plane wave theory of strong acousto-optic interaction in isotropic media, J. Opt. Am., 678 (1979). 43. Korpel, A., and Poon, T., Explicit formalismfor acousto-optic multiple planeA m . , 70, 817 (1980). wave scattering, J . Opt. 44. Poon, T. C . , and Korpel, A., Feynman diagram approach to acousto-optic scattering in the near-Bragg region, J . Opt. A m . , 71, 1202 (1981). 45. Fleck, J. A., Jr.,Moms, J.R., and Feit, M. D., Time-dependentpropagation of high energy laser beams through the atmosphere, Appl. Phys., 10, 129160 (1976). 46. Van Roey, J., van der Donk, J., and Lagasse, P. E., Beam-propagation method: analysis and assessment, J . Opt. A m . , 71, 803 (1981). 47. Yevick, D., and Thylen, L., Analysis of gratings by the beam-propagation method, J . Opt. A m . , 72, 1084 (1983). 48. Johnson, Richard V., and Tanguay, Armand R., Jr., Optical beam propagation method for birefringent phase grating diffraction,Opt. Eng., 25,235249 (1986). 49. Fleck, J. A., and Feit, M. D., Beam propagationin uniaxial anisotropic media, J . Opt. A m . , 73, 920 (1983). 50. Dixon, R. W., Acoustic diffraction of light in anisotropic media, ZEEE J. Quantum Electron., QE-3, 85-93 (1967). 51. Guerin, Jean-Michel, Sound diffraction and the optimizing of acousto-optic modulator efficiency, Proc. SPZE, 200, 200-207 (1985). 52. VanderLugt, A., Moore, G. S., and Mathe, S. S., Multichannel Bragg cells: compensation for acoustic spreading, Appl. Opt., 22, 3906-3912 (1983). 53. Amano, M., and Roos, E., 32 channel acousto-optic Bragg cell for optical computing, Proc. SPZE, 753, 37-42 (1987). 54. Korpel, A., Adler, R., Desmares, P., and Watson, W., A television display using acoustic deflection and modulation of coherent light, Appl. Opt., 5, 1667-1675 (1966). Appl. Opt.,18,4030-4038 (1979). 55. Johnson, Richard V., Scophony light valve, 56. Johnson, Richard V., Guerin,Jean-Michel, and Swanberg,Me1 E., Scophony spatial light modulator, Opt. Eng., 24, 93-100 (1985).

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Acousto-Optic Tunable Filters Milton S. Gottlieb Westinghouse Science and Technology Center Pittsburgh, Pennsylvania

INTRODUCTION The most widespreaduses of the acousto-optic (AO) interaction have been those in which the RF signal driving the transducer is made to control in some fashion a fixed optical beam, generally from some type of laser. The optical beam in these cases is entirely specified, and under system control. We can choose the wavelength, coherence, beam direction, beamspread, etc., to best suit the particular application. The most general operation the cell is that in which the Fourier transform of the input RF signal is produced inthe focal plane of the light beam, through the Bragg relation, OB = F(A,fl.The applicable Bragg relation will, of course, be determined by whether the interaction is isotropic or anisotropic. Common to both types of interactions, however, isthe appearance in the applicable formulas for Bragg angles, of the radio frequency and the wavelength always as the product. Hence, it is really the Fourier transform of this product which is produced. Since the wavelength is constant for thetypical signal processing device, the Fourier transform of RF is generated. For the class of devices discussedin this chapter, of which the tunable filter (AOTF) is the leading member, the light is generally not under independent control, but rather is being characterized by the device. In this process, it .is essentially the Fourier transform of the input light that is under examination, as is the case with a conventional grating spectrometer. devices 197

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can perform a great variety of spectroscopic functions, in many cases more effectively than conventional devices because of their inherent agility, and their capability to directly impose modulation on the light. An issue commonly raised in evaluating the effectiveness of processing methods relates to the advantages of the A 0 over conventional microwave and digital electronics systems. Generally, the advantage is burdened by the necessity to convert the inputelectronic signalsto optical signals, and upon processing convert the optical signals back to electronic signals. This two-way loss may be a very severe handicap when making such comparisons. In comparing spectroscopic types of A 0 devices with their conventional counterparts, on the other hand, there is no comparable handicap going from optical to electronic domains; it is the same for as for conventional devices. The burden, then,arises from the necessity to provide electrical power to establish the interaction between light and sound. The comparison will require that this power burden will be more than compensated by the advantages of the A 0 approach. Thereare several multispectral (i.e., multiwavelength) signal processing schemes, as well as spectroscopic systems which incorporate some aspects of signal processing, which amount to combining spectroscopic analysis and optical signal processing within one system. In such cases, there may be considerable advantage to performing several such functions acousto-optically, and the benefits can be considerable. The subject of AOTFs will be comprehensively reviewedin this chapter, beginning with theory and operation andconcluding with an examination of a large variety of applications. Historically, the collinear AOTF was first to be reported, and the concepts central to its operation will be used to introduce many of the important features. Thiswill be followed by the noncollinear AOTF, whose use far exceeds the former in practice. Exact calculations will be presented of the important device characteristics, such as the resolution and angular aperture. A comparison will be made with other spectroscopic devices, emphasizing the special features and advantages of the AOTF. A principal objective of this chapter is to lead the reader through the steps needed to design and fabricate AOTFs. The chapter begins with a review of candidate AOTF materials, and theguidelines for selecting crystals most suitable for particular devices. This is followed by the design procedure foroptimizing the device to satisfy the intendedsystem requirements. This part concludes with considerations for fabrication of the AOTF, for which the major components will be assembly of the cell, transducer structure, and heat sink. A second major objective is to review several AOTF-based systems and applications that have arisen over the past two decades since the invention

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of the AOTF. The first of these, laser cavity tuning, originally provided the motivation for devising an electronically tunable element, and two leading examples are presented in detail. The most widespread uses for AOTF systems are naturally related to spectrometry. An entire volume would be needed to cover in detail all possible spectrometric systems, and only several illustrative examples have beenselected for this chapter where have already made a significant impact. Examples of commercially available instruments, which are important forcombustion gas monitoring and liquid cell analyzers, are included. The use of the AOTF for several specialized instruments, such as the spectropolarimeter and the fluorescence spectrometer, are gaining rapidly in importance, and these are also described. One of the most intriguing new areas is that of spectral imaging, for which several prototype systems and examples of their use provide some insightinto its possibilities. Finally, we discussthe AOTFin its optical waveguide form which has been exploited for application in fiberoptic communications systems, for diode laser tuning, and for wavelength multiplexed switching. It is hoped that this chapter will stimulate further development on the many more possible applications for the AOTF which exist.

2 THEORY AND OPERATION OF A 0 TUNABLE FILTERS (AOTF) 2.1 Collinear AOTF The operation of the collinear AOTF was anticipated, although not explicitly, by the theory of the anisotropic Bragg diffraction presented by Dixon [l], who derived the equations for the Bragg angles of incidence (Cli) and diffraction (0,) for which there is a strong interaction due toperfect phase matching. These equations take the form

'

where v is the acoustic velocity, X,, is the optical wavelengthinvacuum, and ni and nd are the refractive indices corresponding to the incident and the diffracted light. It is instructive to examine a plot these equations to see how the different regimes may be useful. Such a plot is shown in Fig. 1using typicalvalues of the refractive indices, and theacoustic velocity, for a wavelength of 1 pm. The significant region of this plot for AOTF

200

GOTTLIEB 90

g

30

-$

0

a,

- ~ o l ~ ~

c = l

8

g

of Diffradbn

U.0

0.2 0.4

0.8 1.0

1.4

Frequency

Angles of incidence and diffraction for anisotropic Bragg interaction. For the example shown here, ni = 2.15, nd = v = lo5 cdsec, and A = 1 bm.

operation is that corresponding to theminimum frequencyfor which phase matching can take place. At this frequency, sin €li = -sin ed = 1, and the wave vectors corresponding to the incident and diffracted beams are parallel or antiparallel. The wave vector diagram which describes this interaction is shown in Fig.2 , in which the threewave vectors corresponding to the incident (G) and diffracted (G)light beams, and the acoustic beam, all have their propagation direction normal to the optic axis. For this interaction the vector equation expressing the conservation ofmomentum is

(c)

Equation can be expressed as a scalar equation by substituting the appropriate values of the vectors:

Since the polarization the incident light can be either ordinary or extraordinary, the direction the acoustic vector may be either positive or negative for phase matching. If the incident light is chosen to have the

ACOUSTO-OPTIC TUNABLE FILTERS

201

2 Wave vector diagram for collinear diffraction in birefringent medium. For this example, the incident light, represented by is extraordinary polarized, and the diffractedlight, represented by is ordinary polarized.The acoustic wave vector is represented by E.

smaller the light wave vectors, the roles the curves in Fig. 1 would be reversed. Solving the scalar Eq. for yields f=-

v An

h0

where An = n, - nd.This relation expresses the phase-matching relationship between the incident light wavelength and the acoustic frequency for which this collinear interaction may take place. It implies that the polarization direction of the incident light will be rotated 90" when these conditions are satisfied. These important collinear relationships were first realized by Dixon [l],and later Harris [2] showed that they could be used as the basis for an AOTF. In this situation, Eq. (5) can be considered as the tuning relation for the filter. LiNbO, was chosen as thefirst crystal to demonstrate such a collinear tunable filter The tuning curve expected

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202

for LiNbO,,based on the values no = 2.3, ne = 2.2, and v = X lo5 cm/sec, is shown in Fig. A coupled-wave analysis can be used to calculate some of the important characteristics for this type of interaction, which include the spectral bandwidth, the transmittance, and the acceptance aperture. This analysis yields an expression for the transferof optical power fromthe incident mode, Po, to thecoupled mode, P,. For aninteraction length, L , the power ratio PJP0 between the two modes equals the filter transmittance T , and for perfect phase matching is

where

In Eq. (6a), is the A 0 material density, PA is the acoustic power density, and M2(ij)is the A 0 figure of merit which corresponds to thephotoelastic coefficient pij appropriate for the collinear interaction configuration. The incident optical power at the tunedwavelength will be 100% converted to the orthogonally polarized mode for I'L = The bandwidth and the angular characteristics of the filter cannow be analyzed byallowing a deviation from the perfect phase-matching condition, Ak # 0, where the

600

800

1000

Frequency

Tuning curve for the LiNbO, collinear AOTF.

ACOUSTO-OPTIC TUNABLE

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momentum vector mismatch is Ak = k, - k, - k,. With the mismatch, the filter transmittance becomes

T

=

PL2

+ Ak2/4)L2]ln (r2+ Ak2/4)L2

sin2[(P

Equation (7) does not include the term denoting the small difference in frequency between the incident light and the diffracted light. This frequency difference will simplybe theacoustic frequency, +R, the sign being positive if the incident wave vector is propagating parallel to the acoustic wave vector, and negative if it is propagating antiparallel. This frequency shift is generally of no consequence for A 0 devices used for optical spectrum analysis. Equation (7) can be used to arrive at the optical passband transmission of the filter by allowing Ak to vary as the optical wavelength varies. Following the notation of Harris [2], Ak is related to the wave number change of the light by the relation

where Ay is the change, in wave number, of the optical frequency from the filter center frequency, and where the quantityb is a dispersive constant characteristic of the A 0 material, which may beobtained by differentiation of the Sellmeier equations. In theabsence of ordinary dispersion, b equals 2 1 ~ ( n, ne). Using this value of Ak in Eq. we obtain the frequency response function of the filter: H(Ay) =

b2L2 Ay2)ln IT* sin2f ++b2L2 Ay2

Equation (9) can be recognized as the usual sinc2 filter response expected from a rectangular window function.

2.2 Crystal Symmetry Requirements The complex tensor relationship describing the photoelastic interaction has been fully described in Chapter 2. From that relationship we can see that the collinear interaction specifies a restricted set of photoelastic tensor coefficients for which an acoustic wave can couple the two orthogonally polarized light waves in a birefringent crystal, in which all three waves are copropagating [l].There are two possible couplings which depend on whether the acoustic wave is compressional (longitudinal) or transverse (shear). The simpler cases are the transvetse-wave interactions which result in coupling of orthogonal polarizations. It is well known that such coupling will occur even in isotropic materials, but thatis not relevant to thepresent

GOTTLIEB discussion. For anisotropic materials, the photoelastic tensor components coupling the two polarizations are pa, p55,and p669 all of which are finite valued for all classesof materials. For any of these interactions, theintensity of the diffracted light will be proportional to (pmm cos e),, where 8 is the angle between the light propagation direction and theacoustic propagation direction. Therefore, the diffracted light intensity drops to zero for the collinear interaction, and none of these photoelastic coefficients can be used. The only coefficients that will support a finite collinear coupling intensity with a transverse acoustic wave are p45 and p56. A similar consideration for compressional waves shows that the only usable coefficient is p41.The symmetry properties of the photoelastic tensor forall the crystal classes have been characterized [4], with the result that p45,p569 and p41 are notidentically zero only for noncentrosymmetric crystal classes. These include all crystals belonging to triclinic, monoclinic, and trigonal systems, and also includes the classes 6, and 6/m of the hexagonal system, and 4, 4, and 4/m of the tetragonal system. This places severe limitations on the candidatematerials for thecollinear AOTF, especially when one takes into consideration the other requirements for truly useful AOTFs. There are only three or four suitable crystals (see Table l), but using these, it is possible to construct a collinear AOTF for any optical spectral region from the UV to the far-IR.

2.3 Noncollinear AOTF Phase-Matching Considerations Because the severe restrictions on the choice of materials available for the collinear AOTF, a great deal of interest arose in making a device utilizing noncollinear A 0 interactions while retaining the principal advantages of the collinear approach (such as the large field of view). With the discovery the highly efficient A 0 crystal Te02,the possibility of a highly efficient tunable filter made this particularly attractive. The earliest such effort was reported by Yano and Watanabe who built a far axis TeO, AOTF. The key development of the noncollinear AOTF was made by Chang [6] which resulted in an AOTF with a large angular aperture. The basic concept is to compensate the momentummismatchbetween the wave vectors, due to the change in angle between the incident light wave and the acoustic wave, by the angular change of the birefringence in the plane of interaction. This is accomplishedin the mannerillustrated in Fig. 4. For the extraordinary polarized light, the locus of wave vectors is the ellipse, and for the ordinary polarized light it is the circle; the mismatch compensation will be optimized when the direction the acoustic wave vector is

ACOUSTO-OPTIC TUNABLE FILTERS

205

GOTTLIEB kY

l

kx

2nn,/ho Wave vector diagramfor the noncollinear AOTF, in whichthe tangents to thewave vector surfaces, correspondingto ordinary andextraordinarypolarized light, are parallel. For this example, the incident light is extraordinary polarized and makes an angle with the k, axis,while the diffracted light is ordinary polarized and makes an angle with the k, axis. In the conventional notation, ei= and is measured with respect to the polar (i.e., optic) axis. The acoustic wave, represented by propagates at an angle with respect to the k,, axis.

K,

so chosen that the tangents to the two loci will beparallel for thetwo light wave vectors. For achange in the incident light direction, with the acoustic beam direction and magnitude held fixed, the exact momentum-matching condition will remain nearly satisfied. Consequently, as the angle of incidence, e,,deviates and the frequency is held constant, the center wavelength of the passband remains unchanged. It can be seen from Fig. 2 that the parallel tangent condition is satisfied for the collinear case, that it may be regarded as a special case of the noncollinear AOTE. As can be seen from Fig. the parallel tangent condition is satisfied for any value of 8,by choosing a suitable direction and magnitude of the acoustic wave vector. From simple geometry, we can calculate, a function of ei, the

ACOUSTO-OPTIC TUNABLE

FILTERS

207

required values of the acoustic wave vector direction, and the wavelength dependence of the acoustic frequency. calculational approach easily adaptable to a simple computer program is to compute the coordinates of the light wave vectors, (xi, yi) and (&, yd). These coordinatesare then used to compute the acoustic wave vector direction

and the diffracted light beam angle

The AOTF tuning relation is also obtained geometrically and is

f=

V d b d

-

-b (xd

Yi)'

- xi)2

(12)

The coordinate values themselves can be readoff the wave vector diagram as xi = no cos

ei

yi = no sin € l i

and xd =

na cot ei

n$

+ na cot2 1 - na cot2 ei

The relationship between and eiis independent of the ellipticity of the surface representing ne, and is plotted in Fig. 5. Note that Oi = 90" is the collinear case, while 0" is the case of vanishing birefringence. The exact tuning relation, computed numerically using Eqs. (12)-(14), was approximated by Chang [6] by the expression An An f = -"V sin4 + sin2 2 e i = -F ( 0 J

x

h

For 90" angle of incidence, the tuning relation reduces to that of the collinear AOTF. For a given h, v, and An, f is a maximum for collinear operation, and decreases with decreasing The external angular separation between the incident and diffracted beams, A 0 , is easily calculated from Eq. (11) as A 0 = niei - nd tan-'

k)

GOTTLIEB

208

ei

5 Acoustic beam propagation direction (with respect to polar axis) as a function eifor which the parallel tangent condition will be satisfied for the noncollinear AOTF.

For small angles, Eq. (16) can be approximated as

A@

An sin 2 0 i

(17)

Determination of the AOTF Passband The filter transmissionis determined by the phase-matching condition and is

Equation (18) leads to the spectral resolution of the filter by setting

ALL - 0.451~ from whichwe can calculate the full-width half-maximum (FWHM) spectral passband Ah =

0.9h2 AnL sin2

ACOUSTO-OPTIC TUNABLE

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209

It can be seen from Eq. (20) that for fixed values of L and €li, AA/A2 is the constant 0.9/An sin2 ei, which means that the AOTF resolution expressed in wave numbers is constant with wavelength. Note that the resolution is dependent only on the geometric factors L and eiand not on any material parameters. An estimate of the range of resolution accessible with a noncollinear AOTF design can be seen from the parametric plot shown in Fig. 6. The highest resolution will be obtained with ei= 55"; for interaction lengths from 0.5 to 5 cm the resolution lies in the range of 1 to 10 cm-l. For small values of €li, around the resolution is about 100 times lower. These dimensions are representative of the largest and smallest values which can be reasonably implemented. Exact Calculation of the Angular Aperture One of the most important design features of the noncollinear AOTF is the potential to achieve very large angular apertures. The AOTF angular aperture is defined as that range of incident light beam directions over which the deviation from perfect phase matching is sufficiently small that for a fixed RF frequency the passband of the filter remains relatively unaffected; i.e., the resolution is not degraded. Overthis range of incident angles, the transmission of the filter at the bandcenter will decrease by 3 dB. Because of the nonsymmetric curvature of the indicatrix, the angular

7

? '

100

7.5 degrees

v

c

..-. 15 degrees

W

30 degrees

55 degrees

1

4.5 U.5 3.5 2.5 1.5

Length (cm)

6 Resolution (in wave numbers) ofnoncollinearAOTF for several values

eias a function of interaction lengths from 0.5 to 4.5 cm.

GOTTLIEB

210

aperture will be a function of direction. The two principal direction planes are the polar and azimuthal planes, the polar plane being the plane of incidence, and the azimuthal being the plane perpendicular to the plane of incidence. An exact calculation of the angular aperture requires a detailed numerical calculation. However, simple analytical approximations, valid over a large range of values for angle of incidence, were proposed by Chang [ 7 ] . These analytical approximations for the full angle external to the crystal are A @ = 2n

h0

/ L An)(3 cos2 ei - 1)1

for the polar aperture, and A+ = 2n

h0

/ L An (cos2 ei + 1)

for the azimuthal aperture. The maximum polar angular aperture of the AOTF is achieved for ei = 54.9'. The denominator in Eq. (21) is zero for this value, and the approximation is clearly not valid. It is also in substantial error for small values ei,so that if accurate design values of the angular aperture are required then this approximation may be inadequate. For many typical designs, however, the analytical approximations are useful, especially since they can so easily be incorporated into computer programs. An exact numerical analysis of the angular aperture from the momentum mismatch, A k ( e i ) ,was carried out by Salcedo [ 8 ] .The wave vector diagram shown in Fig. 7 was used to illustrate the effect of noncritical phase matching. When the first derivatives of the wave vector at points A and B are equal, the momentum mismatch due to hei will be minimum. The calculation proceeds by carrying out an exact geometric analysis of the momentum mismatch introduced by a change in the polar angle of incidence, A k ( 8 J . This can be expressed as Ak(h, ei,A e i ) = [ki(h, 8i, A@)

+ k,(h)] - kd(h, ei)

(23)

where k,, is the acoustic wave vector. Its direction and magnitude are fixed regardless of Cli.The momentum values indicated in Fig. 7 are

and

ki(X,€ l i , A e i ) =

kdky" .\/k;sin2 (ei+ Aei)+ (ky")Zcos2(ei + A@)

(25)

ACOUSTO-OPTIC TUNABLE

FILTERS

21l

\

\

\

\

7 Noncritical phase matching: when the wave vector first derivatives at A and B are equal, themomentum mismatch introduced by A@ will be minimum to first order. Inset shows Ak normal to the diffracted wave vector surface, which minimizes [Ak]. (From Ref.

where k y ( X )=

2rrny(h) h0

Note that the exact value of n from the dispersion equation must be used. The calculation of the acoustic wave vector and theacoustic beam direction, ka(h, € l i ) and € l i ) respectively, follow from the parallel tangent condition, and can be calculated as shown in the subsection “Phase-Matching Considerations.” The analysis by Salcedo allows for deviation of the incident wave vector in the azimuthal plane so that the full 3-D acceptance profile can be evaluated. The general expression for the momentum mismatch, with deviations in both the polar and azimuthal planes, A 0 and A+, is Ak(h, e Q 0 , A+) = kd - V k ? + k:

+ 2kikas1

where s1 = cos(Oi + A0)cos

+

-e sin(@, A0)sin

cos A+

(28)

In Eq. (28), the + sign applies to negative uniaxial crystals and the - sign applies to positive uniaxial crystals. The dependences of several of the variables above have not been explicitly indicated, but can be derived from previous equations. In order to calculate the polar and azimuthal angular

212

GOTTLIEB

apertures, it is only necessary to perform the calculation for the range of values of A 0 and A 4 for which the product AkL is lessthan 2.7831. When this value is exceeded, the expression for the AOTF efficiency (q), given by q -sins

(x) AkL

shows that for fixed values of h and f, the phase mismatch will cause the transmission of the AOTF to fall to 50% of its peak value. These expressions are easily incorporated into a computerprogram that calculates the AkL values for full sets of compound angles (polar and azimuthal) and generates the apertureprofile. Examples of these profiles were carried out by Salcedo for thecase of a Tl,AsSe, (TAS) 'AOTF. Several AOTFs have been built which were designed with values of O inear that very wide angular aperture was achieved. These include a TeO, AOTF operating in the near-IR reportedby Dwelle and Katzka [9] and .a TeOz AOTF for the mid-IR reported by Voloshinov and Mironov [lo]. The Etendue The previous sections have described in detail the advantages offered by A 0 devices for spectroscopic applications. For the most part, these advantages accrue from the electronicagility of A 0 devices. However, under certain conditions, a comparison of the spectroscopic characteristics of various devices may reveal that the A 0 device is superior in terms of spectroscopic performance. If the A 0 agility is not a crucial factor, it may be useful in designing a spectroscopic system to compare other devices with the AOTF. It is very useful to have a criterion for making such a comparison because the methods of operation of gratings, prisms, filter wheels, etalons, A 0 devices, etc., are all very different from each other. A criterion for making this comparison was developed by Jacquinot for comparing grating with prism spectrometers, and applied by Melamed [l11 to avariety of dispersive devices. The concept for making such comparisons is termed the etendue. This is the product of the solid angle field of view, R, and the effective area, A , normal to the source, of the device, and is the throughput of the optical instrument. It can be expressed in terms of the relativeluminosity in its image plane, for agiven resolving power. The resolving powerof a spectroscopicinstrument, such as a grating, is generally determined by its dispersion and some geometric factor, such as a slit width. The resolving power can vary between 0 and some maximum value, R,, as limited by the Rayleigh or other resolution criterion. The etendue can be expressed in terms of the instrument's resolving power, that the

ACOUSTO-OPTIC TUNABLE

FILTERS

213

etendue of different dispersive devices can be compared for equal resolving powers. The etendueis defined in the following manner. Figure 8 shows a source of infinitesimal area, illuminating an element of area dA' a distance, r, from the source. If the surface A' is inclined at an angle 4 to the line joining them, and the source (assumed Lambertian of brightness B ) S is inclined at an angle 8,then the flux incident on A' is

where the solid angle subtended by the source as viewed from A' is ds cos W * , and the area elementnormal to the joining line is dA = dA' cos For an optical system whose transmission is T , the definition of the etendue is ER = TAR

(31)

in which A is the area normal to theincident beam direction, andR is the solid angle subtended by the source at thesurface at A . With this definition, comparisons of different instruments can be made for a given resolving power, R = VAA. The units of etendue are L*-steradians. Alternatively, the etendue can be expressed in terms of R and R for a constant area A ; then EA = RR. For any design orientation of the AOTF, collinear or noncollinear, there is a relation between the resolution and the angular aperture, as determinedby the interaction length, L . These relationships for the AOTF follow easily fromthe analytical expressions given in Section 2.1. For the collinear AOTF, the aperture, R , is obtained from the l-D apertures IT

R--AeA+

I

=

"

IV

8 Angles used in defining the etendue.

GOTTLIEB

214

so that the etendue is R = - A =-2AnL AA A.

EA = TRR = 2.rmg0T The situation for the noncollinear AOTF is somewhat more complex because the l-D apertures are not well approximated by the analytical expressions for all values of Oi, as discussed in the subsection “Determination of the AOTF Passband.’’ If accurate values for R are required where the approximations are not valid, then a numerical analysis must be carried out. However, over most of the range where the approximations are suitable, the etendue can be calculated as above:

and R =

2 AnL sin2 l.8Ao

that the etendue is

In a similar fashion, Melamed [l11 has carried out the calculation of the etendue for a number of conventional spectroscopic devices, so that they can be compared with the AOTF. Fubry-Perot Filter. For the Fabry-Perot filter, the resolution issimply related to the angular aperture by R = 2 d R , so that the etendue is

EA = 2rrT By comparing Eqs. and we can see that the etendue of the collinear AOTF is larger by the factor non,. For the available AOTF materials, this factor typically is between 4x and lox. The analysis showsthat the result is exactlythe same for an interference filter, such as thedielectric stack. While a single such filter is not a spectrometer, a side-by-side arrangement such filters with staggered passbands can function as a spectrometer. In such a side-by-side arrangement consisting of M individual filters, the overall etendue will be reduced by the factor M .

ACOUSTO-OPTIC TUNABLE FILTERS

215

The Grating Spectrometer. The etendue of the grating spectrometer will depend upon the grating parameters. The grating angular dispersion is

where is the angle of incidence, which isequal to theangle of diffraction for a Littrow mount. The geometrical factors of the spectrometer are the slit width, W , the slit height, h , and the distance between the grating and the slit, F. The resolving power and angular aperture can be easily expressed in terms of these geometrical factors;

R

=

2F - tan W

and

a = -wh F2

For the grating spectrometer the etendue is

E

=

(9

T A - 2 tan

In making comparisonsof the grating etendue with A 0 (or otherdispersive devices), a typical value of the blaze angle, 8,is The Prism Spectrometer. The etendueof the prism is calculated very much like that of the grating, with the prism dispersion, h(dn/dA),replacing the grating dispersion. Under the same conditions of resolving power, the ratio of prism to grating etendue is

(

E(prism) = " 1 E(grating) 2 tan

) A h dh

(43)

Melamed [l21 has estimated this factor to be about 16 for an NaCl prism at 10 pm. The above expressions will make it relatively simple to compare the efficiencies of the various dispersive devices with the AOTF for any design configuration, normalized for the same resolution. This will be useful in determining if an AOTF is advantageous for any particular application where this efficiency plays a key role. If the AOTF is not competitive, then the system trade-off analysis must be made to determine if the other advantages of the AOTF outweigh a lower efficiency.

216

GOTTLIEB

2.4 Features and Advantages

the

Agility Wavelength Scan Rate. The electronic tunability of the AOTF provides it with the most compelling advantages over the more conventional spectroscopic devices that are mechanically tuned to change wavelength. The minimum random access time for wavelength change is Dlv, where D is the optical aperture, typically about 1 cm. For typical acoustic velocities this leads to a minimum accesstime around 10 ksec. In practice, the access time will be longer if limited by electronic switching speeds and thesettling times of the frequency generators. Frequency selection may be random access, a sequence of predetermined frequencies, or a linear scan. For applications utilizing a linear scan, consideration must be given to ensure that the scan rate is not rapid that the spectral resolution will be degraded. The allowable scan rate will, of course, depend upon the resolution, and other AOTF parameters. The guidelines for estimating this scan rate are simple; from Eqs. (15) and (20) we find that the relation between the wavelength resolution (AA) and the frequency resolution (Ad) is

AA = ( vF An ) F ( O i ) Af

(44)

that the frequency resolution can be expressed as =

1 . 8 1 An ~ F(@) bL

(

The aperture time is = D/v, that for a tuning rate r = dfldt, the frequency range (Af)wan within the optical aperture is

The condition for no degradation of resolution due to scanning is (Aflscan

(

1 . 8 1 An ~ bL

F(ei)

(47)

from which the tuning rate should satisfy

r s

1 . 8 An ~ ~ ~ sin2 20, bLD sin4 Oi

An order of magnitude estimate for r for typical values of the AOTF parameters (v = lo5 cm/sec, An = b = 1.2, L = 1 cm, D = 1 cm, = [l + (sin2 20i)/(sin4 O,)]ln = 4.4) is 31 kWpsec.

ACOUSTO-OPTIC TUNABLE

FILTERS

21 7

+

The expression [l (sin2 20i)/(sin4 willvarybetween2 and 23 over the full range possible. The time required to perform a spectral scan will depend upon the scan range and the AOTF design parameters, but some typical values are useful for order of magnitude estimate. Assuming the same AOTF parameters as above, and for an octave scan of about 1 pm, the RF would have to be scanned from 88.5 to 147.5 MHz. For no loss in spectral resolution, the scan duration cannot beless than 0.89 msec; the number of resolution elements towhich this corresponds is about 190, or 4.7 psec per resolution element. Such rapid data acquisition capability cannot easily be done with conventional spectroscopic techniques. Internal Modulation. The agility of the AOTF is a major advantage for applying modulation functions in order to implement various detection methods. This includes AM, F M , and derivative detection. The simplest of these is AM operation, in which the chopped output from the detector is fed to a lock-in amplifier or some other synchronous system. The intensity of the AOTF output light can be directly chopped (square or sinusoidal wave) by amplitude-modulating the RF input signal. In addition to the excellent stability with which this can be donein comparison to mechanical chopping, it is also possible to modulate at very high rates, should that be desired for optimizing the output signal-to-noise (SNR) ratio. The maximum AM ratewill be limited by the same factors described in the previous section on scan rates; for the same set of parameters used to calculate a typical maximum scan rate, the maximum AM rate would be about 200 kHz. Similarly, the RF input signal to the AOTF can be frequency modulated. In this case, the signal to the transducer is described by f(t) =

W,

+ d sin(o,t)

(49)

where W, is the center frequency, W, is the modulation rate, and d is the frequency deviation. As a result of this FM signal, the peak wavelength passed by the AOTF will also be time dependent, according to h(t) = h,

+

sin(o,f)

where a is the spectral width of the AOTF,and is the wavelength deviation measured in units of This type modulation is central to using the AOTF toperform derivative spectroscopy, the applications of which will be described in a later section. It is the electronic agility of the AOTF which permits FM operation to be done very easily, in comparison to conventional spectroscopic devices, such as gratings, which must be mechanically dithered to achieve the same effect.

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218

3

SPECIFICATIONSOFTHEAOTFDESIGN:MATERIALS AND INTERACTIONS

3.1 Materials forAOTF In Section we noted that thelist of crystals available for use in AOTFs is restricted by the symmetry requirements on the photoelastic tensor. In addition to these limitations, there are more general requirements placed on the A 0 device crystals. These include (1) high optical transmission over the desired spectral range, (2) high uniformity, low scattering, (4) low acoustic losses up to thehighest values of RF required by the device design, (5) reasonably high figure of merit, and (6) suitable mechanical properties so that the crystals can be conveniently cut, polished, and bonded to the transducers. Fortunately, a number of materials satisfying all of the above criteria have been identified, with crystal symmetries that allow both collinear and noncollinear devices to be built over the entire optical spectrum, from the UV to the far-IR. The only crystal available for wavelengths into the vacuum UV is aquartz, which can be used for either collinear or noncollinear designs. It is an excellent optical and acoustical material, is inexpensive and available in very large sizes. However, its A 0 figure of merit is poor, therefore, quartz requires very high RF input powers. Because of the quadratic dependence of power on wavelength, its usefulness is limited to the shorter wavelengths. Crystals available for thevisible and IR toabout 4 pm include lithium niobate (LiNb03) and calcium molybdate (CaMoO,) for collinear AOTFs, and tellurium dioxide (TeO,) as the material of choice for noncollinear AOTFs. TeO, has been used extensively for commercially available devices, and enjoys the most widespread experience in design and use. TeO, is optically active, as is a-quartz, a property which has an impact on certain AOTF designs in which the light is incident at angles near the crystal optic axis. Note that TeO, and a-quartz are the only AOTF materials which exhibit optical activity. In themid- to far-IRspectral range, thallium arsenic selenide (Tl,AsSe, or TAS) is the only available material for both collinear and noncollinear designs. Although it is much more fragile than conventional optical materials, it has been successfully used commercially followingefforts to develop suitable fabrication and handling techniques. More recently, a new class of highly efficient A 0 materials, the mercurous halides have been reported for A 0 devices. The most developed of these is mercurous chloride (Hg,Cl,), which can be used for noncollinear AOTFs over a very large spectral range, from to 20 pm. It has a crystal symmetry and other A 0 properties which are very similar to TeO,, including a high figure

ACOUSTO-OPTIC TUNABLE FILTERS

21

of merit. It is very near to becoming commercially available from sources in the United States and in Czechoslovakia, so that it can be considered for device design. The mercurous halides are very soft materials, chemically very stable, and techniques for fabricating them have also been well developed. All of the crystals discussed above are uniaxial, for which thq design principles are well developed. AOTFs can also be built using biaxial crystals, although none have yet been extensively used for this purpose. An AOTF using one biaxial crystal, thallium phosphorous selenide (Tl,PSe,), has been built [14], although no furtherwork is planned. A higher degree of design flexibility can be achieved with biaxial crystals, so that they may become important in the future. A summary of the important properties of these AOTF crystals is given in Table 1.

3.2 AOTF DesignProcedures Collinear AOTF There are two possible configurations for building a collinear AOTF; the first utilizes longitudinal acoustic wave propagation, and coupling to the optical waveswith the photoelastic coefficient, and the second utilizes shear acoustic wave propagation and coupling with the p56 coefficient. In either case, the crystal orientation is chosen appropriate to thecoefficient. InTAS,forexample,the coupling requires the waves to propagate along the axis, while the p56 coupling requires the waves to propagate along the b axis, with the shearpolarization direction parallel to the axis. The principal difference between these two configurations is the acoustic velocity; in general, shear-wave velocities are about one-half slower than the longitudinal-wavevelocities. The advantage relating to theslower shear velocityis the possibly larger value of the A 0 figure of merit, which increases as lh3.Not all of this advantage may be realized if p56 < as is the case for TAS. A second advantage, especially for operation at short wavelengths, is the lower RF tuning range with shear waves, which tends to simplify the transducer design. A schematic of the basic collinear AOTF is shownfor TAS in Fig.9. In TAS,the acoustic beam energy flowdirection makes an angle of about with respect to the b axis. This is due to the acoustic anisotropy associated with the trigonal crystal symmetry. This phenomenon must be considered when designing an AOTF since it will impact the size of the transducer and the diameterof the optical beam, to ensure that the optical and acoustic fields will fully overlap over the entire active length of the device. Once the A 0 configuration is chosen, the only parameter remaining to be fixed is the interaction length, L , which will determine the resolution,

GOTTLIEB

220

POLARIZING

+

SPLITER

8 B

Basic configuration for the TAS collinear AOTF: compressional acoustic waves corresponding to S,,, (B) shear acoustic waves corresponding to S,*.

the angular aperture, and the RF input power. The mathematical relationships describing these parameters have been discussed in Section 2.1. These relationships are amenable to simple computer programs that will plot, for example, the wavelength dependence of resolution, the field of view, and the acoustic power density for a given diffraction efficiency. The designer must start with that featurewhich has the highest priority for the application, which will dictate some bound on the choice of L . Once L is chosen, the remaining characteristics will be determined by the various relationships. Note that the collinear AOTF does not offer the flexibility to independently choose more than one characteristic. An important limitation that must be kept in mind for collinear AOTF design is the effect of acoustic attenuation, especially at shortwavelengths where the tuning frequencies are high. If a large value of L is chosen in order to achieve high resolution, the acoustic loss may prevent the entire length from contributing to the interaction, the higher the frequency the greater the degradation. In order to take into account these effects, the computer program should evaluate at each wavelength (or equivalently at each input frequency) the attenuation-limited effective interaction length, Len,generally defined as that length for which the acoustic field intensity

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is reduced by dB. At those wavelengths for which L,, < L , the program should substitute LeRfor L in calculating the AOTFcharacteristics. Over a large spectral range, it may be that the AOTF will be crystal lengthlimited at long wavelengths and attenuation-limited at short wavelengths. A limitation on the resolution is also imposed by the optical uniformity of the AOTFcrystal [U]. If the birefringence B = ne - no is not constant over the interaction volume of the crystal, a fixed acoustic frequency will produce exact phase matching for slightly different optical wavelengths in different regions of the crystal. The variation in optical wavelengths for exact phase matching will be related to the variation in the birefringence by v AB AA = -

f

The resolution of an AOTF made from such a crystal cannot be greater than allowed by this variation in wavelength, no matter the value of L . Thus, the maximum resolution of the filter is

and the maximum length of the filter, beyond which there is no increase in resolution, is

An example of this limitation, is shown in Fig. 10 which shows a plot of the optical uniformity needed for maximum length TAS AOTFs for A = pm. For a resolution of 1 cm” an interaction length of 5.5 cm is required (Eq. (20)), and the curve shows that this requires AB < X (Eq. The important question for thedesigner of such high resolution devices is “with whatuniformity can AOTF crystals be grown?” One guide might bethe measured optical uniformity in the best interferometric-grade fused quartz. Using data supplied by several commercial suppliers, this is the order of several parts per million. A more realistic assumption for optical crystals is an orderof magnitude lower, or several parts per In this case, the maximum length the AOTF is between 5 and 10 cm, that 1 cm” resolution appears to be near the limit. Noncollinear AOTF There is a much greater degree of flexibility in designing noncollinear AOTFs because the possibility of choosing the angle of incidence as well as the interaction length, L . Complexity is added to the design

222

I”

GOTTLIEB

-

1

10

100

Maximum Effective Length (cm)

Maximum effective interactionin TAS for the collinear AOTF, as limited by the optical uniformity of the crystal. The optical uniformity isexpressed as the variation of the birefringence, AB = A(n, - ne).

when allowing €ii to vary, since this will also lead to variations in the effective photoelastic coefficient. If power consumption is a primary concern, then the design approach may focus on the optimization of efficiency. Another issue that may be of importance, especially in the case of highly acoustically anisotropic crystals such as TeOz, is the angular dependence of the acoustic velocity and power flow direction, as this may have a large effect on the tuning relation and RF power, as well as on the size and shape of the crystal needed. In order to carry out a complete design, the factors that must be evaluated include the wavelength dependence of the following: (a) tuning relation, (b) spectral resolution, (c) polar and azimuthal angular aperture, (d) RF power requirements, (e) acoustic velocity and power flow angle, and (f) separation between incident and diffracted beams. In addition to these purely AOTF-related parameters, the design must include the transducer and AR coatings after items (a) through have been determined. The procedureuses as its basis the parallel tangent condition which is fundamental for the noncollinear AOTF approach, and for which the mathematical relationships have been given in the subsection “Phase Matching Conditions.’’ The design procedure is easily programmable as an interactive search for the optimum configuration for any application, in which one, ormore,

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operating characteristics may be given priohty. It is generally simpler to have an individual program for each crystal in order to incorporate the orientation dependence of the acoustic properties. The first step of the computer program evaluatesthe acoustic phase, group velocities, and power flow angles, for which the input data would be the principal slow and fast velocities, v, and v,. Using a calculation procedure developed by Murphy [l61 for a wave propagation direction with respect to the slow axis, the phase velocity v ( 0 , ) and power flow angles, as shown in Fig. 11, are

v@,)

=

V(V,sin

=

tan-'

+ ( V , COS

and

v: - v:

+ (v, tan

1

The parameters (a)-(f) can be expressed using the mathematical relationships given in previous sections. convenient flow diagram for the initial design procedure is shownin Fig. 12. The input values of the program are no, ne (note: if the material is significantly dispersive, it may be necessary to incorporate a dispersion formula into the program), v, and v,, and the wavelength limits. Based on the outputvalues of RF tuning, resolution, polar and azimuthal apertures, and RF input power, the next iteration is run by choosing a new value of or L , or both. This procedure continues until an optimum, or at least satisfactory, set of operating char-

Acoustic wave beam propagation direction and energy flowdirection an acoustically anisotropic crystal.

-

GOTTLIEB

ei

v(ei)

I

12 Flow diagram for the design of a noncollinear AOTF.

acteristics is determined. Another factorwhich may be included for optimization is the figure of merit, M,,which will vary with configuration. Although the values of M, for all candidate AOTF crystals are reported in the literature, these are for specific configurations. It may be useful to include calculation of M,,which includes, in general, contributions from several of the photoelastic components, pjjkl. A matrix formulation has been developed by Sovero [l71 for calculating the effective value of M, for arbitrary configuration. The generalized expression for M, is

where &l is a component of the normalized strain tensor for the acoustic mode beingused and is related to the elastic constants throughwellknown equations. This approach can be usedfor any crystal for which there is complete information on the photoelastic and elastic constants and the

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refractive indices. For the most commonly used crystal, TeO,, the values of these constants are C11 = C33 =

Cl2 = C- =

C13 = CM =

in units of lo1, dynes/cm2 p11 = p31 =

p12 = p33

p13 = p- = -0.017

PM =

This procedure was carried out by Sovero to calculate the effective M2 and resolving power of TeO, for values of from to their results are shown in Fig. The curve clearly shows the dramatic decrease in efficiency as the incident light direction is rotated further from the optic axis of the crystal.

3.3 Configurations for Beam Separation In order to achieve efficient operation of the AOTF, it is essential that the optical and acoustical beam directions are accurately aligned in the directions demanded by exact phase matching. Since the basic operation of the AOTF relies only on polarization differences, it is often difficult to separate the diffracted orders with good extinction. Thisis especially true for the collinear AOTF, where there may be no spatial separation at all between the diffracted orders. Several approaches have been devised to deal with these problems, generally at the cost of some added complexity to the overall opticalsystem. The most appropriate approachwill be dictated by the optical and acoustic properties of the crystal, as well as by other design factors. Several of the beam introduction and extraction configurations reported for thecollinear AOTF aresummarized here. The simplest,shown in Fig. 14a, utilizes a highly reflecting filmon the transducer face, and a polarizing beam splitter at the optical inputface that thebeam entering thecrystal is polarized and proceeds to be converted by the collinearly propagating acoustic wave. The inputbeam is reflectedback on itself at the transducer face, where it continues tobe converted. Afterleaving the crystal withthe orthogonal polarization, the polarizing beam splitter reflects it out of the path. In Fig. 14b, the acoustic beamis made collinearwith the optical beam by reflecting off the input optical face at the appropriate angle to ensure collinearity. The input is polarized, and the filtered beam is passed by an analyzer. The arrangement in Fig. utilizes an acoustic wedge which holds the transducer; theacoustic wedge is bonded to the AOTF at

GOTTLIEB

.-

I

0

- 10'

al

iii

'

'

!

, v

,

ao

'

ei (degrees)

B 1

I

I

0

20

..

I

I

10

40

80

8i (degrees)

13 (A) Calculated values of for TeO, AOTF at A (B) Resolution R = A/AA TeO, AOTF at A = 3.39 km.

=

3.39 km;

an appropriately prepared interface; this wedge is cut from the original crystal. The interface is prepared so that the light, incident from the left, is nearly 100% reflected, and the acoustic energy, incident from the wedge, is nearly 100% transmitted across the interface. This requires a very careful design the interface bonding layer. The input light is polarized, and the filtered beam is passed by an analyzer. modification of this scheme is

ACOUSTO-OPTIC TUNABLE FILTERS

-

-

LIGHT BEAM ACOUSTIC BEAM

DPOLARIZER TRANSDUCER POLARIZING BEAM SPLITTER

1 NONCOUINEAR

Figure

Configurations for separating filtered from unfiltered beams in AOTF: (a) collinear, in whichthe light is reflected from the transducer face and is separated with a polarizing beamsplitter; (b) collinear, inwhich the acoustic beam propagates collinearly with the light by reflection from the optical input face; (c) collinear, in which the acoustic beamis introduced into the interaction region across an acoustically transmitting but optically reflecting wedge interface; (d) collinear, same as (c), but the optical beams are separated by bireflectance at the wedge interface; (e) collinear, in which the acoustic walkoff is used to allow optical and acoustic collinear propagation; noncollinear,using spatial separation of beams;and (g) noncollinear, using polarization separation of the beams.

GOTTLIEB shown in Fig. 14d, in which the wedge angle is chosen so that the orthogonally polarized filtered and unfiltered beams are spatially separated by the phenomenon of bireflectance. If the ordinary and extraordinary refractive indices are sufficiently different, the angle between the reflected beams may be as large as several degrees. The configuration illustrated in Fig. 14e is applicable where there is a sufficiently large acoustic walkoff angle that the light beam can be introduced into the crystal at the transducer face. A large acoustic energy flow walkoff angle will allow for a large collinear overlap region. The input and filtered beams are polarization separated. For noncoliinear AOTFs, it is possible to extract the filtered from the unfiltered beam entirely by spatial separation, as shown in Fig. 14f, provided the angular divergence of the beam is not larger than the angular separation between the zero and first diffracted order. In this case, there is no need to polarize the input beam, and both polarizations of the selected wavelength can be obtained simultaneously. This is a useful feature in some applications, such as polarimetry. On the other hand, if the field of view of the input beam is larger than the separation of the orders, the incident and filtered beams must be polarization separated, as shown in Fig. 14g.In this case, the polarizer must have a very highrejection ratio, especially if the incident light isbroadband and the AOTF resolution is high. This is because the unfiltered optical power may be orders of magnitude greater than the filtered, and the SNR would be therefore greatly degraded by low polarization rejection.

3.4 Side-LobeSuppression/Apodization The impulse response of the AOTF, with respect to RF or to optical wavelength corresponds to a sin6 function, as described in Section 2.1. This gives rise to the wavelength side lobes illustrated in Fig. 15, from which it can be seen that for a fixed RF power, there is a substantial amount of optical power transmitted by the AOTF at wavelengths remote. from the bandcenter. A simple calculation shows that if the AOTF is illuminated with white light and excited as to pass light at a fixed bandcenter, about 15% of the optical power passedwill reside outside the F W H M . For some applications this may be adequate, while for others it may result in unacceptably high levels of out-of-band light. The presence' of side lobes is, of course, not peculiar to the AOTF as a spectroscopic device; it is a general property of filters. The typical method utilized to reduce the transmission the filter for wavelengths outside the central passband is to apodize the aperture in order to decrease the level of constructive interference outside the central passband. There is a variety of approaches possible. One simple approach is to pass the light through two

ACOUSTO-OPTIC TUNABLE FILTERS

-20 -15

-5

0

5

15

20

15 Transmittance function of the AOTF; b is the dispersive constant, L is the interaction length,and Ay is the deviation, in wavenumbers, from the filter

center frequency.

stagger-tuned filters with a central wavelength offset just equal to the spacing between their transmission minima and maxima. This results in a single combined transmission maximum at the onehalf maximum point of either filter, and a combined zero at all of the sidebands of both. The penalty is 'the complexity of operating at multiple frequencies. Multiple frequency operation of a single AOTF was first demonstrated by Chang et al. [l81 by driving the transducer in a manner analogous to that foran electro-optic tunable filter (EOTF) electrode array reported by Pinnow Multiple frequencies are applied to theelements, chosen to tailor the passband as to minimize the total out-of-band light. True apodization of the aperture requires that theacoustic field along the direction of light transmission vary in such a way that its Fourier transform corresponds to a function with IOW sideband levels. For example, if the acoustic profile is truncated Gaussian, then the angular distribution of the diffracted light intensity will be its Fourier transform, also Gaussian, with low side lobes. There are two methods for tailoring the .acousticfield profile. In the first, a transducer electrode pattern is fabricated, whosephysical shape will correspond to that of the desired function. Thisisvery similar to the technique used to apodize acoustic surface-wave interdigital transducers, to accomplish a similar purpose. The penalty for this approach, which is

230

GOTTLIEB

very similar to optical aperture shading to reduce diffraction side lobes,is a loss of transmission. This loss of transmission can be regained by increasing the RF input power. Note thatthe fabrication of such atransducer is not especially complicated once the electrodedeposition mask has been generated. The second apodization technique [l81 uses a fixed amplitude weighting function applied to the elements of a transducer array. When the amplitudes and phases applied in each element are all the same, the filter response function is the usual sinc2. On the otherhand, with unequal amplitudes and phases, the response function will be the square of the Fourier transform of the drive voltage profile applied across the transducer array, since the acoustic field intensity profile will, in principle, replicate this. Typically, this will result in a broader passband, but with lower side lobes. The greater the number of elements in the array, the greater can be thesuppression of the side lobes. The advantage over thefixed electrode pattern, which has no phase variation across the profile, is its programmability.

An important design issue that must be addressed with AOTFs for use in imaging applications is the control of image quality and spatial resolution. While the AOTFis inherently capable of yielding very highquality images, this will require careful attention to those factors which may degrade the spatial resolution. A key feature making the AOTF suitable in imaging systems is the large angular aperture. The spatial resolution for any particular design will be determined by the wave vector phase-matching conditions. For a fixed incident light beam direction, the directions of the acoustic wave vector and the diffracted light wave vector must vary in direction with wavelength for exact phase matching. For a given optical beam incident fromafixed direction, there must be adequate angular spread of the acoustic beam energy to satisfy phase matching over the full optical bandwidth. It is the acoustic beam diffraction spread which allows the AOTF tofunction over the full optical bandwidth. From this it follows that phase matching will also result in an angular spread in the diffracted beam direction for optical wavelengths over the full optical bandwidth. It is this angular spread in diffracted beam direction which leads to degradation of the spatial resolution of the imaging AOTF. The degreeof degradation will be determined by the AOTFdesign. Note that theresolution is ultimately limited by aperture diffraction at the AOTF, in accordance withmeasurements reported by Belikov et al. and it may be an objective to approach this limit as closely as possible.

FILTERS

ACOUSTO-OPTIC TUNABLE

231

An estimate of the spatial resolution of the noncollinear AOTF may be obtained from consideration of the phase-matching diagram, as carried out by Suhre etal. Exact phase matching can be expressed using the law of cosines, as

where A is the acoustic wavelength. The parameters ei and A are fixed will vary with producing for this situation, the diffraction angle, e& an angular spread, AO,, with wavelength. If the crystal is dispersive, n, and ni will also vary with wavelength over the optical bandwidth AA. If there is adequate angular spread of the acoustic beam, then there will be an acoustic wave vector available to couple the incident and diffracted light wave vectors. The angular spread of the acoustic wave vector, the diffraction spread, is de, = N L . The value of L is generally selected, along with Q , to yield the desired spectral resolution. For an imaging AOTF, this choice must also take into account the desired spatial resolution. To estimate the magnitude of he, resulting from the design, we restrict the application of Eq. (57) to those wave vector diagrams which satisfy the parallel tangent condition. In this case the relation between Oi and Od is given by tan ed=

k)

tan

e,

from which we can calculate the value of which we can use in Eq. (57) in order toobtain thevalue of A. These values, along with the wavelengthdependent values of n, and n, and ni calculated from the appropriate Sellmeier equations, can now be used to calculate Aedas a function of Oi and AA. As an example of the application of this procedure, we can use an IR imaging systemoperating between 8 and 12 pm using a TAS AOTF. The internal diffracted angular spread was calculated as a function of AA for a range of values of ei from 5" to The results are shown in Fig. 16, fromwhich it canbe seen that for a given AA, A 8 , increases for increasing Oi.This can be qualitatively understood in the following way. For a given and AA, fincreases while L decreases, but L decreases more rapidly, the acoustic diffraction spread increases. As the acoustic diffraction increases, does Aed.These estimated values of ABd can be compared with Rayleigh diffraction from the AOTF aperture, AJD, to determine the degradation of the spatial resolution from the diffraction limit. For example, for a TAS imaging AOTF operatiig at 10 pm, the

GOTTLIEB optical bandpass might typically be 0.5 pm, and have a l-cm optical aperture. Thus, the diffraction-limited spatial resolution is about 1 mrad. Figure 16 shows that the estimated value of Aedis also about 1 mrad, so that there would be no degradation of the filtered image. For a larger optical aperture, or a larger Oi, there would bedegradation. This procedure is applicable to any AOTF and for any wavelengthrange. For most imaging applications, it is probably not necessary to approach the Rayleigh resolution limit. Generally, thefinal image will be formed on a detector array, that the number of elements in the array, and the angular field will determine the limiting spatial resolution. This is usually much less than the diffraction limit. In any case, it is necessary to take intoconsideration the entire optical system when analyzing the AOTF resolution requirements. Another important effect, distinct from the image smear process described above, is the spectral scene shift. understand this process, let us suppose that the spectral resolution is very narrow, and that the field ofview is very small. Then for exact phase matching, the light will be incident exactly at the design angle, €li, and a tuning frequency, fi, will filter the scene with a narrow bandwidth at Al. In order to pass a second wavelength, incident from exactly the same direction, ei, a second frequency,f,, is applied. However, the diffracted beam directions, eld and

with

Acoustic beam spread as function of the AOTF bandpass width, a parameter. (From Ref. 21.)

ACOUSTO-OPTIC TUNABLE

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233

will in general also be different. There aretwo effects that create this difference; the first is the steering resulting from the phase matching, and the second isdue to the variation in refractive indices if the AOTFmaterial dispersion is significant. If the spectral range over which the AOTF is intended to operate is large, then this willmost IiKely be the case. A consequence of such differences in €ld is that the position of the image in the focal plane will shift laterally as thewavelength is scanned. Since most imaging applications require a stationary image, it is important to design the AOTF to compensate for this shift. The procedure fordoing is fairly simple; it consists of creating a wedge or prism angle between the input and output optical faces of the AOTF so that the scene shift, due to refraction from the material dispersion, just balances the scene shift due to the phase matching. This compensationcanbe perfect for anytwo wavelengths within the spectral range. These two wavelengths can be chosen so as to minimize the shift over the entire range. The procedure for minimizing the scene shift is carried out using the relationships for wave vector directions in the AOTF shown in Fig. 17. In that diagram, the two interfaces are the entrance and exit optical faces, whereas the refractive indices for the diffracted beams at wavelengths and are n, and n,, respectively. For normal dispersion, if < h,, then nl > n2.If we define 8, and to be the internal angles that thediffracted beams make with respect to the output face normal, then it can be seen

INCIDENT LIGHT.ki

BEAM,

17 Diagram for the calculation of the wedge angle between the optical input and output faces, used to eliminate the angular shift of the imaged scene between wavelengths h, and h,.

GOTTLIEB that el C If we now define the externalangle that thediffracted beam makes with respect to the exit face normal as e,, then the condition for no scene shift at the two chosen wavelengths is sin 8, = n1 sin 8, = n2 sin or These relationships can now be used to calculate the wedge angle, 8 = - el = eld- ea such that there will be no scene shift. It follows from the previous two equations that 8 1

=

a[&]

The value of eldis determined from the phase-matching conditions, and the wedge angle, e, is then simply

e,

=

eld- ei

where it is assumed that the input light direction is normal to the input face. Note that the correction can be made for either the ,positive- or negative-order diffracted beams, but not for bothsimultaneously. In fact, correction of one will produce a greater scene shift in the other, so that once the wedge is fabricated, the useful order is fixed. Another consequence of the wedge is that the zero-order scene which contains the full spectrum will suffer from severe chromatic aberration. If it is desired to use the zero-order image, it can be separately compensated withan external wedge. The size of the wedge angle will depend, among the factors described above, upon the dispersion of the AOTF crystal. The larger the material dispersion, the smaller the wedge angle correction.

The procedures for fabricating AOTFs aresimilar to thoseused to fabricate other bulk A 0 devices. However, there will typically be greater emphasis for some device parameter domains. For example, it is unusual for the RF to exceed a few hundred megahertz, as is the case for A 0 deflectors for signal processing. While AOTFs most frequently have optical apertures of several square millimeters, it is not unusual for certain applications to

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require apertures upto 30 mm 30 mm. Such apertures leadto very large devices, which is unusually large in comparison to any other A 0 device. These factors will lead to the need for fabrication techniques specialized for such parameters. The steps neededto prepare the body of the AOTF are basically similar to thepreparation of crystals for a variety of optical devices. For production of large numbers of AOTFs of similar design, it is usual to prepare an entire crystal boule forthis purpose. The boule is mounted ona goniometer for x-ray orientation, after which a reference face will be ground on the boule, and it will be placed in a saw for rough cutting the cell bodies to the desired shape. Oxide crystals, such as LiNb03 or TeOz are usually cut on diamond wheels, while more fragile crystals, such as TAS or Hg2C12, are cut using a string saw. After rough cutting, grinding, and polishing is done ona lap with the pieces held in a fixture, such as a plunger jig, which will maintain the orientation accuracy of the reference face ground on the crystal while it was mounted in the x-ray goniometer. Such a fixture may hold a large number of cell bodies for polishing, as shown in Fig. 18, which

Figure Quantities of identical are efficiently fabricated by mounting a large number of cell bodies on a common fixture for performing grinding, polishing, film deposition, transducer bonding and lapping, and electroding.

GOTTLIEB an efficient method of preparing large quantities of identical devices. ‘The most critical surface to be polished is the transducer face, since its orientation with respect to the optic axis of the crystal is the determinant of the polar axis design angle, Oi.In addition, the flatness of the surface mustbeveryhigh in order that the bond between the crystal and the transducer be of high quality.

Transducers The overwhelming majority of AOTFs are designed for operation in the lower range of the RF spectrum. For IR applications, few designs will require frequencies higher than about 50 MHz, while devices designed for the visible seldom require frequencies greater than200 to 300 MHz. In the far-IR, the RF range will lie between about and 30 MHz. The only exceptions to these lower frequencies will be collinear AOTFs for the visible using crystals such as LiNbO,, with high acoustic velocity and high birefringence, where RF inputs up to 1 GHz may be required. The transducer structure almost always consists of LiNbO, plates bonded to the AOTF crystal and then polished to the appropriate thickness. In the case of the very high frequency devices, thin film deposited ZnO transducers have been used although very rarely. A further general distinction between A 0 deflectors and AOTFs is the size of transducer. Typically, deflector transducer dimensionsare of the order of millimeters, while AOTF transducer dimensions are often as large as several centimeters. AOTFs are spectroscopic devices, and thus an important measure of their peraperture. AOTF formance is light gathering power, which scales with optical designs for operation in the IR will, in addition, have to overcome the dependence of RF input power, which leads to larger values of transducer length. Therefore, devices designed for IR applications will require large transducer dimensions. The method of bonding LiNbO, transducers to A 0 crystals most commonly used is that of vacuum compression. This method is very suitable for large area (>l cm2) transducers, but requires considerable care at various stages of the process. This process must be carried out under highvacuum conditions, and requires a system which can maintain lo-’ Torr and hasbeen configured with fixtures designed to bring together the transducer and AOTF crystal immediately after the metal-bonding films have been deposited on them. After themating surfaces have been broughtinto contact with each other, they are immediately placed under pressure for 50 to 2000 psi, depending upon the materials, using a hydraulic system. If this is done within seconds, then a vacuum of 10” is adequate to prevent

ACOUSTO-OPTIC TUNABLE FILTERS oxidation before mating. If the surfaces have been well polished to good flatness, and thefilms deposited with gooduniformity, then near-molecular bonding can occur. Using this technique, compression bonds of indium, tin, aluminum, gold, and silver are routinely made. The inside of the vacuum system in whichthis procedure is carried out is shown in Fig. 19. The two exposed substrates are held on either side of the evaporation sources during film deposition. The system can accommodate multiple sources so that multiple layers of films can be deposited, dependingupon the mechanicalimpedance-matchingdesign being followed. The simplest arrangement is one in which the films are deposited symmetrically on both surfaces. If this is not the case, then a blade shutter may be used to shield one of the surfaces. It is essential that these procedures are carried out in a dust-free atmosphere in order to avoid contaminating the interface with particulates. Even the smallest particles will prevent a suitable acoustic bond to be made between the transducer and the AOTFcrystal, that fabrication must be donein a clean-room facility. After testing the bond to verify its acoustic quality, the transduceris lapped to final thickness; for large-area bonds, special testing procedures are used to ensure that the LiNbO, is uniform in thickness over the entire area. Special polishing fixtures are needed to perform these operations.The final operations are deposition of the top electrodes, and wire bonding. Each design willrequire adeposition mask to define the electrode pattern,which may be dictated by the need to divide the active transducer area into an array of elements. An AOTF onwhich the transducer has been so divided 20. The array designmay be required for impedance isshowninFig. matching, apodization, multiple-drive source, or some other purpose. The interconnect wiring is generally done with gold wire bonds, using conventional wire-bonding apparatus.

4.3

Heat

In order to operate AOTFswith high efficiency, especially at long wavelengths, it may be necessary to use RF input power levels that can reach the thermal damage limit of the transducer structure. Various types of transducer heat sinking have been developed which will allow higher RF power densities to be applied with no damage. The damage generally results from twocauses; excessively hightemperature at the transducer bond which may cause melting other deterioration, andhigh-temperature gradients or differential expansion which may cause stress cracking. Computer programs based on well-established thermal modeling techniques have been developed in order to design AOTF heat sinks and to estimate operating

238

GOTTLIEB

19 Vacuum compression bonding system, in which the metal films are simultaneously deposited on the transducer and the cell body surfaces, which are then brought into contact under calibrated pressure.

ACOUSTO-OPTIC TUNABLE

FILTERS

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20 By series connecting the four elements of thislarge-area L i m o s transducer, the electrical impedance can be increased to near R.

power limits. Such models are used to estimate thetime.evolution of peak temperatures and temperature gradients in order to construct a damage control method using duty cycle parameters as well as heat sinking. The simplest type of thermal management uses fan cooling in a housing designed specificallyfor efficient airflow past the transducer structure.This approach is applicable only for relatively large devices whose sizes are compatible with the mounting of even the smallest blower. An example of an AOTF with such forced-air.cooling is shown in the photograph in Fig. 21. The AOTF is a very large TeO, device with a 30 mm X 60 mm optical aperture andtwo transducers, each 25mm X 28mm.A small muffin fan was mounted directly on the RF mount, and the housing was designed with ducts that the air was drawn into the housing, forced along the transducer, and through ducts to beexhausted. Using this system, each transducer could be powered with 10 W cw, with a temperature rise of no more than 6°C above ambient at the hottest point. Passive heat sinking is more commonly used, and a variety of such well-known electronics techniques is used. One technique well suited to large-area transducers is to contact the transducer with a high thermal conductivity insu-

21 Cooling is provided to high-power mounted on the AOTF holder.

by a fan which is directly

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22 The transducer on a AOTF, whichrequiresveryhigh power densities for long-wavelength IR operation, is provided with a sapphire heat sink, on which the top electrode electrical connections are deposited.

lating slab, such as sapphire, onto which electrodes can be deposited to make the electrical contacts to the transducer electrode elements.Such a structure is shown in Fig. 22. The sapphire slab is contacted intimately to the transducer surface with a very thin layer of thermal conducting paste to ensure good heat transfer. The back surface of the slab contacts the metal housing of the RF mount to remove the heat. A consideration with this approach is the acoustic impedance matching between the transducer and the heat sink, as this may cause loss acoustic power into the heat sink. Generally, this will be only a small loss, but it may be advisable to carefully evaluate the acoustic energy flow across this boundary.

5

SYSTEMS Tuning

The motivation for rapid laser tuning relates to numerous applications for which there is a need for high-speed data acquisition, such remote detection and identification and monitoring of pollution gases, as well as

GOTTLIEB for wavelength-agile optical communications systems. Laser wavelength selection and tuning conventionally use diffraction gratings. A number schemes for high-speed mechanical tuning use rotating gratings and mirrors and multiple gratings. However, it is difficult to achieve random access times less than 1msec withthe required alignment precision by mechanical means. This has led to interest in purely electronic means forcavity tuning. The development of the AOTF has its origins in the need for an electronic method for electronically selecting a single line in a dye laser cavity. It was for this purpose that the collinear AOTF was conceived by Harris in 1971. Harris chose a CaMoO, crystal, which placed the RF tuning range conveniently below 100 MHz. The optical layout for cavity tuning is shown in Fig.23. An acoustic shear wave ismade to propagate collinearly with the optical waves and couple through the pd5 photoelastic tensor coefficient. In this configuration, the shear waveisproducedby mode conversion of a longitudinal wave by reflection at the input optical face. The longitudinal-wave transducer is bonded to the adjacent face, which makes a 62" angle with the input optical face. For the longitudinal wave incident to this face, the acoustic energy is nearly fully converted to anxpropagating shear wave. Alternatively, it is possible to make the face angle and use shear-waveto shear-wave reflection. In this method, the AOTF crystal is immersed in an index-matching fluid to reduce the optical refraction angle, as well as reflection, at theoptical faces. The index-matching fluid is the dye solution itself so that no external dye cell is needed. In order to minimize reflection losses at the other end of the crystal, it was cut at an angle of in the orthogonal plane, and the plane of light TOP

VIEW "

z

Y

I 23 Schematic of a dye laser cavity in which a CaMoO, collinear AOTF is used for wavelength tuning. (From Ref. 22a.)

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polarization is in the plane of incidence at both faces. The difference in refraction angle is used to select the laser cavity polarization. A calcite prism was placed in the beam path to increase this separation to avoid the possibility of competing high-gain oscillations. A Q-switched doubled Nd-YAGlaser, with 100-nsec TEM, mode pulses at A = 5320 with a confocal cavity, was used. With the dye Rhodamine 6G in ethanol, the dye laser was tuned from 5445 to 6225 by varying the AOTF drive between 58.2 and 45 MHz. With a 2.1-cm-long CaMoO, crystal, the AOTF bandwidth is 6.8 A, and with line narrowing within the cavity, a laser line width of 1.35 is obtained. Because of the high-gain conditions, it is possible to make the cavity lase simultaneously at more than a single wavelength, with each near 100% efficiency. Such multipleline operation may be useful for a variety of applications in spectroscopy and communications. Harris demonstrated other multiple-line generation effects by driving the AOTF at power levels greater than thatrequired for 100% efficiency, so that symmetric sideband levels higher than the bandcenter level are produced. Many interesting effects can be produced by varying the duration and peak power of the pump laser. Tuning of a laser cavity with an AOTF was extended to the far-IR by Denes et al. [23]in1988by building a CO, laser cavity containing an AOTF capable of operating from 9 to 11 pm. Themost suitable A 0 crystal for this purpose is TAS, which has extremely low optical losses in this spectral region and a very high optical damage threshold, greater than 1 J/cm2. A schematic of the AOTF tuned cavity is shown in Fig. 24, which consists of the conventional gain medium and end mirrors, to which the AOTF and a polarizing beam splitter are added. Thecollinear TAS AOTF has a carefully designed internal interface which serves an optical as well h

S

24 Schematicof a CO, lasercavitytuninginwhich AOTF is used for wavelength tuning. (From Ref.

a TAS collinear

244

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as anacoustic function. This interface allows the acoustic shear-wave power to couple from the acoustic wedge onto which the transducer is bonded into the interaction region. The interface is cut at an angle of with respect to the B axis of the crystal (the interaction direction), that the optical resonator path has a 90" bend. The shear-wave displacement direction is along the axis, normal to the plane of incidence; for this displacement the shear waves propagate in any direction in the BC plane with no mode conversion. Referring to theschematic, thep-polarized light propagating to the right is split out of the cavity by the polarizing beam splitter; the s-polarized light propagates along the B axis of the crystal as an ordinary polarized wave. In thepresence of the acoustic wave, the tuned lasing wavelength is rotated 90" in polarization direction and upshifted in frequency by the RF. These are now p-polarized, extraordinary waves, reflected (by the process of birefringent reflection) at the interface that they propagate along the C axis. The untuned s-polarized waves, including amplified spontaneous emission (ASE) is reflected (by the process of ordinary reflection) at the interface at an angle of from the C axis, emerging from the crystal at an 11" angle out of the resonator cavity. The tuned light @-polarized) is reflected by the cavity mirror back into AOTF. Ittravels down the AOTFB axis whereit is now downshifted in frequency and reconverted back to s-polarization. The polarizing beam splitter removes any remaining p-polarized light from the cavity so that only the tuned light is coupled out at the output mirror. The design and physical characteristics of the AOTF aredictated by the difficult requirements of laser tuning at 10 pm. The resolution must be high enough to resolve adjacent lines, which are spaced at intervals of between AA = 0.01 pm and 0.027 pm, for wavelengths between 9 and 11 pm. The efficiency of the AOTF must approach 100% under low-gain conditions, which will require a large value of L . The dependencies ofthe resolution and acoustic power density needed for 100% efficiency on the interaction length are shown in Fig. 25a and 25b respectively. From these curves it can be seen that adjacent COz laser lines can be resolved for interaction lengths greater than 2 cm. Depending upon gain conditions in the laser, it is possible that lower resolution, and smaller L , would be adequate. Since the plot shows acoustic power density, allowance must be made for the electromechanical conversion efficiency of the transducer, which will be no greater than about 50%. Assuming that the maximum power loading of the transducer is of the order of 2 W/cmz, the required interaction length is 7 cm. However, note that for the collinear AOTF configuration, shown in the schematic of Fig. the physical length of the crystal need be only one half of the interaction length, since the acoustic wave reflected from the input optical face contributes to thephase-matched

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Interaction Length (cm)

Interaction Length (cm)

25 (a) Resolution of a TAS CO2laser tuning element as a function of length; (b) acoustic power density required for 100% efficiency for a TAS COz laser tuning element.

interaction. It is also important that acoustic attenuation not diminish the acoustic power density over L at the highest frequency needed for line selection. The TAS AOTFis shown in Fig. 26. The experimentally determined values for thetuning curve are shown in Fig. 27; allthe lines between 9 and 11 Km are tuned between 17 and 21 MHz. Several tuned p-branch lines are shown in Fig. 28. The two examples of intracavity tuning of lasers given in this section both utilized collinear AOTFs. While there are distinct advantages in doing it is also possible, and may be more desirable in some cases, to use a

GOTTLIEB

Figure 26 The collinear TAS AOTF built for CO, laser cavity tuning.

noncollinear configuration. The operating principals would be very similar, but we may expect a somewhat greater geometric simplicity since filtered beam extraction is more direct for noncollinear.

5.2 Spectrometry The AOTF offers a number of advantages for spectroscopic analysis that make this device highly desirable in manysystems, both from the viewpoint of performance as well as cost. These advantages result from the electronic agility of the AOTF, as well as the large etendue, as compared to conventional dispersers. Spectrometers based on AOTFs have been built for the visible, near-IR, and mid-IR, several of which are representative and will be described 'in this section. A commercial AOTF rapid-scan spectrophotometer for the visible range was developed very early by the Isomet Corporation and utilized a CaMoO, collinear AOTF. This instrument functioned as a basic scanningabsorption spectrophotometer, useful for routine applications such as multicomponent analysis in studies of physiochemical reactions. The optical tuning range was to 750 nm, either fixed frequency or slewed as rapidly as 1 MHz/p,sec, between and 92 MHz.

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16 l

8

9

I

10 Wavelength ( pm)

I

11

12

27 Tuning curve for the TAS CO2laser cavity tuning element.

Many conventional rapid-scan instruments require that the sample be illuminated with high-intensity broadband light prior to detection, which is not suitable for the analysis of photochemical and photosensitive reactions. The Isomet AOTF was first used by Shipp et al. [24] to perform rapid-scan analysis of fast photochemical reactions. an example of such use, they demonstrated the course of one such reaction, the oxidation of formaldehyde byacid dichromate. A200-nmrangeofwavelengthwas scanned in 11.7 msec and resulted in 128 spectra. More rapid scan rates are possible. More recently, a commercial multiple-component liquid process spectrometer was built by the Combustion Control Division of the Westinghouse Electric Corporation (now a divisionof Rosemount Analytical, Inc.). This instrument, called the LIMOR L, is a multiple-component liquids analyzer that measures those chemical species that have absorption bands in the near-IR, from 0.9 to 2.5 Km. The instrument is shown in Fig. 29. It uses an external sample cell (cuvette) which is connectedto theanalyzer with quartz fiberoptic cable. The transmission range is limited to 2.5 Km by the fiber transmission. This remote operation is advantageous for a variety of monitoring applications. A major advantage of near-IR measurements in liquid process analysis is that the sampling probe is placed

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60 -

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20 10

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20

22

24

-

-

-

.

.. 0 . . . . .. 17.,360 17.400 Freq, MHz

28 Laseroutput signal

AOTF tuning frequency. '

directly in the process stream, so that there is no necessity for extracting samples. A block diagram of the LIMOR L is shown in Fig. 30, which separates the main functional components including the sample cell, the optical bench (which holds the AOTF), the RF electronics, the signal processing, and the interface electronics. The instrument is microprocessor based, and can be remotely operated from a PC-compatible computer. The instrument is built around a TeOz noncollinear AOTF, with RF tuning between 30 and 70 MHz to cover the spectral range. The liquid sample is drawn into the cuvette, and absorption measurements are made at up to five selected wavelengths, with the radiation transmittedfrom the AOTFvia the fiberoptic cable. After passing through the liquid sample, the unabsorbed radiation is conducted by the other fiberoptic cable to the detector in the instrument, a cooled PbS. The processing electronics then takes the absorption measurements and calculates the concentrations of the liquids of interest. The concentrations are displayed on the control panel or can be converted to analog signals for other purposes. Typical liquids which can be measured by this instrument include alcohol, glycerine, styrene, acetic

~ultiple-c~mponent liquid process spectrometer.

acid, amino acid, salt solutions, aromatics, aldehydes, ketones, phenols, and water. Another AOTF spectrometer designed for rapid color analysis in the visible was described by Hallikainen et al. [25]. They have pointed out that diode array-based spectrometers have become available in the past decade, but that in practice they are still slower than AOTF systems. They assembled a system using a commercially available Matsushita TeO, A 0 Model EFL-20, tunable from 380 to '750 nm. A tungsten halogen lamp is used as the source, and a quartz fiberoptic bundle is used to conduct the light to the target, and another bundle is used to collect the reflected light. The output of the collecting fibers is collimated and polarized prior to entering the AOTF. The AOTF RF driver consisted of a voltage-cont oscillator (VCO) and a phase-locked loop (PLL). The output of the is buffered through a broadband amplifier to the desired voltage, and the

250

Figure 30

GOTTLIEB

Block diagram of an AOTF multiple-liquid-component analyzer system.

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R F signal output is fed to the AOTF. The frequency is divided by a programmable counter, and the low-pass filtered output of a PLL regulates the VCO until the divided frequency matches the reference. A microcomputer controls the operation of the spectrometer, which calls the divisions for a specified wavelength from a read-only memory. Up to 61 points can be called, corresponding to a 5-nm sampling interval between 400 and 700 nm. A Hamamatsu R298 photomultiplier is used to detect the reflected light signal. The output of the photomultiplier is converted to a 12-bit signal to the computer, capable to 0.025% accuracy. However, the stability of the light source is the limiting factor. Results reported with this color spectrometer indicate that color resolution is comparable to that of the human eye. Many of the most important applications of absorption spectroscopy require operation in the mid- and far-IR, where the principle molecular absorption bands lie. Several such IR AOTF systems have been developed for specific purposes, utilizing TAS. The first is a combustion monitoring system, designed to perform on-line analysis of the C O and C 0 2 concentrations in combustion products, built and tested by Bardash and Wolga [26] at Cornell University. Conventional exhaust monitors analyze a small sample of the flowing gas and are therefore limited in applicability. By using known absorption spectra of the exhaust gases it should be possible to determine both the partial pressure and the temperature of the constituent gases directly across the flowing stream. Conventional IR spectrometers are not well suited for this because of speed limitations, as well as their unsuitability to operate in harsh environments. The AOTF-based spectrometer built uses a collinear TAS AOTF supplied by Westinghouse , with the requirement that it have adequate resolution to distinguish the vibration-rotation bands in the IR spectrum near 4.3 pm, about 2 cm-l or 0.1%. This corresponds to an interaction length of 5 cm and an optical homogeneity in the crystal birefringence of better than 1 part in lo4. The two principal subsystems of the spectrometer are the electronic system and the optical setup. The electronic system, shown schematically in Fig. 31, consists of the Hewlett-Packard 9836 controlling computer, an H P 8656A frequency synthesizer, a LeCroy signal averager, and an H P 3497A data acquisition unit. The R F power parameters are set by the computer and switched by a Minicircuits ZMSW diode switch, whose output was sent to the R F power amplifier, then to the AOTF. The diode switch output PRF and pulse duration is controlled by a pulse generator driven by a Wavetek signal generator which also synchronized the data acquisition and display electronics. A scanning motor controlled by the data acquisition unit is used so that the AOTF can access either of two optical paths. The optical layout is shown in Fig. 32. The collinear AOTF, a photograph of

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]

4

t I

t

31 Schematic

t an AOTF combustion gas analyzer.

which appears in Fig. uses shear acoustic waves propagating along the crystal B axis. In this configuration, light enters theinput face of the crystal and isreflected at the opposite transducer end by a gold film on thesurface, and exits from the same input face. The two optical paths are the selfcalibration path and the data measurement path, each of which has a broadband light source consisting of a globar and collimating lens. The light from one passes through a calibration absorption cell, and the light from the other passes through the exhaust gas stream. This path, which includes the AOTF,also includes a Rochon polarizing beam splitter, through which the light passes before entering the AOTF; this selects one polarization for the AOTF. The light reflected by the gold layer on the AOTF transducer face passes back into the Rochon prism. The filtered light, whose polarization is rotated go", is deviated by the Rochon. This filtered lightis collected by the turning mirror and directed to a cooled InSb detector. It is necessary to take the ratio of the signal intensity in the measurement to thatin the reference pathin order tomeasure concentra-

ACOUSTO-OPTIC TUNABLE FILTERS AOTF

t

POLARIZING PRISM

BURNER

LENS

32 Optical layout for an AOTF combustion

analyzer.

tions, since the absolute intensity will vary with a number of uncontrolled factors. The system throughput is measured at all wavelengths withno gas in the optical path, and this constitutes the background measurement. The light intensity in the presence of the gas is measured, andits ratio with the background is taken as the gas transmission. The integrated line or band strength is derived from this transmission measurement. The system can be operatedin either ahopping or a scanning mode.In the former, discrete mode, measurements are made at only a set of selected rotation-vibration lines. In the scanning mode the frequency is stepped in small increments, matched to the resolution of the AOTF. Bardash and Wolga have described the following algorithm to determine the temperature and partial pressures from discrete mode measurements. Transmission measurements were made with the reference cell, which contained a mixture of N2 and a known partial pressure of CO at a total pressure one atmosphere. This was used to calibrate the system as follows: The RF is set approxi-

GOTTLIEB

33 The collinear TAS AOTF built for the combustion gas analyzer.

mately at a location between the P and R branches of the fundamental rotation-vibration CO absorption band. Transmitted signalismeasured here, and repeated twice at frequencies 60 kHz higher and lower (corresponding to 3 cm-'). The computer then fits a parabola to these points, finds the extremum, and assumes that this is the spectral bandcenter midwaybetween the P and R branch. To locate agiven spectral line, the computer calculates the frequency where the absorption line should be with respect to the bandcenter, then using a 30-kHz step size with the above procedure, it locates the line to obtain an accurate value for the frequency at line center. The mirror is then turnedso light from the burner enters the AOTF.The frequency isset forthe derived value of line center, and the signal measured. Comparison with the reference measurement is used to derive the value for transmission, compensated for temperature variation. The measurement of flue gases directly in the plant smokestack from industrial combustion processes relating to power generation and manufacturing is rapidly becoming a regulatory requirement worldwide. Control of fuel-air mixtures for optimizing burner function is needed to minimize fuel costs, and reduction of emissions into the atmosphere is mandated to

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reduce pollution levels.Akey requirement for stack gas measurement equipment is reliability with low maintenance. Prior technology for analyzing stack gases involved extracting a gas sample, conditioning it for analysis, and processing it through several instruments. It is now becoming the practice to use in situ instruments for doing the analysis on the gas as it leaves the stack. There aretwo general-methodsemployed, either across the stack measurement or with a probe which isinserted into the gas stream. extraction or sample conditioning is needed for these methods. Infrared absorption is the most effective analysis method to use because it can be applied to a large number of gaseous species, many of which are combustion products. Some typical flue gases and thelocation of their absorption bands are shown in Table 2. The principle methods involving IR absorption are differential absorption, correlation spectroscopy, and derivative spectroscopy. Any of these may be implemented using AOTF-based instruments. A large effort undertaken by the Combustion Control Division the Westinghouse Electric Corporation (now a divisionof Rosemount Analytical, Inc.) led to the development of a stack gas analyzer which incorporated an AOTF and its associated optical and electronic components into a package designed for mounting into a smokestack. The method chosen was differential absorption, in which the absorption at a wavelength in the absorption band of the gas being examined measured, is andits ratio takenwith the absorption of the gas at a wavelength where there is little or no absorption. This ratio is used to determine the gas concentration, similar to the method which employs comparison with a reference cell. The ability to rapidly switch a large number of wavelengths for analysis allows manygases to be measured, and to use algorithms for eliminating interfering absorptions, and to provide zero and range checks without the need for moving elements. The AOTF can function either as the source of the selected IR wavelength, or Table 2 Typical Flue Gases Gas

band

CH4 NO NO2

so2

c02 H20 CO GH,

4.2

IR absorption

center

3.3 p m 5.25, 3.4 4.0 2.7, 2.7 4.5, 3.4

GOTTLIEB

as a tunable detector with a broadband light source to cover the range. The tuned source method issuperior in this application because the AOTF can then also function as a light chopper to discriminate against unchopped background radiation. schematic of the stack gas analyzer system is shownin Fig. There are threemain subsystems:the optical system, the stack-mounted electronic package, and the control and display electronics. The optical system contains the broadband light source (Sic globar), the AOTF module, the detector, and the associated IR collection optics. The stack-mounted elec-

AID

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34

diagram of an AOTF stack gas analyzer system.

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tronics includes the source and detector electronics and serial buses to interconnect to the control electronics. A microcomputer controls the gas concentration algorithms, the displays, and the permanent records. The optical subsystem is a self-contained spectrometer which can operate over a broad range in the mid-IR portion of the spectrum. Radiation from the globar is collected and focused onto the AOTF with a CaF lens. Following the AOTF, another CaF lens collimates the beam, which passes across the stack and is focused by a third CaF lens onto the detector on the otherside of the stack. The filtered and unfiltered beams are separated in angle by so that thespatial separation keeps the unfiltered light from falling on the third lens. The optical elements are prealigned and mounted in fixedpositions in a cylindrical package. The positions of all the elements, including the AOTF, arefixed at thefactory so that no adjustmentsin the field are needed. The stack electronics interfaces with the optical package and consists of the RF drive electronics. The remote microcomputer controls the drive frequency and amplitude from the frequency synthesizer to the AOTF. The detector requires chopped radiation to discriminate background, so a gate switch islocated between the frequency synthesizer and theRF power amplifier, which provides adjustable pulse width and pulse repetition frequency. The output of the detector is integrated over the duration of the acoustic wave so that radiation is measured only during the on time of the AOTF. This analog signal is converted to digital for the microcomputer, which converts it to absorption values and sends the information over the bus to be converted to gas concentrations for display and recording. The system is placed under computer control to operate as an automated analyzer. The control microcomputer is the system master which determineswhich IR wavelengths are to be evaluated and to carry out the necessary computations to derive the gas concentrations. The computer can be programmed to have the AOTF transmit at wavelengths where there is little or no absorption, followed by a wavelength at an absorption band. After taking a predetermined number of samples at each wavelength, averaging the results, the stack electronics sends the concentration information to the control computer. The control computer can be a standard IBM-PC interfaced to the stack electronics with a standard Intel communications protocol. The concentration algorithm uses the conventional differential absorption technique, but more complex algorithms are available in the control computer to allow more complex interferences to be dealt with. Other gases with absorption bands within the spectral range of the instrument can be added simply by introducing the appropriate software. To carry out the gas concentration measurements described here, it is onlynecessary to access a small number of discrete wavelengths. The analyzer system can also be programmed to operatein a scan mode, where

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the frequency synthesizer isincrementedin small steps to producea continuous absorption spectrum. The time required to complete such a scan is determined by the range and the step size. This mode is useful to study new gases to develop the software appropriate to measuring their absorptions.

5.3 Spectropolarimetry There is a need for a class of photometric instrumentation in which the polarization state of the detected light is an important variable. This class, called spectropolarimeters, combines the functions of spectrometers and polarimeters. The AOTFis an ideally suited device for this type instrument, since it has the property of spatially separating each wavelength element into itstwo polarization components. In addition, these operationscan be performed on full 2-D images, as will be described in Section 5.6. Any noncollinear AOTF can be easily configured to be incorporated into such an instrument. Here, the light to be analyzed is incident on the AOTF, which isexcited at somef(h,). The outputfrom the AOTFconsists of three beams: I , ps), I p p ) , and Io - ( I , + I - J, where ps indicates perpendicular (to planeof incidence) polarization, and p , indicates parallel polarization. Three detectors are placed in the focal plane so that intensity measurements of the threebeams can besimultaneously made. From these measurements, a complete description of the spectral dependence of polarization of the incident light can be made. A more complex instrument utilizing these capabilities of the AOTF was assembled byHatano etal. for rapid-scan circular dichroism spectropolarimetry. Circular dichroism is an important analytical method for studying the structure andfunction of complex biologically important molecules. The basis of the method is to determine the spectral dependence of the difference of absorption between left-hand and right-hand circularly polarized light. A closely related phenomenon, magnetic circular dichroism, includes the effect of optical activity induced by an applied magnetic field parallel to thelight propagationdirection. The lattereffect is governed by the molecular electronic and spin states of the constituent molecules. It is of interest to perform these measurements for studying biochemical reactions, which requires the capability to rapidly scan the spectral region of interest. Conventional methods utilize a stress-induced birefringent modulator to produce a h/4 plate, at a fixed wavelength, but this gives only limited information on the processes. By measuring the entire spectral dependence with adequate time and wavelength resolution, it is possible to analyze transient intermediate and chemically unstable species. The

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noncollinear AOTF offers an excellent approach to providing the rapid spectral scan along with the desired light polarization properties. The optical system assembled by Hitano is shown schematically in Fig. 35. It uses a xenon lamp as the light source whose output is collimated for linearly polarized output of the AOTF the input of the TeOz AOTF. The at the selected wavelength is passed through a fused quartz plate stress modulator. The equalintensity beams of the resulting left-hand and righthand circularly polarized light, modulated at 50 kHz by the stress modulator, are made incident on thesample cell. The photodetector follows the sample cell. The 50-kHz modulation of the stress plate, whose induced axes are at to the light polarization direction, produces a dc signal with no sample in the optical path. If an optically active sample is placed in the cell, the relative intensities of left- and right-hand circularly polarized light will be different, and an ac signal component will appear, according to the relation

where A is the light absorbance. This signal is fed to a lock-in amplifier for furthersignal processing. Several illustrative examples of the application of this AOTF spectropolarimeter can be found in

SOURCE

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35 Optical configuration of the spectropolarimeter. (From Ref. 27.)

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5.4 Astronomical Spectrophotometry The AOTF has been incorporated into spectrophotometric systemsby making several modifications to adapt the existing optics to the requirements of the AOTF. Measurements were reported by Bates at the Royal Greenwich Observatory. The detection system consisted of a cooled EM1 9893B photon counter to which the filtered beam was directed and an uncooled photomultiplier for the zero-order beam. Modification of the collection optics is needed as compared with conventional systems because the light incident to the AOTF must be more nearly collimated. A shortfocal-length collimating lens is used to image the telescope exit pupil at the input to the AOTF,and a relay lens is used to reimage the pupil onto the photodetector. The field of view is limited by placing adjustable size stops at the detector focal plane. As with the previously described spectroscopic measurements systems, the AOTF is driven by a frequency synthesizer under the control of a microcomputer. In the work described by Bates, the interfaces were Synertek VIA boards. The functions performed by the spectrophotometer were (a) accept data from the photon-counting tube, (b) accept 8-bit data from the zero-order detector, (c) send frequency control signals to thesynthesizer, (d) display and record the acquired data, (e) operate the control program, which can be varied. The program sequence steps through the selected discrete observation frequencies, each for chosen integration time, and records the photon count at each wavelength for the zero-order and filtered beams. Tests were carried out at theRoyal Greenwich Observatory to compare the AOTF system data with published values for A-type and K-type stars. Compensation to the AOTF data is required for spectral sensitivity and for broadband light scattered in the AOTFcrystal. This was done by tuning the RF for a nontransmitting UV wavelength and measuring the counts once during each sequence. Other corrections include the AOTF transmission profile and the extinction of the atmosphere.. More complex astronomical observations have been made using the AOTF as an imaging spectrometer for the purpose of acquiring information relating to the chemistry, dynamics, and heat transfer of planetary atmospheres. This work was carried out by Watson et al. [29] at the Harvard Observatory, and was an implementation of a near-IR imaging spectrometer, based on the Isomet CaMoO, collinear AOTF, and a cooled CID camera. The AOTFhad resolution and was tunable from 0.65 to 1.4 pm. The CID camera is an intrinsic 100 element array with each element pm square, sensitive from 0.4 to 1.1 pm. Higher-performance arrays have since become available and may be substituted, The telescope was an U20 Cassegrain, from which the image was transmitted to the AOTF

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by relay lenses with an f/10 aperture to match the acceptance angle of the AOTF. A cylindrical lens is inserted in the path to correct for the astigmatism of this particular AOTF; the astigmatism limited the angular resolution to sec of arc. The image signals were processed and sent to a minicomputer for storage. An excellent illustration of the results obtained with this system were observations made on the planetary atmosphere Saturn. A series spectral images over the 8900 spectral band of the CH4absorption is shown in Fig. 36. The intensities of the images were normalized by setting the ring intensity to a constant value. The intensity of the central sphere disappears at the center the methane band, at 8800 A, and a secondary minimum at 8600 A. An increased brightness at the equator can also be seen, which mayresult from the planet’s atmospheric effects. The exposure for the individual images was 2-5 min, giving an SNR of Watson has pointed out that thesensitivity the spectrometer is such that theintensity in each of the filtered images corresponds to the unfiltered light intensity of a G2 star with m,,= These observations were the first done with adequate spectral resolution to allow the mapping of planetary atmospheric

36 Spectral images 29.)

Saturn taken with a CaMoO,

(From Ref.

GOTTLIEB absorption. It is far more flexible than approaches utilizing fixed filters, and the improvements in AOTF system design will allow the spatial resolution to be significantly improved.

5.5 FluorescenceSpectroscopy The use of rapid-scan AOTF methods was applied to fluorescence spectroscopy by Taylor [30] and Kurtz et al. [31], motivated by the growing interest in the use of fluorescent probes to monitor intracellular ion concentrations in livingcells. Fluorescent probes have becomeavailable whose spectral properties vary in response to changes in pH or calcium ion concentration. Using such probes, the ratio of two fluorescent emission intensities can be measured to determine these parameters. Conventional methods using a monochrometer and diode arrayhave disadvantages due to complexity, cost, andinability to simultaneously acquire multiple-wavelength data. A schematic of the AOTFfluorometer described by Kurtz is shown in Fig. 37. It utilizes two AOTFs, which can be rapidly scanned, one to tune the excitation wavelength and the otherto independently tune the emission wavelength. A xenon-mercury arc lamp is used as the light source. To illustrate the technique, data were taken on thespectrum of 10 p M BCEF in a Hepes buffered solution of pH The excitation spectrum was obtained by scanning the AOTFbetween to nm to excite the dye. The emission spectra were taken with the second AOTF tuned to nm, andthis output signal fellon thedetector. Alternatively, the excitation wavelength wasfixed by the first AOTF at nm, and the second AOTF scanned from to nm. A third type of fluorescence measurement was performed, which represents the time-resolved excitation spectra of POLARIZERS

DYE

SCOPE

37 Schematic of the AOTF fluorometer. (From Ref. 31.)

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BCEF at six values of pH, from 5.5 to in l-sec scan time intervals. Some measurements require rapidly alternating the excitation between two wavelengths as rapidly as possible to avoid bleaching phenomena. This is readily done with the AOTF. In another rapid modulation approach, the AOTF can be made to transmit two excitation wavelengths simultaneously, employing two lock-in detectors to separate the two emission spectra. The AOTF flexibility allows a large variety of combinations of excitation and emission measurements to be carried out.

5.6 Spectral Imaging The use of AOTFs for specialized spectral imaging systems (e.g., astronomical, fluorescence microscope, etc.) has been alluded to in prior sections. However, more generalized imaging systems incorporating AOTFs have’recently been developed that lend themselves to a Iarge number of possible applications. One of the objectives of such designs is the greatest use off-the-shelf optical and electronic components, which leads to relatively modest system cost. Many design issues, both AOTF and optical, become apparent with experience with these imaging systems. Most of the AOTF imaging work to date has been in the visible and near-IR spectral range to take advantage of the low cost and ready availability of the optical and sensor components. It is simple to adapt almost any of the charge-coupled device (CCD) TV cameras, which typically incorporate 512 X 512 detector arrays. The system specificationswill include the spectral range, spectral resolution, spatial resolution, and field of view. The AOTF is usually designed in conjunction with the selected optical components. The design parameters will comprise material parameters, ei,L , transducer design, and aperture dimensions. In addition to these, there will be several other designissues relating to image quality. An imaging systemdesigned for portable field use was assembled at Westinghouse STC. A schematic of the optical layout is shown in Fig. and a

25 111.4 TV Input lens

25 mm 111.4 collimalor and relay lens

AcJlF

GOTTLIEB ,

__

,./

,,...

39 Spectral imaging system based on a TeO, AOTF and a standard TV camera. (Courtesy Westinghouse STC.)

photograph in Fig. 39. The AOTF crystal was TeO, with ei= 7.5" and a 1cm 1cm aperture. The AOTF module is shown in Fig. 40. The optics consist of an assembly of a conventional TV camera and photographic lenses. The input was a 25-mm fl1.4 TV lens, in the first focal plane of which was located a field stop to restrict the field of view to lie within the AOTF diffraction angle.A second 25-mm lens functionedas a relay/collimator to provide the required collimation to the AOTF, whose field of view was about 2.7". A telephoto zoom lens was placed in front of the TV camera to allow varying the size of the image to fit the array. This was a standard 70- to 210-mm photographic lens. A black-and-white TV camera rather than a color camera was used in order to take advantage of the higher sensitivity available. Various types of cameras can be used, depending upon the available light levels. Similar AOTF imaging systems have been described by other groups. An imaging spectrometer was built by the Optical Processing Group at the Jet Propulsion Laboratory [32] by Lambert et al., motivated by the need for multispectral imaging in planetary exploration missions. Some of the latter applications have been described by Yu et al. [33] and include both

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40 AOTF module incorporatingTe0, for operation inthe visible through the near-IR.

orbiting and planet-based data collection. In the former case, theimaging system may be useful in analyzing the composition of the planetary atmosphere. The capability to image will be useful in mapping the atmosphere to measure changes with weather conditions. For the surface missions, the mobile vehicle collects rock samples for analysis on earth; it would be the purpose of an imaging spectrometer to perform preliminary classification during collection to facilitate the selection procedure. A breadboard system, consisting of a TeO, AOTF with imaging optics, a CCD camera, and IBM PC was assembled to experimentally demonstrate the imaging measurements of mineral spectral signatures for identification from rocksamples. The breadboard system described by Lambert is shown in the schematic in Fig. 41. It consists an input zoom lens, the AOTF, and a relay lens, followed by another zoom lens at the CCD camera. The respective distances between these elements are designated L1, L,, and L3. All the functions relating to data acquisition, processing, storage, and display are controlled by the IBM PC. The following analysis was used by Lambert to describe the optical response of the imaging system. If a monochromatic point source of light is placed at the input plane, the wave

266

GOTTLIEB

CCD

LENS

ORDER

Schematic of an AOTF imaging breadboard. (From Ref. front, W, emanating from this point source and incident on the AOTF with the paraxial ray assumption is expressed as

Of interest is the light diffracted into the angle by the AOTF grating into the - 1 order, which is the ordinary polarization. Due to dispersive effects, the diffraction angle will be dependent on h. Thus, the - 1 order wave front exiting the AOTF can be expressed as

The wave front at the relay lens at the distance L’ is W, = exp

Finally, the light wave front leaving the relay lens, whose focal length is

f, is

The following important features are aconsequence of these design equations: (a) If the distance L2 between the first focal plane and the relay lens is less than the focal length L , W, is a diverging wave front which can be

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viewed as if originating from a point at a distance LJ/(f - L,) from the relay lens; (b) the input object obtained by the first zoom lens can be treated as being at a distance Lo from the camera, where Lo =

L2f + L3

f-

L2

where L3 is the distance from the relay lens to the camera; (c) the object distance Locan be longer than L, L3; (d) L, and L, can be separately chosen to obtain the desired magnification at the camera, using the zoom lens; (e) the zero- and first-order images at the camera canbe fully separated. The imaging system assembled byLambert et al. was demonstrated for mineralogical mapping by analyzing the contents of Bastnasite rock containing neodymium and samarium fluorocarbonate in silica matix. The neodymium in this rock has absorption bands in the visible, within the range of the TeOz imaging system. A series of spectrally resolved images taken with this system is shown in Fig. The wavelength separation between frames in this assembly is 2.5 nm. The areas rich in neodymium, in the right center portion each frame, changes from light to dark as the wavelength is stepped across the band from 783 to 710 nm.

+

5.7 Communications Semiconductor Laser Tuning Laser cavity tuning using AOTFs has been described in a previous section where the advantages of electronic tunability have been described. The

AOTF multispectral images of bastnaesite. This is a mineral samde

GOTTLIEB concept has particular attraction fortuning semiconductor lasers for optical communications systems, where ultrafast tuning over a relatively wide spectral range would enhance a variety of wavelength-multiplexing schemes. Electronic tuning of DFI3 lasers has been done for narrow tuning ranges by varying injection current. Tuning overa wide spectral range wascarried out by Coquin using A 0 devices in an external semiconductor laser cavity, which allowed tuning at high speeds (less than 10 Fsec), with good accuracy, and over a wide range. A diagram of the external cavity used, which included a GaAS laser, is shown in Fig. The laser is coupled to the cavity with a graded index lens, and within the cavity is an AOTF for tuning and an A 0 modulator whose function will be described later. When the AOTF is tuned to the selected wavelength, it diffracts that light into the rotated polarization. As has been pointed out in the previous section on cavity tuning, an effect of the AOTF operation is to frequency-shift the filtered light on eachpass through the AOTF, always in the samedirection; this phenomenon would render the AOTFuseless for stablecw operation. The purpose of the A 0 modulator is to provide an equal and opposite frequency shift to that of the AOTF, that there is no net shift for each round trip of the light. Since for an A 0 modulator, the diffraction angle varies as the product of the light wavelength and the drive frequency, the diffraction angle is fixed, as the wavelength is varied with tuning. Coquin also points out that by providing a phase shift between the RF input of the AOTF and the modulator, it becomes possible to interpolate between modes of the cavity. Tuning over the entirelaser gain profile of 35 nm was accomplished with a fixed mechanical setting the components in the

"+

0 43 External cavity configurationfor an source. (From Ref. 34.)

tunable semiconductor laser

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cavity, although the efficiency and output may vary greatly over the spectrum. TeOz AOTFs can be used for tuning lasers in the important 1.3- and 1.55-pm wavelength ranges. Wavelength Multiplexing One of the most important potential uses of the AOTF for communication applications is to provide the wavelength selection required for broadband systems requiring fast switching between optical carriers. A number of communication system concepts employing AOTFs for multiwavelength selection were demonstrated by Cheung et al. [35-371 which are described in this section. The first of these, an optical network withmicrowave subcarriers [35] operates in the 1.3- to 1.56-pm range, and uses one fixed wavelength transmitterheceiver pair per channel; the wavelength-division multiplexing isdone with a Te02 AOTF which is coupled to optical fibers. A schematic of the system is shown in Fig. 44; it is based on four laser transmitters, each at a different wavelength, each modulated by a different RF carrier modulated with its own PR/FSK signal, with a frequency deviation of 50 MHz. The unique feature of this system is the AOTF ability to perform wavelength selection at the receiver. With the AOTF it is possible to simultaneously receive any combination of channels without interference. The laser signals are polarization filtered and combined by a 4 x 4 star coupler, from which the output beam is collimated and passed through a polarizing beam splitter before going to the AOTF. In order to demonstrate the system functions, the AOTF was driven by two RF tones simultaneously through an RF power combiner, with more being possible. The limitation is the power density that can be applied to the transducer. The signal is detected by a pinFET detector followed by filters for signal separation. Biterror rates were measured, with little degradation due to simultaneous multiwavelength operation. The small degradation is due to heterodyning at the detector of the light components diffracted by different frequencies. The wavelength-division multiplexingconcept was extended by Cheung et al. [36] to greater channel capacity using an integrated optic version of the AOTF, to bedescribed in more detail in a later section. The principle advantage of the integrated optic version of the AOTF is the lower RF drive power requirements for high diffraction efficiency, that it is possible to simultaneously drive a greater number of channels. This AOTF kas fabricated on x-cut LiNbO,, into which Ti was indiffused to form a single-mode optical waveguide. The interaction length was 2.5 cm, resulting in a spectral resolution of 1.0 nm and a drive power of 180 nW for efficiency. The experimental setup consisted of 16 lasers in the 1.53- to 1.56-pm range, each tuned to a wavelength separated by about 2 nm,

GOTTLIEB

/-

U

h -1.2975

\

h=

+

cl

g

-

Experimental setup for AOTF wavelength separation. (From Ref.

combined by a 16 X 16 star coupler. One output the star coupler was collimated and passed through a polarizing beam splitter. Sixteen-channel wavelength-division multiplexing was demonstrated with crosstalk levels below - 15 dB, which are suitable for many applications. In a variation of the above system demonstration Cheung et al.

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carried out a demonstration of simultaneousfive-wavelengthselection, with a wavelength separation of 2.2 nm, again using anintegrated optic AOTF. In this network, each channel is assigned a different transmission wavelength, which can be used to transmit information either at baseband or at microwave subcarrier frequencies. By combining multiple wavelengths with multiple subcarriers in order toallow multiple services for each user, very efficient utilization of the available fiber bandwidth is achieved, the number of channels in the network being N M ,where N is the number of optical wavelengths and M is the number of subcarriers on eachwavelength. The demonstrationsystem used eight lasers operating at eight different wavelengths from 1.53 to 1.55 pm, with 2.2-nm separation, such that this separation corresponded to 3 the AOTF resolution. The modulation was a 30 Mb/sec PR FSK signal on five subcarrier frequencies between 1.1and 1.5 G&. The modulated laser signals were polarization filtered and combined by star couplers. The collimated output beam was polarization filtered before passing into the AOTF. The outputbeam was coupled into a single-mode fiber and subsequently into the detector. The bit error rate withallfive channels operating waswhich demonstrates the feasibility ofdense wavelength-division multiplexing using AOTF filtering.

5.8 CoherenceDetection It is well known that low levels of coherent, or spectrally very narrow radiation, can be detected in the presence of high-level broadband background radiation by using the techniqueof derivative spectroscopy.While the technique can be implemented with any dispersive device, Chang [38] utilized an AOTF to obtain a high sensitivity for discriminating laser radiation at 0.6328 pm against a white light background. A great advantage of using the AOTF to perform derivative spectroscopy is its capability of purely electronic FM operation, while others require mechanical modulation of some component, an important feature for remote systems requiring high reliability. Derivative detectionrelies upon the large rate of change of light intensity with wavelength of a spectrally narrow radiation. The signal is obtained by frequency modulating the RF input to the AOTF, that the center wavelength of the filtered passband varies with time as

Ac

= X0

+ a8 COS(WJ)

where is the modulation frequency and is the amplitude of the wavelength excursion (in units of the AOTFbandwidth, If the spectral

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72

linewidth, centered at A,, is very narrow compared to the AOTF bandwidth, the signal produced by the AOTF will be P =

PLTosinc2(ho - A,

+

cos(o,t))

where PL is the incident light intensity and Tois the peak filter transmission (determined by the RF input power).Figure 45 shows frequency modulation the RF input leads to an AM signal in the presence narrow-band radiation. If the AM signal is detected with a lock-in amplifier tuned to the modulation frequency, very high SNR enhancement can be obtained. This enhancementcan be understood by examining the Fourier components the signal at themodulating frequency. These components are Po,PI, Pz, etc., where

P

=

Po

+ t/z(P1 cos(o,t) + P2 COS(20,t) +

*

m)

45 The upper curve shows how frequency modulation of the AOTF FW input results in an amplitude modulated optical signal. The lower figure showsthe resulting AM signal detected at the modulation frequency.

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2

The amplitude of each term is Po = P2T$(Ac) P, = P2 =

(73)

PLTO

(74)

.\/z a8S’(Ac) P , T d a a8 4S(Ac)2

where S&) is the sinc function. For a narrow spectral line the signal power at the first and second harmonics are P1 = 1.28P,

(76)

and P2 = 1.282P0

(77)

In order to determine the sensitivity of derivative signal detection for wavelengths in the infrared against thermal background, we assume the Planck radiation law:

[

-1

- l]

H(A) = c , A - ~ exp(:)

To a good approximation for thewavelength range from about 2 to 11 pm, the first wavelength derivative is -= dH(A)

dA

H(A)[(b - 5A)A2]

(79)

and the second waveIength derivative is

- -= d2H(A) d2A

5.48A - d H(A)[

A2

]

Using these expressions together with a typical AOTF design, the SNR enhancement at several wavelengths, for both the first and second harmonic signals, is shown in Table 3. Derivative detection can be performed with AOTFs in anyspectral range and with either collinear or noncollinear designs. Some results are shown in this section for measurements that were done at Westinghouse STC at A = 3.39 pm and A = 9.5 pm. The AOTFs used in this work were TAS, with Oi= 35.5” and L = 15 mm. Two devices were used, one optimized for to 5 pm and the other for 9 to 11 pm. The purpose of these measurements was to demonstrate the ability of the derivative technique to

or

274

GOTTLIEB

Table SNR for Direct Detection and First and Second Derivative Signals for a Narrow Spectral Line against Thermal Background Wavelength (bm)

P;lP;,

PJPB

Oscilloscope

Recorder

.

Lock-in Amplifier

I

Function Generator

46 Block diagram of the derivative detection system.

detect the presence of infrared laser radiation against high thermal background. A He-Ne laser was used as a 3.39-pm source, and a line-tunable COz laser for 9.5 pm. In both cases, the laser linewidth was much lessthan the AOTF resolution, which was about 25 cm". block diagram of the experimental system is shown in Fig. An InSb detector was used for the short wavelength, and a MCT detector for long wavelengths. The AOTFs were driven by a Fluke (Model RF signal generator, which was linearly frequency swept at a very low rate (
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AOTF tothe narrow laser line was recorded by amplitude modulating the RF signal at l-kHz rate during the linear sweep. The derivative spectrum of the laser line was taken by frequency modulating the RF input to the AOTF with an FM deviation of 99 kHz. The FWHM of the AOTF was 400 kHz, so that thedeviation is near optimum for producing the maximum FM signal amplitude. The direct spectrum of the laser taken by linearly sweeping the RF and the derivative spectrum of the laser line are shown in Fig. 47a and b respectively. Note that the zero crossings occur at the peak of the transmission and at each sideband peak. The thermal background was a Sic globar at 1340°C, whose radiation was incident on the AOTF after being combined with that from the laser. The frequency dependence of the direct signal of this thermal source is shown in Fig. 48a. If the system response were flat with respect to wavelength, the blackbody direct signal wouldhave its peak at about 1.8 pm. The measured response is quite different because of other factors; these include the spectral response of the detector, the quadratic wavelength dependence of the A 0 efficiency, and thefrequency dependence of the transducer. The neteffect of all of these is represented by the measured curve. The derivative signal taken in the same way as for the laser is shown in Fig. 48b. In order to test the ability of derivative detection to discriminate the laser against the high background, the two sources were adjusted to the same brightness (within the AOTF resolution). The direct signal and the derivative signal of these combined sources are shown in Fig. 49a and 49b. It is easily seen that the background is greatly suppressed in comparison with the laser signal. The derivative laser signal is 30 dB greater than that of the blackbody, which was easily verified by attenuating the laser by this amount and detecting its presence in the background. Similar measurements replacing the He-Ne laser with a CO2 laser, and the InSb detector with the MCT detector, produced similar results.

Waveguide Much activity since 1975 was stimulated in the field of integrated optical waveguides directed at two aspects of optical signal processing areas, one involving analysisof R F signals, and the otherinvolving analysis of optical signals.Much of the motivation for either was related to the need to miniaturize optical systems and by the need to reduce their cost, possibly by batch fabrication of integrated optics. Parallel developments in fiberoptic technology was a further stimulus, since it seemed natural to couple together these two guided-wave media. At the same time, there was ex-

GOTTLIEB

4 6 4 8

52

54 Frequency. MHz

58

52

54 56 Frequency, MHz

sa

60

62

(a)

46

48

60

62

(W

47 (a) Direct spectrum a (b) corresponding derivative spectrum.

line taken with aTAS AOTF;

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B

46

I

I

I

4a

50

52

56 Frequency, MHz

48

50

52

5854 56 Frequency, MHz

I

I

l

58

60

62

60

62

48 (a) Direct spectrum ablackbodyradiation source taken with a TAS AOTF; (b) corresponding derivative spectrum.

278

46

GOTTLIEB

48

52

58

60

62

Frequency, MHz

49 (a) Direct spectrum of a 3.39-pm laser source combined with a blackbody radiation source

equal radiant intensity at3.39 km; (b) derivative spectrum of the combined sources taken with a AOTF with 99-kHz FM deviation.

plosive growth in the technology related to acoustic surface waves, which seemed an ideal way to control light beams in waveguides. There is a variety of factors making waveguide systems attractive for different areas of application, but probably none more compelling than for optical communications. A major problem with commercially available bulk optical components, such as AOTFs, foruse in high-density wavelength-divisionmultiplexed systems, is the high RF power requirements. For guided-wave AOtinteractions, the dimensions of both the optical and acoustic beams are reduced greatly, except for that of the interaction length. The effect of these reduced dimensions is to drastically reduce the RF drive power requirements for efficient diffraction by about two orders of magnitude. With such a reduction, it becomes feasible to design an AOTF that can support 100 simultaneously operating wavelength channels. The most commonplanar optical waveguide is asymmetric,bounded on one side by air, or some other medium of low refractive index, n,, and on the other side by a substrate of higher refractive index, n3. The principal guiding medium layer has a bulk refractive index n2,which is intermediate

279

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I

46

48

I

I

I

52

I

I

I

58

60

62

Frequency, MHz (b)

Continued.

between n, and n2, and a thickness, t, on the orderof the light wavelength or less, so that only one or a few discrete propagation modes can be supported. with bulk wave devices, there are two basic waveguide modes, TE and TM, based essentially on the plane of polarization. For TM modes the polarization direction ( E field) is normal to the plane of the waveguide, and for TE modes the polarization direction lies in the waveguide plane. The effective index of the mode, neff,lies between that of the substrate and bulk guiding layer, n3 > nett > n2, and will be determined by the value of tlA. In addition, it will be different for the TE and TM modes for any given value of t l X . The momentum, or propagation vector of the guided beam, is defined as p = 2.~n,~f/A,,, exactly as the k vector is defined for unguided light wavepropagation. Of great significance for A 0 interactions in optical waveguides is the observation that anisotropic interactions may occur even in waveguide media that are isotropic. The anisotropy arises from the modal dependence of since TE and TM modes will have different values of neH.Also, the magnitude of the effective birefringence, neff(TE) - neff(TM),can be chosen by varying the guide layer thickness. In addition, the effective photoelastic coefficients for guidedwave interactions will be more complex than those for bulk wave. Con-

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280

sequently, there is a relaxation of the crystal symmetry requirements for useful anisotropic-based devices, such as the AOTF. The acoustic wave for the integrated optic AOTF is generated by an acoustic surface wave (ASW) transducer which is fabricated on the guide surface. The substrate must be a suitable piezoelectric material, such as LiNbO,, and the transducer must be of the interdigital type which efficiently generates theASW. The energy in the guided light waveis confined to the thin guide layer region and it is readily apparent that the acoustic energy must also be confined to the same guide layer region in order for the interaction to be efficient. This occurs very naturally with ASW, for which the strain amplitude will be large only to a depth on the order of an acoustic wavelength. For a well-designed integrated optic A 0 device, the overlap between the optical and the acoustic fields will be near unity. The guide layer is formed on the LiNb03 surface by the process of indiffusion of Ti to a depth of several micrometers. This slightly alters the refractive indices of the substrate to form the light guide. Light can be coupled into theguiding layer by several methods, themost commonbeing the edge coupler, which introduces the light via an optical fiber or a lens to focus the external beam at the edge of the guide. A schematic of an integrated optic AOTF is shown in Fig. in which the incident light beam and theASW are made to propagatecollinearly. The required phasematching condition for the collinear AOTJ? in the waveguide is =

+ KASW

(81).

where the acoustic wave vector K will couple theTE and TM optical modes. The input light is made pure TE by means of the integrated optic mode selector at the input edge. The mode selector is an appropriately designed metal/dielectric layer deposited on the surface. For optical wavelengths that satisfy the phase-matching condition of Eq. (81) there will be a con-

z

50 Integrated optic LiNbO, AOTF.

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version of the TE mode to a TM mode, i.e., a rotation of the plane polarization. The collinearly propagating light beams pass under another optical mode selector at the opposite edgeof the waveguide. This second mode selector is chosen to pass TM modes only, that only the phasematched wavelength istransmitted to theedge the waveguide, where it is coupled out, either by another fiber or collected by a lens. Complete mode conversion of the light has been achieved with only 8 mwof RF power, about 250 times less than the bulk-wave counterpart. Design and fabrication improvements can further improve the power requirements, channel crosstalk, and the number of wavelengths that can be supported.

REFERENCES Dixon, R. W., Acoustic diffraction of light in anisotropic media, IEEE J . Quant. Electron. QE-3, Harris, E., and Wallace, R. W., Acousto-optic tunable filter, J . Opt. Soc.

Am., Nieh, T. K., and Harris, E., Aperture-bandwidthcharacteristics of the Am., acousto-optic filter, J. Opt. Nye, J. F., Physical properties of crystals, Oxford: Clarendon Press, Yano, T., and Watanabe, A., Acousto-optic TeO, tunable filter using far off-axis anisotropic Bragg diffraction,Appl. Opt., Chang, I. C.,Analysis of the noncollinear acousto-optic filter, Electron. Lett., Chang, I. C. ,Tunable acousto-optic filters: an overview, Opt. Eng., ( Salcedo, J. R., Phase-matching in acousto-optic filters. I: Uniaxial crystals, submitted. Dwelle, R., and Katzka, P., Large field of view AOTFs, Proc. SPZE, 753, Voloshinov, V. B., and Mironov, 0. V., Wide aperture acousto-optic filter for the mid-IR range, Opt. Spectrosc. (USSR), Melamed, N. T., and Gottlieb, M., A comparison of various dispersive devices, Westinghouse Research Report No. 85-1Cl-OPREP-R1, Melamed, N. T., The etendueof a filter and of a filter spectrometer, Westinghouse Research Memo No. 85-1Cl-OPREP-M1, Gottlieb, M., Goutzoulis, A. P., and Singh, N. B., Fabrication and characterization of mercurous chloride acousto-optic devices, Appl. Opt., Gottlieb, M., and Singh,N. B., Growth, characterization and device design: thallium phosphorous selenide crystals, in Growth and Characterization Acousto-Optic Materials (N.B. Singhand D. Todd, eds.), Trans. Tech. Publ., Zurich, pp.

GOTTLIEB Gottlieb, M., and Kun, Z., Temporal response of high resolution acoustooptic tunable filters, Appl. Opt., Murphy, J., and Gad, M., Aversatile program for computing and displaying the bulk acoustic wave properties of anisotropic crystals, Proceedings of the IEEE Ultrasonics Symposium, pp. Sovero, E. A., and Khoshnevisan, M., A generalized method for designing acousto-optic tunable filters, Proceedings of the IEEE Ultrasonics Symposium, pp. Chang, I. C., Katzka, P., Jacob, J., and Estrin, Programmable acoustooptic filter, Proceedings of the IEEE Ultrasonics Symposium, pp. Pinnow, D., Abrams, R. L., Lotspeich, J. F., Henderson, D., Stephens, R., and Walker, C., An electro-optic tunable filter, Appl. Phys. Lett., Belikov, I. B., Buimistryvk, G., Voloshinov, V., Magdich, L., Mitkin, M., and Parygin, V., Acousto-optic image filtering, Sov. Tech. Phys. Lett., Suhre, D. R., Gottlieb, M., Taylor, L. H., and Melamed, N. resolution of imaging noncollineartunable filters, Opt. Eng.,

T., Spatial

Harris, E., Nieh, T. K., and Feigelson, R. S., CaMoO, electronically tunable filter, Appl. Phys. Lett., Taylor, D. J., Harris, E., Nieh, T. K., and Hansch, T. W., Electronic tuning of a dye laser using the acousto-optic filter, Appl. Phys. Lett., Denes, L. J., Gottlieb, M., Singh, N. B., Suhre, D. R., Buhay, H., and Conroy, J. J., Rapid tuning mechanism for CO, lasers, Proc. SPIE, Shipp, W. S., Biggins, J., and Wade, C., Performance characteristics of an electronically tunable acousto-optic filter for fast scanning spectrophotometry, Rev. Sci. Instrum., Hallikainen, J., Parkkinen, J., and Jaaskelainen, T., Acousto-optic color spectrometer, Rev. Sci. Instrum., Bardash, M., and Wolga, G. J., Acousto-optic spectrometer system used to monitor combustion processes, Appl. Opt., Hatano, M., Nozowa, T., Murakami, T., and Yamamoto, T., New type of rapid scanning circular dichroism spectropolarimeterusing an acoustic optical filter, Rev. Sci. Instrum., Bates, B., Halliwell, D., and Findlay, D., Astronomical spectrophotometry with an acousto-optic filter spectrometer, Appl. Opt., Watson, R. B., Rappaport, A., and Frederick, E. E., Imaging spectrometer study of Jupiter and Saturn, Icurus, Lansing Taylor, D., Salmon, Edward, and Jacobson, Ken, A Practical Guide to Light Microscopy for Biologists, University Science Books, to be published.

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Kurtz, I., Dwelle, R., and Katzka, P., Rapid scanning fluorescence spectroscopy using and acousto-optictunable filter, Rev. Sci. Instrum., Lambert, J., Chao, T., Yu, and Cheng, L., Acousto-optic tunable filter (AOTF) for imaging spectrometerfor NASA applications:Breadboard demonstration, Proc. SPIE, Yu, J., Chao, T. H., and Cheng, L., Acousto-optic tunable filter (AOTF) imaging spectrometer for NASA applications: systems issues, Proc. SPIE, Coquuin, G . A., and Cheung, K. W., Electronically tunable external cavity semiconductor laser, Electron. Len., Cheung, K. W., Liew, C., and Lo, C. N., Experimental demonstration of multiwavelength optical network with microwave subcamers, Electron. Lett., Cheung, K.W., Smith, D. A., Baran, and Hef'ner, B., Multiple channel operation of integrated acousto-optic tunable filter, Electron. Lett., Cheung, K.,Liew, and Lo, C., Simultaneous five wavelength filtering at nm wavelength separation using integrated-optic acousto-optic tunable filter with subcamer detection, Electron. Lett., Chang, I. C., Laser detection utilizing tunable acoustic-optic filters, IEEE J . Quantum. Electron., QE-14,

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5 Transducer Design Akis P. Goutzoulis Westinghouse Science and Technology Center Pittsburgh, Pennsylvania

William

Beaudet

Harris Corporation Melbourne, Florida

1 INTRODUCTION In Chapters 2, 3, and 4, we discussed the device design methodology that includes material selection, interaction geometry, acoustic mode and orientation selection, as well as transducer geometry specification. In this chapter we address the design and the interfacing of the transducer structure which launches the acoustic wave into the acousto-optic (AO) device. typical transducer structure consists of a metal top electrode, a p i e m electric crystal, and one (or more)metal bonding layer which attaches the piezoelectric crystal to the substrate and which is used as a bottom electrode. The performance of the device as measured by its bandwidth, impedance, conversion efficiency, and voltage standing-wave ratio (VSWR) largely depends on thecharacteristics of the transducer structure used. These characteristics are determined, among other things, by the number, composition, dimensions, and natural properties (e.g. ,mechanical impedance) the various layers and the substrate. the complexity of the transducer structure and the device operating frequency increase, the overall transducer behavior becomes more complex, and the number and accuracy the calculations necessary to predict the device performance increase as well. It is therefore desirable that the device designer not only is able to analyze and design such structures, but is also able to efficiently and accurately predict the overall transducer structure performance regardless of the transducer complexity involved. 285

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AND GOUTZOULIS

In this chapter we first present a comprehensive analysis of the transducer structure (Section 2). The analysis of the various bonding layers is presented via equivalent circuits through the use of a transmission line equivalent matrix analysis to predict the device electrical impedance and transducer conversion efficiency. We also discuss various performance parameters which canbe employed in order toevaluate the overall transducer design. The effects the various layers in simple transducer configurations are described next along with techniques that allow broadband operation with minimum conversion loss. We then discuss various materials issues, and we emphasizethe materials that can be used as bonding layers because they dramatically affect the amount of acoustic energy transferred from the transducer into the A 0 substrate. Note that several discussions on bonding and transducer materials can also be found in various sections of Chapter 6. However, the objectives of these discussions are related to the various fabricational processes the A 0 devices rather than to efficient the transfer of the acoustic energy from the transducer to the A 0 crystal. In Section we present a computer program which is based on the analysis presented in Section 2. We use this program in conjunction with three design examples covering the MHz, MHz, and GHz frequency ranges, in order toshow the use of the design methodology as well as of the program itself, for the study and analysis of simple and complex transducer structures. When appropriate we present actual experimental results to show the agreement between theory andexperiment. These threedesign examples also serve asgood opportunities for theanalysis and understanding of generic transducer issues such as theeffectiveness acoustic quarter-wave matching. We complete the transducer design by describing the electrical matching and power delivery networks (Section For this purpose we discuss impedance matching techniques appropriate for simple transducers structures, phased array transducers, and multichannel devices. In each case we explain the design philosophy followed in matching the device, we present the network used, and we show the performance improvement achieved in an actual A 0 device. We close this section by noting that in Appendix A we providea design program from the St. Petersburg StateAcademy of Aerospace Instrumentation which combines the overall A 0 deflector design methodology (including A 0 material selection, interaction geometry, acoustic mode propagation, orientation selection and transducer geometry specification) with the transducer design methodology (including transducer material selection, acoustic and electric impedance matching). This “single” program can be used to adjust (interactively) the electric impedance matching network so that in conjunction with the A 0 bandshape, the desired A 0

TRANSDUCER DESIGN

287

1

L Single-port

deviceconfiguration.

deflector frequency response can be achieved. relatively easily, that it can be used for

This program can be modified modulators and AOTFs.

2 TRANSDUCER ANALYSIS The majority of A 0 devices are single-port one-dimensional (l-D) structures and use a piezoelectric transducer to generate bulk acoustic waves which then propagate in the crystal (Fig. 1). A less common A 0 configuration is the one found in two-dimensional A 0 devices, e.g., X-Y deflectors or scanners, and involves two'transducers which are orthogonal to each other. The analysis of either of these A 0 structures is based on the analysis of a single-port l-D multilayered A 0 structure, such as the one shown in Fig. 2. To simplify suchan analysis the following assumptions will be made aboutthe transducer-A0crystal structure: (1) the transducer dimensions are large compared to the acoustic wavelength (A,) in the piezoelectric film, (2) the transducer crystal symmetry is chosen that the transducer is excited in a pure l-D acoustic mode and the generated acoustic wave propagates toward the thickness direction, i.e., into theA 0 crystal, the A 0 crystal has a crystal symmetry that is appropriate for the desired propagation mode, (4) the various electrode andbonding layers

2

- - - -- --- - -

N-l

N tN

-.

9 Multilayered single-port nected to a source.

device structure with the transducer con-

288

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transmit the acoustic power without mode conversion, and (5) the acoustic energy generated by the transducer propagates into the material such that theinitial beam size is defined by the dimensions of the topelectrode. The goal of our analysis isthe derivation of simple, closed-form expressions for the input complex impedance and~fromthis the untuned conversion efficiency of the transducer. Using these expressions, the device designer can then study and optimize the top electrode area, the electrode/ bonding layer thickness, and the acoustic impedance(s). These serve as a best condition starting point for the latter addition of an electrical matching network (covered in Section 4).

2.1 TransducerEquivalentCircuitAnalysis Typical devices use transducer structures that generate planar volume acoustic waves and satisfy the assumptions described earlier. Thesedevices can be analyzed by using the l-D transducer model developed by Mason [l] and extended by Berlincourt [2], Sitting [3-51, and others [6-91. This l-D model was developed in order to predict the input impedance, conversion loss, and bandwidth (BW) characteristics of a multilayered transducer structure such as the oneof Fig. 2. The results of this l-D analysis are summarized by the equivalent circuit shown in Fig. 3. Here the pie-

I I

I I

Equivalent circuit model summarizingthe Mason l-D analysis results.

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289

zoelectric film is represented by the Mason equivalent circuit [l],the top and bottom electrode layers are treated as transmission lines, the topelectrode free surface is treated as an acoustic short, and the crystal is represented by an impedance load The term COis the clamped capacitance of the transducer and is given by

where E is the relative dielectric constant, is the dielectric constant of free space, A . is the cross-sectional area of the transducer defined by the dimensions of the top electrode,and to is the thickness of the piezoelectric crystal. Note that COis the capacitance of the transducer when all mechanical vibrations are prevented, i.e., the clamped capacitance. Theelectrical equivalent of the piezoelectric layer acoustic impedance Z , is given by

R. (Ohms) where zo =

=

@* AOZO

is defined as POVO

with p. and V , being the mass density and acoustic wave velocity of the piezoelectric film respectively. The parameter Q, used in Eq. (2) is given by

where h = e/EEO, and e is the piezoelectric stress constant. Equation (2) can also be written as R. (Ohms) =

1 -

(5)

2foC0k2 where f o = Vo/Ao = V0/2t0is the half-wave resonant frequency of the transducer and k is the electromechanical coupling constant. Note that transducers of one orof integer multiples of an acoustic wavelength thickness will not generate an acoustic wave that can propagate into the substrate because there will be phase cancellation of the piezoelectrically induced stress. This implies that the absoluteBW of the transducer canr,otexceed 2f0. In practice, however, careful design is required for low VSWR (e.g., <2.0) devices of fractional BW exceeding the piezoelectric k (i.e., for longitudinal LiNb03 and 0.68 for shearLiNbO,). For an ideal lossless

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AND GOUTZOULIS

transducer the parameters k , C,, andf, are sufficientto describe the overall transducer operation. Note that in the equivalent circuit of Fig. 3 the transformer is a 1:l ideal transformer and 8, = wf/f0, where f is the frequency. The quantity Z4is an electrical impedance that may represent not only the A 0 crystal but any number of delay media, and depends on the combination of bonding layer and the substrate. We start the analysis by representing the top and bottom electrodes as lossy transmission lines of length t , at frequency = 2wf, terminated by an impedance load 2, with characteristic impedance 2, and attenuation coefficient a. For such a transmission line the general expression for the input impedance is given by

2, = 2,

2, + Zc tanh[(a 2, + 2, tanh[(a

+ jp)t]

+ jp)t]

l

where p = 2w/A, and A is the acoustic wavelength inside the transmission line. It can be shown [lo] that a layer having a mechanical impedance Z, loaded by air (the mechanical impedance of the air (Zair)is much smaller than 2 , ) is equivalent to a lossless electrical transmission line of characteristic impedance Zc = Z, loaded by a short circuit. The surface of the top electrode oppositeto thetransducer is free, which is equivalent to an acoustic short (i.e., 2, = 0); thus using Eq. (6) we find that the input impedance of the top electrode is equal to where the subscript TM stands for “top metal,” andwhere Zm, am, and t,, are the specific mechanical impedance, the acoustic attenuation coefficient, and thethickness of the topmetal electrode respectively, and where , ,p = 2dA, and A,, is the acoustic wavelength inside the top metal electrode. For the purposes of this analysis it is convenient to normalize 2,and all other impedances by 2,(the specific acoustic impedance of the piezoelectric layer). These normalized impedances are represented by For the case of the normalized impedance is given by =

,+rvf

tanh[(aTM + iPTM)tTMl

Reasoning as above we find that the normalized impedance, bottom metal electrode is given by

(8)

of the

Having calculated and we can now reduce the equivalent circuit of Fig. 3 to thatof Fig.4. To analyze this new circuit we can useloop equations

291

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Reduced equivalent circuit of the transducer. to find the input impedance = VJZJ, where R2 and R3 are the electrical equivalents of and and are given by R2 = Razz and R, = R$,: By definition an ideal transformer satisfies the relations V , = V ; and Z4 = I2 + 1,. With these in mind and with reference to Fig. 4 we can now write the following loop equations:

v,=--I , + 14 W

-

z, + 12 + 13 W

O

O

+

I4 V , = V T’ -- - -14 + - = -I1 pc, joC, koC,

I,

csc

+ V,

-jR, csc

+ V,

0

=

Z2R2 + jZ2Rotan

+ (I2 + Z3)( -jR,

0

=

Z3R3 + jZ3Rotan

+ (I2 +

Combining Eq. (11) with Eqs. (12) and (13) we obtain

v, =

[ig + - (Il

[:-j + [211,+

12

+ I,) jR, cot OO)Z2 + ( - j R , csc eo)Z3

0 = - I,

(R,

0 =

( -jR, csc €),)I2

-

+ (R3 - jR, cot e0)Z3

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AND GOUTZOULIS

For a convenient solution of 2,we canrepresent Eqs. (14)-(16) in a matrix form: -i -i -i WC0

WC0

WC0

- R, - jRo cot

-jR, csc

WC0

- -jR, csc eo

[j

(17)

R, - jR, cot

- WC,

From the matrix Eq. (17) we can now easily find the solution for Z , = VJZ1 which is given by 2,= D/All,where D is the determinant of the 3 X 3 matrix and Allt,isgiven by R, - jR, cot All =

-jR,

csc

-jRo csc R,

-

jR, cot

Proceeding as indicated above we find that the solution for Z1 is given by

+

1

(z2 z3)sin eo + 2j(l - cos (1 z,z3)sin eo - j ( z z + Z~)COS

+

Equation (19) is the closed-form expression for thecomplex impedance of the input transducer asa function of frequency, transducer capacitance and impedance (i.e., C, and R,), and complex normalized impedances of the top and bottom metal electrodesand 23 respectively). We note that in Eq. (19) the first term represents an electrical impedance due to the capacitance of the layer, whereas thesecond term represents the acoustic impedance of the device. In Eq. (19) the only unknown parameter is contained in the expression for z3which, as we can see from Eq. is z, and represents the combined impedance of any number of delay media connected to the bottom electrode. Such delay media include additional bonding or matching layers and the crystal. To find a general solution to this problem we must work backwards,i.e., from the crystal toward the bottom metal electrode. -Let us assume that there are N additional delay media: N - 1 additional bonding layers (designated by to zN+,) and the crystal (designated by zN+3= zAo). This situation is shown schematically in Fig. 5 . We proceed by first assuming that the N - 1 bonding layer is mounted directly onto the crystal which we consider

TRANSDUCER DESIGN """""

z

B

""""-

"_""""

"

"

16 _"

-

" " "

GOUTZOULIS BEAUDET AND

294

as anknfinitely” long delay medium. Under this assumption we set the normalized impedance z ~ of +the ~Nth layer as

where and are the mass density and sound velocity of the A 0 crystal respectively. We can now proceed by using the normalized version of Eq. to write the expressions for zN+2, . . . , 2 5 , and 2 4 as follows: zN+2

= 2LN+2

+ ZLN+2 tanh[(aL.N+2 + jPLN+2ltLN+2I + zAO tanh[(aLN+2 + jPLN+2)fLN+21

ZLN+2

where zLi= ZLi/Zo,aLi,Ai = 2dPLi,and f L i denote thenormalized specific mechanical impedance, attenuation coefficient, acoustic wavelength, and thickness of the ith delay layer respectively. Equations (8), (9), and (19)-(23) contain all the information necessary to predict the input impedance of the complete transducer structure (consisting of N delay media) as a function of frequency and forvarious physical parameters of the various layers. The A 0 device designer must evaluate these equations backwards, i.e., from to zl, over the frequency band of interest and for various combinations of layers and layer parameters.

2.2 TransducerDesignEvaluationCriteria The transducer designer must evaluate and compare the various transducer design choices in order toarrive at theoptimum transducer/bonding structure. In general, the evaluation criteria vary from application to application. However, since most A 0 deflector and modulator applications involve signal processing or computing, typical RF system design criteria, such as conversion loss (CL measured in dB), reflection coefficient (r), and VSWR are sufficient. Note that in some applications the maximum RF power that can be applied safely on the transducer is also important. This is because aside from the obvious A 0 device safety issue, the maximum RF power figure determines the maximum amount of diffracted light (in conjunction with the power of the input light source) which is a very

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295

important figure in many applications especially those involving tripleproduct processors and AOTFs. Furthermore, the maximum RF power level in conjunction with the RF threshold level (defined as theRF power level that results in a diffracted optical beam power that equalsthe optical scattering level) determines the available input signal-to-noise ratio and dynamic range which in turn may determine the performance of the overall system. In the next section we discuss the CL, r, and VSWR criteria and we show how they relate to the previously derived equations. Optimizing these parameters by matching the device impedance with an RF delivery network will be presented in Section 4. The complex input impedance the A 0 device, given by Eq. (19), can be rewritten as -

&l

Z , = R , + j X,--

In Eq. (24), R, + jX, represents the complex acoustic impedance of the device, whereas the term j/wC, represents the electrical impedance due to thecapacitance of the piezoelectric layer. The real part (R,) of the acoustic impedance is defined as theradiation resistance. Electrical power dissipated in R, represents acoustic power flowing away from the transducer into the crystal. Equation (24) is the expression of the input impedance of a single transducer. The impedance of a mosaic [l13 of K transducers connected in series is KZ1. If the K elements are connected in parallel, the input impedance is Z J K . It is important to keep theserelations in mind since they are necessary for calculating the impedance of a transducer that consists of multiple electrodes and various interconnection patterns. Once the input impedance of the transducer is determined, the conversion loss (CL) figure of the transducercan be calculated. CL is defined as

where PS is the maximum power available (under matched conditions) from the source to which the transducer is connected, andPINis the power absorbed by the radiation resistance [12]. If the transducer is connected directly to a generator with real impedance, Rg, the transducer is called “untuned.” Figure shows the equivalent circuit used for untuned CL calculations. Aside R, and Z,, Fig. 6 also shows a series resistance R,, which represents the real part of a series contact impedance. This series impedance arises mainly from the thin bond wire which is usedfor electric contact to the top electrode and its real part (R,) is typically in the 0.1-

GOUTZOULIS AND BEAUDET

6 Equivalent circuit for untuned conversion loss calculations.

2 R range. The imaginary part (Xse)of this series impedance is usually inductive and in the 0.1-1 nH range. For high-frequency (>l G&) device designs this inductive component could become significant and the designer would need to include it in the overall design. To calculate the power (PIN) absorbedby Z1 we can apply standard ac circuit analysis on the equivalent circuit of Fig. 6 and find that

where the asterisk denotes complex conjugate. We are interested in the real part of PINbecause it represents the acoustic power that flows into the A 0 crystal. Setting R; = R, + R,, and with reference to Fig. 6 we can describe the voltage V , by

v, = R;V'Z1 + Z1 By substituting Eq. (27) into Eq. (26) and after some simple algebraic calculations we find that the real partof P, is given by Re[P,]

=

(Rg + R,,

IV' I2Ra + R,)' + (X, - l/dJ'

Maximum power willbe delivered to thetransducer undermatched impedance conditions. This occurs when Z1 is real and the radiation resistance matches that of the source, i.e., R, = R, and R , = 0. Underthese conditions we find (from Eq. (28)) that the maximum available power is given by

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297

Substituting Eqs. (28) and (29) into Eq. (25) we find that the conversion loss is given by

CL (dB) =

log

(R,

+ R,, + R,,)’ +,( X , - ll0C0)~ 4R,Rll

1

For most applications the device is required to have minimum conversion losses, typically better than 3 dB. This implies that the transducer impedance is well matched to the impedance of the source, we will see in Sections 3 and this may not be possible without the use of an external matching network. Note thatin Eq. (30) we can include the effects of the bonding wire inductance (X,) by substituting the term X , - l/oCo by X , + X,, - l / ~ C o . The coefficient l? is defined as the ratio of the voltage reflected back into the source to the voltage incident on the transducer terminals and is determined by the load impedance only. With reference to Fig. 6 we find that the reflection coefficient for the untuned device is given by

r = Z1 + R,,

- Rg 2 1 + R,, + R, From Eq. (31) we see that when 2,+ R,, = R,, the reflection coefficient is zero. However in this case CL is not 0 dB because part of the incident power is dissipated by R,,. To have both CL = dB and r = 0 we require that R, = 0 and 2,= R,. If reflections do occur, at some position along the unmatched transmission line the incident and the reflected waves will add in phase to give a voltage maximum (Emax)and at another position they will add out of phase to give a voltage minimum (Emin).These positions are stationary and give rise to a standing wave. VSWR is a measure of the strength of this standing wave and is defined

where the subscripts “inc” and “ref” refer to the incident and reflected waves respectively. Based on the definitions and VSWR we can easily show that the two measures relate as follows:

and VSWR - 1 = VSWR

+

298

BEAUDET

ANDGOUTZOULIS

Note that the absolute magnitude of r can be used to describe the efficiency of power transmission via the following relationship % Power reflected = Ir12 (35) 100

Typical commercially available A 0 devices have input impedances of 50 fl and VSWR values of 1.5 < VSWR < 2.1 over the full BW of the device. This means that thereflected power is in the 4-12.6% range. Furthermore, most deflectors and modulators have maximum input drive levels of 0.52 W, whereas AOTFs can vary widely from one-half to tens of watts.

2.3 Wideband TransducerConsiderations Having developed closed-form expressions for the impedanceof the transducer we are now able. to study and analyze the effects of the various parameters of the transducer, electrode, and bonding layers. Recall that the transducerconversion loss (Eq. (30)) contains bothelectrical and acoustic components. It would be desirable to separate the effects of the two and study the corresponding responses independently, which can be accomplished if we assume low coupling figures ( k < 0.3). The majority of bulk state-of-the-art A 0 devices use LiNbO, transducers in configurations with k figures in the 0.49-0.68 range (see Section 2.4). It is thus necessary to study the combined effect of the two responses, a task that leads to quite cumbersome analytical expressions which provide little (if any) intuitive insight. The alternative solution is to use a computer program which calculatesthe input impedance, and the corresponding performance figure:, as a function of the impedance and the thickness of the electrode and the bonding layers, and over the frequency range of interest. InSection 3 we describe such a computerprogram which is based on the formulation presented in Section 2, and which can be used to study the effects of the layer parameters. Before we use this program, however, it is worthwhile to briefly examine the effects of the various layers in verysimple transducer configurations. This will help the designer gain some insight in order to succeed in the most difficult task in transducer design, namely broadband operation with minimum conversion loss. In general, when the various layers in the path of the acoustic wave have specific impedances that are different fromZ, and they behave mismatched transmission lineswhich transform the real load into a complex one. The amount of transformation depends on the degree of mismatch, and it usually results in shifted and deformed CL curves which may have significant ripples in the passband. They may also result in sig-

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299

nificant phase distortion, which fortunately is not a problem for most A 0 device applications. Using Mason’sequivalent circuit Sitting [4] and Meitzler and Sitting [l31 have analyzed the response of simplified acoustic transducer structures for which they assumed R, = l/o,Co. This eliminates the losses obtained with an untuned transducer andmakes the CL shapedepend on the characteristics of the acoustic layers only. For 0.5 < k < 0.7 the main findings of their work can be summarized as follows: (1) When the electrode and the bonding layers are acoustically thin (i.e.,fo/foi C 0.02, wherefoi is the halfwave frequency of the ith layer) broadband operation with minimum conversion loss is generally possible if the transducer and the A 0 crystal characteristics impedances satisfy 0.8 ZAdZo 2.0. (2) When Z, = and the electrodes are acoustically thin, a symmetric wideband response is possible if the bonding layer is a quarter-wavelength thick. (3) Minimum CL is achieved with no adsorbing layer on thesurface of the top (i.e., the surface is air-backed). (4) The top electrode should be kept as thin as possible, because as it gets thicker the overall response shifts toward lower frequencies and significant ripple may appear within the passband. When ZBM matches ZAo there is no effect, however, whenf,lf,,, < 1 the device response shifts toward higher frequencies if ZBM/Z,o C whereas it shifts toward lower frequencies when ZBM/ZAo > 1. (6) When the impedance of the bonding material is an orderof magnitude lowerthan 2,and the 3-dB BWis generally a few percent of the centerfrequency f,. Finally note that when fO/fOBM 0.002 the 3-dB BW increases to 30% ~41. In practice the situation is far more complex since we generally deal with (1) significant mismatches between Z, and ZAo, and (2) transducer structures that consist of several layers. In almost all cases we can use acoustically thin, air-backed top electrodes thereby eliminating unnecessary conversion losses and band shifting. On the otherhand and in direct analogy with microwave and optical antireflection coatingtechniques, broad, symmetric passbands can beachieved via the use of bond layer thicknesses that are multiples of a quarter-wavelength at f,. The objective is to match two media of different characteristic impedances and minimize the reflection coefficient at thevarious interfaces. This can be achieved by choosing the characteristic impedance of any bondinglayer to obtain equalreflection factors to the adjacent layers. Thus, the large reflection arising between mismatched 2, and ZAo is minimized because it is broken up into many small ones. The design of quarter-wave (N4) acoustic transmission line matching is based on its microwave counterpart [15-171, and it has been extensively

-

300

ANDGOUTZOULIS

BEAUDET

applied to transducers of bulk acoustic delay lines [4,6, 14, 18, 1'91. Using the equivalent microwave formulation we can easily show that the characteristic impedance, ZB, of a single N 4 bonding layer designed to match Zo and ZAo is given by

ZB

=

ZB

=

(36) Broader acoustic BW is achieved if the front half of the transducer itself is treated as a N 4 matching layer in addition to the N 4 matching layer bonded to it In this case the characteristic impedance of a single bonding N 4 layer is given by: (37)

Fdr two N 4 bonding layers used in a Z ~ - Z B 1 - Z ~ - Z A oconfiguration, the characteristic impedances are given by zB1

z!n"23,",

(38)

ZA"Zd,",

(39)

and =

In practice it is difficult to achieve adequate dimensional control for multiN 4 configurations, and even more .difficult to identify and use suitable bonding materials with characteristic impedances that satisfy the N 4 configuration requirements. For these reasons most broadband A 0 device 'designs use a single N 4 bonding layer. Two N 4 bonding layers are used when large mismatches exist between Zo and ZAo.. Note that the N4matching scheme creates ripples in the passband which results in increased phase nonlinearities especially for the multi-N4 configurations. On the other hand, if 2,and ZAo are significantly mismatched, the use of a N4bonding layer with a characteristic impedance equaling the geometric mean of the adjacent layers will improve both the passband and the phase distortion. In all cases the BW improvements, the phase response and the dimensional sensitivity of the various N4-matching strategies must be analyzed indetail via the use of a computer program and in conjunction with the available materials choices.

2.4 Transducer,Electrode,andBonding

Materials

..

The transducer material is selected primarily because of its ele-t romechanical coupling performance (i.e., large k ) since most A 0 applications require very efficient A 0 devices. As such the typical material of choice is LiNb0, which has relatively high coupling figures for both shear and longitudinal operation (0.68 and 0.49, respectively), as well as low dissipation loss. LiNbO, is bonded in the form of a thin platelet (-250 Fm)

TRANSDUCER DESIGN,

301

and is then reduced to the properthickness via (1) a combination of coarse (3-5 pm) and fine (0.5-5 pm) mechanical polishing (using various grades of diamond compounds) and/or chemical etching, and (2) coarse mechanical polishing followed by ion milling. When optimized [21] both thinning techniques give similar results for transducer thicknesses as low as 0.45 pm. For thinner transducers the ion-milling approach is preferred because it offers higher precision and control. Using ion-milling techniques pm thin transducers for acoustic delay lines operating at 11 GHz have been reported [22]. When the ease of transducer fabrication is of primary importance, the typical material of choice is ZnO which can be deposited to the proper thickness via thin-film deposition techniques, such as vacuum evaporation or sputtering, without the need for adhesive bonding and mechanical polishing. With this technique A 0 devices operating at 10 GHz have been reported [23]. Table 1shows the acoustic properties of LiNbO, and ZnO for various crystal cuts and wave modes. The 36" Y longitudinal (L) and X shear (S) cuts in LiNbO, produce composite modes where the indicated component predominates (for more details see [24] and [25]). Note that aside these two transducer materials, there are many other less popular materials [26281 including CdS, LiIO,, Si02, AlN, PZT-7A, SPN, etc., which may be appropriate for specialized A 0 device applications. Another importantfactor that must be considered in choosing the transducer material is the acoustic and electric impedance matching. The former must be considered in conjunction with the A 0 substrate and thebonding layers used. The latter depends,among other things, on thesize and number of transducers. For example in single, large-area transducers the resulting low impedance at high frequencies makes materials with high dielectric constants unattractive. This can often be mitigated by serially

Table 1 Acoustic Properties of LiNbO, and Material

Mode

Cut

k

Velocity (dsec) ~~~~

LiNbO, LiNbO, LiNbO, LiNbO,

Y

L L S S

Y X

L S Source: Refs.

X

4800

Z (lo9 g/sec-m*)

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AND GOUTZOULIS

connecting multiple transducer sections. This solution is frequently used in AOTFs and deflectors. The choice of the transducer material is also affected by its power-handling capability. Transducer damage occurs if the classical dielectric breakdown field is exceeded. In practice, A 0 devices with 0.5-pm thin LiNbO, transducers and top electrodedimensions of 150 X 100 Fm2 canbe subjectedto CW RF powers of 500 mWwithout damage. In ZnO the critical dielectric breakdown is determined primarily by processing factors. For example, pinholes generated during the evaporation process or pressure applied to the transducer during wire bonding cause transducer failures at RF powers much lower than those determined by the critical dielectric breakdown. For these reasons LiNbO, transducers are generally accepted as having a higher power-handling capability. The choice of the bonding layer may dramatically affect the amount of acoustic energy transferred since the bonding layer provides the molecular contact between the transducer andthe A 0 crystal. Fortunately, the device designer has available a number of electrode and bonding layer materials that the acoustic impedance matching can be optimized. Table 2 shows the velocities and characteristic mechanical impedances of the most useful metals as well as of the epoxy. As Table2 shows, for both the longitudinal and shear waves there is a wide range of bonding layer impedances that cover the 2.86-69.7 X lo9 g/sec-m2 andthe 1.34-37.0 X lo9 g/sec.m2 ranges respectively. These impedance ranges cover those requiredby most combinations of transducer and A 0 substrate materials. However, when it comes to fabrication some of these materials present serious problems during deposition while some others require special handling in order to avoid oxidation and subsequent bond failure. It is thus important that the designer be aware not only the basic acoustic characteristics of these materials but also of the practical implications associated with each material. Unfortunately thereis no single source of information available that fully covers this issue. The following brief discussion indicates some of these issues and is based on the experience of several members of the Westinghouse Science and Technology Center Thin Film Laboratory As a general rule, the thickness of any metal layer should not exceed 5 Fm because the metal becomes stressed and shows a tendency to pull up from the substrate. Thus, the designer must keep the bonding layers as thin as possible as to avoid stresses and insure a good bond. For thermal deposition (the most usual bonding technique for A 0 devices) typical deposition rates are -100 h m i n , with typical deposition systems operating from 10" toTorr. Bonding temperatures in the 400-700°C range are preferred for good adhesion. Aluminum (Al) is a relatively easy and soft material to handle and evaporates at moderatetemperatures atTorr).It wetswell

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to the evaporation sourceand it adheres better thanmost bonding metals, although better adhesion is achieved if it is buffered with chromium. Unfortunately it oxidizes easily, which means that the full bond operation must be performed rather quickly in order to avoid bond contamination. In most cases some type of protection is advisable usually in the form of thin (100-300 A) chromium layers. Chromium (Cr) has excellent adhesive capabilities and thus it is used almost exclusively for the support other metals. It is regularly used as the buffer layer between electrodes and transducer, and between the various bonding layer(s) and the A 0 substrate. However, it doesstress, and films thicker than 300 tend to pull up. It evaporatesat rather moderate temperatures (-837°C at lo-* Torr); however, it may oxidize and thus it should be protected. Copper (Cu) evaporates at about 727°C (at lo-* Torr), however, it is not easily deposited because it has a tendency to move toward the cold ends of the filament and eventually shorts theconnections of the filament. This forces its evaporation via a resistance source (boat) or via E-beam techniques (the lattersignificantly complicates the A 0 device fabrication). In general, it is a violent metal and oxidizes badly although it does not contaminate the depositionsystem. Epoxy resin mixed to a very low viscosity is considered as the simplest and most convenient way to form a bond. Unfortunatelyin most cases the resulting performance is unacceptable. Thisis because it is hard to control its thickness and its parallelism with respect to both the transducerand the A 0 substrate surfaces. Bonding layers as thick as 1 pm are possible but require a high degree of cleanlinesswhen deposited in order to avoid inclusion of dust particles. Furthermore its mechanical impedance may vary as a function of time and it mismatches those of most A 0 substrates and transducer materials. In general,isitnot recommended for broadband devices or for devices above 100 MHz; however, it may be acceptable for low-frequency, narrowband operation. Gold (Au) is an easy material to,work with and oneof the most popular electrode choices. Unfortunately ithas a poor adhesioncapability and thus it needs a buffer layer. Most frequently itis used as top electrode because it adheres well with gold interconnection wires. Note that for longitudinal waves its acoustic impedance is rather high and thus it is a mismatch for most A 0 substrates. Indium (In) is the easiest and softest bonding material and gives good bonds at low temperatures (-487°C atTorr) because of its high ductility. Maximumdeposited thickness should be less than 10 pm because it tends to deform under mechanical polishing. Unfortunately it is very

TRANSDUCER DESIGN lossy and at 1 GHz even small thicknesses (e.g., 1 pm) result in unacceptable loss (-8 dB). Lead(Pb)evaporates at low temperatures (-342°C atTorr) and is considered as a very difficult material to work with for reasons: (1) it oxidizes quickly after the bond is formed and thus it must be protected immediately and effectively, and (2) it is toxicand contaminates the vacuum system, which must be thoroughly cleaned for subsequent operations. The latter implies that we cannot deposit a different metal after lead is evaporated without breaking the vacuum, which is undesirable because it often leads to unacceptable surface contaminationand thus bond failure. Nickel (Ni) is a hard metal thatwets well and evaporatesat rather high temperatures (927°C atTorr).Itpresentsa problem in that it alloys rapidly with the refractorymetals of the depositionsystem. This limits the maximum thickness of the deposited layer to about 500 A. Platinum (Pt) requires a very high evaporation temperature (1292°C at Torr) and in general it is difficult to evaporate. Typical thicknesses are in the tens of Angstroms and thus it is not very useful for most A 0 devices. Much thicker films (-10 pm) can be deposited via sputtering. It does not oxidize easily and it does not adhere well. Silver (Ag) is easy to evaporate (574°C at lo-’ Torr), but it has poor adhesion properties and thus it requires a buffer layer. Note that it is one of the few metals that do not interact with the mercurous halide class of A 0 crystals with which it forms stable bonds. Tin (Sn) is also easy to evaporate (682°C at Torr) but it crystallizes in different phases and this often.results in stressed and cracked A 0 substrates. This is especially true with soft A 0 materials such as Tl,AsS,, which can be split in two if used in small sizes (e.g., 15 10 5 mm3). This problem can be eliminated if a thin layer of a soft metalbuffer (e.g., In) is used between the Sn and the A 0 substrate. Titanium (Ti) oxidizes very easily and it is hard to evaporate (1067°C atTorr).It alloys rapidly with therefractory metals and thus only small thicknesses can be deposited. If necessary, sputtering techniquescan be used to about 2 pm. Thicker films are not advised because it is a high stress metal that tends to “flake-off.” Zinc (Zn) is easy to evaporate (127°C at lo-* Torr) but it is toxic and contaminates the vacuum system. It should be avoided if not absolutely necessary. The previous discussion indicated that the choice of the bonding and electrode materialsmay affect significantly both the overalldevice design and the device fabrication. The adhesion and oxidation properties of the electrode andbonding metals make the use of a thin(100-200 A) Cr layer

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on both surfaces of the transducer as well as the surface of the A 0 crystal almost mandatory. Although for most devices these adhesive layers are (by themselves) acoustically thin, in reality they are parts of the electrodes and bonding layers which may not necessarily be acoustically thin. Thus, it is a good practice to always examine the effects of these extra layers especially if the A 0 device operates above 1 GHz. This is accomplished by calculating the composite impedance for a two-layer top electrode and treating the remaining layers as additional delay layers. Note that for transducer designs where N 4 acoustic matching requires prohibitively large (>5 pm) bonding metal thickness, the bonding metal may be replaced by a thin crystalline platelet of the appropriatethickness. Indeed, at least one such device has been reported where a 66-pm-thick SiO, platelet was used for A/4 matching between a LiNb03 transducer and a TeO, A 0 substrate. The final parameter of interest is the mechanical impedance of the A 0 crystal. This is the one parameter for which the transducer designer has no choice given that the A 0 crystal is usually determined by system considerations and rarely by the transducer design. Table 3 shows the densities, acoustic velocities, and mechanical impedances of most popular A 0 substrates as a function of the acoustic mode. Comparing Tables 1,2, and we conclude that there is a considerable overlap in acoustic impedances between transducers, bonding metals, and A 0 substrates. This implies that transducer Structures with well-matched layers are possible. As we will see this is indeed the case even for materials like TeO, and the mercurous halides (Hg,Cl,,Hg,Br,, and Hg,12) which have impedances (for shear waves along [llo]) of about an order of magnitude lower than LiNb03 transducers.

3 COMPUTER-AIDEDTRANSDUCERDESIGN Due to the large number of parameters involved, the transducer design theory described previously is best used inthe form of a computer program. To the best of our knowledge the first published computer-aided transducer design was developed by Hopp who used it for the design of bulk microwave acoustic delay lines. In Appendix B we show a FORTRAN program which is based on the methodology presented earlier, a more complex version of which has been used at Westinghouse STC for the study and development of a variety of A 0 devices, extending over the 10 MHz-4 GHz frequency range. Most of these designs have been reduced to practical devices successfully. The program is named DESIGN.FOR andit should be used in conjunction with three subroutines TLIMP, TRAIMP, and CONEFF. All programs are self-explanatory and have been

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Table 3 Selected A 0 Device Materials Material

Acoustic mode

LiNbO, LiNbO, TiO, Ti02

L [loo] [100]35° L [l101 8030L [loo] 3630L [OOl]

PbMoO, 5960 Fused Silica TeO, 6.0 TeO, GaP GaP GaP GaP Tl,AsS,

L L [OOl] [l101

6460L [l101 L [loo] 6650L [l111 S [l101 L [loo]

Density (g/cm3)

Acoustic velocity (&sec)

Impedance (lo9 g/sec.m2)

4.64 4.64

6570 3600

30.5 16.7

4.23 4.23

7930

33.5

6.95 2.2

6.0 3.72 4.13 24.2 4.13 4.13 4.13

620 5850 4130

6.2 13.3

2150

HgzCl,7.81

[l101

2.71

347

7.31 2

S [l101

2.00

273

m

m

Hg24 Tl,AsSe, 18.6

[l101 L [loo] 2050

7.7 1.96 9.05

Tl,AsS,

L [loo] 2300

6.46

Ge

L [l111

5.33

29.3

17.1

254 14.9 5500

Source: Refs.

written in a simple form which is readily executable with the Microsoft V50 FORTRAN compiler. DESIGN.FOR calculates the transducer input complex impedance and the conversion loss for 200 points over the frequency range specified by the user. The program first calculates the complex impedance (Z2RR + jZ2II) of the top electrode,which can have up to two metal layers. It then calculates the complex impedance of the bottom electrode (Z3RR + jZ3II), whichcanhave up to five metal layers plus the substrate. These complex impedances are calculated via the use of the subroutine TLIMP which calculates the complex impedance of a transmission line according

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to Eq. (6). The program proceeds with the calculation of the complex impedance of the transducer structure (ZTR + jZTI) according to Eq. (19) and via the use of subroutine TRAIMP. ZTR and ZTI are thenused to calculate the transducer conversion loss (CL) viathe subroutine CONEFF and according to Eq. (30). These calculations are repeated 200 times over the frequency range specified by the user. The results are stored in the arrays ZAR (real part of the transducer impedance),ZAI (imaginary part of the transducer impedance), and CLL (conversion loss). The user must supply an appropriatel-D plot subroutine todisplay ZAR, ZAI,and CLL as a function of frequency. DESIGN.FOR can be modified to include additional layers for either the top or bottom electrode according to the design methodology presented in Section 2. DESIGN.FOR can be used to study and analyze simple or complex transducer structures, thereby gaining useful insight in the overall transducer design. Moreover it can be used to study the relative meritsof the various broadband acoustic-matching techniques described in Section 2.3. The overall transducer design philosophy and the use of DESIGN.FOR is best demonstrated via the use of some specific transducer design examples. In the following three sections we present three such examples, and we discuss the material choices made as well as various other issues peculiar each example.

3.1 Design Example 1: 200-400

LiNbOB Transducer on

The first example involves the design of an A 0 deflector which uses a longitudinal LiNbO, 36" Y-cut transducer on T13AsS4A 0 substrate. For this example the 3-dB BW requirement is 200 MHz centered at fo = 300 MHz. The top electrode is required to have a rectangular shape of dimensions L = pm and H = 530 pm. The length L was determined from the A 0 interaction length (at A = 830 nm), whereas the height H was set from acoustic beam height requirements. For this device we will use a Au topelectrode with Cr for good adhesion on both transducerfaces and on the T13AsS4substrate. Thiswill result in a configuration Au-CrLiNb0,-Cr-X-Cr-Tl,AsS4, where X is the unknown bonding layer(s). For the first design iteration, and in order to keep the Au layer acoustically thin, we will set its thickness to 0.2 pm. (We will examine the effects of the top electrode's thickness in more detail later.) Thethickness of all Cr layers will be kept to 100 A, which is a typical thickness for Cr adhesive layers at frequencies below 1 GHz. For this iteration the only unknown data are(1) the transducerthickness to and (2) the bonding layers and their thicknesses. The former can be estimated from to = V0/2f0 = 12.3 pm.

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We note, however, that in practice the transducer must always be thinner because the resonant frequency of the transducer is alwayslower thanf, = V0/2t0.This frequency loading effect is mainlydue to (1) mass loading due to thefinite thickness of the top electrode[S] and (2) k loading [38], which occurs when k # 0, in which case the center frequency of the transducer is given by

($

tan - = For X-cut shear LiNb03 transducers ( k = 0.68) the k loading has a profound effect since it lowers the center frequency to about 77% of that predicted by fo = V0/2t0. On the other hand, for 36" Y-cut longitudinal LiNbO, transducers ( k = 0.49) the k loading lowers the center frequency to about 90% of that predicted by fo = V0/2t0.The practical aspects of the transducer loading have been analyzed in detail by Weinert [39]. The designer can use DESIGN.FOR to study the combined effects of both frequency loading mechanisms. Because of the wide BWrequirement a good initial guess for thebonding layer can be made in conjunction with a single N 4 matching layer. Use of Eq. (36) with = 34.8 lo9 g/sec-m2and Z,, = 13.3 X lo9 g/sec-m2 gives 2, = 21.5 X lo9g/sec-m2.From Table 2, we see that thebest choices are Pb (22.4 lo9 g/sec-m2),Sn (24.6 X lo9 g/sec.m2), and A1 (17.3 lo9 g/sec-m2). Given the oxidation and contamination problems with Pb, it is wise to start our design with the next best choice, namely Sn. The thickness for Sn can be determined from ts, = Vs,/4f0 = 2.77 pm. With these in mindthe initial formof the transducer structure is Au-Cr-LiNb0,Cr-Sn-Cr-Tl,AsS,, and the corresponding thicknesses are 0.2 pm-100 A-12.3 pm-100 A-2.77 pm-100 A. We are now ready to use DESIGN.FOR to optimize the overall structure. We will concentrate on CL since our objective is its minimization over a 3-dB BW of 200 MHz. Running the program for the above data we see that theoverall response is asymmetric and centered around 260 MHz (Fig. 7). Our first goal is to shift the center of the response to 300 MHz, which is accomplished by reducing the transducer thickness. By using successively smaller to values, we arrive at an optimum value of to = 10 pm. As Fig. 7 suggests, as to is reduced from 12.3 to 10 pm, CL shifts to a higher center frequency while at thesame time it becomes more symmetric. If to is reduced to less than 10 pm, CL will become even more symmetric but it will shift to an unacceptably high center frequency. Thus we will keep to = 10 pm and we try to optimize CL by varying the thickness of Sn. This isshowninFig. from whichwe see the following: (1) CL

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500

Frequency (MHz)

7 Effects of transducer thickness (to) on the device conversion loss (CL) for a 2.77-pm-thick Sn matching layer for design example 1.

0'

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l

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8 Effects of Sn thickness on the device conversion loss (CL) for a 10pm-thick LiNbO, transducer for design example 1.

31l

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becomes symmetric for ts, = 3.1 pm, (2) as tSn increases the transducer loading changes and CL moves slightly to lower frequencies, and (3) for ts, > 3.1 pm CL becomes asymmetric. We note that the choice ts, = 3.1 pm achieves both a symmetric CL response and a center frequency of 300 MHz, and it is within 10% of the value predicted by ts, = Vs,/4f0. From Fig. 8 we see that a 3.1-pm-thick Sn bonding layer does satisfy the BW requirements. In fact, theresulting 3-dB BW is 250MHz, whereas the 200-MHz BW is achieved with a ripple of 2 0.85 dB, which isacceptable even for very demanding applications. The +0.85-dB 200 MHz performance is achieved with a worst-case CL figure of -3.8 dB. Since these results correspond to a device impedance -25 Cn, significant improvement in CL can be achieved with electric impedance matching. We should now question whether better results can be achieved using the Pb orA1 choices. This is easily accomplished by repeating and optimizing the above procedure for each of these materials. The so-determined optimized results are shown in Fig. 9 for to = 10 pm, and for fPb = 1.8 pm, = 5.3 pm, and ts, = 3.1 pm. As expected, and as Fig. 9 suggests, Pb gives better results than Sn, specifically; a 200-MHz BW with a ripple only &0.45 dB. On the other hand, Sn is superior to A1 which gives a 2 1.25-dB, 200-MHz BW. From these data we conclude that the difference between Pb and Sn is not large enough to justify Pb as the material of

" 0

0 '

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500

Frequency

9 Optimized device conversion loss (CL) for 1.8-pm Pb, 3.1-pm Sn, and matching layers with 10-pm a LiNbO, transducer for design example

5.3-pm A1 1.

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choice especially when considering the problems associated with it, and therefore Sn is the material of choice. It is worthwhile to compare the performance obtained with Sn and that obtained with ideal N4 matching layers determined from (A) the typical N4 matching microwave formulation (Eq. (36)), (B) the combination of a N4 transducer layer and a single N4 bonding layer (Eq. (37)), and (C) the combination of a N4 transducer layer and two N4 bonding layers (Eqs. (38) and (39)). Such a comparison will give us an idea of how close Sn is to an ideal N4 matching layer. Using Eqs. (36)-(39) we find that the ideal impedances are (A) = 21.5 X lo9 g/sec.m2, (B) 2, = 18.33 X lo9 g/sec.m2, and (C)Z,, = 23.04 lo9 g/sec-m2,and Zm = 15.23 X lo9 g/sec.m2 for the above three N4 matching cases respectively. Assuming that the above ideal impedances correspond to materials with sound velocities of 3000 d s e c , we find that the ideal N4 thicknesses are 2.5 pm. Using DESIGN.FOR in conjunction with the above datawe can optimize the above three ideal scenarios and arrive at thefinal results shown in Fig. 10. Note that in all cases we used to = 10 pm, and that the optimized thicknesses are (A) c, = 2.7 pm, (B) c, = 2.6 pm, and (C)tsl = 2.8 pm and tm = 2.5 pm. In Fig. 10 we also show the CL response obtained with a thin 200-A Cr bond (D). The dataof Fig. 10 suggest that (1) the thin Cr

m;[ -1

-9

.>

S

-2 I

I

I

Frequency (MHz)

Optimized device conversion (CL) for threedifferent types of ideal N 4 layers: (A) Z, = 21.5 lo9 g/sec-m2,(B) Z, = 18.33 lo9 g/sec-mz, (C) Z,, = 23.04 lo9 g/sec.mz and 2, = 15.23 109 g/sec.m2. Curve (D) corresponds to a thin 200-A chromium bond.

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bond has a 3-dB BW of 130 MHz, which is not acceptable, (2) case (A) has a 3-dB BW of 255 MHz and a 0.7-dB, 200-MHz BW, (3) case (B) has a 3-dB BWof234 MHz and a 1.7-dB, 200-MHz BW, and (4) case (C) offers the best performance with a 3-dB BW of 272 MHz and a 0.45-dB BWof 200 MHz. Although in terms ofBW flatness and actual loss all three ideal cases offer better performance than Sn, thebest case (C) advantage is only 1 dB, which means that for all practical purposes Sn gives a nearly ideal performance. The last parameter we need to examine is the thickness of the Au top electrode (cm). Figure 11 shows the CL response for to = 10 pm, C,,= 3.1 pm for cm varying in the 0.1-1 pm range. These curves show that no serious effect occurs for cm N25 (i.e., pm), however, for largercm values CL becomes asymmetric and shifts toward lower frequencies. It is thus a good practice to keep the top electrode acoustically thin that we have one less parameter to worry about! Note that a similar case can be made for the Cr adhesive layers. To demonstrate the overall design procedure and the value the program DESIGN.FOR, we build an experimental "&ASS, A 0 device according to the results of design example 1. The various layer (measured) thicknesses were TAU= 0.2 pm, all Cr layers were 100-A LiNbO, = 9.7 pm, T,, = 3.0 pm, and the top electrode dimensions were L = 450 pm and H = 500 pm. The CL response of the device without any additional

0 -9

5-

-8

E -7

9

-6

.-

-5

2 >

6c

-2 0

Frequency (MHz)

11 Effect top electrode thickness on the device conversion design example 1.

(CL)

BEAUDET GOUTZOULIS AND

314

electric impedance matching is shown in Fig. 12. we can see there is very good agreement with the calculated response, especially if we take into account the slightly thinner transducer and Sn layers. CL is centered at slightly higher frequency; however, it has a very symmetric shape and 'a 3-dB BW of 265 MHz, which is in good agreement with the 250-MHz predicted figure. The actual CL value at the center of the CL curve is at -3.4 dB, whereas the program has predicted -3.8 dB. Note that the dip of the curve is about - 1.1dB fromthe highest peak, whereas DESIGN.FOR had predicted - 1.7 dB. To our experience the results of DESIGN.FOR agree very well with the results obtained from actual devices. Quite often the actual CL is broader and smoother than the calculated one, the CL of the design example 1 being one such example. In practice the control of the transducer and metal layers thickness is such that the actual data agree with those from DESIGN.FOR to about * O S dB.

3.2 Design Example 2: 20-40 MHz LiNbOB Transducer on Hg,CI2 Substrate The second design example involves an anisotropic (birefringent) shear [l101 Hg2Cl, A 0 cell with a 3-dB BWof 20 MHz centered at 30 MHz and a shear LiNbO, X-cut transducer. This is a challenging problem because

0 -9

-2

-l 0

0 200

300 Frequency (MHz)

400

500

12 Measured conversion (CL) an experimental untuned Tl,AsS, device build accordingto design example 1. The transducer thickness was 9.7 km, and the Sn thickness was 3.0 km.

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there is a large difference between the impedances of LiNbO, and Hg2C12 (22.6 X 10 g/sec.m2 versus 2.71 X lo9g/sec.mz, respectively). Furthermore the selection of the bond layer material is dictated not only by impedancematching considerations but also by the need to form a bond that will be mechanically strong and stable,and chemically compatible with the Hg2C12 substrate. This latter consideration severely limits the choice of bond materials. It is well known [40, 411 that most metals in contact with Hg2Cl, are not stable and willchemically react. In these cases the metal film becomes severely corroded, whereas the crystal surface becomes greatly pitted and deformed. It is also known that Ag films deposited on Hg,Cl? are stable but do undergo a chemical reaction to form a complex Ag compound. Most other metals subsequently deposited on the Ag are also chemically unstable. One exception is Pb, which in contact with the Ag layer substrate is chemically stable and a bond with good mechanical integrity can be formed by vacuum deposition. The alternative solution in to first cover the Hg2C12substrate with an inert layer and then deposit the desired metal. This solution can be implemented with the combination of MgF, (V = 4200 m/sec and = 12.81 X lo9 g/sec.m2) and In. For this design example we can use DESIGN.FOR to analyze the performance of the above two bond options. For the anisotropic A 0 interaction (at A = 0.6328 pm), the length of the top electrode must be 3.35 mm [35]. Assuming that there is no restriction on the height of the top electrode, we could choose H such that the resulting top electrode area brings the real part of the transducer impedance as close to 50 Cl as possible. This may eliminate the need for an external electric impedance matching network thereby simplifying the overall device fabrication. For both bond options we will use an acoustically thin (0.2 pm) Ag top electrode with an adhesive layer of Cr (100 A) on the top surface of the transducer. Use of the program shows that for the Pb/Ag option the transducer thickness is 70 pm and theoptimum Pb thickness (for N 4 matching) is 8.0 pm. This is a rather thick Pb layer and may result in bond peel-off. To eliminate this risk we can deposit two 4-pm-thick Pb layers with an acoustically thin (100 A) Ag layer between them for better adhesion. Thus, for this option the optimum transducer structure becomes Ag-Cr-LiNb0,Ag-Pb-Ag-Pd-Ag-Hg,Cl,with the following corresponding thicknesses: 0.2 pm-100 A-70 pm-100 A-4.0 pm-100 A-4.0 pm-2000 A. For the In/MgF2 option the transducer thickness is 66 pm, the In layer is 8.1 pm thick and the MgF2layer is 0.2pm thick. For this bond the complete transducer structure is Ag-Cr-LiNb0,-Cr-In-MgF2-Hg2C12 and has the following thicknesses: 0.2 pm-100 A-66 pm-100 A-8.1 pm-2000 A. The resulting, optimized CL responses are shown in Fig. 13. For comparison purposes we also show the CL response for the ideal case of two

GOUTZOULIS AND BEAUDET -5

-4

E U) U)

0

45

15

Frequency

a

13 Optimized conversion loss (CL) for (a) 8.0-pm thin Pb with 2000 and 70-pm-thick transducer, (b) 8.1 pm thin In with 2000-a thin MgFz and a 66-pm-thick transducer, and (c) two ideal matching layers 25-km-thick with Z,, = 9.1 X lo9 g/sec.mz and Z, = 3.67 X lo9 g/sec-m2 anda66-pm-thick transducer.

25-km-thick N 4 matching layers with Z,, = 9.1 X lo9g/sec-m2and 2, = 3.67 x lo9 g/sec.m2, respectively. Both ideal layers are assumed to have a sound velocity of V = 3000 &sec and are used in conjunction with a 66-pm-thick transducer. The dataof Fig. 13show that theideal bond option offers the broadest and smoothest CL response, with a -0.75-dB average loss over the band interest. In terms practical solutions and for maximum BW, Pb/Ag is the best choice, whereas for.minima1ripple In/MgF2 is preferred. Note that the 1.3-dB ripple the Pb/Ag option can be reduced if we take advantage of the birefringent A 0 bandshape [42] whichcan be used to weight down the two lobes of the CL response. The Pb/Ag bond offers a 3-dB BW 23 MHz, which satisfies the design goal. Furthermore over the 20-40 MHz band the average insertion loss is about 1.5 dB and the average real impedance is 57 CR. The latter could be acceptable for operation with a 50 CR source and it was accomplished by optimizing H . ‘Figure 14 shows the dramatic effect of H on CL for the optimized Pb/Ag bond and for L = 3.35 mm. It can be seen that the H = mm choice results in a minimal-loss, very symmetric CL response. We note, however, that the use rectangular top electrodes (such as the3.35 X 4.0 mm2 electrode of this example) in conjunction with highly acoust-

TRANSDUCER DESIGN

31 7

Effect of the top electrode height ( H ) on the device conversion loss (CL)for the optimized PbIAg bond design example 2 with L = 3.35 mm.

ically anisotropic A 0 materials (such as Hg2C12or Te02)often results in unacceptable acoustic spread, which places a severe limitation on long aperture A 0 deflectors. This important effectcan be counteracted by the application of apodized electrodes in which the shapeof the top electrode is used to control the spreadingof the acoustic energy. Insuch cases minimization of the acoustic spread shapes the top electrode and may 50-Q impedance. In thesecases matching prevent scaling the total area for of the transducer impedance to 50 Q must be achieved via an external impedance matching network. We have fabricated an experimental Hg2C12device with the optimum layer thicknesses but with a X 3.35 mm2square top electrode.Figure 15 shows the measured CL response which is in very goodagreement with the response predicted via the computer program. Once again the measured CL response has asomewhat broader 3-dB BW (27 MHz versus 23 MHz); however, it has a slightly deeper midband dip. The latter is due mainly to the use of smaller H and secondarily to small mismatches occurring at the Ag-Hg2C12interface. We close this design example by noting the practical implications of the Pb/Ag bond choice. The Pb/Ag structure is very sensitive to oxidation and deterioration and additional features are required for a stable structure. To prevent the exposed Pb film from oxidization, the exposed Pb surface must be protected by a coating of a thin Ag film after the

GOUTZOULIS AND BEAUDET

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.f

>

-2

c

S

-1

15

20

25

30

Frequency (MHz)

Measured conversion loss (CL) of an experimental untuned Hg,Cl, device build according to design example 2. The top electrode dimensions were 3.35 X 3.35 mm2, the Pb layer was 7.0 km thick and the Ag layer 2000 thick. transducer bond has been made. After the LiNbO, transducer is bonded to the Hg2Clz we need to grind and polish the transducer to 70-pm thickness. This is usually done in a water slurry of polishing compound which would allow moistureto bedrawn into the Pblayer between the transducer and the crystal. The Pd bonding layer in contact with the moisture would deteriorate very quickly in this process. This danger can be eliminated by using a thin film of UV light-cured cement around the periphery of the LiNbO, prior to grinding. This forms a seal that keeps moisture from the Pb interface. A diagram showingthe elementsof the resulting rather complex transducer structure is shown in Fig. 16.

3.3

Design Example 3: 1.35-2.7 GHz LiNb03 Transducer on LiNb03 Substrate

The final design example involves a high-frequency anisotropic shear [loo] 35" LiNbO, A 0 deflector centered at 2.0 GHz with a 3-dB BW of 1.35 GHz. For this example the length of the top electrode is equal to the birefringent interaction length, which is 115 pm at 830 nm. Using Eqs. (36)-(39) we find that the impedances for the three ideal N 4 matching options are (1) Z , = 19.43 lo9g/sec-m2,(2) 2, = 18.47 X lo9 g/sec.m2, and (3) Z,, = 19.85 X lo9 g/sec.m2 and Zm = 17.44 lo9 g/sec.mz.

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From Table 2 we see that only Ag and Cu have acceptable impedances, and thus we will use these in conjunction with Au top electrode and 75A-thick adhesive Cr layers. Use of DESIGN.FOR shows that the resulting three optimized transducer structures are (1)Au-Cr-LiNb0,-Cr-Cu-Cr-LiNbO, with thicknesses 750 A-75A-0.58 km-75 81-0.32 pm-75 A, (2) Au-Cr-LiNb0,Cr-Ag-Cr-LiNbO, with thicknesses 750 A-75 A-0.62 pm-75 A-0.36 pm-75 A, and (3) Au-Cr-LiNb0,-Cr-Cu-Ag-Cr-LiNbO, with thicknesses 750 A-75 A-0.62 km-75 A-0.3 pm-0.2 pm-75 A. For all cases the top electrodeheight H is 50 pm and was determined with the objective of maximizing the real electric impedance (10-12 Cl for all cases). Smaller H values will increase the impedance even more, but the resulting top electrode surface will be rather small for bonding the Auconnection wire. The CL responses of the above three structures (Fig. 17) have a 3-dB BW of at least 2 GHz, and thus they all satisfy the design BW goal. The two N4-layer bond does offer the smoothest BW, but it is the most complicated. On the other hand, response the of the Cu structure is very similar with that of the two N4-layer structure and thus it is preferred if Cu is to be used. The response of the Ag bond has the smallest loss(1 dB less than the other options) and a shape that can somewhat correct the midband dip resulting from the wideband anisotropic A 0 interaction. Note that over

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the band of interest theaverage real impedances for the three bond options are 10, 11, and 12 R respectively, and thus further impedance matching via an external matching network is required. We emphasize that for high-frequency designs the tolerances of the various thicknesses are very critical and high deposition accuracy is required. This can bedemonstrated in the presentdesign example by varying the thickness of the top electrode. The resulting effect is shown in Fig. 18, where we vary the thickness of the Au layer from to lo00 to 1250 A. It can be seen that this rather small change has a profound effect on the overall response, and it can significantly deteriorate the overall performance. Similar effects can be observed by varying the adhesive Cr layers from to 150 or by varying the transducer thickness by 0.1 pm. 4 ELECTRICAL MATCHING AND POWERDELIVERY The last part of the transducer designinvolves the electrical matching network and the delivery of electrical power to the transducer electrode area. For this problem we must consider the amount and uniformity of the reflected electric power in addition to theconversion loss parameter used in the bond design. The amount of the reflectedpower relates to the efficiency of power transfer, whereas the uniformity of the reflections affects the amountof ripple in the responseof the device as well as its phase linearity. In general, these quantities can be determined by plotting the VSWR as a function of frequency. Figure 19 shows a plot of the loss (in dB) resulting from the reflections as a function of VSWR. The plot of Fig. 19 is based on the formulation discussed in Section 2.2 and described via Eqs. (32)-(35). In practice the VSWR specification is lessthan 2.1, which corresponds to about 0.6 dB of power loss. Tighter VSWR specifications call for lower reflections that are usually based on the driving amplifier response to a nonideal load or response uniformity rather than a lower absolute conversion loss. The design of efficient electrical impedance-matching networks is a wellknown problem in electrical and microwave engineering, and it has been well formulated and analyzed in various previous publications (see, for example, Furthermore there are severalcommercially available, inexpensive, electrical impedance-matching software packages which can efficiently solve very complex impedance-matching problems. The user of these softwarepackages is typicallyrequired to provide the measured complex impedance values of the unmatched device, as well as a set of desired specifications which include the device impedance and VSWR. Based on these data theprogram can calculate variousmatching networks of varying complexity whichsatisfy the desired specifications. (An example of an

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interactive electric impedance-matching network program is contained in the program in the Appendix A, providedby the St. Petersburg State Academy of Aerospace Instrumentation.) Inview of the availability of the formulation, analysis, and computer-aided design solutions, wewill not discuss this problem in detail. Instead, we will provide a qualitative overview emphasizing problems particular to the various types of A 0 transducer structures. 4.1 Simple Two-Element Matching Circuit A simplified electrical equivalent circuit for a typical A 0 device is shown in Fig. 20. For low-frequency devices ( C l GHz) with untuned impedances that result to a few dB of conversion loss, a modest matching network can be produced by resonating the parallel-plate capacitance with a parallel coil and following with a series reactive element to cancel any residual reactance. Figure 21 illustrates this approach with a slow shear TeOzdevice example. The device has a 40-pm-thick shear LiNbO, transducer with a 0.5-pm-thick Au top electrode and an overall active area of 8 mm2. The bond layers from the transducer toward the TeO, substrate consist of a 0.1-pm Au, 1.3-pm Cu, 7.6-pm Sn, 1.3-pm In, and0.1-pm Au. The desired operating frequency extends from 37.5 to 62.5 MHz. The untuned device impedance is shown as curve A on the Smith chart of Fig. 21 (a detailed

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20 Simplified electrical equivalent circuit for typical ducer structures.

A 0 device trans-

explanation of the Smith chart can be found in [45]). shunt inductor of 470 nH translates the impedance along a constant-conductance circle (curve B). series inductance of 96-nH centers the matched impedance, curve C, around the real axis. Figure 22 shows the effect of impedance matching in terms of reflection loss. The untuned loss was less than 2 dB over the passband and the ripple was over 1.5 dB, whereas the tuned conversion loss is no more than 0.5 dB and the ripple has been reduced to under 0.3 dB. The corresponding effect on VSWR is shown in Fig. 23 and itmay be significant for the overall system performance. Fig. 23 shows, the untuned VSWR of 4 is reduced to 2. In general, this simple two-element matching technique very often produces a device useful for laboratory experiments. In the frequency range of a few hundred megahertz to the order of 1 GHz theshunt inductorcan often be implemented right on the device transducer surface with a bond wire shunting the active electrode to ground. photograph of an processor utilizing two slow shear TeO, devices similar to theexample described is shown in Fig. 24.Chip inductors are mounted on printed circuit cards covering the device electrodes. It can be seen that thesimple matching network allowsa compact implementation.

In Chapter 1 we described the advantages of using phased array transducers, one of which is the control of the overall transducer impedance by placing electrodes in series and/orin parallel combinations. Figure 25 shows the electrode configuration used for a longitudinal TeO, operating from 250 to MHz. For this example placing each half of the electrodes in a common busincreases the device impedance, over thatof a single commonarea device, by a factor of 4. For anuncut array half of the elements would connect to theincoming signal and half would connectto thesignal return. For the device of Fig. 25 the original area is cut in half for each segment

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21 (Bottom) Example of a two-element matchingnetworkforaslow shear TeO, deflector covering the MHz range. (Top) Curve A of the Smith chart shows the impedance of the untuned device, curve B shows the effect a 470-nH shunt inductor, and curve C shows,the effect of a series 96-nH inductance.

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Figure 24 processorusing two slow shear TeO, devices similar to that discussed in the example of Figure 21. (Courtesy of Harris Corporation.)

RETURN^ 25 Twelve-electrode phased arraytransducerconfiguration used for a longitudinal TeOz device operating from 250 to 450 MHz.

TRANSDUCER DESIGN and the two segments are electrically connected in series. This must be done as the opposing sides of the bond area operate at a different electrical potential. The equivalent impedance area now consists of four sets of series electrodes, each containing 3 of the total 12 electrode areas. This produces a design area of 1/4 (sections) times 3/12 (elements). The resulting impedance for this configuration is about R which is much more acceptable than the under 1R impedance that would be produced by the full area in parallel, or even the 2.5-R impedance possible withthe uncut phased array. We recall that the transducer design methods presented earlier can be applied to any transducer area given that the resulting impedances are scalable. In practice, however, and in order to view the actual untuned conversion loss, it is helpful to reduce the design area so that it corresponds to the effective area achieved after the appropriate interconnections. For this device a four-element ladder matching network can be used as shown in Fig. 26. The interconnecting bond wires are combined into an external series inductor of about 5 nH in series with the device bond impedance. The impedance of this structure is plotted in the Smith chart of Fig. 26 as curve A. The first stage of the matching network is an additional 9-nH series inductor and a 12-nH shunt inductor the effect of which is shown in curve B. The matched impedance (curve C) is then obtained with an additional 5-nH series inductance and a 13-pF shunt capacitor at the RF connector. The device was constructed with a 7.0-pmthick LiNb03 transducer and has an effective area 0.15 mm2. The top electrode is a 0.6-km-thick Au layer and the bond is a 0.4-pm In layer between two 0.05-pm Au layers. The unmatched device had an untuned conversion loss of about 1.5 to 3.5 dB over the passband (Fig. 27). After matching, the conversion loss is reduced to less than 0.5 dB. Figure 28 shows the corresponding unmatched and matched VSWRs. It can be seen that the worst-case-matched VSWR is below 1.8 over the full passband. Figure 29 shows the actual TeO, device. Air-wound inductors were adjusted (while the performance was measured via a network analyzer) by changing the spacing between windings. At these operating frequencies (i.e., below 500 MHz) adjustable capacitors may also be used, 4.3 Multichannel Power Delivery Often implementation constraints can dominate the selection of a power delivery network. This is especially true for the networks used in conjunction with multichannel A 0 devices. Figure 30 shows a 64-e1ectrode7 200-pm, center-to-center-spacing, power delivery network used for a 64channel shear GaP A 0 deflector. The .network provides spatial separation for theinco.ming signal lines. The transmission lines serve several purposes:

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Figure 26 (Bottom) Four-element ladder matching network for the phased array transducer of the longitudinal 250-450 MHz TeO, device. (Top) Curve A of the Smith chart shows the impedance of the unmatched device, curve B shows the effect of the 9-nH series inductor and the 12-nH shunt inductor, and curve C shows the effect of the full matching network.

(1) they provide a matching element; (2) they separate the 64 channels spatially; and (3) they maintain the element-to-element electrical isolation. The implementation of the matching network (a section of which is shown in Fig. 31) is constrained to a length of 1.3 in. This allows sufficient length to separate the connectors for the incoming signals while limiting the pack-

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Figure 27 Untuned and tuned conversion loss for the four-element ladder matching network example of Figure 26.

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29 Photograph of the phasedarray TeOzdevice showing the four-element matching network. (Courtesy of Hams Corporation.)

age to a reasonable size. The shunt inductor at the device load (shown in the two previous matching-network examples) isomitted here dueto electrical crosstalk considerations. The bond wires are kept as short and as close to the ground planes as possible. Curve A in the Smith chart of Fig. 31 shows the impedance of a single channel including a very small bond inductance of about 0.2 nH. The66-R transmission line rotates the impedance (curve B), allowing a nominal shunt capacitance of 3 pF tobring the response to the real axis (curve C). The untuned conversion loss shown in Fig. 32is obtained from design values of a 0.2-pm-thick Au electrode layer of 0.17 mm2area ona 1.44-pm-thick shear LiNb03 transducer. The bond is a 0.3-km-thick Ag layer sandwiched between two 0.2-pm-thick Au layers. Note, unlike the previous examples, the measured values are further from the design values. This is because as the operating frequencies increase, the simple transducer model described earlier does notcompletely characterize the device impedance. Parasitic field couplings become in-

TRANSDUCER

30 Power delivery network for a 64-channel shear GaP (Courtesy of Harris Corporation.)

331

deflector.

creasingly significantat higher operating frequencies, requiring special fabrication care especially above 1 GHz. The power delivery network lowers the matched VSWR to about 2.1 (Fig. 33). Figure shows the complete package of the "channel deflector. While preserving a compact package size, the device is able achieve better than 30-dB signal isolation; an important criterion unique to multichannel device operation.

GOUTZOULIS AND BEAUDET

31 (Bottom) Section of the &channel power delivery network. (Top) Curve A of the Smith chart shows the impedance of a single channel including a bond inductance of about 0.2 nH. Curve B shows the effect of a transmission line which rotates the impedance thereby allowing a shunt capacitor of 3 pF to bring the response to the real axis (curve C).

4.4 High-FrequencyDeviceConsiderations There are some general guidelines in selecting an approach to electrically match A 0 devices. At frequencies below 1 GHz lumped-element designs provide good results with minimal investment in components and good

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34 Photograph of the complete 64-channel shear GaP device package. (Courtesy of Hams Corporation.)

flexibility in implementation.As operating frequencies extend above 1 GHz matching withdistributed components yields more acceptable results. This requires fabrication of transmission line substrates. Design iterations can be reduced by careful attention to parasitic coupling as a modification to the starting point impedance. At frequencies above 2.5 GHz wave mode propagation becomesa concern. The RF power delivery accesses the device electrode surface in a coplanar manner throughbond wires for signal path

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and return. Transmission line networkscouple better when the device interface includes a coplanar wave launch. This level of RF design requires a field-competent design package. Although many devices have been assembled using less sophisticated approaches to matching, one should not expect reliable implementation using lumped elements o r even impedancemodeled transmission lines at frequencies above 2.5 GHz. When accurate models are not available, careful measurement of the device impedance in the final field conditions (i.e., with appropriate mounts andcovers) may produce arealistic estimate of parasitic elements toallow a successfulmatch implementation. An estimate of the match stability may be judgedby applying a literal “ruleof thumb.” If the VSWR changes with yourthumb on the device cover, stray coupling is likely to be a problem in operation.

ACKNOWLEDGMENTS Akis Goutzoulis thanks Bob Weinertof Westinghouse STC for many fruitful philosophical discussions and technical recommendations concerning the optimization of acoustic impedance-matching procedures. He also thanks Betty Blankenship, Harry Buhay, andMilt Gottlieb, also of Westinghouse STC, for their expert technical advice concerning the use of various metals as bonding layers.

REFERENCES 1. Mason, W. P,, Electromechanical Transducers and Wave Filters, 2nd ed. Van Nostrand, New York, 1948, pp. 201-209, 399-404. 2. Berlincourt, D. A., Curran, D. R., and Jaffe, H., Physical Acoustics, Vol. 1A (W. P. Mason, ed.), Academic Press, New York, 1964, pp. 233-242. 3. Sitting, E. K., Transmission parameters of thickness-drivenpiezoelectric transducers arranged in multilayer configurations,IEEE Trans. Sonics Ultrasonics, SU-14, 167-174 (1967). 4. Sitting, E. K., Effects of bonding and electrode layers on the transmission parameters of piezoelectric transducers used in ultrasonic digital delay lines, IEEE Trans. Sonics Ultrasonics, SU-16,2-9 (1969). 5. Sitting, E.K., Warner, A. W., and Cook,H. D., “Bonded Piezoelectric Transducers for Frequencies Beyond 100 MHz,” Ultrasonics, 108-112, April 1969. 6. Kossoff, G . , The effects of backing and matching on the performance of piezoelectric ceramic transducers, IEEE Trans. Sonics Ultrasonics, SU-I3, 20-30 (1966). 7. McSkimin, H. J., Transducer design for ultrasonics delay lines, J. Acousr. Soc. A m . , 27, 302-309 (1955). 8. Reeder, T. M., and Winslow, D. W., Characteristics of microwave acoustic transducers for volumewave excitation, IEEE Trans.MicrowaveTheory Techniques, MTT-17, 927-941 (1969).

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9. Hopp, T., Computer-aided design of bulk microwave acoustic delay lines, Report number NTIS (1974). 10. Hueter, T. F., and Bolt, R. H., Sonics: Techniques for the Use Sound and Ultrasound in Engineering and Sciences, Wiley, New York, 1965, p. 39. A thin film mosaic transducer for bulk 11. Weinert, R. W., and deKlerk, waves, IEEE Trans. Sonics Ultrasonics, SU-19, 354-357 (1972). 12. Onoe, M,,Relationships between input admittance and transmission characteristics ofan ultrasonic delay line, IRE Trans. Ultrason. Eng., UE-9,42-46 (1962). 13. Meitzler, A. H., and Sitting, E. K., Characterization of piezoelectric transducers used in ultrasonic devices operating above 0.1 GHz, J . Appl. Phys., 40(11) (1969). 14. Inamura, T.,The effect of bonding materialson the characteristics of ultrasonic delay lines with piezoelectric transducers, Japan. J. Appl. Phys., 9, 255-259 (1970). 15. Collin, R. E., Theory and design of wide-band multisection quarter-wave transformers, Proc. IRE, 43, 179-185 (1955). 16. Riblet, H., General synthesis of quarter-wave impedance transformers, IRE Trans., MTT-5, 36-43 (1957). 17. Young,L., Tables for cascaded homogeneous quarter-wave transformers, IRE Trans., MTT-7,233-237 (1959). 18. Kittinger, E.,and Rehwald, W., Improvement of echo shape in low impedance materials, Ultrasonics, 211-215 (1977). 19. Goll, J., and Auld, B., Multilayer impedance matching schemes for broadbanding of water loaded piezoelectric transducers and high Q electric resonators, IEE Trans. Sonics Ultrasonics, SU-22, 52-53 (1975). 20. Desilets, C., Fraser, J., and Kino, G., The design of efficient broad-band piezoelectric transducers,IEEE Trans. Sonics Ultrasonics, SU-25,115-125 (1978). 21. Bagshaw, J. M., and Willats, T. F., Anisotropic Bragg cells, GEC J . Res., 2, 96-103 (1984). 22. Huang, H., Knox, J. D.,Turski, Z., Wargo, R., and Hanak, J. J.,Fabrication of submicron LiNbO, transducers for microwave acoustic (bulk) delay lines, Appl. Phys. Lett., 24, 109-111 (1974). 23. Kirchner, E. K., Deposited transducer technology for use with acousto-optic bulk wave devices,SPZE, 214 (acousto-optic bulk wave devices), 102-109 (1979). 24. Warner, A., Onoe, M,, and Coquin, G. A., Determination of elastic and piezoelectric constantsfor crystals . . . ,J. Acous. A m . , 42,1223-1231 (1967). 25. Foster, N.F., and Meitzler, A.H., Insertion loss and coupling factors in thinfilm transducers, J . Appl. Phys., 39, 4460-4461 (1968). 26. Meitzler,A. H., in Ultrasonic Transducer Materials (0.E, Mattiat, ed.), Plenum, New York, 1971. 27. Jaffe, H., and Berlincourt, D. A., Piezoelectric transducer materials, Proc. IEEE, 53, 1372-1386 (1965). 28. Spenser, E. G., Lenzo, P. V., and Ballman, A. A., Dielectric materials for electro-optic, elastooptic, and ultrasonic device applications, Proc. IEEE, 55, 2074-2108 (1967).

TRANSDUCER DESIGN Temperature dependence of the elastic, 29. Smith, R. T., andWelsh, F. piezoelectric, and dielectric constants of lithium tantalate and lithiumniobate, J . Appl. PhyS., 42,2219-2230 (1971). 30. Gottlieb, M., Buhay, H., andBlankenship, B., WestinghouseScience & Technology Center, Pittsburgh, Pennsylvania,January 17,1992, private communication. 31. Slobodnik, A. J., Jr., Delmonico, R. T., and Conway, E. D., Microwave Acoustics Handbook,Vol. 3, Bulk Wave Velocities, TR-80-188,National Technical Information Services, Springfield VA, 1980. 32. American Institute of Physics Handbook, McGraw-Hill, NewYork, 1963, pp. 3-88. 33. Katzka, P., and Dwelle, R., Large spectral bandwidth acousto-optic tunable filters, Poster paper,IEEE I986 Ultrasonics Symposium, Williamsburg, VA. 34. Chang, I. C., Selection of materials for acousto-optical devices, Opt. Eng., 24, 132-137 (1985). 35. Goutzoulis, A. P., andGottlieb, M., Characteristics and designof mercurous halide Bragg cells for optical signal processing, Opt. Eng.,27,157-163 (1988). 36. Elston, G., Amano, M., and Lucero,J., Material tradeoff for widebandB r a g cells, Proc. SPIE (Advances in Materialsfor Active Optics),567,150-158 (1985). IEEE 1988 Ultrasonics 37. Chang, I. C., High performance wideband Bragg cells, Symposium, 1988, pp. 435-438. 38. Onoe, M., Tiersten, H. F., and Meitzler, A. H., Shiftin the location of resonant frequencies causedby large electromechanical coupling in thicknessmode resonators, J . Acoust. Soc. A m . , 36-42 (1963). 39. Weinert, R.W., Very high-frequency piezoelectrictransducers, IEEE Trans. Sonics Ultrasonics, SU-24, 48-54 (1977). 40. Gottlieb, M., Goutzoulis, A. P., and Singh, B., N. Mercurous chloride (HgzClz) acousto-optic devices,Proceedings of the IEEE Ultrasonics Symposium, 1986, pp. 423-427. 41. Gottlieb, M., Goutzoulis, A. P., and Singh, N. B., Fabrication and characterization of mercurous chloride acousto-optic devices, Appl. Opt.,26,46814687 (1987). 42. Dixon, R. W., Acoustic diffraction of light in anisotropic media, IEEE J . Quantum Electron., QE-3, 85-93 (1967). 43. Bademian, L., Parallel-channel acousto-optic modulation, Opt. Eng., 25,303308 (1986). 44. Mattaei, G. L., Young,L., and Jones, E. M. T., Microwave Filters, Impedance Matching Networks and Coupling Structures, McGraw-Hill, New York, 1964. 45. Rosenbaum, J. F., Bulk Acoustic Wave Theory and Devices, Artech House, Norwood, MA, 1988.

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6 Acousto-Optic Device Manufacturing Vjacheslav G. Nefedov St. Petersburg State Academy

Aerospace Instrumentation St. Petersburg, Russia

Dennis R. Pape Photonic Systems Incorporated Melbourne, Florida

1 INTRODUCTION Acousto-optic (AO) devices combine physical features found in both ultrasonic delay lines and optical windows. Like an ultrasonic delay line, the A 0 device has a piezoelectric transducer mechanically bonded to an acoustic substrate, as shown in Fig. 1. Also like an ultrasonic delay line, an impedance-matching network is used to efficiently couple RF energy into the transducer. Like an optical window, the acoustic medium is a transparent optical block polished to a high degree of parallelism, flatness, and surface quality. It is not surprising, then, to find that the manufacture of A 0 devices combines technologies and processes found in both the manufacture of ultrasonic delay lines and optical windows. Indeed the proliferation of A 0 device manufacturing capability throughout the world is a result of the mature development of ultrasonic delay line and optical window manufacturing processes and the relative ease with which they can be combined to produce an device. A flowchart containing the primary steps in the manufacture of an A 0 device is shown in Fig. 2. The manufacturing process starts with the growth of the A 0 device material, and, if a platelet transducer is used, the transducer material as well. The A 0 device material, usually in boule form, is oriented and rectangular optical blocks, with dimensions and orientation determined by the device design, are cut. The optical'faces as well as the

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Acousto-optic device showing piezoelectric transducer structure with impedance-matching network and transparent optical cell block.

transducer bonding surface of the A 0 device optical block are then polished. An antireflection coating is then applied to the optical faces. If a platelet transducer materialis used, this material is also,oriented and cut, again with dimensions and orientation determined by device design. The transducer platelet material is also polished. This completes that portion of the manufacturing process that utilizes optical window processing techniques. The A 0 device optical blocks are now ready for the application of the transducer. Here manufacturing techniques used in the production of ultrasonic delay lines are employed. Two types of transducers can be used: thin film and platelet. If a thin-film transducer is used, the device optical block is placed in a vacuum chamber where the thin film transducer is deposited. If a platelet transducer is used, the platelet transducer is prepared and bonded to thedevice optical block. The platelet is then reduced in thickness to achieve the appropriate device center frequency. A metallic electrode is then deposited on top of the piezoelectric material. An impedance matching circuit is designed to match the impedance of the A 0 device to the electronic driver. The A 0 device and theimpedancematching circuit are then mounted in the device housing. An RF connector on the housing is electrically connected to theinput side of the impedance-matching circuit while wires from the output side are bonded to the topelectrode of the A 0 device. This completes that portion of the manufacturing process that utilizes ultrasonic delay line processing techniques. Finally, an acoustic absorber is attached to the end of the device to frustrate acoustic reflections in the device. This completesthe fabrication of the A 0 device.

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2 ACOUSTO-OPTICDEVICEOPTICAL WINDOW MANUFACTURING The starting point in the manufacture an device is the preparation the device optical window block. The choice the device block material is usually determined by the type of device being produced and the specific device performance required, as discussed in Chapters 2, and 4. Table 1 shows the parameters of the most often used materials.

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Material Growth In general, the starting material for the A 0 device optical window block as well as the platelet transducer is a boule of single-crystal A 0 material. A 0 materials are grown usingstandard crystal growth techniques including directional sublimation, the Bridgman technique, and the Czochralski technique (someA 0 devices are also made from amorphous andpolycrystalline materials) [l].In the Czochralski growth technique, as shown in Fig. 3, powder of the crystal to be grown is placed in a platinum (or other nonreacting material) crucible. A heating element surrounding thecrucible is used to melt the powder. The temperature of the melt is also precisely controlled with the heating element during growth. A seed crystal, attached to a rotating rod (typically 60 rpm), is lowered into the melt. the rod is slowly withdrawn, material from the melt solidifies on the seed. Continued slow withdrawalof the rod,typically at ratesof 1to 10 mmh, results in the formation of a crystal boule.

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2.2 Material Orientation After the boule is grown, the direction of the principal crystal axes are determined. These axes can be found knowing the growth direction and the symmetry of the crystal as well as by observing the decayed crystal faces on the surface of the boule. The directionof the axes can be determined, for a piezoelectric material, by knowing the sign of the piezoelectric modulus and measuring the response of the crystal to a clamping deformation [2]. piezoelectric tester used to measure the polarity of the piezoelectric response is shown in Fig. The procedure used for determiningthe direction of the crystalline axis in a piezoelectric material is illustrated in Fig. 5 for L i m o 3 grown along the z axis. The crystalline facet along the boule can be used to find the position of the crystal plane of symmetry which is the yz plane. Thus, the position of the y axis is determined. In order to find its direction, the polarity of the piezoelectric response to clamping deformation applied along y axis at the point a is measured. If the piezoelectric response and the sign of the piezoelectric modulus are positive, the axis y at the point

Piezoelectric tester used to determine crystal axes direction. (Photo .courtesy of St. Petersburg State Academy of Aerospace Instrumentation.)

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5 LiNbOJ crystalline

345

orientation procedure.

is in the positive direction. Similarly, the positive direction of the t axis can be found. The direction andsign of the x axis follows from geometric considerations.

2.3 Optical Window Block Sawing Once the boule has been oriented the A 0 device optical window blocks are cut. The boule is cut with a sawing machine with reciprocally moving metallic saws and abrasive pulp (water with abrasive powder). A sawing machine is shown in Fig: The oriented crystal boule is fastened on the saw table with easilymeltable compounds or plaster.A section sawed from a GaPboule is shown inthe upper portionof Fig. 7. The lower left portion shows a device optical block cut from the boule section. After sawing, the device blocks must be tested for opticalhomogeneity. The opticalwindow surfaces of the device block are polished to allow optical inspectionof the material (thesawed pieces in Fig. 7 have been polished). Thedevice blocks are inspection polished on a standard opticalpolishing machine, shown in Fig. 8. The material is tested for defects (bubbles, cracks, fissures, etc.) by illuminating the device block with a polarized collimated light beam -A homogeneous transmitted optical beam indicates no defects are present. Optical window blocks passing the optical quality test then undergo final orientation. The required accuracy of the device optical window block final orientation depends upon the type of A 0 interaction. For example, for an

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6 Optical window block sawingmachine. Corporation.)

NEFEDOV AND

(Photo courtesy of Harris

isotropic interaction, the orientation accuracy must be greater than30 arc minutes. For an anisotropic interaction, the orientation accuracy varies from parts of arc minutes to several arc minutes. For example, for anisotropic diffraction using the slow shear mode in Te02, the [l101 acoustic face must be oriented with accuracy greater than 40 arc minutes and the [OOl] optical face greater than arc minutes. The final Orientation is made with an x-ray goniometer This instrument, shown in Fig. 9, measures the intensity of x rays Bragg diffracted by the crystal as a function orientation angle. With a priori knowledge of the crystalline structure of the material, the orientation of the material can be determined from the angular x-ray intensity profile.

Optical

Block Surface

After sawing, the A 0 device optical window blocks are finish-polished. Four surfaces of the device blocks are polished: the two optical window

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7 Acousto-optic device optical window block manufcturing:(upper) section of GaP boule;(lower left) optical block; (lower right) optical block with bonded platelet transducer. (Photo courteryof Hams Corporation.)

surfaces, the transducer bonding surface, and the surface opposite the transducer bonding surface. Finish polishing is performed in the same optical polishing machine used to perform the inspection polish, shown in Fig. 8. Both coarse and finepolishing abrasives are used to obtain a highquality optical window. The optical window surfaces are typically polished parallel to 30 arc seconds with flatness and a 10-5 scratch dig surface quality. The acoustic transducer bonding surface and the opposite device block surface are also optically polished to the same specifications. Figure 10 shows TeOz optical window blocks mounted foracoustic bonding surface polishing.

2.5 Optical Window Block Antireflection Coating It is desirable to reduce optical losses at the device block windows by using antireflection coatings. Both single and multilayer AR coatings can

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8 Optical polishing machine. (Photo courtesy

Harris Corporation.)

be used. A single-layer AR coating is designed such that the reflections from the AR coating surface cancel in phase and amplitude the reflections from the optical device block window surface. The thickness of the layer must therefore be an odd number of 1/4wavelengths. The intensity I , of a reflected beam from a single surface is [4]

[:I:1’

I=I, -

where Io is the intensity the incident beam and p is the ratio of the indices of the two materials at the interface. Table 2 shows the calculated ratio of the intensity of the reflected beam to the incident beam as well as the transmitted beam ( I t = 1 - I,) to the incident beam the four most commonly used A 0 materials (optical wavelength A = 0.63 nm) when no AR coating is used.

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I

9 X-ray crystal orientation goniometer. (Photo courtesyof St. Petersburg State Academy of Aerospace Instrumentation.)

In order that the two reflected beams from an AR coated surface cancel completely, they must be equal intensity. It is thus necessary that p be the same at both the interfaces: -=nair ~ A w Ra t

coat substrate

Since nair = 1.0, the index

refraction of the AR coating ltAR

must

be As shown in Table most A 0 materials have high refractive indices, usually between 2.0 and Thus the index a singlelayer AR coating will vary between about and Most single-layer AR coatings use chloride or fluoride compounds Magnesium fluoride, with an index of at nm, and cerium fluoride, with an index of are commonly usedcoatings. Silicon dioxide ( n = and aluminum oxide (n = films, easily produced by reacting sputtering in a dc magnetron sputtering system; are also used.

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10 TeO, opticalwindowblocksmountedforacousticbondingsurface polishing. (Photo courtesy of Hams Corporation.)

Table 2 Transmission and Reflection Coefficients for Acousto-OpticSubstrates Without Measured Calculated AR coating Material GaP LiNbO, PbMoO, TeO,

R,(%)

RR, ,((%%))

With AR (Si02) coating

R,(%)

R,(%)

R,(%)

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MANUFACTURING

3.51,

For normal incidence, the single-pass reflectance from an AR coated surface is 2

R = [

sub sub

-

nAR coat

n%.R coat

3’

Table 2 shows the theoretically calculated and experimentally measured reflection and transmission ( l - R ) coefficients of SiO, films deposited on LiNb03, Te02, Gap,and PbMoO,. Multilayer AR coatings can also beusedwhenlower reflectivity or broadband optical illumination is desired. After the antireflection coating is applied the device block optical window surfaces are covered with a protective paint to prevent scratches and mechanical damage during subsequent device processing.

3 PIEZOELECTRICTRANSDUCER MANUFACTURING The piezoelectric transducer is a multilayer structure mechanically bonded to theA 0 substrate. The transducer structure, asshown in Fig. 11, consists of a piezoelectric material sandwiched between top and bottom metallic layers. This structure is mechanically attached to theA 0 substrate through the bottom metallic bonding layer. nonmetallic bonding layer can also be used in which case a separate metallic bottom electrode layer is required.) The piezoelectric material converts electrical energy into acoustic energy. The bottom electrodebondinglayer is designed not only to attach the transducer structure to the substrate but also to efficiently couple the acoustic energy into the substrate. The topmetallic layer serves as the top electrode andits geometry defines the initial length and width of the sound column. Two types of transducer structures are used in A 0 devices, thin film and platelet [6]. Thin-filmtransducers areformed directly on thetransducer surface of the device optical window block by thin-film deposition techniques. The piezoelectric layer is typically polycrystalline. Platelet transducers are single-crystal platelets of piezoelectric materials whichare bonded to the transducer surface. One of the key performance parameters in transducer technology is the efficiency with which the appliedelectrical energy can be converted into acoustic energy. The conversion efficiency is determined by the piezoelectric coupling coefficient of the transducer material as well as its dielectricconstant, frequency constant, acoustic impedance, electrical resistivity, and breakdownvoltage. Table 3 shows the values of the main properties of the most widely used piezoelectric materials for piezoelectric transducer manufacturing.

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/

Piezoelectrictransducerstructure. The piezoelectric coupling coefficientisdirectly proportional to the electrical to acoustic conversion efficiency and is thus the main parameter determining transducer efficiency. The dielectric constant determines the electrical capacity of the piezoelectric transducer and affectselectrical impedance matching. The impedance of the transducer determines the degree to which acoustic energy is coupled into the bonding layers and A 0 substrate. The optimal thickness of the piezoelectric material is established by the resonance condition that the thickness d of the transducer be nominally one-half of the acousticwavelength:

where is the acoustic velocity of the piezoelectric material and fo is the resonance frequency. The frequency constant, fo X d , determinesthe thickness the piezoelectric material at the desired operating frequency, and thus, the fabrication technology of the piezoelectric layer (thick trans-

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NEFEDOV A N D PAPE

ducers, i.e. ,those operating below 100 MHz usually require a platelet since it is difficult to deposit a high-performance thick piezoelectric thin film). All of the parameter values shown in Table 3 are for bulk single-crystal materials. Since thin-film piezoelectric layers are typically polycrystalline , these parameters can vary and therefore must be controlled during the manufacturing process. The piezoelectric transducer is under the influence of internal mechanical stresses. These internal stresses (actually the ratio between the internal stress and the bonding cohesion) affect the operation of the A 0 device and can cause partial or full destruction of the piezoelectric transducer. Moreover, they can even destroy the A 0 substrate. Internal stresses can be divided into two classes: (1) those stresses caused by differences in the properties of the bonding materials and (2) those stresses caused by structural imperfections in the materials within the piezoelectric transducer which occur during the manufacturing process. Thermal stresses caused by the difference in the thermal properties of the transducer materials belong to the first group. Stresses within the layers of transducer structure belong to the second group. In this group, stresses within the thin-film piezoelectric layer are most important, as they can, even without the destruction of the piezoelectric transducer, considerably decrease piezoelectric properties. Minimization of these stresses are considered in the discussion on thin-film piezoelectric transducers. Thermal stresses are caused by temperature variations during the manufacturing process. The main source of thermal stress in the transducer structure is the difference in the thermal coefficients of linear expansion of the piezoelectric material and the A 0 substrate. In order to minimize thermal stresses the thermal coefficients of linear expansion of the transducer material should be closely matched to the A 0 substrate and transducer manufacturing processes should be employed which use minimal heating. Usually, materials for the piezoelectric transducer and A 0 substrate as well as their orientation are chosen in such a way to maximize the efficiency of acoustic wave generation and A 0 interaction. Given these materials, an estimate of the difference in thermal coefficients of linear expansion and the allowable level of thermal stresses should be determined in order to choose the appropriate transducer manufacturing process. Because most piezoelectric and A 0 materials are monocrystals or patterned films, the thermal coefficient of linear expansion depends both on the orientation of the materials. Figures 12-18 show the distributions and difference in the thermal coefficient of linear expansion for the most common orientations of the piezoelectric material and the A 0 substrate. In these figures TeO, and LiNb0, are chosen as A 0 substrates (curve l),and LiNbO, and ZnO

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Y TC LE X 106/"K)

of Figure 12 Acousto-optic crystal substrate and transducer thermal coefficient of linear expansion: (1)A 0 crystal [LiNbO, (loo)], (2) piezoelectric transducer [LiNbO, ( y + 36")], (3) difference [2-11.

Figure 13 Acousto-optic crystal substrate and transducer thermal coefficient of linear expansion: (1) A 0 crystal [TeO, (OOl)], (2) piezoelectric transducer [LiNbO, ( y 36")], (3) difference [2-11.

+

356

Acousto-optic crystal substrate and transducer thermal coefficient of linear expansion: (1)A 0 crystal [TeO, (110)], (2) piezoelectric transducer [LiNbO, (loo)], (3) difference [2-11.

Aco~sto-opticcrystal substrate and transducer thermal coefficient of linear expansion: (1) A 0 crystal [TeO, (110)], (2) piezoelectric transducer [LiNbO, ( y + 163")], (3) difference [2-11.

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Acousto-optic crystal substrate and transducer thermalcoefficient of linear expansion:(1) A 0 crystal [LiNbO, (loo)],(2) piezoelectric transducer [ZnO (OOl)], difference [2-l].

Acousto-optic crystal substrate and transducer thermalcoefficient linear expansion: (1) crystal [TeO, (OOl)], (2) piezoelectric transducer [ZnO (OOl)], difference [2-l].

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Acousto-optic crystal substrate and transducer thermal coefficient of linear expansion: (1) A 0 crystal [TeO, (llo)], (2) piezoelectric transducer [ZnO (loo)], difference (2-11.

as the piezoelectric material (curve 2). Curve is the difference in the thermal coefficients of linear expansion (TCLE). These plots are in units of 106/K. From thesecurves we cansee that forseveral combinations of materials there is a considerable difference in the thermal coefficients of linear expansion. a rule of thumb, the difference in the thermal coefficients of linear expansion should not exceed 0.1 to 1.0 106/K in order topreserve the integrity of bonded materials if a high-temperature manufacturing process is used. The actual stresses in a particular layer is determined by the strength of materials, adhesion forces, and manufacturing temperature levels. 3.1 . Thin-Film Transducer Fabrication Thin-film piezoelectric transducers are formed directly on the substrate using vacuum deposition technology. The thin-film transducer has a number of advantages over a platelet transducer: (1) no transducer bonding layer is required which mayintroduce extrainsertion losses, (2) the platelet reduction process is eliminated, electrical impedance matching is simpler due to thelower capacitance of the thin-film piezoelectric transducer, and (4) thin-film transducers can be deposited on large areas and curved

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surfaces. The primary disadvantage of the thin-film piezoelectric transducer is its much lower piezoelectric coupling coefficient than the platelet transducer. The simplicity, reproducibility, and relatively low production costs of thin-film transducer fabrication, involving only film deposition processes, over the more involved processes required to fabricate platelet transducers (particularly at higher frequencies) led to thepreference of this transducer technology by some A 0 device manufacturers. Although most of the commercially available A 0 devices have platelet transducers, thin-film transducers remain the preferred approach among some manufacturers. Ultrasonic transducers have been fabricated using thin films of AIN, CdS, LiNb03 and ZnO [7]. ZnO has the highest piezoelectric coupling coefficient (see Table of these piezoelectric thin-film materials and is the usual choice for thin-film transducer fabrication in A 0 device manufacturing. ZnO Deposition Technology ZnO can be deposited using thermal evaporation techniques but the film quality is poor [7]. The highest-quality ZnO films are formed by the ion sputtering process. In this process the ZnO deposition material forms the cathode of an anode-cathode assembly inside a vacuum chamber. An inert rare gas, typically Ar, introduced into thevacuum chamber at low pressure becomes ionized when a high voltage (either dc or RF) is applied across the anode-cathode assembly. Accelerated by the electric field between the anode and the cathode, theAr+ ions bombard the cathode and cause ZnO atoms to be ejected. The ZnO atoms diffuse to the A 0 substrate where they are deposited into a thin film and form the piezoelectric transducer. Various ion sputtering anode-cathode configurations have been employed to deposit ZnO including the diode triode and magnetron [ll].The diode configuration, where the anodeserves as theA 0 substrate holder, typically yieldspoor quality films due to substrateheating and film damage caused by secondary electron bombardment. Also, the diode configuration requires a relatively high Ar gas pressure which results in film contamination from Ar atoms trapped in the ZnO film. The triode configuration uses an auxiliary thermionic cathode to inject electrons into the Ar gas to create ionization. Unlike the diode configuration, electron emission is independent of gas pressure and thus the triode configuration can be operated at lower gas pressures. Nevertheless, this configuration too suffers from substrate heating, film contamination from the thermionic cathode material, and thermionic cathode decay if reactive gasses are used in conjunction with Ar (in order tomodify the properties of the deposited film).

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The magnetron sputteringconfiguration overcomes the secondary electron induced substrate heating problem which is the major disadvantage of both the diode and triode sputteringconfigurations for the production of highquality ZnOthin-film transducers. Several different types of magnetron sputtering designs (cylindrical, planar, and magnetron gun) have been developed for thin-film deposition. The planar magnetron sputtering configuration is the most widely used[12]. The main elements of the planar magnetron sputtering source, shown in Fig. 19 for both circular and rectangular geometries, are a planar circular cathode target parallel to an anode surface, usually grounded, that serves as the substrate holder. permanent magnet underneath the cathode creates a circular closed path where the magnetic field lines are perpendicular to the cathode surface. The magnetic field confines the plasma to the circular closed-path region. The electrons are captured by the magnetic fieldand, because of the crossed electric and magnetic fields, move in long helical paths through the argon gas. The trajectory of the secondary electrons emitted by the cathode due to ion bombardment, however, is bent away from the substrate. These unwanted secondary electrons are captured by a ground shield, thus eliminating substrate heating. In addition, the probability an electron colliding with an argon atom is greatly increased in this system because of its helical path. This results in higher film growth speeds than that available with either the diode or triode systems. Film growth speeds of 15 p d h r havebeenachievedwithmagnetron sputtering systems. The increased

l/ Figure 19 Circular and rectangular planar magnetron sputtering sources. Curved lins> rcprsscnt magnetic field lines

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collision probability also allows the system to be operated at even lower gas pressures than the diode system, thus reducing film contamination. Figure 20 shows a photograph of a circular planar magnetron cathode assembly whichis used for thin-film piezoelectric transducer manufacturing at the St. Petersburg State Academy of Aerospace Instrumentation. The operation of a magnetron deposition unit is as follows. A 0 substrates areplaced on theanode holder and loaded into thesystem chamber. Pa, After pumping the chamber down to a pressure of about 1.3 X gases are backstreamed into the chamber to a pressure of about 0.1 Pa. A voltage of approximately 300 to 400 V is applied between the anode and cathode,which creates an abnormalglow discharge concentrated near the target. Plasma ions then begin to bombard the target and sputtering is initiated. The sputtered atoms, condensing on the substrate, form the thin-film transducer. ZnO Film Characteristics ZnO is a hexagonal (wurtzite) crystal of class 6mm. ZnO films produced by standard vacuum deposition techniques on metal substrates (as in A 0

20 Circular planar magnetron cathode assembly. (Photo courtesy of St. Petersburg State Academy of Aerospace Instrumentation.)

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NEFEDOV AAlD PAPE

transducer fabrication) are not epitaxial but instead are polycrystalline structures with varying degrees of misorientation between individual crystallites [7]. A uniformly oriented polycrystallinefilm will, however,exhibit a piezoelectric coupling constant close to that of the bulk single-crystal material. A group of crystallites in a polycrystalline film with the same crystallographic orientation forms a "texture." A polycrystallinefilm can be characterized by threeparameters: (1) thetextureratio & l , the ratio of crystallites with c-axis orientation perpendicular to the(hk.l) plane to the total number of crystallites in the film, (2) the misorientation angle the angular spread of the crystallites orientation about the c-axis direction, and (3) the c-axis direction angle 8, the angle between the c axis and the normal to the film plane. The magnitude of the ZnO thin-film piezoelectric coupling constant as a function of 8 for various values (with &k.[ = 100%) is shown in Fig. [7,13]. The 21 (where the electric field is along the direction 8 = longitudinal mode coupling is maximum when the c axis is parallel to the electric field while shear mode coupling is maximum when the c axis is inclined at anangle of about 30". a increases, the piezoelectric coupling constant decreases (with no coupling when the film crystallites are randomly ordered). In addition,nonuniform orientation results in the simultaneous generation both longitudinal and shear waves. From the figure we see thata c-axis orientation parallel to theelectric field is optimum for longitudinal mode transducers (where the longitudinal mode coupling is maximum and no shear mode coupling occurs) and a c axis orientation inclined to theelectric field by about 40" is optimum for shear modetransducers (where no longitudinal mode coupling occurs). Thin films of ZnO, like other wurtzite class crystals, grow primarily with the (00.1) plane parallel to thesubstrate surface, i.e., the c axis is oriented perpendicular to the substrate [7]. With the piezoelectric film sandwiched between electrodes parallel to the A 0 substrate (i.e., the electric field is parallel to the c axis), this orientation yields a longitudinal mode transducer. Pure shear mode transducers (where the c axis is inclined to the normal by about 40", as shown in Fig. 21) can be formed by obliquely depositing the film [14]. (The crystalline structure of the metallic electrode upon which the piezoelectric material is deposited does not appreciably impact the ZnOfilm orientation. It is important, however, that themetallic surface be clean and smooth [7].) ZnO Film Quality and Deposition Parameters A number of factors, both equipment and process related, influence the type and quality of a sputtered thin-film piezoelectric transducer. Equip-

363

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0.2

30

60

90

9 (degrees)

KS

0.3

0.2

9 (degrees)

21 ZnO piezoelectric coupling constant vs. orientation angle for various values: (a) longitudinal mode and (b) shear mode.

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.NEFEDOV AND PAPE

ment factors include (1) the type of pumpdown system, (2) the maximum available vacuum, the type and construction of the magnetron sputtering system, and (4) the method for gas composition mixing and backstreaming to the vacuum chamber. Process factors include (1) glow discharge parameters, (2) gas composition and pressure, thermaland temporal parameters of the sputtering process, and (4) geometry of the substratekarget arrangement. Pumpdown systems employing oilmust contain adequatecryogenic trapping for high-quality thin-film piezoelectric transducer deposition.Oil vapor affects the structure of the deposited film and contamination of the transducer substrate surface reduces film adhesion. Also, organic compounds in the vacuum chamber affect the crystallographicstructure of ZnO films [8]. Pumpdown systemswithout oil or oil vapor are ideally preferred. The maximum available vacuum must be highin order to provide a sufficiently clean deposition environment. The type and construction of the magnetron sputtering system determines the configuration of the substrate holder and the maximum area over which film uniformity can be maintained. The type of supplied voltage (ac or dc) determines the target material. If dc sputtering is used, the targetmust be electrically conductive to remove electrical charges generated on its surface. Usually, metallic targets are used. If ac sputtering is used, the target can alsobe made of semiconducting and dielectric materials. The target also determines the gas composition. The method for mixing the working gas and backstreaming it into the vacuum chamber influence chemical reactions, gas mixture uniformity, and stability of glow discharge parameters within the vacuum chamber [15,16]. Stability is particularly important because if the discharge extinguishes during sputtering, crystalline disorientation occurs and the film’s piezoelectric coupling constant is reduced. Film growth speed decisively determines the film’s texture characteristics. When the film growth speed decreases, the atoms depositedon the substrate have sufficient time to become incorporated within the existing crystal lattice before another layer is deposited. more uniform film generally results from aslow film growthspeed. (Onemust, however, take into account the bombardment by high-energy particles which can considerably change the dependence between growth speed and film quality [17,181.) Rhk.Jon film growth The dependenceof the film structure (texture ratio speed is shown in Fig. [19]. Below the boundary growth speed V , the crystallites form with the (00.1) plane orientation (c-axis orientation perpendicular to the film surface). Above this speed, the number of (00.1)

MANUFACTURING ACOUSTO-OPTIC DEVICE

365 . .

I

I

.-

I

2

75

-

!?!

a

50 .

25

I

0

0.14

0.28

0.42

0.53

Growth Speed (nrnls)

22 Dependence growth speed v.

ZnO film structure(textureration

R ~ ~ on , , )film

oriented crystallites decreases and crystallites with both (10.0) and the (li.O) orientation axis in plane of film) begin to form resulting in a mixture of both perpendicular and horizontal c-axis orientations. The boundaryfilmgrowth speed increases with increasing substrate temperature. An elevated substrate temperatureincreases atom mobility, providing close to equilibrium conditions where (00.1) planes form parallel to the film substrate. Unfortunately, it is not possible to increase v b substantially through substrate heating because the atoms will begin to reevaporate from the substrate surface. The limitation in growth speed severely limits the practicality of obtaining films withthicknesses greater than10 pm (i.e., of ZnO transducers with center frequencies below about MHz). For example, when v b = 0.25 ndsec, it takes 9 hr to obtain a 10-pm-thick film. Such an extended deposition period requires a sputtering system with a very high degree of temporal stability. The growth process can be made considerably shorter by using a twostage sputtering process [20]. It has been found that the deposition speed influences the film's texture pattern even at the earliest stages film deposition (up to thicknesses of 0.1 to 0.3 pm). At this early stage the

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orienting sublayer is formed. Once the orienting sublayer is formed, the film growth speed can be accelerated without a decrease in film quality. This two-stage growth process can yield films with thicknesses up toseveral tens of micrometers. During the first stage, sputtering is carried out at a speed lower than the boundary speed (typically0.05 to 0.1 ndsec). During the second stage, the speed can be increased to 1to 2 ndsec. Thick films have been obtainedwith texture patternaxis angular spreads corresponding to thatassociated with the first-stage growth speed. This two-stage process can reduce the time needed to deposit a 10-pm film from 9 to 3 hr. The film growthspeed, the uniformity of film thickness, and thequality of the crystal structure also depend on thedistance between the target and the substrate. To reduce film defects the particle mean free path length must be longer than the distance between the target and the substrate. Table 4 showsthe required particle mean free pathlength for different gas pressures. Given that the working pressure in the magnetron sputtering system is usually about 0.1 Pa, the distance between the target and the substrate must be less than about 5 cm. The sputtering target size and the distance between the substrate and the target also influence the thickness uniformity. The geometry forthesubstrate(A)/target (B) assemblyis shown in Fig. 23. For a film with radius R, equal to the radius of the sputtering zone R , a thickness nonuniformity of less than 2.5% can be achieved if the distance between the target and the substrate, H , as well as the target radius, R , is appropriately chosen, as shown in the graph in Fig. 24. For a flat target = 0), the ratio HIR must be between 0.8 and 1.0 cm. This means that if the distance between the target and the substrate (determined by gas pressure) is chosen to be cm, the sputtering zone diameter must bemore than8 to 10 cm in order toobtain the given thickness nonuniformity. The sputtering zone diameterin turn determinesthe target size and thus the mechanical design of the magnetron. Table 4 MeanFreePath between Particle Collisions free

MeanPressure (Pa>

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23 Geometryforsputteringsubstratekargetassembly.

1.5

-

1.3

-

0.9

-,

P (degrees) 24 ZnO Film thickness nonuniformity as a function of substratekarget geometry and target orientation.

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NEFEDOV ANLI PAPE

It is possible to deposit films withanisotropic properties in the substrate plane by introducing asymmetry in the growth conditions, e.g., by changing the incident angle of the sputtered material. By choosing the right angle, the c axis of the film crystallites can be forced to form either horizontally or vertically in the film plane. These biaxial growth patterns can be used to produce efficient shear wave piezoelectric transducers. As shown inFig. 21, the piezoelectric coefficient for the shear mode has two maximums: 4 = 30" (Ks= and 4 = 90" (Ks= 0.31). Films for efficient shear wave piezoelectric transducers either must have the tilted pattern axis, or this axis must be in the film plane. Experiments show that if the substrate is tilted up to the pattern with the tilted c axis is formed, whereas if the tilt angle is more than the c axis lies in the substrate plane. Different incident angles of the material particles sputtered from the target surface result in crystal surface nonuniformity over the substrate surface. The smallest tilt angle is in the central part of the film. The tilt angle 0 increases from the centerto the border, where crystallites with the (11.0) and (10.0) orientations appear. ZnO Piezoelectric Thin-Film Transducer Performance ZnO films have been deposited for longitudinal acoustic wave excitation with frequencies from 1 to 10 GHz [15,21-231. One way to characterize the quality of a deposited thin film is to measure the angular spread of Bragg diffracted x rays from the film surface in the goniometer setup shown in Fig. 9. The resulting "rocking curve" [2] is a measure of the spread in the misorientation angle a. Figure 25 shows rocking curves for various thicknesses of ZnO films deposited in a planar magnetron sputtering system by a Zn target sputtering in an Ar-0, gas mixture: (a) 2 pm, (b) pm, (c) 8 pm, and (d) 12 pm. The sputtering parameters for this film were target diameter, 120 mm; distance between the target and the substrate, 50 mm; voltage, between 350 and V; current, between 0.2 and 1.0 A; Ar-0, ratio,l:3; gas mixture pressure, 0.13 Pa; growth speed, 0.25 ndsec; substrate temperature, 250°C. The substrate materials are SiO,,LiNbO,, and A1203previously metallized with Al. The ZnO films deposited under these conditions have the following crystal pattern parameters: Rm,l = 99-loo%, a = &5", and 8 = 3". These parameters make it possible to achieve a piezoelectric coupling constant coefficient of K L = 0.25 (i.e., 90% of that found in monocrystal ZnO). Current research activities in ZnO thin-film transducer deposition have concentrated on (1) increasing film thicknesses up to 35 to 50 pm without texture decay, (2) depositing films on a number of A 0 materials (e.g., TeO,, PbMoO,, NaBiMoO), and (3) depositing films with a tilted c-axis orientation.

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I

::

(oo.2;

-

2.4 pm 20

30

40

60

0 1 .

+:>;

(00.2)

20 (deg)kr, 18

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30

40

50

70 I%

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25 Rocking curves various thicknesses ZnO films deposited in .a planar magnetron sputtering system by a Zn target sputtering in an Ar-0, gas mixture: (a) 2 pm, 4 pm, (c) 8 pm and (d) 12 pm.

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The primary limitation in increasing film thickness is the accompanying increase in internal stresses caused by both film texture pattern imperfection and differences in the thermalcoefficients of linear expansion between the film and the substrate. we noted earlier, these stresses may not exceed the strength of the ZnO film and the substrate and adhesion forces. For LiNbO,, SiO,, Gap, and A1203 crystals, films with thickness up to about 50 p m can be deposited with the required pattern. Rocking curves from a 50-pm-thick film with R , , , = = = and K L = 0.24 are shown in Fig. 26. Both the sample and the x-ray detector were rotated in Fig. 26(a), while only the sample was rotated in Fig. 26(b). A bottom A1 electrode with a'thickness between 0.5 and 1 pm provides both good ZnO adhesion to the A 0 substrate and internal stress decoupling.

+

I%

0

20

30

40

60

Rocking curves from a 50-p,m-thick film with R,,, = 98%, = (a) both the sample and the x-ray detector rotated and (b) sample only rotated.

4

=

6", and K L =

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As the thermalcoefficient of linear expansion for A1 is higher than that of ZnO or the A 0 substrate, an A1 film can reduce the internal stresses in the transducer film and the A 0 substrate. The high level of internal stresses in ZnO films and the low strength of TeOz and PbMoO, crystals make it impossible to deposit thin-film piezoelectric transducers directly on these materials [24]. For these materials other methods for stress decoupling between the piezoelectric transducer and theA 0 substrate have to be used including deposition of a buffer layer and reducing substrate temperature. As the buffer layer, an A1 electrode of half-wave thickness can be used for frequencies from MHz to 1 GHz, W2 ranges from 32 to 3.2 pm. Low substrate temperature, unfortunately, resultsin low film quality. Thehighest-quality film results from a trade-off between the characteristics of themultilayer structure, theA 0 substrate, theadhesion sublayer, the ground layer, the orienting sublayer, thepiezoelectric film, and the top electrode. Figure 27 shows rocking curves for a 3-pm (7.27(a)) and 8-pm (7.27(b)) ZnO film deposited as a multilayer structure on an (001) TeO, crystal. The texture parameters for this ZnO film are thefollowing: for athickness of 3 pm (Fig. 7.27(a)) Rnk.,= 99%, = +6", 8 = +7"; for a thickness Of 8 pm (Fig. 7.27(b)) Rnk,l = 97%, (T = 8', 8 = For shear acoustic wave generation in the GHz region, e.g., for anisotropic diffraction in LiNb03 crystals [25,26], the films must have either tilted = 30') or horizontal = 90') c-axis orientations. Furthermore, it is necessary that in the film plane, the axis should be oriented in the direction that will yield the most efficient A 0 interaction in the A 0 substrate. Figure 28 shows rocking curves for a ZnO film with a tilted axis (with sample and detector rotated in 7.28(a) and sample only rotated in 7.28(b)), while Figs. 29 and 30 show films witha horizontal axis (in each case showing both the sample and detector rotatod profile in (a) and the sample-only rotated profile in (b)). In thetilted c-axis profile, the axis tilt angle is between 25 and 40', while in the horizontal axis either the(11.0) and (10.0) planes (Fig. 7.29) or only the (10.0) plane (Fig. 7.30) are parallel to the film plane. The disorientation angle of the axis in the film plane can be experimentally measured with a piezoelectric tester using a piezoelectric response diagram with the tilted acoustic probe pulse generation. For the film with the (10.0) plane orientation, this angle is = 10".

3.2 Platelet TransducerFabrication Platelet transducers are fabricatedby first mechanically bonding a singlecrystal piezoelectric plate to the A 0 substrate and thenreducing the plate thickness to achieve the required transducer resonance frequency. While

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27 Rocking curves for a 3-wm (a) and a multilayer structure on an (001) TeO, crystal.

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the manufacturing process for platelet transducers is more complicated than that for theproduction of thin-film transducers, a platelet transducer can provide distinct performance advantages. The generally superior performance of the platelet transducer makes it the most commonly used transducer by the majority of commercial and custom device manufacturers. The material of choice for the piezoelectric platelet is lithium niobate (LiNbO,). The piezoelectric coupling coefficient of LiNbO, is large (approximately a factor of 2 larger than that of ZnO, both for longitudinal

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28 Rocking curves for a ZnO film with atilted c axis: (a) both the sample and the x-ray detector rotated and (b) sample only rotated.

and shear modes) (Table 3). LiNb03 also has the requisite physical properties (good mechanical strength, hardness, and stability) necessary to withstand the bonding and reduction process. The material is produced in large scale throughout the world and thus is relatively inexpensive and easy to obtain. The manufacturing process for a platelet transducer consists of the following steps: (1) manufacturing the piezoelectric platelet, (2) depositing

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the bottom electrode, (3) bonding the platelet to the A 0 substrate, (4) reducing the platelet to the required thickness, and (b) depositing the top electrode on the platelet surface. Manufacturing the piezoelectric platelet involves the same steps asthat for the A 0 substrate (as discussed in Section 1). A boule of LiNbO, is grown and oriented. Platelets of the material are then removed from the boule by sawing. The platelets are individually oriented with an accuracy greater than 30 arc minutes. Finally, the bonding surface of the platelet is polished. Two LiNbO, orientations exhibit large piezoelectric coupling, the yz plane orientation and the plane orientation. Figure 31(a) shows the piezoelectric coupling-of LiNbO, in the yz plane and Fig. 31(b) shows the coupling in the plane For longitudinal excitation, the 36" Y-cut orientation in the yz plane is preferred because no shear mode.coupling is present. In this direction the longitudinal mode piezoelectric coupling constant is 0.49. For shear mode excitation, either the 163" Y-cut orien-

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30 Rocking curves for a ZnO filmwithhorizontal c axis with (10.0) plane parallel to the film plane: (a) both the sample and the x-ray detector rotated and (b) sample only rotated.

tation in the yz plane or an X-cut orientation inthe xy plane is preferred. The X-cut orientation is usually usedto excite shear waves in A 0 deflector devices because (1) it has a higher shear mode coupling constant (0.48 versus (2) it excites a pure mode and there is n o coupling to the quasilongitudinal mode. There is, however, coupling to the orthogonal shear mode. In those cases where orthogonal shear mode coupling must be suppressed, the Y-cut orientation in the yz plane is used. The thickness of the platelet is usually minimized to limit the amount of material that must be removed during the reduction process. The platelet must be thick enough, however, to withstand the bonding process. Usually,

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31 LiNbO, piezocoupling vs. orientation angle: (a)

plane and (b) xy

plane [27].

a platelet thickness of 1 to 2 mm is used. shown in Fig. 32.

LiNb03 platelet transducer is

Transducer Platelet Bonding Bonding the piezoelectric platelet to the substrate is a critical part of the platelet transducer manufacturing process. The quality of the bond determines in large part theefficiency, frequency, and passband performance of the device. bonding layer with lowacoustic loss and an acoustic impedance closely matched to thatof the adjoining substrate is desired. If the loss is high or the acoustic impedance is poorly matched, the efficiency of the device will be poor and the bandwidth will be severely restricted unless the layer is made extremely thin. Propertiesof material used for bonding the bonding layer, as well as the electrode, are shown in Table 5.

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The commonly used methods for bonding the piezoelectric platelet to the substrate are[28,29] (1) adhesive bonding, (2) thermocompression bonding, cold vacuum compression bonding, and (4) optical contact bonding. Adhesive Bonding Adhesive bonding with organic compounds (e.g., epoxy, varnish, stopcock grease, silicon oil, phenyl compounds, etc.) is a relatively easy way to attach a transducer to an substrate. TeOz Bragg cell devices fabricated with transducers bonded with a thin epoxy layer (less than 1 pm thick) have demonstrated good performance at frequencies up to 160 MHz [29]. Epoxy-bonded transducers have also been reported to work as high as 250 to MHz The utility of this technique above this frequency is limited, however, due to the large acoustic impedance mismatch between the organic compound and the adjacent piezoelectric material and the A 0 substrate. The acoustic impedance of organic compounds is typically an order of magnitude smaller than both the bottom metallic electrode layer and the A 0 substrate (see Table 5). The bond thickness must be made “acoustically

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32 LINbO,platelettransducers:(right)sawed, (left) photoresistprotected for bonding. (Photo courtesy of Hams Corporation).

thin” in order that such a large mismatch will not substantially reduce the bandwidth of the transducer. Indeed, above 100 MHz the layer thickness cannot exceed several tenths of micrometers, or severe bandwidth reduction occurs Not only are such thin bonds difficult to fabricate (although 0.1-pm-thick epoxy bonds have been reported but thin bonds increase the requirements for substrate surface flatness and polishing quality. In addition, if high-frequency operation is required, this thin layer cannot provide the mechanical strength necessary for themechanical reduction of the LiNbO, platelet. Thermocompression Bonding Metal layers, with acoustic impedances more closelymatched to the adjoining materials than those of organic compounds, can be used to join the piezoelectric transducer to theA 0 substrate with thermocompression bonding Using the thermocompression bonding technique, metal surfaces can be bonded without the application of the destructively high temperatures necessary to melt the metals.

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In the thermocompression bonding process both the transducer bottom electrode and theA 0 substrate are coated with a metal layer. Gold, silver, aluminum, indium, and tin have been used (see Chapter 5). The metal surfaces are then brought together under the mutual application of heat and pressure. Typical bonding temperatures arebetween 250°C and 350"C, and pressures are lo8 Pa applied over a period of one-half hour or more. The resulting plastic deformation and diffusion occurring at the interface results in a rugged, uniform bond. Thermocompression bonding consists of twosteps:(1) metallic film deposition on the surfaces to be bonded and (2) application of pressure and temperature to achieve bonding. These two steps can be performed either in one vacuum chamber (without breaking vacuum) or in different vacuum chambers. When performed without breaking vacuum, the metallic surfaces are protectedagainst dust and oxidation, and the processing time is shortened. Itis difficult,however, to control thequality of the deposited films, and the device for mechanical positioning and applying pressure to the bonded materials must be very precise.In thesecond case, the surfaces to be bonded are easily aligned. The bonding surfaces, once exposed to air, however, quickly develop an oxidation layer, which mustbe eliminated through longer bonding time. Figure 33 shows a photograph of the equipment used for the thermal deposition of the bonding layers on thepiezoelectric platelet and the A 0 substrate prior tothermocompression bonding. Figure shows the inside of the thermocompression bonding apparatus. The thermocompression bonding technique uses high temperatures and, for thebest bond, should be performed without breaking vacuum after the bonding layer deposition. Because of the high temperatures, only those materials with almost identical thermalcoefficients linear expansion can be reliably bonded. For the material combinations shown in Figs. 12-18, only a LiNbO, platelet bonded to a LiNbOj(Fig. 12) or a TeO, (Fig. 15) substrate satisfies this condition. Thermocompression ultrasonic bonding [33]is a modification to the thermocompression bonding technique. In addition to heat and pressure, ultrasonic energy is also applied. This results in lower temperature and pressure requirements. Italso allows the bonding process to be performed in the ambient. Figure 35 shows a thermocompression ultrasonic bonding apparatus [33]. Longitudinal acoustic waves (typically 18 kHz with a power of 0.4 W) are excited by a transducerand transmitted via a horn waveguide to thebonding surface. ball joint provides the ability to align the waveguide directly to the bond surface. A glass pressure platethermally isolates thepiezoelectric layer from the waveguide. The substrateis clamped in a holder.A heating

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33 Vacuum equipment for metal evaporation. (Photo courtesy of St. Petersburg State Academy of Aerospace Instrumentation.)

coil around the holder provides heat for the bonding process. Instead of requiring 400°C and lo8 Pa (as is the case for thermocompression bonding) bonds using gold, indium, and silver have been made at lower temperatures and an order of magnitude lower pressures Pa). Another advantage of this method is that the application the ultrasonic energy breaks down the oxidization layer on thebonding surface. Thus a high-quality bond can be achieved by using different machines for the bond layer deposition and the bonding. A LiNbO, platelet thermocompression ultrasonic bonded to a quartz crystal using a Ni-Cr/Au bonding layer 0.15 p,m thick was reduced to a thickness of 2.5 p,m corresponding to a device center frequency of 1.5 GHz Despite the reduction in temperature, materials with dissimilar coefficients linear expansion still may fracture as the transducer is cooled back to room temperature. ColdVacuumCompressionBonding Cold vacuum compression bonding at room temperature eliminates the stresses induced in either of the pre-

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34 Thermocompressionbondingapparatus. (Photo courtesy of St. Petersburg State Academy of Aerospace Instrumentation.)

viously described thermocompression bonding techniques [35]. It is the bonding technique of choice for many A 0 device manufacturers. In this process, both the platelet transducer andthe A 0 substrate are coated with the metallic bonding layer and immediately brought into contact under a high veryhighvacuum (at least to 10” Pa). Theshorttimeand vacuum prevent the formation of an oxidation layer which will cause unreliable bonding. A pressure of lo9 Pa isapplied to thetransducer assembly to achieve the bond. A photograph of a cold vacuum compression bonding apparatus is shown in Fig. 36. Indium [36], silver, tin, and gold have been used as bond layers in cold vacuum compression bonding. A LiNbO, platelet cold vacuum compression bonded to a spinel crystal using a gold bonding layer 0.3 pm thick was reduced to a thickness of 0.24 pm corresponding to a device center frequency of 10 GHz [37]. The device in theright-hand side of Fig. 7 shows a GaP cell with a cold-vacuum compression-bonded LiNbO,platelet transducer.

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35 Thermocompression ultrasonic bonding apparatus schematic

Optical Contact Bonding Optical contact bonding eliminates the necessity for the bonding material Optical contact bonding occurs between two highly polished surfaces when the gap between them is less than tens of Angstroms. Cohesive forces appearing between the surfaces result in a bond which can be as strong as that of the substrate material itself. The strength of the cohesive force between the flat surfaces of two materials is a function of the dielectric constant of the materials and the distance between the two surfaces The A 0 device transducer structure must contain a metallic electrode layer between the optically polished piezoelectric transducer platelet and the substrate. In orderto make.an adequateoptical contact bond, the electrode metallic layer between the piezoelectric transducer and the A 0 substrate must satisfy two requirements: (1) the layer thickness must be limited, and (2) the electrical resistivity and acoustic attenuation of the electrode layer must be low. One of the conventional materials for this

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Figure 36 Cold vacuum compression bonding apparatus. (Photo courtesy of Harris Corporation.)

layer is Au. A Cu electrode layer with a Cr adhesive sublayer can also be used. A disadvantage of an electrode made of Cu, however, is its low corrosion stability. It is possible to increase this stability if Cr is used not only as the adhesion sublayer, but as a protective layer deposited over the Cu layer. The thickness of the adhesive Cr sublayer is 10 to 15 nm, and the thickness of electrical conductive Cu layer is 25 to 30 nm. Electrical resistivities for the sublayer and the layer are 0.7 X ohm-cm and 0.7 x ohm-cm, respectively. The thickness of the protective layer is approximately equal to 15 nm. The process for optically contact bonding-the piezoelectric transducer platelet to the surface of the A 0 substrate has the following steps: (1) deposition of the metallic electrode layer on the A 0 substrate, (2) contacting the platelet to the substrate using water, and (3) removing the water from the bond region.

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The piezoelectric transducer is first placed on the water-moistened surface of the A 0 substrate. When the piezoelectric transducer platelet is positioned at the right place on the A 0 substrate surface, the platelet is lightly clamped to the substrate. An optical probe should show that the interference fringes in the contact layer have disappeared. If the surfaces are well cleaned, the contact process is easy and fast. Next a pressure of approximately lo6 Pa is applied to the assembled piezoelectric transducer in order to remove water from the contact region. Optical contact technology considerably simplifies the manufacturing process for A 0 devices and has two advantages over the metallic compression bonding techniques: (1) piezoelectric bonding is made without vacuum, and it becomes possible to position the plate on the A 0 substrate more accurately, (2) no loss or passband distortion occurs due to the bonding layer. Optical contact technology can be realized on widely used A 0 substrates such as fused and crystal quartz, Ge, TeO,, PbMoO, [41]. Transducer Platelet Reduction The thickness of the transducer platelet is reduced to the thickness that will produce the desired device center frequency. This thickness is nominally the thickness of the resonance frequency, but its exact dimension is modified by the surrounding materials (see Chapter 6). Figure 37 shows roughly the thickness of a LiNbO, platelet transducer for a given device operating frequency for both longitudinal and shear acoustic modes. Two techniques are commonly used for platelet reduction: mechanical lapping and ion milling [7]. Mechanical lapping involves the removal of the platelet material using abrasive compounds. The procedure is usually performed by hand, one device at a time. Platelet transducers as thin as 0.4 pm are routinely produced using this method. Ion milling involves the removal of material by sputtering. This procedure is performed in lieu of mechanical lapping when transducer thicknesses below 1 pm are required. Ion-milled transducers 0.25 pm thick have been achieved. Prior to reduction the bond region of the transducer is protected with optical paint to prevent it from being damaged. Mechanical Reduction The thickness of the piezoelectric platelet can be gradually reduced through a process of mechanical lapping with coarse abrasive grit and then finish polishing with fine polishing grit. The mechanical lapping jig is essentially the same apparatus as that used for optical window polishing (Fig. 8). The A 0 substrate is blocked on all sides with pieces of the same material as that of the platelet transducer. The entire assembly is lapped by hand using a slurry of water and carborundum or diamond grit. A schedule of a typical reduction of LiNbO, is

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Unloaded Transducer Resonant Frequency (MHz)

Figure 37 LiNbO, thickness vs. nominal resonance frequency.

Table 6 LiNbO, Mechanical Reduction Schedule Grit sue (pm)

Coarse 25 9 5 1 0.5 0.2

Reduction time

Reduction (pm)

30 min 30 min 30 min 30 min 1 hr 1 hr 4 hr

2 mm-600 600-300 300-100 100-10 10-4 4- 1 1-0.5

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shown in Table 6 [42]. Starting with a coarse grit, a 2-mm-thick Lm03 platelet can be reduced to about 10 pm using successively smaller grit sizes in,about 2 hr. The platelet can be reduced to a final thickness of 0.4 pm with careful polishing over another 6-hr period. Chemical polishing can be used after mechanical lapping to remove the abrasion groves in the platelet surface. High-frequency devices finished with a chemical polish are reported to have lower insertion loss than those without the chemical polish [42]. A GaP deflector with a LiNbO, transducer mechanically reduced to 1 pm thickness is shown in Fig. 38. Ion Milling While high-frequency platelet transducers can be finish-lapped by mechanical polishing techniques for operation at frequenciesover 1GHz, this approach is difficult to reproduce in a reliable manner and it requires skilled opticians. Ion milling is an excellent microthinning technique for frequen-

Figure 38 GaP cell with LiNbO, platelet transducer reduced to 1 Fm. (Photo courtesy of Harris Corporation.)

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cies above 1 GHz. Ion milling was originally used for thinning transducers for bulk acoustic delay lines. Delay lines with frequency operation as high as 11.5 GHz have been achieved [36]. Rosenbaum et al. have reported A 0 deflectors with LiNbO, ion-milled transducers that operate at 1 GHz [43]. Shear LiNbO, A 0 deflectors using ion-milled LiNbO, transducers with thicknesses of 0.3 pm operating at 3.5 GHz have been demonstrated at Westinghouse STC [44]. In the ion-milling process, atoms are removed from the target surface by bombardment with energetic ions. Atoms are ejected, or sputtered, from the substrate as a result of momentum transferred to them by the impact of the beam ions on the substrate. This is significantly different from plasma etching where chemical reactions dominate rather than physical ion bombardment process. The average number of atoms ejected per incident ion is referred to as the sputtering yield. For incident ions in the 400 to 1000 eV energy range, sputtering yields are on the order of 0.1 to 10 atoms per incident ion. In general, the yield is affected by the target material through the binding energy between atoms, which is of the order of 1 to 10 eV, depending on the material. The typical ion-milling beam energy is a few thousand electrovolts range because at higher energies the yield is reduced (the ions penetrate deeper into the substrate giving less energy to the surface atoms). The impact angle is important since for ions incident at more oblique angles to the substrate, more energy is transferred to the atoms near the surface, and this permits more atoms to escape from the surface. The ion-milling process has some important inherent features which include (1) no significant lower limit on the feature size that can be etched, (2) good control of the slope of the etched features, (3) any material can be ion-milled, and (4) excellent repeatability form run to run and uniformity within a run. Ion milling can reduce the platelet thickness at a rate of tens to hundreds of Angstroms per minute, so that total minute times are in the range of a few hours, depending on the starting thickness and the beam power used. Depending on the beam power, significant heating of the substrate may occur since it absorbs energy from the ion beam; thus intermittent operation may be required for system cooldown to avoid thermal damage to the substrates. This cooling causes no serious deterioration even at submicrometer thicknesses [43,44]. In general, ion milling is nonreactive, and it is carried out in argon atmosphere around 1.3 x Pa. It is important to carefully monitor the etch depth as the finish thickness is approached. Optical techniques, as well as control methods peculiar to the ion-milling process, can be used for precise thickness control. Figure 39 shows a typical ion-milling system made by Veeco Instruments Inc. which can operate on substrates as wide as 3 in. Prior to ion milling,

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39 Photograph of a3-inion-millingsystemmadeby Veeco Instruments Inc. The vacuum system is shown at the left whereas the control electronics for the ion milling are shown at right. (Courtesy of Westinghouse Electric Corporation.)

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the transducer is mechanically thinned to a few micrometers. The transducer/AO crystal structure is then mounted in a target fixture assembly (Fig. left). Before inserting the target fixture into ion-milling the system, a glass plate with an appropriate aperture is set on top of the transducer (Fig. center). The plate shields the remaining transducer structure from unwanted ion milling, whereas the aperture allows thinning only at a specific location on the transducer surface (the shape and area of the thinned part of the surface is determined by the shape and area of the aperture). Figure shows an example of a finished,ion-milled well with dimensions x 2.0 mmz in a LiNbO, transducer (the area and shape the well are similar to that of the shielding plate shown in the center of Fig. A deposited Au top electrode within the well is also visible. The waves around the well are characteristic the ion-milling process and are due to edge milling occumng fromoff-axis ions. The uniformity of the milling process is demonstrated in Fig. which shows the interference fringes obtained with an ion-milled LiNbO, transducer 0.3 Fm thick. The small number of wide fringes showsthat excellent uniformity has beenachieved;

Photograph of the fixturing for holding the A 0 device (left), etching mask (center) and actual A 0 device (right). (Courtesy Westinghouse Electric Corporation.)

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41 Photograph of mounted device in the fixture of Fig. 2, showing the finished ion-milled well in the transducer, with deposited top electrode. The dimensions of the ion-milled well are 1.5 X 2.0 mm2. (Courtesy of Westinghouse Electric Corporation.)

over an area of 100 X 100 pm2 the uniformity waswithin 10% of the transducer thickness or f15 nm. It has been reported that devices with transducers ion-milled to pm exhibited similar performance to those mechanically lapped to these dimensions The primary advantage of this approach (asidefrom not requiring askilled optician) is the ability to remove and test thedevice periodically during reduction-a procedure not possible with the parallel alignment tolerance requirement in the mechanical reduction process.

3.3 Top Electrode Definition The piezoelectric transducer substratemanufacturing process ends with the deposition anddefinition of a metallic electrode on topof the piezoelectric substrate surface. The top electrode not only provides the means to drive the transducer,but it alsodefines the height and width of the sound column, an integral part of an optimum A 0 design.

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42 Photograph of an ion-milled LiNbO, transducer with a thickness of 0.3 Fm. The small number of wide fringes shows the excellent uniformity of the pmz) was within 10% of the transthinned transducer which (over an area of

ducer thickness. (Courtesyof Westinghouse Electric Corporation.) The top electrode material is chosen to be both thick enough to provide a stable substrate for the attachment of the bond wire yet thin enough that excessive transducer loading and passband distortion are avoided. The specific material and thickness are optimized through a transducer impedance-matching analysis as discussed in Chapter 5 . Common top electrode materials include copper, aluminum, and gold. Typically the top electrode is fabricated using a single material a few tenths of a micrometer thick. Usually, a “lift-off’ photolithographic technique is used to define the electrode. photolithographic resist is applied to thepiezoelectric substrate surface and exposed witha mask the desired electrode shape. The exposed resist is then removedfrom the surface leaving an opening in the resist. The top electrode metal materialis then deposited on the resist. Removing the resist leaves the top electrode metallization in the desired shape. This process avoids the use of chemical

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metal etches which can damage the bonding layer. A GaP deflector with a top electrode is shown in Fig. If the thin-film transducer process is used, the top electrode can be deposited in the same vacuum cycle as the piezoelectric layer. Figure 44 shows a sputtering system with two magnetrons which can deposit both the metal electrode andthe piezoelectric layer. A high-quality A1 electrode can be formedfrom a target made of an Al-Cu-Si alloy. The copperreduces the surface roughness and the silicon improves the aluminum adhesion. Optimum deposition occurs when the substrate has a temperature of 160 to 200°C. The A1 forms in the [loo] orientation with the texture axis perpendicular to the substrate. The mean crystallite size is 0.5 pm. A typical electrode is 0.3 to 0.5 pm thick. Typical growth rates are 2 ndsec.

43 GaP deflector with top electrode defined. (Photo courtesy of Harris Corporation.)

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44 Dual magnetronsputteringapparatus. (Photo courtesy tersburg State Academy Aerospace Instrumentation.)

St. Pe-

4 FINAL DEVICE ASSEMBLY Once the fabrication of the transducer on the optica€block is completed, the device is ready for final assembly. An impedance-matching circuit is designed to match the impedance of the A 0 device to the electronic driver. The A 0 device and the impedance-matching circuit are then mounted in the A 0 device housing. An RF connector on the housing is electrically connected to the input side of the impedance-matching circuit while wires from the output side are bonded to the top electrode of the A 0 device. Finally, anacoustic absorber is attached tothe endof the device to frustrate acoustic reflections in the device. 4.1 Impedance-MatchingCircuit Once the fabrication of the transducer is complete,the RF impedance of the device ismeasured with a network analyzer.An impedance-matching network is then designed to match the impedance of the device to that of the external sourcedriver(typically 50 Cl). Thisnetworktypicallyconsists of discrete capacitors and inductors arranged in a pi-shaped circuit on a circuit board.

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Microstrip transmission lineelements also be used to simulate capacitors and inductors [&l. microstrip transmission line impedance-matching network is shown in Fig. The network consist of a series a high-impedance line shunted to groundandaserieslow-impedanceline. The networkis approximately equivalent to a series inductor, a shunt inductor, and a shunt capacitor. The input to the circuit is attached to an F W connector (typically SMA) on the device housing, while the output to the circuit is attached to the device transducer.

The device is attached to the impedance-matching circuit via wire bonding. The choice of the bond wire material andthe bonding mechanism is usually governed by the composition of the transducer top electrode

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material. It is desirable to bond like materials together. Thus, if gold is used as the top electrode material, gold wire is used for the wire bond, and similarly for aluminum top electrode and aluminum wire. (When dissimilar metals are bonded,e.g., aluminum and gold, an intermetalliccompound can which can cause the wire bond to degrade and fail Gold wire is typically thermocompression bonded to the top electrode while aluminum wire is ultrasonically bonded at room temperature. Figure shows a photograph of a wire-bonding machine.

An acoustic absorber is usually attached to the back surface of the device to frustrate internal acoustic reflections. A metal or epoxy material with an impedance matched to the A 0 substrate is used. further reduce unwanted A 0 interaction, abevel can also be cut in the back surface prior to the attachment of the impedance-matching circuit.

46 Wire-bonding machine. (Photo courtesy

Harris Corporation.)

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Assembled acousto-optic cavity dumper device. (Photo courtesy of Hams Corporation.)

The A 0 device, with the impedance-matching network and acoustic absorbed, is mountedin a rectangular housing. The housing has openings on the side for optical illumination and mounting holes on the bottom for attaching opticalmounting hardware. Thehousing mayalso have additional features, such as cooling, for specific device requirements. finished cavity dumper device with cooling tubes in the housing is shown in Fig. A finished multichannel A 0 deflector is shown in Fig. 48.

The authors would like to thank V. Kulakov for the English translation of the work of Professor N. G. Nefedov, which was written originally in Russian. The authors also thank P. Fadeev of the St. Petersburg State Academy of Aerospace Instrumentation for his contribution to the dis-

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48 Assembled multichannel device. (Photo courtesy of St. Petersburg State Academy Aerospace Instrumentation.) cussion on platelet transducers and A. Goutzoulis and M. Gottlieb of Westinghouse Science and Technology Center forcontributing the section on transducer thinning via ion-milling techniques. D. R. Pape wishes to acknowledge stimulating conversations with B. Beaudet and E. Bryant of the Harris Corporation and M. Shah of MVM Electronics concerning the fabrication of A 0 devices. The photographs from the St. Petersburg State Academy of Aerospace Instrumentation were taken by N. M. Jakovleva, and the photographs from the Harris Corporation were taken by Ron Carman and furnished by John Watkins and Ed Bryant.

1. Castelli, L., Lithium niobate applications in optics and acousto-optics, Laser FocuslElectro-Optics, December 1985, pp. 120-123. 2. Bond, W. L., Crystal Technology, Wiley, New York, 1976. 3. Efremov, A . A . , and Salnikov, Ju.V., Manufacturing and Testing of Optical Workpieces, Vyshaja Shkola, Moscow, USSR, 1983. (Russian) Hecht, E., Optics, Addison-Wesley, Reading, MA, 1987, Chap.

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5. Krylova, T. N., Interference Coatings: Optical Properties and Study Methods, Mashinostroenie, Leningrad, USSR, 1973. (Russian) 6. Reeder, T. M., and Winslow, D. K., Characteristics of microwave acoustic transducers for volume wave excitation, ZEEE Trans. Microwave Theory Tech., MTT-17, 927-941 (1969). 7. Foster, N. F., Piezoelectric and piezoresistive properties of films, in Handbook of Thin Film Technology (L. Maisse and R. Glang, eds.), McGrawHill, New York, 1970, Chap. 15. 8. Chji, R., Yamozaki, O . , Wasa, K., et al., New sputtering system for manufacturing ZnO thin film SAW devices, J. Vac. Sci. Tech., 15, 1601-1604 (1978). 9. Foster, N. F., Crystallographic orientation of zinc oxide films deposited by triode sputtering, J . Vac. Sci. Tech., 6 , 111-114 (1969). 10. Mochalov, B. F., Streltsova, N. N., and Shermergor, T. D., Deposition of ZnO piezoelectric films by ion-plasma sputtering methods, Electron. Tekh., Ser. 6, No. IZ (Z36), 126-128 (1979). (Russian) 11. Danilin, B. S., Mochalov, B. F., Streltsova, N. N., et al., Zinc oxide piezoelectric film deposition in a magnetron ion sputtering system, Elektron. Tekh., Ser. 3, No. 3(87), 62-65 (1980). (Russian) 12. Waits, R.K., Planar magnetron sputtering, in Thin Film Processes, Academic Press, New York, 1978, Chap. 11-4. 13. Kenigsberg, N. L., Piezoelectric coefficients of patterned zinc oxide films, Acustich. Zh., 35, 368-370 (1989). (Russian) 14. Foster, N. F., The deposition and measurementof zinc imideshear mode and other thin film transducers, J . Vac. Sci. Tech., 6 , 111 (1969). 15. Shermergor, T. D.,and Streltsova, N. N., Film Piezoelectrics, Radio i Sviaz, Moscow, USSR, 1986. (Russian) 16. Foster, N. F., The deposition and piezoelectric characteristics of sputtered lithium niobate films, Appl. Phys. Lett., 40,420-421 (1969). 17. Tominaga, K., Iwamura, S., Fujita, I., et al., Influence of bombardment by energetic atoms on c-axis orientation of ZnO films, Jap. J. Appl. Phys., 21, 999-1002 (1982). 18. Kotelianskiy, I. B., and Luzanov, V. A., Crystallization of patterned zinc oxide filmsunder the conditions of bombardment by high-power oxygenparticles, Fiz. Khim. Obrabotka Mater., No. 4, 14-19 (1989). (Russian) 19. Grankin, I. M., Kalnaja, G.I., and Prishepa, N. N., High oriented zinc oxide films, Zzv. AN SSSR, Neorgan. Mater. 132,820-823 (1982). (Russian) 20. Bukharev, V. I., Mochalov, B. F., Streltsova, N. N., et al., Experimental study of pattern properties of zinc oxide films deposited with a magnetron method, Elektron. Tekh., Ser. 10, No. 5(29), 35-38 (1982). (Russian) 21. Nefedov, V. G., Gusev, 0.B., Mikhailov, V. N., et al., Technological process of piezoelectric transducer manufacturing based on zinc oxide films,Inform. Add., No. 90-91, Leningrad, TsOONTZ-ONZ NZZVSh, (1990). (Russian) B., Nefedov, V. G., Mikhailov, V. N., et al., Investivation on 22. Gusev, possibility to manufacture acousto-optic modulators with zinc oxide piezo-

NEFEDOV A N D PAPE

23.

24. 25. 26.

27. 28. 29. 30. 31.

32.

33. 34.

35.

36.

37.

electric transducers for the metric and decimetric ranges, Abstracts of Reports of All-Union Conference on Optical Information Processing, LIAP , Leningrad, USSR, 1988. (Russian) Nefedov, V. G., Gusev, 0. B . , Mikhailov, V. N., Gabaraiev, 0. G., et al., Zinc oxide films for acousto-optic and acoustoelectronic devices, Abstracts of Reports of XV All-Union Conference Acoustoelectronics and Physical Acoustics, LIAP, Leningrad, Part 3, USSR, 1991. (Russian) Kirgtn, E. K., and Yaeger, D. R., Today’s capabilities of microwave (0.218 GHz) acousto-optic devices, Proc. SPZE, 90 (1976). Soos, J. I., Rosemeier, R. Q. ,McFerrin, T. P. , and Sheerer, R. L. , 2.5 GHz bandwidth shear Bragg cells, Proc. SPZE, 936 (1988). Demidov, A. Ja., Zadorin, A. S . , and Pugovkin, A. V., Wideband abnormal light diffraction by hypersound in a LiNbO, crystal, in Acousto-optic Methods and Information Processing Technology, LETI, Leningrad, Vol. 142, USSR, 1980. (Russian) Rosenbaum, J. F. , Bulk Acoustic Wave Theory and Devices, Artech House, Boston, 1988, Chap. 4. Morozov, A. I., Proklov, V. V., and Stankovsky, B. F., Piezoelectric Transducers for Radioelectronic Devices, Radio i Sviaz, Moscow, USSR, 1981. (Russian) Uchida, N., and Niizeki, N., Acoustooptic deflection materials and techniques, Proc. ZEEE, 61, 1073-1092 (1973). Chang, I. C., Acoustoptic devices and applications, ZEEE Trans. Sonics U1trasonics, SU-23, 2-21 (1976). Sittig, E. , Effects of bonding and electrode layers on the transmission parameters of piezoelectric transducers used in ultrasonic digital delay lines, IEEE Trans. Sonics Ultrasonics, SU-16, 2-10 (1969). Konig, W. F., Lambert, L. B. , and Schilling, D. L., The bandwidth, insertion loss, and reflection coefficient of ultrasonic delay lines for backing materials and finite thickness bonds, IRE Znt. Conv. Rec., Pt 6, 9 , 285-295 (1961). Larson, J. D. , and Winslow , D. K. , Ultrasonically welded piezoelectric transducer, ZEEE Trans. Sonics Ultrasonics, SU-18, 142-152 (1971). Uchida, N., Fukunish, S., and Saito, S., Performance of single-crystal LiNbO, transducers operating above 1 GHz, ZEEE Trans. Sonics Ultrasonics, SU-20, 285-287 (1973). Sittig, E. K . , and Cook, H. D. ,A method for preparing and bonding ultrasonic transducers used in high frequency digital delay lines, Proc. ZEEE, 56, 13751376 (1968). Warner, A. W . , and Meitzler, A. H., Performance of bonded, single-crystal LiNbO, and LiGaO, as ultrasonic transducers operating above 100 MHz, Proc. ZEEE, 56, 1376-1377 (1968). Huang, H. G., Knox, J. D., Turski, Z., Wargo, R., and Hanak, J. J., Fabrication of submicron LiNbO, transducers for microwave acoustic (bulk) delay lines, Appl. Phys. Lett., 24, 109-111 (1974).

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38. Eschler, H. , Oberbacher, R. , Weidinger, F. , and Zeitler, K.-H. , Sirnens Forsch und Entwickl., 4 , 180 (1975). 39. Torgashin, A. N., and Gabaraiev, 0. G., Optical contact technology and its use in acousto-optics, Acousto-Optic Devices and Their Applications, RIO SOGU, Ordzhonikidze, USSR, 1989, pp. 56-62. (Russian) 40. Lifshitz, M. E., Theory of molecular adhesion forces between condensed matters, D A N USSR, 97, 643-646 (1957). (Russian) 41. Tavaciev, A. F., Talalaev, M. A., Torgashin, A. N., et al., Use of optical contact in acousto-optic device manufacturing technology, Abstracts of Reports of XI11 All-Union Conference on Acoustoelectronics and Quantum Acoustics, Kiev, Part 11, USSR, 1986, pp. 338-339. (Russian) 42. Private conversation with Ed Bryant, Harris Corporation, Melbourne, FL, December 1992. 43. Rosenbaum, J. ,Price, M. ,Bonney, R. ,and Zehl, 0.,Fabrication of wideband Bragg cells using thermocompression bonding and ion beam milling, IEEE Trans. Sonics Ultrasonics, SU-32 , 49-55 (1985). 44. Private communication with M. Gottlieb and A. Goutzoulis, Westinghouse STC, Pittsburgh, PA, September 1992. 45. Bagshaw, J. M., and Willats, T. F., Anisotropic Bragg cells, GEC J . Res., 2, 96-103 (1984). 46. Young, E. H., and Yao, S-K., Design considerations for acousto-optic devices, Proc. IEEE, 69, 54-64 (1981). 47. Glaser, A. , and Subak-Sharpe, G. E. , Integrated Circuit Engineering, AddisonWesley, Reading, MA, 1979, Chap. 16.

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Testing of Acousto-Optic Devices Akis P. Goutzoulis and Milton S. Gottlieb Westinghouse Science and Technology Center Pittsburgh, Pennsylvania

Dennis R. Pape Photonic Systems Incorporated Melbourne, Florida

1 INTRODUCTION The testing of acousto-optic (AO) devices is the step that follows the device fabrication and its main purpose is to determine the degree to which the design goals have been achieved. The detailed testing of experimental A 0 devices, which are based on new designs or fabrication techniques, is often of crucial importance because it may reveal performance issues and/or effects not previously estimated or even known. Similarly, testing is important for characterizing new A 0 materials and estimating their performance when used in conjunction with specific device designs and applications. In this chapter we describe in detail a variety of different tests that can be performed on the four basic A 0 devices: single-channel deflectors (Section 2) , multichannel deflectors (Section 3) , modulators (Section 4) , and tunable filters (AOTF) (Section 5 ) . Since all A 0 devices involve electric, acoustic, and optical parameters, the tests must cover all three domains to the degree necessary for each device type and the application. In general, the tests and test procedures depend mainly on the A 0 device type, although several tests are common among all devices. These common tests involve (1) the acoustic pulse echo which shows the transducer bond quality, (2) the Schlieren imaging which shows the quality and characteristics of the propagating acoustic field, (3) the electric impedance, reflection 403

loss, and voltage standing-wave ratio (VSWR), which determine the electrical performance of the device, (4) the optical scattering which determines the quality of the crystal used, and (5) the acoustic attenuation of the crystal. Tests specific to deflector devices include (1) the overall frequency response or bandwidth which is determined by the acoustic, electric, and A 0 interaction responses, (2) the diffraction efficiency which determines the amount of light diffracted on a specific order, (3) the third-order intermodulation products which determine the level of spurious, unwanted intermodulation signals, (4) the single- or two-tone dynamic range, and (5) the time bandwidth product which relates to the number of resolvable elements and is of crucial importance for high-resolution spectrum analyzers and correlators. Multichannel deflectors require, in addition to the above tests, several tests that are concernedwith the (1) performance uniformity from channel-to-channel, (2) channel-to channel isolation which includes electric and acoustic crosstalk and affects the device dynamic range, and channel-to-channel phase and time uniformity of the input signal. The tests peculiar to themodulars include the (1) determination of the rise time, which is vital for digital applications, (2) modulation bandwidth, which is important for analog modulation applications, (3) modulation transfer function, which is critical for applications with stringent linearity requirements, and (4) modulation contrast ratio. AOTFs also require their own characteristic tests, which include the (1) determination of the tuning relation, (2) optical bandwidth, (3) spectral resolution, which is a key parameter for spectroscopic applications, (4) out-of-band transmission, which can seriously degrade the overall resolution, (5) RF power dependence of transmission, polarization rejection ratio, which is very important for overlapping diffracted and undiffracted orders, (7) spectral dependence of the spatial separation of the various orders, (8) angular aperture or field of view, and (9) spatial resolution of spectral images, which is important for spectral imaging applications. In the following sections we describe all the above tests with enough detail to allow the reader to successfully test any device. However, we emphasizethat each custom device design may require refinements of these test procedures.

2

DEFLECTOR TESTING

The full and precise characterization of an deflector requires several tests, which include acoustic echo measurements, Schlieren imaging, electric impedance, frequency response, scattering measurements, third-order intermodulation products, dynamic range, time-bandwidth product, and

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acoustic attenuation. The purpose, setup, and procedure for performing these tests are discussed in this section.

AcousticEcho Measurements One of the most critical steps in fabricating an A 0 device is the bonding of the transducer to the A 0 crystal. Following bonding, there are many steps in the fabrication procedure before the transducer structure is completed. Therefore, it is critical to assure before proceeding with these later steps that thebond is good, to thedegree that it can be tested atthis point. Since the transducer is, in general, not polished to its final thickness on bonding, the test cannot ensure that the mechanical bond, as determined by the bond layer thicknesses and composition, is correct according to the design. The test can, however, at least indicate that a continuous mechanical bond, with good contact .between the transducer and the crystal has been made. This is a quick, routine type of test, which issuitable forquality control when producing large numbers of similar devices. The basis of the procedure is to examine the acoustic pulse echo pattern produced by a small, movable electrode. A schematic of the measurement setupis shown in Fig. 1. The metallic bond layer forms the ground electrode, while the top surface of the transducer will normally have no conducting layer on it.*A movable top probe electrode can be easily made from a polished metal disc, about 5 mm or smaller in diameter, which is held gently in

1 Schematic of test setup forexaminingtransducerbondqualitywith movable electrode.

WVlZOULIS, W I I Z I E B , AND PAPE

(a>

2 Oscilloscope display of test patternsfrom (a)good bond, showing undistorted input pulse and return echo pulses, (b) poor bond, showing distortion of input pulse due to reflection of acoustic energy within transducer, and (c) undistorted input pulse for b. contact on the selected area of the transducer. pulse width small in comparison to thetravel time across the crystal is set, usually on the order of a few microseconds. With the probe held in contact with the transducer, the frequency is tuned until return echos are observed on theoscilloscope. If the transducer has not yet been thinned, this will be at some low frequency, around 5 MHz for typical bonding thicknesses. The pattern seen from a good bond is shown in the oscilloscopetrace in Fig. 2(a); the input pulse is undistorted and the echo pulses are reasonably clean replicas of the input pulse. The test involves probing the entire transducer area to ensure that the bond is uniform. An example of the test results obtained from a poor bond is shown in the oscilloscope trace in Fig. 2(b), whereas for comparison purposes we show in Fig. 2(c) the input pulse obtained when the probe is not in contact with the transducer. It can be seen that the pulse of Fig. 2(b) is distorted due to high reflection of acoustic energy within the transducer plate. In the region of a poor mechanical bond, the acoustic energy cannot be transmitted to the crystal. This diagnostic test easily shows suchpoor transmission, and the probeserves to pick up even a small such region if the transducer area is well sampled.

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WUZOUL,IS, W m E B , AND PAPE

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2.2 Schlieren Imaging High-performance A 0 processors require A 0 deflectors with uniform, well-collimated acoustic beams (in the plane perpendicular to the plane of the A 0 interaction) without acoustic reflections from the sides of the A 0 crystal and without beam walkoff. These requirements are even more important in multichannel devices where the lack of highly collimated acoustic beams may result in severe crosstalk which limits the dynamic range and thus the usefulness of the device. In general, a uniform and well-collimated acoustic beam is achieved byusing a carefully oriented A 0 crystal in conjunction with (1) apodized transducer electrodes [l],or (2) acoustic collimating modes in materials such as GaP or (3) cylindrical transducers that focus the acoustic beam Regardless of the collimating technique(s) used, however, it is always necessary to examine the quality of the resulting acoustic pattern. This can be achieved via the use of the knife-edge method used by Toepler to examine Variations in the index of refraction of a medium, and which is known as schlieren imaging The schlieren imaging allows the observation of the phase variations generated in the A 0 crystal along the sound path, and it can be explained with the aid of Fig. 3. Collimated light from a laser illuminates the crystal which isdriven by a single RF tone. The acoustic grating(s) induced by the propagating acoustic beam(s) results in variations in the index of refraction, which causes variations in optical path through the deflector. These optical path variations result in emergent optical wavefronts that aredistorted. Lens L, focuses the undistorted (zero order) and distorted (diffracted orders) wave forms. At the focal plane a slit is used to pass only the first diffracted order, which is subsequently imaged onto a photographic film. Any shadow formed on the film reveals an angular displacement the optical beam, and thus it indicates the rate

DEFLECTOR

ORDER

3 Schematic of schlieren imaging system for observing the 2-D acoustic protile of

deflectors.

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409

and location of the change of refractive index across the input optical plane of the deflector; i.e., itprovides a mapping of the propagating 2-D sound beam. Figure 4 shows the photograph of an experimental schlieren imaging system as well as the schlieren image itselfat the far right of the photograph. The device under test is a S[110] TeO, deflector which uses a diamondshaped apodized top electrodedesigned to produce awell-collimatedacoustic beam. Figure 5a shows the schlieren image obtained from a similar device which uses nonapodized, rectangular-shaped top electrodes. Itcan be seen that the resulting sound profile is nonuniform, and it contains at least six acoustic sidelobes on each side of the main lobe, as well asacoustic reflections from both sides of the crystal. In Fig. 5b weshow the schlieren image from an L[lOO] A 0 deflector in which the selfcollimating acoustic mode results in a highly collimated, uniform acoustic profile free.from side lobes or acoustic reflections. Schlieren imaging is also useful for testing the orientation in materials with high elastic anisotropy such as TeO,, Hg,Cl,, and Hg,Br,. In these

Figure 4 Photograph of an experimental schlieren imaging system used with a S[ TeO, deflector with apodized, diamond-shaped top electrodes. (Courtesy of Westinghouse Electric Corp.)

410

WUi"ZOUL.IS, W1TLIEB, AND PAPE

5 (a) Example of a nonuniform, noncollimated 2-D sound profile from a TeOz deflector with nonapodized, squared top electrodes. (b) Example of a uniform, well-collimated 2-D sound profile from a L[lOO] TI,AsS, deflector in which the specificacoustic propagation direction used resultsin self-collimation of the acoustic beam.

TESTING OF ACOUSTO-OPTIC DEVICES

41 l

(b)

6 (a) Example of the electrical impedance of a GHz L[lOO] LiNbO, deflector matched to 50 R. (b) Example of the return for the deflector of Fig. 5(b), covering the GHz range. (c) Example of the VSWR the deflector of Fig. 5(b).

materials the elastic anisotropy leads to a significant difference in direction between the group and phase velocities. This may result in significant acoustic walkoff, which limits the maximum usable aperture of the deflector. For example, for shear waves propagatingin the [l101plane of Hg2Br2 a misorientation is multiplied by a factor of 20, so for propagation in long-

412

1

WUIZOVLIS, WTi'LIEB, ANDPAPE

m /

GHr M2

Figure

Continued.

delay devices the transducer face must be oriented to 0.1" or better.Since typically a good x-ray from an etched surface can provide an orientation to an accuracy of O S " , a potential for beamwalkoff as much as 10" exists if only x-ray orientation is used. Schlieren imaging can be used to overcome this orientation problem in conjunction with a temporary, low-frequency transducer mounted on a ground test face of the crystal. From the measured schlieren imaging walkoff angle, a correction is calculated for the surface and the face is reground. second schlieren test follows the regrinding to verify the calculation and the followed correction.

2.3 ElectricalImpedanceTesting The electrical impedance and the return loss of an deflector can be easily measured via the use of a standard network analyzer. The test is usually automated and the results are plotted as a function of frequency. The impedance is plotted on a typical Smith chart, whereas thereflection loss is plotted in dB versus frequency. From the reflection loss data we can easily calculate the transmitted power as a function of frequency thereby determining the electrical bandwidth of the deflector. In a similar way we can also measure the VSWR of the deflector. Figures 6(a, b) show examples of the impedance and return loss of a matched L[100] LiNb03 deflector centered at1GHz with a 3-dB bandwidth of 500 MHz. Figure 6(a) shows that the electric impedance covering the 0.75-1.25 GHz band is very close to 50 CR with the worse

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413

case real impedance being about 43 at a frequency of840 MHz. Figure 6(b) shows that the worse case return loss, over the band of interest, is 14 dB at 1.25 GHz. This means that the worst-case power transfer to the transducer is 96% and that only 4% of the power is reflected. Figure 6(b) also shows that this particular deflector has a wide 3-dB electrical bandwidth which exceeds 950 MHz. In practice, however, the acceptable electrical bandwidth corresponds to a VSWR of 5 2 or a return loss of better than 9.5 dB. In this case the electrical bandwidth of the deflector is over 850 MHz and covers the 0.65-1.5 GHz range. Finally, in Fig. 6(c) we show the VSWR of the deflectorover the 0.75-1.25 GHz range which satisfies 1.1 SVSWR

The frequency response or bandwidth (BW) of an deflector is determined by the product of the electric, acoustic, and interaction responses [5]. Each of these responses is determined by various factors which depend on the deflector design, the material, and the fabrication technique used. TheBW of a deflector can be measured via the use of an power spectrum analyzer [6] (Fig.7). In this systema collimated optical beam of uniform intensity is incident on the deflector which is driven by a leveled RF sweep of center frequency!, and bandwidth 2Af. The sound field propagates at an angle, €li, with respect to the optical beam which propagates along the axis. The angle €li is set such that theBragg condition issatisfied for f,. Fourier transform lens collects and separates the diffracted and undiffracted orders and focuses the first diffracted order onto a linear detector array, the output of which is an exact replica of the deflector BW. Using spatial Fourier transformanalysis [6,7] we canrelate

fc f INPUT RF SWEEP

+FL +

7 Schematic an acousto-opticpower spectrum analyzer used to evaluate the bandwidth an deflector.

WUl'ZOULIS, W Z Z I E B , AND PAPE

41

distance, x , at the focal plane and RF frequency, f, in the A 0 deflector bY x = (+)f

where h is the optical wavelength, FL is the focal length the Fourier transform lens, and V is the velocity of sound in the material. Figure 8(a) shows an example of BW testing using the system Fig. 7, for the case a L[lOO] LiNb03 deflector driven by a 1-GHz BW sweepcentered at 1 GHz. For this example the deflector has an actual 3-dB BW covering the - 1350 MHz range. By varying the angle €li we obtain different A 0 responses, the envelope of which is independent of the interaction response, and representsa replica of the combined electric and acoustic responses. Since it is possible that the electroacoustic response is broader than the interaction re-

(a) Exampleof A 0 frequency response for anL[lOO] LimoBdeflector. centered at 1GHz. The horizontal represents frequency(100MHz per major division) from 500 to 1500 MHz.The vertical axis represents diffraction efficiency (1%W per major division).(b) Example of electroacoustic frequency response for the example of Fig. 8(a). Five different A 0 responses have been recorded and optimized at different Bragg angles. (c) Schematic of a single-detector acoustooptic system used to evaluate the bandwidthof an A 0 deflector.

415

TESTING OF ACOUSTO-OPTIC DEVICES

CTOR

OUTPUT TRIGGER TRIGGER

SWEEP GENERATOR

INPUT

OSCILLOSCOPE

sponse, an input RF sweep BW larger than that expected for the A 0 BW should be used in orderto measure the true electroacoustic BW. Figure 8(b) shows an example the electroacoustic response obtained for the previous deflector example. Five different A 0 responses have been recorded for which8, was optimized formaximum response at 750,875,1000,

41

WUlZOUJ5IS. W T I Z I E B , AND PAPE

1125, and 1250 MHz, respectively. It can be seen that the electroacoustic response in the 750-950 MHz range is about 2.5 dB higher than that in the 1200-1400 MHz range. This information is not apparent from Fig. 8(a), where the interaction was optimized at -1150 MHz in order to obtain the widest possible smooth response centeredat 1GHz. Note that for a fixed tIi the output of the detector array represents the averageBW response of the deflector over an A 0 time aperture determined by the width (D,along the axis) and the position of the input opticalbeam in the plane. By using a small D and probing different parts of the deflector in the plane, we can measure theA 0 response as a functionof position relative to the transducer. Thisallows a coarse examination of the effects of acoustic attenuation and the acoustic beam spreading, and helps identify the optimum operating area of the deflector. An alternativesystem for measuring the BW of an A 0 deflector is shown in Fig. 8(c). This system is similar to the spectrum analyzer shown in Fig. 7, with the exception of a single-element detector which has replaced the detector array at thelocation of the first diffracted order. Inthis system, the focal length of the Fourier transform lensis adjusted so that all of the first-order diffracted lightover the deflection BW is captured by the singleelement detector. The output of the detector is input to an oscilloscope triggered by the swept FW input to the deflector. The temporal trace on the oscilloscope is then a display of the power in the first-order diffracted optical beam versus FW frequency. Thedisplay can easily be converted to diffraction efficiency versus RF frequency by manually scaling the output to the productof the opticalpower in the zero-order opticalbeam and the RF power input to the deflector.

2.5 Scattering Measurements deflectors aretransmissive optical components, andthey include scattering sources such as [8] (1)surface imperfections and contamination, (2) permanent index fluctuations due to imperfections in the A 0 crystal lattice structure, and bulk particulates including smallbubbles, inclusions, and contamination. Theangular dependence and strengthof the scatteredlight depends on several factors, the most important of which are the size of the scatterers relative to the optical wavelength, their periodicity and relative population, and the propagationand polarization of the opticalbeam. The types and origins of scattering can be measured and characterizedby various techniques and instruments,including low-angle transmissive scatterometers formeasuring the bidirectionaltransmission distribution function birefringent interferometry formeasuring the optical homogeneity of the bulk [lo], various surface roughness profiling techniques, etc. The

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41 7

results of the scattering measurementscan be used not only in comparing A 0 deflectors but also in the modeling of A 0 systems with the goal predicting their ultimate performance [ll]. The light scattered by the A 0 crystal acts as noise that limits the performance of the A 0 deflector. Thisis most important when the deflector is used in an RF spectrum analyzer or channelized receiver, where the scattered light is very frequently the limiting factor of the system dynamic range (DR). For these applications, the important scattering parameters are (1) the level of the zero-order scattering that extends overpassband the of the device and (2) the sidelobe level of the first-order diffracted beam. The zero-order scattering level determines the DR floor or equivalently the minimum (or threshold) level of the input RF signal that produces a detectable output. The sidelobe level of the first-order diffracted beam determines theminimum detectable level of a weak RF signal in the presence of a strong RF signal, when the frequency separation of the two signals equals the frequency separation of the peak and the sidelobe. Furthermore, the increase of the output sidelobes and the widening of the diffracted beam result in decreased system resolution and increased crosstalk among parallel output channels. Once theA 0 deflector has been fabricated, an accurate characterization of the zero-order scatteringand the diffracted beam sidelobe structurecan be made by using the deflector in an power spectrum analyzer configuration and accurately recording the profiles of the zero and first diffracted orders [12, 131. This is also useful prior to deflector fabricationin (1) selecting anA 0 crystal adequate quality, and (2) gaining some idea about the diffracted beam sidelobe structure by observing the sidelobe structure the zero order, because in general the former resembles an attenuated version of the latter. This is more valid for isotropic A 0 interaction and less for anisotropic where polarization filtering [14, 151 between the two orders is used to reduce the overall scattering level and improve the diffracted beam profile. The schematic of such a scattering system is shown in Fig. 9. A laser beam is expanded through a two-lens system ( L , and L,) to give a collimated beam of diameter D.This beam is used the as probe for the scattering measurements from the test crystal or device. After passing through the A 0 crystal the emerging beam is focused onto the slit of a beam scanner. This scanner consists of a very narrow (10-25 km) slit with anoptical fiber probe attached immediately behind the slit. The slit/fiber assembly is in turn joined to amotorized linear drive. The fiber transmitslight the passing through the slit onto a photomultiplier (PM), the output of which is fed to alogarithmic amplifier (LOG AMP). Since typical PMssaturate atvery low optical power levels (-1 kW) an optical attenuator is used prior to

AND PAPE

WuIzOUL,IS, Wlli!,IEB,

418 GAUSSIAN-PROFILE COLLIMATOR

l

A 0 DEVICE

MOTOR-DRIVEN SCANNING SLIT

F3

FIBER-OPTIC COLLECTOR

9 Schematic of a scanning, slit-based scattering measurement system.

the PM in order tomatch the DR of the slit-fiber-PM subsystem with that of the spectrum analyzer optical system. The output of the amplifier is displayed on an X-Y recorder, the X-input being driven with a signal proportional to the linear displacement of the slit. Thus, the output from the X-Y recorder provides a spatial intensity profile of the focused beam incident on the slit. By comparing the profiles with and without the test crystal or device in the optical path, a quantitative measure of the scattering of the beam by the crystal is obtained. The diameter D of the probing beam isdetermined by the magnification of the lens system L,-L,: D =

where is the diameter of the collimated laser beam and Fl and F, are the focal lengths of lenses L 1 and L2 respectively. Use of a relatively large probing beam effectively averages any localized imperfections in the crystal and provides a realistic measure of the scattering limitations of a particular device or crystal boule. The same system can be used prior to deflector fabrication with a narrow probing beam in order to identify the least scattering region(s) in the material and thusaccurately determine the transducer and top electrodelocations for optimized performance. To identify the region of zero-order scattering that extends over the deflector’s passband or thefrequency separation the peak andsidelobes,

TESTING OF ACOUSTO-OPTIC DEVICES

41 9

we must translate the linear displacement Ax of the scanning slit to an RF frequency scale Af. This can be done from the relation =

VAX hF3

where F, is the focal length of the focusing lens L,. For a given A 0 material and RF resolution, Eq. (3) determines the minimum practical F, (in conjunction with the slit width in order to perform a meaningful sampling of the scattering profile. This is because as F, decreases does the width of the focused beam and thus for large d, the sidelobe structure may be smoothed or even lost because of the spatial integration over the width of the slit. Much finer sidelobe structure information can be obtained if we take into account the continuous spatial integration performed by the slit and deconvolve the results. For many A 0 applications, however, this type of-informationmay be unnecessary because a similar spatial integration is performed by the output detector arrays, which in most cases have widths compatible with those of the scanning slits [16]. A photograph of a laboratory scattering measuring system is shown in Fig. 10. The optical part consists of a 3-mW He-Ne laser beam (not shown in Fig. 10) which isfocused by a 10 X objective lens onto a 25-pm-diameter spatial filter. The resulting filtered beam is collimated by a spherical lens ( F L = 70 mm), passed through a sample two-channel A 0 deflector, and is then focused by a 175-mm focal length lens onto the scanning slit assembly. The latter consists of a 25-pm (W) X 2500 pm ( H ) scanning slit mounted on a scanning motor drive which has a travel distance of 10 mm and is readable to20 pm. A precision micrometer screw drives the slit and the associated fiberoptic collector probe across the focal plane. Automatic scan with controller direction and speed is accomplished with use of a scan control unit. An output from 0-100 mV is available whichisused for correlating the position of the slit with respect to the X axis of the X-Y recorder. The fiberoptic collector is 0.9 m long and consists of a fiberoptic bundle housed in a flexible stainless steel sheath. Thecollector terminates in a special adaptor which includes a filter cavity to allow neutral density filters to beinserted between the fiber probe and the PM. The PM assembly contains a thermoelectric water-cooled PM with temperature control, power supply, water pump, water reservoir container, and an S1 photosurface with spectral response from 300 nm to 1.1pm. The output of the PM drives a LOG AMP, which in turn drives the X-Y recorder. The scanning slit, motor drive, control unit, adaptor, and PM assemblyare Gamma Scientific Models 700-10-65A, 700-10-70, SG-1, 2020-6, and DC-45A, whereas the LOG AMP is a HP 7563A. The LOG AMP has a 55-dB optical DR, whereas the PM has a 45 dB DR and saturates for input optical power

WUlZOVLJS, Wli'LIEB, AND PAPE

Figure 10 Photograph an experimentalscatteringmeasurementsystem. (Courtesy of Westinghouse Electric Corp.)

levels of 2 pW. Use of He-Ne lasers (or infrared laser diodes) with power levels of several milliwatts in conjunction with neutral density filters extends the system DR to over 70 dB. An example of a first-order diffracted beam scattering profile taken by the system of Fig. 10 is shown in Fig. 11. The A 0 deflector used in this example and was is a L[100] T13AsS4with a 200-MHz BW and a TBW of considered for use ina channelized receiver. Figure 11shows thatthe focused probe beam has no sidelobes to at least dB, and thus in principle it allows the detection a weak single-tone signal(at about -40 dB)separated from a strong single tone by 10 MHz. However, the scattering the T13AsS4 ,crystal enlarges the widthof the diffracted beam and introduces sidelobes that significantly deteriorate this detection capability. Specifically,the power the weak signal must now increase by at least 8 dB (to dB)in order to allow discrimination from the sidelobe structure. Some demanding A 0 applications require deflectors with sidelobes suppressed to better than dB at A = nm. The testing of these deflectors demand that the probebeam has an adequateGaussian profile so that when focused it shows no sidelobes to at least- dB. In practice

TESTING OF ACOUSTO-OPTIC DEVICES

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0-

-5 -

-m

-10

-

-15

-

'CI

2-20c

c

-25

-

-30

-

/Scattering /Input

Profile Beam Profile

fc

+ 20MHz

f,.+ 10 MHz

Frequency

C '

Example of a scattering profile from an experimental deflector.

this is possible with a good optical design in conjunction with carefully selected single-mode laser diodesand precision spatial filters. Such designs typically usea lens to collimate the laser diode light followedby a Keplerian expander with a spatial filter to eliminate the noisy components of the laser beam profile that generateunwanted sidelobes. Note that thespatial filter truncates the Gaussian profile and this results in distorted, sinc-type sidelobes weighted by the Gaussian profile. Hecht has studied this effect and has shown that for a dB sidelobelevel a perfect Gaussian profile must be maintained to at least the -29-dB points. For a given source size this determines the beam angular divergence that must 'be maintained through the system and it sets the f-numbers of the lenses as well as the width of the spatial filter.

422

WUlZOUL.IS, W77LIEl3, AAD PAPE

Figure 12 shows a miniaturized laser diode collimator which was designed using the above principles, and which is used for scattering measurements of a line-illuminated GaP deflector. The collimator uses commercially available, multiple-element lenses designed for operation with laser diodes, and an in-house-built precision spatial filter assembly. Figure 13(a) shows the profile of the resulting Gaussian probe beam, which has a clean, Gaussian-like shape with minimal distortion to at least the -29 dB points. When this beam is focused (Fig. 14(a)), the resulting sidelobes are about -41 dB, which is marginally acceptable for our purposes. A significant improvement of several dB is possible if the collimator’s output is passed through a single-mode fiber, which acts as a filter that virtually eliminates already suppressed modesand remaining noisycomponents [17]. Figure 13(b) shows the Gaussian profile resulting from propagating the beam of Fig. 13(a) through a 12-cm-long74/85-~mfiber segment. It can be seen that the beam has a broader, nearly Gaussian profile with no sidelobes to atleast the -36.5-dB level. When this profile is focused (Fig.

12 Photograph a miniaturized laser diode collimator with spatial filtering used scattering measurements a line-illuminated GaP deflector. (Courtesy Westinghouse Electric Corp.)

TESTING OF ACOUSTO-OPTIC DEVZCES

-1

\

-1

-25

-35

2.0 Distance (mm)

13 Gaussian profiles from(a) the miniaturized collimator Fig. 12, and (b) when the miniaturized collimator is used in conjunction witha 4/85-~msinglemode fiber.

14(b)), asmall sidelobe appearsat the - 44-dB level, whereas most of the noisy sidelobe structure appears at the -48-dB level. Note that an additional 1-2 dB reductionin sidelobe level is possible if the fiberis subjected to mode striping.

2.6 DiffractionEfficiency Measurements The diffraction efficiency, q, of an A 0 deflector is defined as the ratioI,/ I , of the first-order diffracted beam power to the zero-order transmitted

0

-5 0

5

m^

S

.-m C

(U

-20 -25

-30

c

-

-35

-4 5 -50

-1.6

-0.8 0 Distance

0.8

1.6

14 FocusedGaussianprofilesfrom (a)the miniaturizedcollimator of Fig. 12, and (b) when the miniaturized collimatoris used in conjunctionwith a 12cm 4/85-pm single-modefiber.

beam power, and for the frequency for which exact momentum matching occurs is given by [l81

where

In Eq. ( 9 , X is the optical wavelength, M2 is an material figure of merit, L is the interaction length, H is the transducer height, and P, is the acoustic power. The diffraction efficiency can be easily measured with a calibrated detector which measures Io at the input face of the deflector and Zl at the first diffracted order. The variation of the applied P, with frequency can be eliminated by normalizing the measured ZJZ0 by the applied P, and expressing the results in percent per watt (%/W). This procedure

TESTING OF ACOUSTO-OPTIC DEVICES

425

can be repeated for different RF frequencies that q can be plotted as a function of the input RF frequency. Since q depends on H , care must be taken so that the height of the optical beam is less than H.

2.7 Third-Order lntermodulation Product Testing The presence of multiple acoustic waves in an A 0 deflector results in multiple diffracted beams which contain spurious intermodulation products. The mechanisms responsible for these spurious signals are not only multiple optical diffraction due to the presence multiple tones simultaneously in the deflector [l91 but also material dependent acoustic nonlinearities [20, 211. When two tones of frequenciesfi and fz are present in the deflector, the strongest in-band spurious signals are the two-tone (or third-order) intermodulation products (IMP) 2fl-f2 and 2f2-fl,which are of major concern in A 0 spectrum analyzer systems since they limit the two-tone DR. Hecht [l91 has shown that the intensityof the third-order IMPS due to multiple optical diffraction is given by ZZ,l

=

q3 -

where q is the diffraction efficiency of the main diffracted modes at fi or dB) deflectors,q must be less than 0.02. This low efficiency in conjunction with typical detector arrays of dB dynamic range makes the detection of Zz,l via power spectrum analysis-type techniques very difficult and inaccurate. A more effective technique involves an interferometric Mach-Zender-type scheme in conjunction with an RF spectrum analyzer [21]. Figure 15 shows the schematic of this approach in which the deflector under test is fed with two equal-amplitude RF tones of frequencies fl and fz at a level that a predetermined q is produced. The two-tone diffracted beam is made to interfere with the diffracted beam from a reference deflector drivenby a single tone at frequency f3. The output is detected by a high-gain, lownoise detector/amplifier system and is then analyzed by an RF spectrum analyzer, which allows the simultaneousdisplay of the intensities of all the spectral componentsof interest. Note that for accurate measurements the two-tone RF input to the deflectormust be IMP free to better than10 dB below the minimum IMP level expected from the deflector. The system of Fig. 15 can operate without the reference deflector[22]; however, in this case the detector/amplifiersystem is required to have an RF bandwidth equal to2fz-f1. For multi-GHz deflectors this is nottrivial a task, especially whenwe consider the low-noise requirement. The detection

fz. Equation (6) shows that forwide-DR (e.g.,

426

WK'ZOULJS, WK'LIEB, AND PAPE Input Laser

Amplifier

Schematic of an interferometric system for IMP characterization of

deflectors. bandwidth can be significantly reduced with the addition of the reference deflector. This is because the latter acts as a mixer and downconverts the IMP bandwidth, BW-, given by BW- = (2f2-fJ - (2f1-f2) = 3(f2-f1) (7) to a much lower center frequency, equal to 0.5(f1 + f2) - f3, for which the low-noise requirement can be easily accomplished. Figure 16 shows the measured IMP level [23] using the system of Fig. 15 in conjunction withtwo T13AsS, deflectors at frequencies fi = 830 MHz, f2 = 838 MHz, and f3 = MHz, and for q = 0.05. For this example IMP levels as low as -31 dB (relative to the main diffracted tones) were measured, the limiting factor being the scattering of the A 0 crystal. Note thatby focusing the input optical beam onto thetest deflector, we can probe different areas of the sound field. This allows the measurement of the IMP level as a function of the distance from the transducer, which isvery important for large TBWP deflectors when they areused in channelized receiver applications. It also provides the ability to distinguish between the IMP level produced by multiple optical diffraction and by acoustic nonlinearities [22].

2.8 Determination of Dynamic Range Once the diffraction efficiency, third-order IMP, and the scattering level over the passband of the deflector are measured, we can determine the

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427

16 Photograph of themaindiffracted tones and thethird-order IMPs for a Tl,AsS, deflector with f, = MHz, f2 = 838 MHz, = 0.05, at A = 633 nm. For this example the reference deflector was drivenby an 800-MHz tone.

deflector DR. The useful DR largely depends on the specific application, most frequently however, it is the spurious-free dynamic range (DR,). DR, is defined as the input level variation range over which spurious signals are not developed above the minimum detectable signal level. For A 0 deflectors the level of the spurious signals isequal to thelevel of the thirdorder IMPs, whereas the minimum detectable signal is equal to the zeroorder scattering extending over the deflector passband. To obtain DR2 we plot the relative diffracted optical powers (in dB) the main diffracted tones at fi and f, versus the input RF power level (in dBm). The DR, is then determined bymeasuring the range from the interception the IMP curve and thecrystal scattering to theinterception of the main diffracted tone curve and the crystal scattering. In addition to the measured IMP curve, it is often useful to plot the IMPcurve determined by the multiple optical diffraction becauseit sets the limit of maximum theoretical spurious-free dynamic range(DR2T)in any deflector. Comparison of DR, and DRzTallows'us to determine how much improvement is possible in a specific deflector if acoustic nonlinearities were to be reduced. An example of an actual DR plot determined by the above procedure is shown in Fig. 17 for the case of a deflector operating over the

GOUlZOULIS, GOTTLIEB, AND PAPE

428

550-1050 MHz range [23]. For this example DR, = 30.7 dB and DR2, = 38.9 dB, which implies that an improvement of 8.2 dB would be possible if the acoustic nonlinearities that limit DR, were eliminated. The plot of Fig. 17 also shows the single-tone dynamic range (DR,) which is defined as the power range from the maximum acceptable safe input power level (P,,,) to the crystal scattering level. For the example of Fig. 17 Pmax= 26 dBm and thus DR, = 53.7 dB. Regarding DR, we note that when safety is not an issue P,,, is determined by the maximum acceptable deviation from a linear response. Typically the acceptable deviation is 1 dB, and the input power level to which this occurs is called the 1-dB compression point.

2.9 Time-Bandwidth Product The most important parameter of an A 0 deflector is its time-bandwidth product (TBWP) defined as the product of the time aperture ( T A ) and BW. The TBWP is equivalent [25]to the number of resolvable elements, defined as the ratio of maximum deflection angle over the angular spread

10

ti -10

:

n ; -20

.-0

c,

Q

U

-30

Q)

4-

0

-40 .n Q)

.L -50

-

c,

Q

Q,

-60

Figure 17 Example of a DR plot for the case of a Tl,AsS, deflector operating over the 550- 1050 MHz range where acoustic nonlinearities limit the spurious-free DR.

TESTING OF ACOUSTO-OPTIC DEVICES

429

of the diffraction-limited optical beam. Depending on the application, TBWP determines different system performance parameters. For example, for spectrum analyzers it determines the frequency resolution, for space-integrating correlators it determines the processing gain, and for time-integrating correlators it determines the number of parallel correlations (or, equivalently, the delay resolution of the correlation). It is well known that the BW of the deflector is determined [5] by the product of electric, acoustic, and A 0 interaction BWs. The useful TA is determined [26] by the (1) optical aperture, (2) acoustic attenuation, (3) geometric spreading of the acoustic beam due to diffraction from a finitewidth transducer, and (4) in some cases, by the spreading of the acoustic beam due to elastic anisotropy in the A 0 crystal [3]. Given the number of factors affecting the TBWP, it is often necessary to perform a test in order to verify the predicted TBWP performance. This is most often accomplished by using the deflector in an A 0 power spectrum analyzer in conjunction with a detector array (Fig. 18). The deflector is driven by two sine waves of equal amplitude which are separated in frequency by Af. By gradually reducing Af and observing, at the output of the detector array, the depth of the dip relative to the height of the two peaks we can determine the actual resolution of the deflector. The minimum acceptable depth is determined by the Rayleigh criterion [27, 281, which states that two spots are barely resolved by a diffraction limited system when the central dip between them is 19% of the maximum intensity of each spot. Once the Rayleigh resolution has been reached, Af must be measured in the R F domain via an R F spectrum analyzer. From the measured Af resolution and BW we can determine the actual TBWP.

WAVEFORM

Figure 18 Schematic of an A 0 power spectrum analyzer driven by two tones used to determine the frequency resolution of an A 0 deflector.

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In designingfrequency resolution experiments, much considerationmust be given to the pixel width of the detector array (along the direction of sound propagation) relative to the width of the focused spot. Using Eq. (1) we find that the distance, W, between the lowest and highest frequencies at the frequency planeof the spectrum analyzer of Fig. 18, is equal to W = XFL(BW) V Sampling theory requires that the detector arraysamples W at least twice per resolvable spot, which means that the pixel width, Dp, must satisfy

Dp

Wl2TBWP

(9)

If Eq. 9 is not satisfied, the detector array undersamples the output and this results in resolution loss. In practice, thefocal length of L3 is selected that the resulting W satisfies Eq. 9 for a given array with pixel size Dp. For example, for L[lOO] a LiNbO, deflector with BW=500 MHz, TA=2.0 psec, and a detector arraywith Dp= 10 pm, we find fromEq. 9 that W 2 20 mm. Subsequently, use of Eq. 8 with W 1 20 mm, shows that FL must be at least 415 mm at X = 633 nm. An experimental frequency resolution testing system is shown in Fig. 19. It is used for the testingof a L[100] LiNb03 deflector which operates over the 0.75-1.25 GHz range with a theoretical TBWP of1100 spots. Figure 20 shows the best resolution achieved with a detector array of Dp= 19 pm, when used with FL = 175 mm. This particular example demonstrates undersampling with W= 8.44 mm and a theoretical system TBWP of only 222, i.e., a theoreticalAf of 2.25 MHz. This is indeed the case as the RF spectrum analyzer measurement of the inputtwo tones shows (Fig. 21). Figure 22 shows the best resolution achieved with a detector arrayof Dp= 11 km, when used with FL=580 mm. For this setup W=27.9 mm, and thus a theoretical system TBWP of 1268 spots can be resolved. The data of Fig. 22 correspond to an experimentalAf of 494 kHz (Fig. 23) or an experimental TBWP of1012,which isin good agreement with the theoretical TBWP of 1100. In addition to detector undersampling, lens (L3)aberrations can also result in resolution loss because they increase the width of the focused spot, thereby increasing Af and thus reducing TBWP (note that by definition the maximum TBWP assumes diffraction-limited spots). Resolution loss alsooccurs when a nonuniform optical beamis used, because it always has a higher-frequency content than a uniform beam, and thus a wider spot when focused. Hecht[6] has studied thewidening the focused spot when a Gaussian beam profile is used, and has shown that little widening

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431

I Figure Laboratory power spectrum analyzer used for frequency resolution testing of an L[lOO] LiNbO, deflector. (Courtesy of Westinghouse Electric Corp.)

Figure 20 Example of frequency resolution measurements demonstratingundersampling usingthe system of Fig. 19.The test deflector is a 500-MHz L[lOO] LiNbO, with a theoretical TBWP of 1100. For this exampleFL is 175 mm and D, is 19 Wm.

432

WUl'ZOU5IS, WlTLIEB,

A M ) PAPE

21 RF spectrumanalyzer photograph showinga2.25-MHz separation for the two tones used in the example of Fig. 20.

22 Example of frequency resolution measurements demonstrating sufficient sampling usingthe system of Fig. 19. The test deflector is a 500-MHz L[100] LiNbO, with atheoretical TBWP of 1100. For this example withFL is 580 mm and D, is 11 p,m.

TESTING OF ACOUSTO-OPTIC DEVICES

23 RF spectrum analyzer photograph showing a 494-kHz separation for the two tones used in the example of Fig. 22.

occurs (55% of uniform case) when the truncation ratio is 0.75; i.e., the intensity of the Gaussian beam at the edges of the deflector is down by exp( - 1.125). In this case the resolution loss is about 5% and the TBWP is reduced to 95%.

2.10 AcousticAttenuationMeasurement The acoustic attenuation of most A 0 crystals used for A 0 devices are well known and documented in the literature [29]. Quite frequently, however, it is necessary to make an attenuation measurement on a device crystal because (1) there may be significant variation from one crystal batch to another, (2) a different orientation is used for which a good measurement has not yet been performed, and the crystal has been prepared by a new process [30-321. There are classical techniques for measuring the acoustic attenuation in solids, which are well described in the literatureon acoustics. These techniques require specialized apparatus, while an adequate measurement can often be done by an A 0 probe method, forwhich the necessary apparatus is typically foundin laboratories where A 0 device work is done. A convenient setup for measuring acoustic attenuation by the optical probe method is illustrated in Fig. 24. Since it is usually most

WUlZOULJS, Wi'TL,IEB, AND PAPE ROTATION TABLE

OSCILLOSCOPE

OSCILLATOR

24 Schematic a system employing the optical probe method uring the acoustic attenuation in device crystal.

meas-

useful to determine the frequency dependence of the attenuation in order to verify the expected p dependence for high-purity crystals it is helpful to bond a fairly low frequency (-20-30 MHz) transducer to the crystal, and perform the measurements on thehigher harmonics as well as on the fundamental frequency. Depending on thebond impedance match, it is often possible to obtain data beyond the ninth harmonic. The measurement accuracy can be optimized by working with a small laser beam diameter, e.g., 1 mm, in order to maintain good spatial resolution. For each frequency, the Bragg angle is optimizedfor peaksignal level. pulsed input RF signal is used, with pulse width, T,, that is small in comparison to the device time aperture The intensity of the diffracted signal, is measured for several positions of the incident laser beam at distance, d , from the transducer. If the input RF power level is set so that the diffracted signal intensity nearest to the transducer, I,, is well within the linear range of the device, then as the laser beam is translated to

TESTING OF ACOUSTO-OPTIC DEVICES

435

some distance d, the corresponding diffracted beam intensity will decrease according to In this equation a is a frequency-dependent attenuation constant which is approximately equal to where a, is the attenuation constant per unit length at 1 GHz, f is the frequency inG&, and m = 2 for most crystals of interest In general, it is difficult to obtain an accurate estimate of the attenuation coefficient by this method, even when the attenuation coefficient is high. However, the overall accuracy can be greatly improved by making as many measurement as there are laser beam diameters along the crystal length, and obtain a(f)for a given frequency, from the slope of a plot of loglo(Z/Zo) against d. This procedure is carried out at as many frequencies as can be accessed withhigher harmonics. By usingthe various a(f)values, the value of the coefficient a, can beobtained from a best fitto a quadraticdependence.

3 A 0 MULTICHANNEL DEFLECTOR TESTING multichannel deflector is constructed in the same way as a common single-channel device with the replication of single channels on a common A 0 substrate. Therefore most of the procedures employed in testing an individual channel of a multichannel deflector are the same as thoseused to test a single-channel device. These common procedures include acoustic echo, schlieren imaging, electrical impedance and VSWR, BW, scattering, diffraction efficiency, and third-order IMP. The additional tests required for a multichannel deflector include the channel-to-channel performance uniformity, channel-to-channel isolation, and thesignal-phase error. These additional test procedures are described in this section. 3.1 Channel-to-ChannelPerformance Uniformity The measurement of channel-to-channel performance uniformity entails comparing the results of the performance measurements of the individual channels of the multichannel device. Each channel of the multichannel deflector is individually tested with all other channels OFF. For electrical testing the same experimental setup and procedures used to test a singlechannel device are employed. For optical testing almost the same experimental setup and procedures as that used to test a single-channel device can also be employed. The experimental setup is modified so that the

WVlZOULIS, WlTL.IEB, ANZ) PAPE

436

multichannel device is mounted ona vertical translation stage. Each channel is tested by translating the cell that the channel is illuminated in the same way as that used for single-channel Bragg cell testing. Typically the performance of any one channel shouldnot vary bymore than & 20% from the average performance of all of the channels.

3.2 Channel-to-ChannelIsolation The measurement of channel-to-channel isolation entails the measurement of crosstalk (an undesired signal appearing in one channel as a result of coupling from other channels). A crosstalk measurement typically determines the intensity of a signal in a nominally OFF channel due to the presence of a signal in a neighboring ON channel. The crosstalk level is usually defined as the ratio of the intensity of the signal in the OFFchannel to the intensity of the signal in the neighboring ON channel. Crosstalk in a multichannel Bragg cell results from both electrical and acoustic coupling between channels, as shown in Fig. 25. Electrical crosstalk arises primarily from coupling between the individual electrode matching networks and/or thetransmission lines connected to each of the multiple transducers. Acoustic crosstalk arises from the diffraction spreading of the acoustic beam fromone channel intoneighboring channels. Acoustic crosstalk increases as a function of distance from the transducer plane.

3.3 ElectricalCrosstalk Measurement Electrical crosstalk can be conveniently and unambiguously measured with an RF network analyzer Two adjacent channels of the multichannel device are connected to the transmission and reflection ports of the analyzer. The frequency source of the analyzer is swept through the bandwidth

RF Crosstalk

Acoustic Crosstalk

25 Multichanneldeflectorcrosstalk.

TESTING OF ACOUSTO-OPTIC DEVICES

437

of the device. The electrical transmission (crosstalk) through the two channels is then displayed directly on the analyzer as a function of frequency. Electrical crosstalk can also be measured using one of the “acoustic” crosstalk measurement techniques described below. Near the transducer, acoustic crosstalk is negligible since the acoustic beam divergence is negligible. An acoustic crosstalk measurement made near the transducer plane thus measures electrical crosstalk [36]. High-performance multichannel devices exhibit electrical crosstalk levels less than - 40 dB [37].

3.4 AcousticCrosstalkMeasurement Acoustic crosstalk, as discussed above, increases as a function of distance from the transducer plane. Acoustic crosstalk measurements involve measuring the intensity of the undesired diffracted optical beam from a nominally OFF channel due to thepresence a signal in an ON channel. The acoustic crosstalk measurement techniques described here actually measure the total crosstalk (both electrical and acoustic) between channels. One optical setup formeasuring acoustic crosstalk is shown [36]in Fig. 26. An optical beam is focused within a channel of the multichannel device.

PHOTOMULTIPLIER TUBE DETECTOR

LASER

SPECTRUM ANALYZER

12 M H z MODULATION

SIGNAL GENERATOR

26 Multichanneldeflectorcrosstalkmeasurementsetup.

GOuIzOUL.ZS, W'ZTLIEB, AND PAPE

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'

The device is mounted on a translation stage that measurements can be made at different positions along the length of the channel. The diffracted optical beam is collected by a photomultiplier tube detector whose output is fed to a spectrum analyzer. The output of the spectrum analyzer is connected to a strip chart recorder driven at the same rate as the multichannel cell translation stage. modulated carrier is fed to the channel and the intensity of the detected modulated output, Io, is recorded. modulated carrier is then fed to an adjacent channel (where now the illuminated channel is OFF). The intensity of this detected modulated output, I,, is also recorded. The crosstalk is defined as the ratio (in dB) of I , to Io. plot of the adjacent channel crosstalk in a 64-channel TeO, longitudinal mode multichannel cell (center frequency 400 MHz, bandwidth 200 MHz, transducer height pm, transducer center-to-center spacing 250 km) isshown[36]inFig. 27. The graph clearlyshows the spatial dependence the crosstalk. In most applications crosstalk levels less than -30 dB are desired. By measuring the spatial dependence of the acoustic crosstalk the useful TA of the device can be determined. Another crosstalk measurement setup is shown [38] in Fig. 28. The entire aperture of the multichannel Bragg cell is illuminated with a single colli-

t -100.0 0.0 0

.o 50

2.0 100

3.0 150

'

4.0 200

5.0 250

27 Multichanneldeflectorcrosstalkmeasurement.

6.0 DISTANCE (mm) 300 TIME-BANOWITH PROOUCT

TESTING OF ACOUSTO-OPTIC DEVICES

439

28 Intensity profile multichannel deflector crosstalk measurement setup

mated optical beam. A pair of lenses is used to form an image the acoustic waves withineach channel using the schlieren imaging technique. Here thezero-order light is blocked by a schlieren stop in the Fourier plane the optical system and the image isformed using the first-order diffracted light. An optical power meter is mounted on a two-dimensional translation stage in the image plane and is scanned orthogonal to the acoustic propagation direction across the images of the individual channels. pinhole in front the photodetector is used to provide good spatial resolution. The opticalpower meter output, as a functionof the scan distance, yields an intensity profile the acoustic waves ineach channel. Intensityprofiles at different locationsin the multichannel cell can be obtainedby translating the optical power meter in the direction of acoustic propagation. Acoustic crosstalk ismeasured by activating a channel andscanning the photodetector across the image of the ON channel as well as the adjacent OFF channels. The crosstalk level is defined as the ratio of the signal intensity measured in an OFF channel to the signal intensity measured in the neighboring ON channel. An example of a measurement taken using the above procedure is shown [39] in Fig. 29. Here a scan is made across the schlieren image of a multichannel device where two adjacent channels are simultaneously activated. Thesignal in the neighboring channel to the right the ON pair of channels is about 32 dB below the signal in the ON channels, indicating the crosstalk level at this scan location is about - dB. The accuracy of this approach may be less than desired as some

Intensity profile multichannel deflector crosstalk measurement

of the intensity of the signal measured in the OFF channel may be the result of spurious light scatter. (This background light scatter could be measured in a scan prior to activating the ON channel and then subtracted from the crosstalk level measured from the ON channel scan.) The previously described measuring technique overcomes this difficulty.

The measurement of channel-to-channel phase or time nonuniformity entails measuring the difference in the signal time-of-arrival between channels. Signal time of arrival is defined as thetime a signal is optically detected relative to thetime the signal is applied to themultichannel device. Channel-to-channel phase or time nonuniformity is the result of electrical phase differences between the matching networks and/or the transmission lines connected to each of the multiple transducers and acoustic and optical path differences between channels. An experimental setup for measuring channel-to-channel phase nonuniformity is shown [40] in Fig. 30. The optical setup is the same as that used in the first acoustic crosstalk measurement technique. A modulated RF carrier is fed into one channelof the multichannel device as well as to the reference input of a network analyzer. The output from the photomultiplier tube is connected to thetest input of the network analyzer. The network analyzer compares the phase of the modulated input to thephase

441

TESTING OF ACOUSTO-OPTIC DEVICES Multichannel Bragg Cell Swept Frequency Source

Mixer Photomultiplier Tube Detector

Network Analyzer

30 Electrical multichannel deflector phase nonuniformity measurement

setup

of the modulated output detected by a photomultiplier tube detector. detect the modulated output, the output from thephotomultiplier tube is mixed with the carrier. The phase difference between the input and output is displayed directly on the network analyzer as a function of frequency. A linear phase variation across the band is the result of a time delay between the input and output andcan be removed by adjusting a time delay in the reference channel. This measurement serves as a reference. The same measurement is then made of adjacent channels. A typical multichannel deflector has & 10" of channel-to-channel phase nonuniformity. An alternative optical approach to measuring channel-to-channel phase nonuniformity is shown in Fig. 31. The entire aperture of the multichannel Bragg cell is illuminated with a collimated optical beam. A lens is used to form the 2-D Fourier transform of the signals in the device in the back focal plane of the lens. The optical intensity distribution in this plane gives the power spectrum in the acoustic propagation dimension and phase difference between channels in the orthogonal dimension. Phase differences between adjacent channels result in an optical fringe pattern which is shifted vertically away from the transform center in proportion to the phase difference. Since the origin of the transform pattern is not known exactly, a series of phase difference measurements can be made between sequential pairs of channels for a relative phase difference measurement.

W U l Z O W I S , W T I Z I E B , AND PAPE

LIGHT

31 Opticalmultichanneldeflectorphasenonuniformity setup [NI.

I measurement

This measurement technique might be attractive when the application is direction of arrival signal processing, but it is not as accurateas the electrical technique described above.

MODULATOR TESTING

4

Most of the modulator tests(acoustic echo, schlieren imaging, electric, acoustic, and interaction BW, scattering, diffraction efficiency, thirdorder IMP, and VSWR) are similar to those of the deflectors. In addition, the modulator must be tested for its risetime (t,), modulation bandwidth (BW,), modulation transfer function (MTF), and modulation contrast ratio (MCR). These additional tests are unique for modulators, and fortunately they can be performedwith the same test setup, a schematic of which is shown in Fig. 32.

4.1 RisetimeTesting The risetime, t,, of an modulator determinesthe maximum digital data rate usable, and thusit is of primary importance forapplications involving digital modulation. The 10-90% t, depends on the transit time of the acoustic wave across the input optical beam, and is defined [41] as t, =

1.33 W, V

where W, is the l/$ radius of the laser beam incident on theacoustic field of the modulator, and V is the acoustic velocity. Equation (12) shows that

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443

t 32 Schematic of a system used for testing the risetime an

modulator.

for a given material and configuration, t, is proportional to W,. This means that for small t, values (e.g., 110 nsec) focused optical beams should be used. This is because typical narrow collimated optical beams have a diameter of 20.5 mm which, for most materials, results in t, of several tens of nanoseconds. Figure 32 shows the schematic of a risetime test system which employs focused optical beams. In this system light from a laser source is collimated via lens L1 and is subsequently focused onto the sound field by lens L2. The diffracted optical beam is collected and focused onto a single-element high-speed detector by lens L,, which has a focal length of F3. The distances between modulator, L, and detector is 2F,. The output of the detector is displayed on an oscilloscope along withthe envelope of the modulated RF input signal. The latter is generated by mixing the output of a pulse generator with a sine wave whose frequency equals the center frequency, f,, of the modulator. For these tests the outputof the pulse generator is usually a square pulse train with risetime significantly smaller than that expected from the modulator. By observing the 10-90% t,of the detected pulses, we can determine the t, of the modulator for the specific W, used. Figure 33 shows an example of t, testing for the case of a Te02 modulator with f, = 60 MHz. For this example 2w, 80 pm and the resulting 1090% t, is 90 nsec, which isin good agreement with the t, = 86.6-nsec value predicted from Eq. (12). Figure 33 also shows the envelope of the modulating RF input signal, which has a t, < nsec. By using different combinations of lenses L, and L2 we can generate various focused beam sizes which result in different t, values. This information can be used to generate a plot of f, versus the input spotsize, which can be used to verify the design of the modulator and determine the ex-

-

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WUlZOULJS, Wl'TLIEB, ANLI PAPE

Example of modulator risetime measurement using the system of Fig. 32, for S[llO] TeO, modulator withf, = 60 MHz and 2w0 = 80 pm.

pected data rate as a function of the size of the input optical beam. An example of such a plot is shown in Fig. for a L[100]Tl,AsS, modulator of fc = MHz, which was tested with four different spotsizes. In performing the f, test careful attention should be given to various factors which can seriously degrade the accuracy of the measurements. Since focused optical beams are used, we must ensure that the zero and first diffractedorder beams are well separated. This means that angular the spread ( s e d ) of the diffracted beam satisfies 20B. In principle, can be somewhat different from the angular spread of the input optical beam However, in practice is the limiting factor, and therefore care must be taken in selecting the f-numbers of the L,-L, lenses. Note that in addition to the proper f-numbers, lenses L1-L2must also be of adequate quality in order to avoid aberrations which increase W, thereby increasing fr.

TESTING OF ACOUSTO-OPTIC DEVICES

445

1

34 Example of a risetime

optical beam diameter plot for a L[lOO] modulator of 480-MHz center frequency.

When the modulator is used for analog rather than digital applications, the modulation bandwidth (BW,,,) rather than t, is of importance. The SW, associated with a 3-dB falloff in output intensity is defined [26] as 0.5 SW,,, = tr

and thus one can use the measured t, value to evaluate SW,,,. The alternative is to use the system of Fig. 32 in conjunction with different sine wave modulating signals (instead of a pulse train) to directly determine SW,,, for a given By varying the frequency of the modulating sine wave and observing the voltage at the detector’s output, we can identify the frequency f,,, = SW,,, for which the output intensity drops by 50%. An example of this test is shown in Figs.35(a),(b), which show twooscilloscope photographs of the S[110] TeO, modulator’s output for a 100-kHz and a 5.5-MHz modulating sine wave, respectively. For this example the 5.5MHz frequency has about 50% of the low-frequency tone (i.e., 100 kHz)

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WUlZOULIS, WiTLIEB, AA!D PAPE

35 Example of modulation bandwidth testing for a TeO, modulator with fc = 60 MHz and 2w, = 80 pm. (a) 100-kHz tone, and (b) f, = 5.5MHz tone with half the amplitude of the 100-kHz case (in both cases the lower line corresponds to 0 V).

TESTING OF ACOUSTO-OPTIC DEVICES

447

amplitude, and thus it corresponds to f, = SW, = 5.5 MHz. For higheraccuracy measurements, the oscilloscope shouldbe replaced by an RF spectrum analyzer, which will allow the precise characterization of both the amplitude and frequency of the detected signal. Note, however, that in this case the f, will correspond to the frequency that is lower by 6 dB since the 3-dB SW, is defined with respect to theintensity rather than the RF power of the detected signal.

4.3

Modulation TransferFunctionTesting

For analog applications with stringent linearity requirements, the modulation transfer function rather thanSW, is important. MTF is defined [26] as

where = 2wJVis the acoustic transit time. By combining Eqs. (14), (12), and (13) we can show that the MTF can be expressed as a function of the flf, ratio:

m

=

exp

[ -0.69g)2]

where f, = SW,. The MTF can be evaluated by measuring the voltage at the output of the detector as a function of the modulating frequency using the setup of Fig. 32. These data are then normalized by the voltage measured at a very low modulating frequency (i.e., near DC). The experimentally determined MTFis then obtainedby plotting the normalized data as a function of the ratio flf,. Figure 36 shows an example of the calculated and measured MTF for the S[110] TeO, modulator with 2 4 , = pm and f, = BW, = 5.5 MHz. It can be seen that there is excellent agreement between the calculated and measured data. 4.4 ContrastRatioTesting The modulation contrast ratio determines the visibility or contrast of the modulation maxima and minima, and is given by

where I,,,,, and Imin are themaximum and minimum values of the intensity for a given modulation. The MCR is a maximum and equal to unity if the minima are zero, and zero if there is no longer visible modulation. For a

WUl'ZOULJS. Wli'UEB, AND PAPE

1.2 1.4 1.6 1.8 2.0

36 Measured and calculated modulation transfer function for a TeO, modulator withf, = 60 MHz, 2w, = 80 pm, and c, = nsec.

given modulation MCR is measured using the system of Fig. 32 simply by observing the maximum and minimum values of the detected voltage on the oscilloscope. For example, the MCR for Figs. 35(a), and (b) is 0.86 and 0.46 respectively. In a similar manner we can evaluate the static contrast ratio (SCR) defined as

In evaluating SCR caremust be taken in eliminating the RF leakage which may significantly deteriorate the SCR of the modulator which is usually caused by scattering from the crystal. 5

TESTING

The majority of tests required for characterizing the are quite different from those required for deflectors or modulators. This is because of the substantially different nature of an as compared with that of a deflector or a modulator, as well as because of the diversity and types of applicationswhich are different than those of deflectors or mod-

TESTING O F ACOUSTO-OPTIC DEVICES

449

ulators. The common tests are acoustic echo, schlieren imaging, electrical impedance and VSWR, scattering and acoustic attenuation. The additional AOTF tests include (1) tuning relation, (2) optical BW, (3) spectral resolution, out-of-band transmission, (5) RF power dependence of transmission, (6) polarization rejection ratio, (7) spatial separation of orders, (8) angular aperture, and (9) spatial resolution of spectral images. These tests are described in this section.

The most important AOTF test is the verification of the AOTF tuning relation defined as

where V is the acoustic velocity, An is the birefringence,and Fis a function only of the design angle of incidence Oi. Note that F(Oi) is unity for the collinear AOTF and is a numerically evaluated function for the noncollinear AOTF. Thepurpose in verifying the tuning relation is to ensure that the crystal configuration conforms to thatof the design to the desired degree of accuracy. The tuning agreement willbe affected by the accuracy to which the design angle Oi conforms. Since to each value of Oi there is a corresponding acoustic propagation angle, O,, and since generally V = V(O,), an error in crystal orientation will change the tuning relation. Itmay be important to takeinto consideration the temperature coefficients of the acoustic velocity, as well as the refractive indices, as these, too, may have a significant impact on the measurement. A typical setup used in order to perform this test is shown schematically in Fig. 37. A laser source is used to provide a well-calibrated wavelength standard. Thebasic instrument of the test setup is a sweep frequency RF signal generator, whose sweep rate can be adjusted to a low rate, typically less than 1 MHdmin. The output from the sweep generator is chopped by an RF switch which is controlled by a square-wave generator at a rate of about 1 kHz. The square-wave generator is also usedas the reference forlock-in a amplifier which receives the AOTF signal from the detector. An X-Yrecorder is used to provide a plot of the AOTFsignal as a functi?q~of the sweep frequency. By using a second wavelength in the AOTFspectral range, agood fit the tuning curve over the entirerange can be obtained. Anexample of a typical tuning curve is shown in Fig. 38, for thecase a Tl,AsSe, (TAS) AOTF covering the 8-12 pm range. In general, very high precision can be achieved with this technique with commonly available laboratory signal generators.

450

WUIZOULIS, WiTLIEB, AND PAPE

DETECTOR C

AOTF

Y-CHANNEL

RECORDER I I

1 SWITCH

SQUARE WAVE GENERATOR

X-CHANNEL REFERENCE

A

SWEEP FREQUENCY SIGNAL GENERATOR

37 Schematic of a test system for measuring the tuning relation of the AOTF.

5.2 Optical

Test

The 3-dB optical BW of the AOTF, is defined as the spectral range over which the transmission efficiency for a fixed RF drive power remains above and is a very important characteristic for broadband AOTF applications [ M ] .The test setup used to measure theoptical BW is verysimilar to thatshown in Fig. 37, withthe difference that thelaser source is replaced with a broadband light source, preferably one which closely approximates a blackbody emitter. Although an incandescent filament source may be used for the near-UV and visible, a heated Sic rod or a globar is typically used to cover the entire range from the visible through the far-IR. Its operating temperaturecan be adjustedto optimize it for any spectral range and choice of detector, andits lack of protective envelope avoids associated

TESTING OF ACOUSTO-OPTIC DEVICES

8

9

10 Wavelength (

451

urn)

38 Example of a tuning curve for a

11

12

AOTF for the 8-12 pm

range.

absorption limitations. Note that theAOTF optical BW is determined by the transduceracoustic and electric BW and by the h-* dependence of the A 0 diffraction efficiency (see Eq. (5)). The measurement consists of scanning the RF over the full range of interest at a constantdrive power level whilerecording the AOTFfiltered light signal. The magnitude of the signal must be normalized to take into account the spectral intensityof the source,as well asthe spectralsensitivity of the detector, both of which can vary greatly over any sizable spectral range. Note that frequently it is necessary to use two different detector types to adequatelycover the spectralrange of interest. Anexample of an optical BW scan is shown in Fig.39 for the case of a TAS AOTF with an incident angle Ol = 35" and an interaction length of 1cm. For accurateresults the nonlinearitiesfrom all sources must be avoided. For example, theAOTF drive power should be kept below that value for which the diffraction efficiency exceeds 50% for any wavelength within the range of interest. Another sourceof nonlinearity is the detectoritself, especially IR detectors such as InSb or MC". Therefore, itis goodpractice either to calibrate the detector nonlinearity and provide a compensation for it or toreduce the highest signal level belowthe onset of unacceptable nonlinearity. This can be done either by reduction of the RF drive power

W m O U L I S , W 2 1 z I E B , AA!D PAPE

452

$

2.5

5.0

Wavelength

39 Example of an optical bandwidth curve for a typical

AOTF.

or by reduction of the incident source intensitywith neutral-densityfilters. Note that well-calibrated neutral-density filters can be used to determine the detector linearity.

5.3 Spectral Resolution Test The spectral resolutionis a key characteristic of any spectroscopic device, and thus it is routinely measured for AOTFs In general,two different methods are used in order to ensure that the device has been well characterized. Thefirst method is similar to the oneused for testing thetuning relation. Using this method in conjunction with a laser source, a scan is taken as a function of the input frequency. The scan provides the frequency for peak transmission as well as the frequency width (Af) that corresponds to the full-width half-maximum (FWHM) intensity points. Using fo and Af, we can then calculate the spectral resolutionwhich is given by R = fJAf = XJAX. An example of such a scan is shown in Fig. for the case of a TAS AOTF. For this example R = 32.5. Depending on the resolution criterion chosen, the frequency separation between the peak and first zero the transmitted signal can also be designated. For highresolution AOTFs, it is important that the scan rate is slow enough as not to degrade the measurement. It has been observed frequently with AOTFs that the spectral resolution as determined with the above method may not correspond well with that observed when the AOTF is used to analyze broader light sources. In principle, the impulse response the device should be the same in the

v,)

TESTING OF ACOUSTO-OPTIC DEVICES

453

Frequency

40 Example of a spectral resolution test for the case of a TAS AOTF.

frequency space as in the wavelength space, and a scan of either frequency or wavelength should produce the same result. In practice, this is often not the case. The reason for this is due to the imperfections in the acoustic field distribution, which may arise from irregularities in the transducer structure.If there arecomponents of the acoustic field which depart from that of the designed distribution, then these componentsmay phase match withoptical wavelengths that lie beyondthe design resolution width. If the resolution test is performed with the laser, then there will be no wavelength components to phase match with these stray acoustic compo-

454

W W O m I S , W m I E B , AND PAPE

nents, and the response appears to conform to the design response. For this reason, it is more reliable to measure the spectral resolution with a fixed RF applied to the AOTF,and record the light signal while scanning the wavelength of the source. A schematic for this type of measurement is shown in Fig. A simple mechanically scanned grating monochrometer is used, such as a Jarrell-Ashmodel 82 with motorized drive, which provides an output voltage related to the wavelength for the X-channel of the recorder. Of course, it is necessary to provide appropriate slits on themonochrometer to assure that the instantaneous spectral width of the source beam is substantially less than the AOTF spectral width. Otherwise, it would be necessary to deconvolve the monochrometer bandpass from the signal to obtain the AOTF resolution.

5.4 Out-of-BandTransmission The transmission curve in the immediate region of the main peak should reflect the shape of a sinc2 function. Any significant departures from this shape, in the form of additional transmission, is likely due to acoustic field

A

x-Y

41 Schematic a test system for measuring the spectral resolution of an AOTF with a broadband input light source.

TESTING OF ACOUSTO-OPTIC DEVICES

455

irregularities. Closely associated with this type of resolution degradation is the appearance of transmitted light at wavelengths more remote from the main peak, i.e., far out-of-band transmission. This type of irregularity may be associated with the presence of acoustic field components propagating in directions far off from the design direction. Such components typically arise from the unintentional reflections of the acoustic beam by the boundaries of the A 0 crystal. Such reflections are not unexpected, since it is very difficult to completely absorb the acoustic energy at the crystal end opposite the transducer. It is common practice to wedge this crystal end that the direction of the reflected energy does not phasematch with the incident light within the intended spectral range of the AOTF. If this condition is not satisfied, phase matching at some wavelength may be satisfied for frequencies far from the design frequency for that wavelength. Out-of-band transmission can be tested using the setup in Fig. by choosing a number of RF frequencies within the range of the device, the number depending upon the overall RF range. For each frequency the AOTF output signal is recorded as the wavelength is scanned over the entire spectral band of interest. For this test, the sensitivity the postdetector amplifier should be increased that this background transmission can be measured. For a well-designed and fabricated device, the background level should be 30 to 40 dB below the main peak value. For several applications it is necessary to evaluate the integrated out-of-band light intensity relative to the integrated intensity under the main transmission peak. In general, it is common practice to use bandpass optical filters to restrict the incident light beam range in order tominimize the out-of-band energy. Such a bandpass filter may also be used in conjunction with this test in order to measure the most meaningful quantity for the intended AOTF application. When evaluating the test results it is important to keep in mindthat thesinc2function side lobes integrated from the firstside lobe to infinity will contribute about 5% to the transmission outside the main peak.

5.5 RF Power Dependence of Transmission It is important to experimentally establish the regime of linearity for an AOTF in order to ensure that thedevice operates properly. The setup for this test is shown in Fig. 42, and utilizes an RF power meter between the input amplifier and the AOTF, and either a broadband source or different wavelength lasers. The AOTFmust be driven CW, and therefore the modulation the optical beam is obtained with a mechanical beam chopper. The chopped optical signal ismeasured on an oscilloscope. Note

WVlZOULJS, W l T L I E B , AND PAPE

456

4

OSCILLOSCOPE

SIGNAL

42 Schematic of test system for measuring the linearity of the AOTF transmission vs.the RF drive power.

that if the impedance of the AOTF is not constant, the measurementmust be done for several optical wavelengths. This is because the electromechanical conversion efficiency varies with frequency, and the diffraction efficiency primarily reflects the acoustic rather than the electrical power density. Before proceeding with the measurement, the detection system should be calibrated forlinearity and if necessary the light intensity should be reduced sufficiently that it lies in the linear detection region. The measurements areeasily done manually, and consist RF power level vs diffracted signal level.Plotting andanalyzing the results in the usual manner will indicate thepower level which should not be exceeded for any desired degree of linearity. Closely associated with the above power transmission characteristicsat the wavelength peak, is the power dependence of the sidelobetransmission. It may be useful to verify by test that the power dependence of the intensity ratio of the peak to sidelobe agreewith the theoretical predictions.For a nonapodized transducer, the first and second sidelobe peaks should be down by 13 dB and 17 dB respectively, for diffraction efficiencies below 50%. the inputRF level increases, the peak-to-sidelobe ratio decreases because the nonlinear AOTF response. This is undesirable because it

TESTING OF ACOUSTO-OPTIC DEVICES

457

results in high levels of out-of-band transmission. Thus, measurement of this ratio will help optimize the AOTF operation that the out-of-band light is restricted to that caused by acoustic field irregularities or possible misalignment of the AOTFin its mount. Note thatsuch misalignment can cause unsymmetrical sidebands with higher than expected transmission.

5.6 Polarization RejectionRatio The operation of the AOTF is based upon the birefringent properties of the A 0 crystal, which may depart in some respects from ideal behavior, thereby degrading device performance. In particular, it is assumed that the filtered radiation will be 100% polarized, the positive- and negativeorder polarization being orthogonal to each other. This is of crucial importance if the inputangular field exceeds the angular separation between the zero and first diffracted orders. In this case the polarization of the filtered light must be used in order to separate it from the undiffracted light. For example, if the AOTFcrystal isstrained, theremay be sufficient strain birefringence in the optical path to cause some rotation of the unfiltered light, part of which will then appear in the diffracted beam. Furthermore, for the case of optically active AOTF crystals, low-incidentangle designs could allow unacceptably high levels of unfiltered radiation into the output beam. For these reasons, it is desirable to test the AOTF for its polarization rejection ratiosince it may limit the DR of the device. The experimental setupis similar to that of Fig. with the addition of a polarizer andan analyzer at the inputand the outputof the AOTF.Note that the input polarizer should be of high quality because the test result can be no better than that permitted by its rejection ratio.If an unpolarized laser is used, the output optical beam will consist of three components: the zero orderwith intensity Io,and the + 1 and - 1diffracted orders with intensities and respectively. The polarizer is then used to select the input polarization, whereas the analyzer is usedto select the appropriate component at the AOTF output.For this test theRF drive power should be set for 50% diffractionefficiency, that 1+1= = 0.510.By measuring the intensities of each of the three output componentswe can calculate thetwo rejection ratios: Z0/Z+*and Zo/Z-l. The measurementcan be performed with an expanded optical beam that fills the AOTF aperture or with an unexpanded beam which is used to probe individual portions of the aperture in case of nonuniform strains. If the rejection ratio is an important parameter, it may be useful to perform the test at more than one wavelength since strain birefringence is dependent not only on the geometry but also on the wavelength.

458

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WUlZOUL.IS, W l T L I E B , AND PAPE

SpatialSeparation of Orders

The spatial structure of the optical beam exiting the AOTF is somewhat complex when examined in detail. However, for some applications, the details of this structure can be very important and therefore they must be characterized. This spatial structure is illustrated in Fig. 43. For an unpolarized input beam, there are four beams which appear in the output. In addition to the two first-order diffracted beams, the two polarizations in the zero order are also separated because of the birefringence of the crystal. Note that theactual separation of the orders will depend upon the (1) incidence angle Of, (2) direction of light propagation with respect to the optic axis, and path length in the crystal. The measurement the angular separation between the various orders is carried out using a laser source and a single-element detector mounted on a translation stage. Since the angular separation between the two zeroorder beams is quite small, the light beam must be well collimated and the detector plane sufficiently distant from the AOTF so that the beams will be spatially separated. The diffracted order beams will generally be between l"and 10" from the zero order. Note that these measurements must be performed at two wavelengths to fully account for dispersive effects.

5.8 AngularApertureTest The angular aperture or field of view (FOV) of the AOTF is defined as the angular field over which any input light ray may arrive and be transmitted at no less than 50% of the transmission at the optimum phasematched arrival angle. The determination of the angular aperture is carried

%=L-

+

Figure 43 Directions and polarization of the zero-order, positive and negative, first-order beams for an AOTF.

l"TING

OF ACOUSTO-OPTIC DEVICES

459

out at a fixed wavelengthand for afixed RF power. This test is most easily carried out by mounting the AOTF on a goniometer as illustrated in Fig. 44.The AOTFis held in a fixed position with its input opticalface located at the center of the goniometer, while the laser source and the detector are held on arms which are free to rotate about the AOTF. The measurement consists of determining the transmission ratio T(8) = Z(8)/Zp,where 8 is the angle of the laser with respect to theAOTF and I,, is the intensity of a perfectly phase-matched beam. It is important that theRF drive power be set at a level well below the nonlinear range in order to measure the true angular aperture. The AOTF of Fig. 44 is positioned in order to measure the polar aperture; for measuring the azimuthal aperture the AOTF must be rotated andmounted orthogonal to the plane of incidence. Note that the transmitted intensity distribution in the azimuthal plane is symmetrical about the center. However, this is not the case in the polar plane, especially for large values of the incidence angle, €li.For large FOV designs it is important to consider the effect of optical reflection losses, especially when AR coatings have been applied to the device. Depending

LASER

'h DETECTOR

\ -

/

GONIOMETER MOUNT

Determination of the angular aperture of an AOTFby measuring the transmission as the incident laser beam is rotated about the input face of the AOTF.

460

WVlZOULlS, W T I L I E B , AND PAPE

upon their design, the coatings themselves may contribute significantly to the angular variation of the transmission, and this effect should be separately evaluated from that due to the interaction. It was mentioned earlier that forOi the angular aperture (as represented on a polar plot)can be very complex, especially in certain singular directions. characterize this behavior, the must be mounted at measured angles between the polar and azimuthal planes. The measurement will be restricted by vignetting by the crystal near these singular values, where the angular aperture may be toolarge to allow even a small ray to exit the crystal output face.

5.9 Spatial Resolution of Spectral Images Optical systems whichincorporate for spectral imaging require an additional testwhich relates to thetransfer function of the or simply to the image quality resulting from the simplified method for characterizing the transfer function is shownin Fig. and uses an imaging camera. standard resolution chart is placed at a convenient distance, L , from the input to the The distance and the chart line spacings are chosen that a line pair of the chart will lie at theresolution limit of the The resolution limit can be specified as theangular separation, 8, between the line pairs at the limit, at the distance, L. This angle can be compared with the diffraction limited resolution angle from the aperture (=l.ZA/D).In general, the diffraction limit will be much smaller for an operating near the visible, while for at long-wave IR, the resolution may well be aperture diffraction limited. Figure shows an example of the chartimaged through a TeO, operating in the visible, and displayed on a TV monitor. From this photograph, it can be seen that theline pairs become indistinguishablebetween the small scale numbers 5 and For this example it is easy to verify, by

Fiol0 =

-6

45 Spatial resolution test an AOTF with an imaging camera by determining just resolved line pair on a standard resolution chart.

TESTING OF ACOUSTO-OPTIC DEVICES

461

41

aa

Example of a spectral image from a TeO, AOTF displayed on a TV monitor

examining the zero order image, that the image degradation is due to the interaction and not to the crystal or the TV camera.

The authorswould liketo thank Dr. D. K. Davies of Westinghouse Science and Technology Center forhis help in obtaining some of the experimental results presented in this chapter.

Bademian, L., Parallelchannel acousto-optic modulation, Opt. Eng., Hecht, D. L.,and Petrie, G . W., Acousto-optic diffraction from acoustic anisotropic shear modes in gallium phosphite, IEEE 1980 Ultrasonics Symposium Proceedings, Cohen, M.G . , Optical study of ultrasonic diffraction and focusing in anisotropic media, J. Appl. Phys., Longhurst, R. Geometrical and Physical Optics, Wiley, New York, Chang, I. C., and Hecht, D. L., Characteristics of acousto-optic devices for signal processors, Opt. Eng., 21,

WUIZOULIS, W l i ' Z I E B , AND PAPE 6. Hecht, D. L., Spectrum analysis using acousto-optic devices, Opt. Eng., 16, 461-466 (1977). 7. Goodman, J. W., Introduction to Fourier Optics, McGraw-Hill, New York, 1968. 8. Stover, J. C., Bjork, D. R., Brown, R. B.,and Lee, J. N.,Experimental measurement of. very small angle stray light optical performance of selected acousto-optic materials, Mater. Sci. Forum, 61, 57-92 (1990). 9. Stover, J. C., and Cady, F. M., Measurement of low angle scatter, Opt. Eng., 24,404-407 (1985). 10. Henningsen, T.,and Singh, N. B., Crystal characterization by use of birefringence interferometry, J . Cryst. Growth, 96, 114-118 (1989). 11. Brown, R.B., Craig, A. E., and Lee, J. N., Predictionsof stray light modeling on the ultimate performance of A 0 processors, Proc. SPZE, 936,29-37 (1988). 12.Goutzoulis, A., Gottlieb, M., Davies,K.,and Kun, Z., Thalliumarsenic sulfide acousto-optic Bragg cells,Appl. Opt., 24, 4183-4188 (1985). 13. Singh, N. B., Davies, D. K., Gottlieb, M., Goutzoulis, A., Mazelsky, R., and Glisman, M. E., On the quality of mercurous chloride crystals, Mater. Lett., 397-400 (1989). 14. Dixon, R. W., Acoustic diffraction of light in anisotropic media, IEEE J. Quantum Electron., QE-3, 85-93 (1967). 15. Hecht, D. L., Variable bandshapes in birefringent acousto-optic diffraction in LiNbOB,J. Opt. Soc. A m . , 66, 1094 (1976). 16. Goutzoulis, A. P., and Kumar, B.K. V., Detector size effects on peak-tosidelobe ratio in bulk acousto-optic spectrum analyzer, Opt. Eng., 24, 908912 (1985). 17. Hammer, J. M., and Neil, C. C., Adjustable modules for high-power (> 7.5 mW CW) coupling of diode lasers to single-mode fibers, ZEEE J . Lightwave Technol., L T - l , 485-494 (1983). 18.Chang, I. C., Acousto-opticdevices and applications, IEEE Trans. Sonia Ultrasonics, SU-23, 2-22 (1976). 19. Hecht, D., Multifrequency acousto-optic diffraction, ZEEE Trans. Sonia UItrasonics, SU-24, 7-18 (1977). 20. Chang, I. C., Nonlinearacousticeffects in widebandacousto-opticBragg cells, in Proceedings of the CLEOS Conference, 1983. 21. Shah, M. L., and Zerwekh, P. S., Intermodulation in wideband Bragg cells, 1983 lEEE Ultrasonics Symposium Proceedings, 1983, pp. 441-444. 22. Pape,D., Acousto-opticBraggcell intermodulation products, 1986 IEEE Ultrasonics Symposium Proceedings, 1986, pp. 387-391. 23. Goutzoulis, A., Davies, D., and Gottlieb, M., Thallium arsenic sulfide Bragg cells for acousto-optic spectrum analysis, Opt. Comm., 57, 93-96 (1986). 24. Elston, G., and Kellman, P., The effects of acoustic nonlinearitiesin acoustooptic signal processing systems, 1983IEEE Ultrasonics Symposium Proceedings, 1983, pp. 449-453.

TESTING OF ACOUSTO-OPTIC DEVICES

463

25. Korpel, A., Adler, R., Desmares, P., and Watson, W. ,A television display using acoustic deflection and modulation of coherent light, Appl. Opt., 5, 1667-1675 (1966). 26. Young, E. H., and Yao, S-K., Design considerations for acousto-optic devices, Proc. IEEE, 69, 54-64 (1981). 27. Randolph, J., and Momson, J., Rayleigh-equivalent resolution of acoustooptic deflection cells, Appl. Opt., 10, 1453-1454 (1971). 28. Chang, I. C., Cadieux, R., and Petrie, G., Wideband acousto-optic Bragg cells, 1981 ZEEE Ultrasonics Symposium, 1981, pp. 735-739. N., Acousto-optic deflection materials and techniques, 29. Uchida, N., and Niizei, Proc. ZEEE, 61, 1073-1092 (1973). 30. Roland, G., Gottlieb, M., and Feichtner, J. D., Optoacoustic properties of thallium arsenic sulfide, Appl. Phys. Lett., 21, 52-54 (1972). 31. Issacs, T. J., Gottlieb, M., and Feichtner, J. D., Optoacoustic properties of thallium phosphrous selenide,Tl,Pse,, Appl. Phys. Lett., 24,107-109 (1974). 32. Singh, N. B., Gottlieb,M., and Goutzoulis, A.P., Mercurous bromide acoustooptic devices, J. Cryst. Growth, 89, 527-530 (1988). 33. Bolef, D., in Physical Acowstics(W. P. Mason, ed.), Vol. IV,Part A, Academic Press, New York, 1966, p. 113. 34. Spenser, E.G., Lenzo, P. V., and Bellman, A. A., Dielectric materials for electro-optic, elasto-optic, and ultrasonic device applications, Proc. IEEE, 55,2074-2108 (1967). 35. Beaudet, W. R., Hams Corporation, private conversation, 1992. 36. Pape, D. R., Multichannel Bragg cellsfor optical systolic matrix processing, Topical Meeting on Optical Computing, March 18-20,1985, Incline Village, N V , Tech. Digest, Paper TuC6-1, 1985. 37. Beaudet, W. R., Popek, M., and Pape, D. R., Advances in multichannel Bragg cell technology, Proc. SPZE, 639,28-33 (1986). 38. Lin, Crosstalk characteristics of multichannel acousto-optic Bragg cells, Proc. SPZE, 936, 76-84 (1988). 39. Lin, S., and Boughton, R. Some performance characteristics of a channel Bragg cell with self-collimating acoustic waves, Optical Society of AmericaAnnualMeeting, Oct. 15-20, Orlando, FL. Tech. Digest, Paper MG1, 1989. 40. Lee, J. P. Y., Simple phase-tracking measurement technique for multichannel Bragg cells, Opt. Eng., 27, 677-683 (1988). 41. Maydan, D., Acousto-optical pulsemodulators, IEEE J . Quantum Electron. , QE-6, 15-24 (1970). 42. Singh, N. B. ,Gottlieb, M., and Goutzoulis, A. P.,Devices madefrom vaporphase-grown mercurous chloride crystals, J. Cryst. Growth, 82,274-278 (1987). 43. Singh, N. B., Denes, L. J., and Gottlieb, M., Growth and characterization of large Tl,AsSe, crystals for collinear AOTF devices, J. Cryst. Growth, 92, 13-16 (1988).

464 44.

WUlZOUL.IS, W l ' l U E B , A M ) PAPE Steinbruegge,K. B., Gottlieb, M., and Feichtner,J. D., Automated acoustooptic tunable filter infrared analyzer, Proc. SPZE, Feichtner, J. D., Gottlieb, M., and Conroy, J., Tunable acousto-opticfilters and their applications to spectroscopy, Proc. SPZE,

Computer-Aided Design Program for Acousto-Optic Deflectors. Oleg St. Petersburg State Academy

Gusev

Aerospace Instrumentation St. Petersburg, Russia

In general, the total frequency-dependentefficiency of an A 0 device is

where is the A 0 efficiency, q D is the efficiency loss associated with the diffraction acoustic energy outside the illumination aperture of the device, is the efficiency loss associated with acoustic attenuation in the deflector, and qTRAN is the loss associated with converting electric energy into acoustic energy at the transducer. The first term in Eq. (A.l) is discussed in Chapter 1 on A 0 deflectors, in Chapter 2 for A 0 modulators, and in Chapter for A 0 tunable filters. The second and third terms are primarily present only in deflectors and tunable filters and are discussed in Chapter 1 and Chapter respectively. The fourth term is discussed in Chapter 4. In Fig. A.l we provide a computer-aided design program from the St. Petersburg StateAcademy of Aerospace Instrumentation,which calculates the overallefficiency an A 0 deflector. Theprogram calculates the A 0 efficiency for an isotropic Bragg interaction using user-supplied device operating parameters,A 0 material characteristics,and transducer length. (The program can be modified to include the routine from the isotropic design program shown in Chapter 1 in Fig. which calculates a nominal value of L. The program can also be modified to include the other A 0

APPENDIX A OPEN 'PLOTDATA-1' FOR OUTPUT #l OPEN 'PLOTDATAQ' FOR OUTPUT #2 OPEN 'PLOTDATA-Y FOR OUTPUT #3 OPEN'PLOTDATAJ' FOR OUTPUT #4 OPEN 'PLOTDATAB' FOR OUTPUT #5 OPEN "PLOTDATA-6' FOR OUTPUT #6 OPEN 'PLOTDATA-7' FOR OUTPUT #7 OPEN 'PLOTDATA-C FOR OUTPUT #8 PRINT 'HARDCOPY ? YES 1, NO 0 INPUT N PRINT 'ELECTRICAL RESPONSE7 YES l,ELECTROOPTICAL RESPONSE? YES INPUT XX1 Pl=3.14159 F9=3E+08 FFO=F9 PRINT 'CENTRAL FREQUENCY FS..',FS;'GW FFF=.333 PRINT 'RELATIVE BANDWIDTH FFF=',FFF FF1 =FFO'FFF PRINT "BANDWIDTHFFl=;FFl W0=3E+O8/(F9*SQR(2.1)) P=l PRINT 'MAXIMUM BRAGG ANGLE MISMATCH P=',P PRINT 'ELECTRIC WAVELENGTHIN DIELECTRIC WO=';WO;'pTI' L1=.006 PRINT 'LENGTH OF LOAD TRANSMISSION LINE Ll=';Ll ;'pTI' LO=Ll/WO PRINT 'WAVELENGTH OF LOAD TRANSMISSION LINE LO=':LO 20 =20 2W;ZO;'Ohm' PRINT 'CHARACTERISTIC IMPEDANCE OF LOAD TRANSMISSION LINE T=.000003 PRINT TIME APERTURE T=';T E=38.6 PRINT 'DIELECTRIC CONSTANT OF PIUOELECTRICS E=';E L8=.0025 PRINT "TOP ELECTRODE LENGTH L8=';L8;'mm U7=4200 PRINT 'ACOUSTIC VELOCITY IN A 0 SUBSTRATE U7=';U7;'dsec' D9=T'U7 PRINT 'OPTICAL APERTURE D9=';D9;'m' F5=F9-.5'FFF'F9 PRINT 'LOWEST FREQUENCY F5=';F5;'Hzm PO=1 PRINT 'GROUP VELOCITY ANISOTROPY RATIO PO=';PO H=SQR(U7"2'T/F5'PO)

-

-

-

Computer-aideddesignprogramfor

-

deflectors.

467 PR~NT"TOPELECTRODE WIDTH (NEAR ZONE C O ~ D ~ T ~ o H=";H;"m" N) H=.0004 PRINT "CORRECTEDTOP ELETRODE HEIGHT H=";H;"m" N0=2.412 L9=6.328E-07 PRINT "OPTICAL WAVELENGTH L9=";L9;"mN PRINT "REFRACTIVE INDEX NO=*;NO U 1=4790 PRINT *ACOUSTIC VELOCITY IN PlEZOELECTRlCS u1=";u1 ;"dsec" R6=50 PRINT "SOURCE IMPEDANCE RW;R6;"0hmn K0=.49 PRINT "REFERENCE ELECTROMEC~ICAL COUPLING COEFFICIENT=";KO K6=KOA2/(1-K0"2) PRINT "REFERENCE ELECTRIC COUPLING COEFFICIENT OF EQUIV. NET.K6=";K6 K6=.2 ~RINT 'ELECTRIC COUPLING COEFF. OF EQUIV. NETWORK PIEZOEL. TRANSD. K6=";K6 Q9=4 PRINT "FIGURE OF MERIT OF LCR CIRCUT Q9=";Q9 C9=E*8.85E-l2*L8*H*2~F9/Ul RlNT 'STATIC CAPACIT. OF SINGLE ELEM. PIEZOEL. TRANSD. C9=";C9;"F" 01 =I PRINT "CO DECREAS. COEFF. FOR MULTIELEM. PIEZOEL. TRANSD. 01=";1 c9=c9/1 ~RINT "CO DECREASED=';C9;"FN R 9= 1/( 2 * P I * F9* C 9* K6*Q9) PRINT "RADIATION RESISTANCE OF PIEZOEL. TRANSD. R9=';R9;"0hmn c2=0 PRINT "SOURCE CAPACITANCE C2=";C2;"F" C3-0 cco=o PRINT 'CAPACITANCE PARALLEL TO LOAD TRANS.LINE INPUT CCO=";CCO;"~F' INT 'CAPACITANCE PARALLEL TO C9 C3=";C3;"Fn C8=C9+C2+C3 PRINT "TOTAL CAPACIT. C9+C2+C3=";C8;'Fn K8=C9*K6/(C9+C2+C3) PRINT "ELECTRIC COUPL.COEFF. WITH PARALLEL CAPACIT. K8=";K8 RE^ * IF NO EXTERNAL SERIAL CAPACIT. C4=0 C4=0 PRINT 'EXT~RNALCAPACIT. SERIAL TO c9+c2+C3=";C4;'Fn GOSUB 3470 R3=1/(2*PI*FO*CO*K*Q) F'RINT "RADIATION RESISTANCE R3=";R3;'0hmn PRINT "ELECTRIC COUPLING COEFF. WITH EXTERNALCAPACIT. K=";K PRINT 'FIGURE OF MERIT OF EQUIV. NETW. WITH EXTERNALCAPACIT. Q=";Q

.I Continued

468

APPENDIX A

PRINT"STAT. CAPACIT. OF EQUIV. NET. WITH EXTERN. CAPACIT CO=";CO;"F" REM STOP PRINT "LCR RESONANT FREQ. WITH EXTERN. CAPACIT. FO=";FO;"Hz" PRINT "UPSHIFTED PIEZOEL.TRANSD. RESONANT FREQ. F7=";F7;"Hz" DO=U 1/2/F7 PRINT "PIEZOELEM. THICKNESS WITHOUT BOND DO=";DO;"m* L2=1/( (2*PI*FO)"2*CO) GOTO 930 PRINT "CORRECTIVE INDUCTANCE PARALLEL TO CO =";L2;"H" 930 K9=1 PRINT "INDUCTANCE INCREASE RATIO K9=";K9 L3=L2/K9 PRINT 'CORRECTIVE INDUCTANCE PARAL. TO LOAD TRANS. LINE=';L3;"HU PRINT "LOAD TRANSM. LINE CHARACTERISTIC IMPEDANCE -";ZO;"Ohm" PRINT 'DIELECTRIC CONSTANT E=2.1' L5=3E+ 1 1/SQ R(2.1 )/F0/4 PRINT "Q-W TRANSFORMER LENGTH (GENERAT.TRANSM.LINE)=";L5;"mm" 0 5 =1 PRINT "Q-W TRANSFORMER SHORTENING RATIO 05=";05 L5=L5*05 PRINT 'SHORTENED Q-W TRANSF. LENGTH (GENERAT.TRANSM.LINE)=";L5;"mm" U3=3E+1 lISQR(2.1) U4=2*PI*FO M3=( U3/U4)*ATN( l/(K9*U4*CO*ZO)) PRINT 'INDUCTIVE STUB LENGTH ZO=';M3;"mm' Q6=2* PI*L9*L8/( NO*(U7/F0)"2) PRINT "KLEIN-COOK PARAMETER Q6=';Q6 A=l.451 E-12 PRINT 'ACOUSTIC ATENUATION PARAMETER A=";A;'Np/sec" M2=3.43E-17 PRINT 'A0 FIGURE OF MERIT M2=';M2;'sec**3/gM S0=(1.23*M2*L8/H)*l E+18 PRINT "DIFFRACTION EFFICIENCY SO=';SO;"%NVt" GOTO 1240 T5=SQR( 1-SIN( L9*F9/2/U7)"2) PRINT 'BRAGG ANGLE COSINE T5=';T5 Q7=( P P 2 "M2* 1E+07*MO*X7)/(H*( L9*.0 1*T5)"2)/4 PRINT 'Q7=';Q7 QO=Q7* S IN(P I*X7/(2*N9))/( PI*X7/N9/2) PRINT 'DIFFR. EFFIC. WITH BRAGG ANGLE ADJUSTMENT QO=";QO;"YooNVt' AF=FFO*FFF 1240 REM IF N = 0 GOTO 2080 PRINT #1 ELECTROOPTICAL FRECUENCY RESPONSE FOR AOD" PRINT #1 WITH MATCHING NETWORK BASED ON" 11"

Figure A.l

Continued

APPENDIX A

469

GOTO 1290 PRINT #1,," LUMPED INDUCTANCE AT LOAD TRANSMISSION LINE INPUT" REM GOTO 1310 1290 PRINT #1,," SHORTENED INDUCTIVE STUB AT LOAD TRANSMISSION LINE" GOTO 1320 AND EXTERNAL SERAL AND PARALLEL CAPACITANCES" 1310 PRINT #l,," 1320 PRINT #1,," AND QUARTER-WAVE TRANSFORMER WITH FREQUENCY RESPONSES" PRINT #1,," A 0 INTERACTION AND ACOUSTIC AlTENUATION" PRINT #1,," LiNbO3 => Te02 [OOl] AOM : MARK [TENZOR 901" PRINT #l,," SIGNAL PARAMETERS" PRINT #1,,"Central frequency .......................................................... =';FO;'Hz' PRINT #1 ,,"Time aperture ................................................................. ='. T;"sec" PRINT #1,,"Relative bandwidth ........................................................ =';FFF PRINT #l,," Bandwidth.......................................................................... =".FFl PRINT #1,," ACOUSTO OPTIC SUBSTRATE" PRINT #1,,'Te02 N[001], U[OOl], E- perpendicular to [OOl]" PRINT #1,,'Acoustic wave direction..................................................... - [OOl]" PRINT #1,,"Optical wave polarity................. = perpendicular to [OOl]" PRINT #1,,'Optical wave direction...................................................... [lOO]" PRINT #1,,"Acousto optic interaction................................ isotropic" PRINT #1,,"Acoustic velocity (longitudinal) ......................... =';U7;'m/sec' PRINT #1,,"Acoustic wave attenuation....................................... =';A;'Np/sec' PRINT #1,,'Klein Cook parameter (without mismatch).........=';Q6 PRINT #1,,'Bragg angle mismatch........................................................ =";P PRINT #1 ,,'Acousto optic figure of merit ................................ =';M2;'sec*'3/gU PRINT # 1,,'Diffraction efficiency (without losses). .............. ..=';SO;'%/Wt" PRINT #1,,'Optical aperture................................................................... =';D9;'m' GOTO 1610 PRINT #1,,'Diffrac. eff. with Bragg angle adjustement...............=';QO;'%/Bt" 1610 PRINT #1,,' PIEZOELEKTRIC TRANSDUCER" PRINT #l,,'LiNb03 Y+36 deg.' PRINT #1 ,,'Dielectric constant with constant strain...................... =';E PRINT #l,, 'ElectromechaniCal coupling coefficient......................... =';KO PRINT #1,,'Electric coupling coeff. for equvalent network =';K6 PRINT #1,,'Figure of merit of LCR circuit...................................... =';Q9 PRINT #l,,'Top electrode width.............................................................=' ;H;"m" PRINT #l,,'Top electrode length.............................................................. =' ;L8;"mN PRINT #1,,'Static capacitance of clamped transduser =';C9;"Fm PRINT # 1,,"Radiation resistanse................................................................ =';RS;"Ohm" PRINT #1 ,,'Acoustic velocity with constant strain .......................... =';U1 ;'m/sec' PRINT #1,, 'PIEZOEL.TRANSD.PARAMETERWITH FEEDER AND EXTER.CAPAIT.' PRINT #1,,* Piezoel.transd. feeder capacitance.................................... =";C2;'F' PRINT #1,,'Capacit.parall.to load transm.line input........................... =";CCO;'F" REM PRINT #1,,"Exter.capacit.ser.to piezoel.transd.+feeder........=";C4;"F" PRINT #1,,"Electric coupl.coeff. with parallel capacit. ...............=';K

-

-

-

-

-

-

...................

Figure A.l

Continued

APPENDIX A

470

PRINT #1,;LCR figure of merit with exter. capacit. ......................=' ;Q PRINT #l,;Stat. capacit. of piezoel.transd. + exter.capacit.';CO;'F" PRINT # l ,,'Radiat.resistance with exter. capacit. =';R3;'0hm' IF C4=0 THEN 1900 PRINT #l,,'Central frequency FO= ...........';FO;'HZ' PRINT # l ,,'Piezoelectric transducerresonant frequency' PRINT # l ,,'upshifted due to external capacitance =';F7;'HZ' ;DO;'m' 1900 PRINT #l,,'Piezoelement thickness without bond DO PRINT # l ,,' Matching network parameters' PRINT #l,,'Generator impedance for Q-W transformer =';R6;'Ohm' GOTO1960 PRINT # l ,,'Corrective inductance parallel to CO+C2+C3 =';L2;'H' 1960 PRINT #l,,'Correct.induct. paralleltoload trans.linein. ..=';L3;'Hm GOTO1990 PRINT #l,,'Corrective inductan............................................. lumped' REM GOTO 2000 1990 PRINT # l ,,'Corrective inductance shorted inductive stub' 2000 PRINT #l,,'lnductance increase ratio =';K9 =';Ll;'m' PRINT # l ,,'Load transmssion line length PRINT #l,,'Normalized load transmission line wavelength =';L0 PRINT # l ,,'Transmission linedielectrcs teflon,diel.const. ..=2.1' 05=0 THEN 2050 PRINT # l ,,'@W transformer shortening ratio =';05 2050 PRINT # l ,,'Q-W transformer width =';LS;'mm' ST0 P 2080 REM PUT CALL TO PLOT SETUP ROUTINE HERE FOR F=.5 TO 1.501 STEP .0125 GOSUB 3100 WRITE # l , F,13 NEXT F FOR F=.5 TO 1.501 STEP .0125 GOSUB 3010 WRITE #2, F, M9 NEXT F FOR 2-1.25 TO 1.75 STEP .25 R5=ZO'Z GOTO 2160 PRINT 'Loadtransmission line input impedance =';R5;'0hm' 2160 Z4=SQR(R6'R5) REM IF N=O GOTO 2250 PRINT #l,,'Gener.impedance to load transm.charac.impedance ratio 7 PRINT # l ,,'Q-W transf. charac.' impedance =';Z4;'0hm" REM IF N=O GOTO 2250 PRINT #l,,'lnductive stub charact. impedance =';ZO;'Ohm'

...................

.....................

...............

...........=' ......

.....

............................ ........................ ...................

...........................

...................................

................ ...........

Continued

.....

APPENDIX

471

PRINT # l ,,'Inductive stub length with charac. impedance ZO....=" ;M3;'mm' 2250 FOR F=.5 TO 1.5 STEP .0125 GOSUB 2950 GOSUB 2620 TT=2'PI'F'.25'05 A4=ZO'R B4=ZO9X+Z4'TAN(TT) C4=Z4-ZO'X'TAN(TT) D4=ZO'R'TAN(TT) C44=C4*C4+D4'D4 R4=(A4'C4+B4'D4)IC44 X4=(B4'C4-A4'D4)IC44 KK1 l=(Z4'R4-R6)*(Z4'R4-R6) KK12=(Z4'X4'X4'Z4) Kl=KKll+KK12 KKl3=(Z4'R4+R6)'(Z4'R4+R6) K2=KK13+KK12 G4=1-KllK2 REM G4=(1-6"2) GOSUB 3010 M5=G4'M9 GOSUB

-

-

REM B1 Electroopt.freq.response normalized by Klein Cook parameter M6=M5'13 F<.998 OR F>1.01 THEN 2540 GO=SQR(Kl/K2) N=O GOTO 2540 SO=(l+ABS(GO))/(l-ABS(G0)) PRINT #l,,'Reflection coefficent at frequency F=l........... =';GO PRINT #l,.'VSWR at frequency F=l =';SO 2540 XX1=1 THEN 2565 IF Z=1.25 THEN WRITE F,M6 Z=1.5 THEN WRITE #4, F,M6 IF Z=1.75 THEN WRITE #5, F,M6 GOTO 2570 2565 Z=1.25 THEN WRITE #6, F,G4 Z=1.5 THEN WRITE #7, F,G4 Z=1.75 THEN WRITE #8, F,G4 2570 REM NEXT F REM last statement 2470 next NEXT Z CLOSE # l CLOSE #2 CLOSE

.........................

Continued

472

APPENDIX

CLOSE #4 CLOSE CLOSE #6 CLOSE #7 CLOSE END func 2620 NN=F-l/F G5=1+Q'Q'NN8NN BO=R5'2'PI'FO'CO/Z Gl=BO'K'Q/G5 REM 'Inductance parallel to CO add '=-1/F' to B1 REM Inductive stub parallel to CO add '-Tl' to B1 B1=(F'G5-K0NN'Q"2)/G5 B2=BO'B1 REM Denormalized G8=G1 & B8=B2 G8=GlR0 B8=B2/ZO B5=2'PI'F'LO B3=B2+SlN(BS)/COS(BS) C=l-B2*SIN(B5)/COS(B5) D=Gl'SIN(B5)/COS(BS) GS=C*C+D*D G=(Gl'C+B3*D)/G9 R E M 'Inductance parallel to load trans. line input add '-KS'BOIF' to B R E M 'Induc.stubparal. toload trans.line input add 'f'2'pi'fO*zO*ccO'to B R E M Inductive stub parallel to load trans. line input add '-BO'Tl' to B B=(B3'C-G1'D)/G9-BO'T1+F'2'PI'FO'ZO*CCO REM *Denonnaked compon. of input conduc. of load tran. line P9=G & D9=B P9=G/ZO DS=B/ZO R=G/(G'G+B'B) X=-B/(G'G+B'B) REM 'Denormalized components of load trans. line input imped. & X9=X R9=R'ZO X9=X'ZO RETURN 2950 REM Reactive conductance of shorted stub 71' AO=U4'M3/U3 AAl=SIN(AO'F)/COS(AO'F) AA12=U4*CO'ZO'AAl T1=1/AA12 RETURN 3010 REM Acoustic attenuation frequencyresponse FF=FO'F

-

-

Continued

APPENDIX Al=A'T'FF'FF IF A1>100 THEN 3070 MS=(l-EXP(-Al))/Al GOTO 3080 M9=1 3080 RETURN 3090 REM A0 interaction frequencyresponse 3100 ll=.25'Q6*(F*F-PgF) ll=O THEN 3135 12=SIN(ll) l3=(l2/ll)*(l2/ll) GOTO 3140 3135 13=1 3140 RETURN REM Transversal dimensions of rectangular coaxial line H=.3 PRINT 'Width of central conductor';H;'mm' H1=.2 PRINT 'Dielectric thickness';Hl;'mm' H2=H+2'Hl PRINT 'Facewidth';H2;'mmm L8=2 PR1NT 'Length of central conductor';L8;'mm' Z0=18.5 PRINT 'Characteristic impedance';ZO;'Ohm' E9=2.1 PRINT 'Dielectric constant of waveguidedielectrics';E9 Wl=H2'(EXP(ZO*SQR(E9)/59.952)'(L8/H2+H/H2)-1) PRINT 'Face1ength';Wl;'mm' PRINT PRINTTransversal dimensions of microcoaxial rectangular' GOTO 3370 PRINT 'loadtransmissionline' PRINT Q-W transformer' 3370 PRINT 'shorted inductive stub' PRINT PRINT 'characteristic impedance';ZO;'Ohm' PRINT 'Dielectricc teflon ';E9 PRINT PRINT 'Width of central conductor';H;'mm' PRINT 'Length of central conductor0;L8;'mm' PRINT 'Facewidthm;H2;'mm' PRINT 'Face1ength';Wl;'mm' END 3470 REM & Q of PT equivalentnetwork with external serial capacit.

-

Continued

APPENDIX

474

-

* C4 externalcapacitanceserial C7=C8'( 1 IF C4=0 THEN 3520 GOTO 3540 3520 U=O GOTO 3550 3540 U=C7/C4 3550 1+U) Q5=SQR((l+K8)'(l+U)/(l+K8+U)) Q=Q9'Q5 FO=F9'Q5 F9=FO/Q5 F7=FO/Q5 C6=C7/K8 C5=C7/( 1+U) CO=C5*CS/(C5+CS) RETURN

to CO

Continued

interaction geometries.) The program calculates an optimized transducer height that no losses are associated with diffraction. The program can be used interactively to design an electrical impedancematching network given user-supplied values of the equivalent network of the piezoelectric transducer. An electrical equivalent circuit for a typical A 0 deflector transducer is shown inChapter in Fig.20. The user supplies the electrical coupling coefficient k ( = C,&,), the figure of meiit = l/ooCAR),and the series resonant frequency of the equivalent circuit. A simple two-stage matching network connected to the transducer via a transmission line is designed (similar to that shown in Chapter in Fig. 21) which resonates the parallel-plate capacitor with an inductor (Lo)followed in series by quarter-wave transformer [24]. Once the circuit is designed, the user can vary 2,the ratio of the load impedance R, to thetransmission line impedance The program in Fig. A . l is configured to calculate the diffraction efficiency of a longitudinal mode 100-MHz bandwidth, 3-psec timeaperture TeOzdeflector. RF power is delivered to the device via a microcoaxial waveguide structure with an internal conductor cross section equal to the piezoelectric transducer electrode size (2.5 X 0.4 mm). The output from the program providing all of the design information is shown in Fig. A.2. The program also provides calculated values for the parametersin Eq. (A.l) as a function of frequency. The program can be interfaced to a

APPENLIIX A

476

0.60

0.70 0.90 1.00 1.10 1.20 1.30 Relative Frequency (FC=3OOMHz)

1.40 1.50

Relative transducer efficiency vs. relative frequency for 1OO-MHz bandwidth, 3-hsec time-aperture deflector using different Z values.

0.60

0.90 1.00 RelativeFrequency

0.70

1.10

1.20 1.30 MHz)

1.50

Relative device efficiency vs. relative frequency for 1OO"Hz bandwidth, 3-hsec time-aperture deflector using different Z values.

APPENDIX A

477

graphics routine which allows the user to interactively design the A 0 deflector and electrical impedance-matching network to achieve a desired frequency response. Figure A.3 shows composite plot of qa, and for this device. Three curves are shown for corresponding to different values of the impedance ratio 2.Figure shows the composite diffraction efficiency q for this device using the three curves from the previous plot. The most uniform bandshape is that with Z = 1.50. A few of the many A 0 devices designed at the St. Petersburg State Academy of Aerospace Instrumentation are shown in Fig. A S .

A 0 devices designed and fabricatedat the St. Petersburg State Academy of Aerospace Instrumentation.

This Page Intentionally Left Blank

A Computer Program for the Analysis and Design of Transducer Structures P. Goutzoulis Westinghouse Science and Technology Center Pittsburgh, Pennsylvania

! ! ! ! !

DESIGN.FOR

T H I S I S A TRANSDUCERDESIGN PROGRAM THAT I S BASED ON THE THEORY D E S C R I B E D I N CHAPTER 5. I T USESTHESUBROUTINES T L I M PT, R A I M P , AND CONEFF I N ORDER TO CALCULATETHEIMPEDANCE ! O F AT R A N S M I S S I O NL I N ET, H EI M P E D A N C E O F THE TRANSDUCER, AND ! THETRANSDUCERCONVERSIONLOSS,ALSOACCORDINGTOTHETHEORY ! I T CALCULATESTHECOMPLEXIMPEDANCE(Z2RR+jZ2211) FOR ! A TOPELECTRODEWITHUPTO 2 L A Y E R S( T 2 AND TA),ANDTHE ! COMPLEX IMPEDANCE O F THEBOTTOMELECTRODECZ3RR*)Z31I)WITH ! UP TO 5 D E L A YL A Y E R S( T 3T, 4 , 75, T 6 T, 7 ) I. TT H E NU S E ST R A I M P ! TOCALCULATETHEFINALIMPEDANCE FOR THE INPUT TRANSDUCER. ! THEUSERCANADD AS MANY LAYERS AS NEEDED OR BYPASSTHE ONE ! NOTNEEDED B Y USINGZEROTHICKNESS.ATTHEEND O F THE ! CALCULATIONSTHEUSERNEEDSA l - DP L O TR O U T I N E TO I N S P E C T ! THECONVERSIONLOSS(CLL),ANDTHEREAL A PARTS O F THE ! INPUTIMPEDANCE CZAR AND Z A I ) AS A F U N C T I O N OF FREQUENCY. ! THE PROGRAM I S ! SETUPFOR A T L 3 A s S 4E X A M P L EW I T H [ L 1 L I N b O 3 TRANSDUCER, ! 1 0 0A OF CR AT EACH TRANSDUCER FACE AND ON THE A 0 CRYSTAL, ! Sn AS T H EB O N D I N GM E D I U M( L / 4 @ 3 0 0 MHt.2.8 AND ! A u A S THE TOP ELECTRODE. THE FREQUENCY RANGE O F INTEREST ! I S2 0 0 - 4 0 0M H z T . HE PROGRAM COVERS T H E1 0 0 - 5 0 0M H z RANGE. ! D O U B L EP R E C I S I O N KK,RSE,PI,Ul,U2,U3,U4,US,U6,U7,A2,A3,A4,A5, 1 Z2C,Z3C,Z4C,Z5C,Z6C,Z7C,ZAO,ZOO,Tl,T2,T3,T4,T5,T6,T7,

2

OFO,AO,EO,EV,CO,RO,FFO,FF,FFI,B2,B3,B4,B5,B6,B7,

3 4

22RR,Z211,Z3RR,Z311,Z4RR,Z411,Z5RR,2511,~6RR,~611,~7RR,~711,

6

OF,ZARR,ZAII,TKC3,DPZ

THO,ZTR,ZTI,CL,RG,TAA,ZAC,TA,UA,BA,Tll,A6,A7,T22,T55, !

APPENDIX B REAL !

COMPLEX Cl,C2,C3,C4,CS,CIN,COUT,CA,CB,CC,CD,CE !

PI-3.14159265 ! ! SOURCE bND WIRE SERIES IMPEDANCE (Ohms)

RG-50.0 RSE-0.5 ! ! TRANSDUCER COUPLING COEFFICIENT (Squared) KK-.49+0.49 ! ! VELOCITIES (m/aec)

U1-7400.0 U2-3378.0 U3-6650.2 U493320.0 US-2250.0 U6-U3 u7-u3

UA-U3 ! ! ATTENUATION COEFFICIENTS

42-0.0 A390.0 A4-0.0 AS-0.0

6610.0 A790.0 DPZ 0.0

-

! ! MECHANICRL IMPEDANCES (gr/acc.m*+2)

Z2C-65.2E9 23Cg47.2E9 Z4C-24.6E9 ZSC-Z3C Z6C=Z3C 27C-23C ZAC-ZJC ! CRYSTAL IMPEDANCE Cgr/aec.m++21 ZAO-13.3E9 ! TRANSDUCER IMPEDANCE (gr/sec.m+*2) 200-34.8E9 ! ! NORMALIZATION OF IMPEDANCES

zAc-zAc/zoo z2c-z2c/z00 Z3C-Z3C/ZOO Z4C-Z4C/ZOO zsc-z5c/zoo Z6C-Z6C/ZOO Z7C-Z7C/ZOO

ZAO-ZAO/ZOO ! ! THICKNESS ( m )

11-10.OE-6 T292000.1 €-l 0 13-1 0O.OE-l0

APPENDIX B

! !

481

(mxm)

! !

! !

! !

! ! !

! ! ! !

! !

!

!

!

!

!

!

TLIMP
!

! !

APPENDIX B

482 THO-(FFI)/FFO !

OF-2.*PI+FFI CALL TRAIMP~OF,RO,CO,Z2RR,Z2II,Z3RR,Z3II,THO,ZTR,ZTI~ ZARCII-ZTR ZAI(I)-ZTI !

CALL CONEFF(ZTR,ZTI,RSE,RG,CL) CLLC I )-CL WRITE(+,1001) FFIIlE6, ZTR, ZTI, CL CONTINUE 1000 1001 FORMATC4
CALL A l-D SUBROUTINE TO PLOTZAR,ZAI.CL AS A FUNCTION OF FREQUENCY IN ORDER TO INSPECT CL AND RA.

STOP END C Subroutines used the transducer design program. THIS PROGRAM CONTAINS THE SUBROUTINES REQUIRED BY THE TRANSDUCER DESIGN PROGRAM:DESIGN.FOR ! !

SUBROUTINE TLIMP ( Z C , Z N l R , Z N l I , A , B . T , Z N R . Z N I ) !

THIS SUBROUTINE CALCULATES THE COMPLEX IMPEDANCE
! ! ! ! !

! ! !

DOUBLE PRECISION ZC,ZN1R,ZN1I,A,B,T,ZNR,ZNI,TAR,TAI,Al,B1,NUMTR, 1 DENT,NUM1R,NUM2R,NUMR,NUMlI,NUM2I,NUMI,DENZl,DENZ2,DENZ,NUMTI !

A1 -A+T B1 -BIT ! ! ! !

HERE WE CALCULATE THE REAL AND IMAGINARY PARTS OF TANH
NUMTR.EXPC2.*A1 )-EXP<-2.+Al) NUMTI=2.~DSIN(2.~3.14159*Bl) DENT~EXP~2.+A1~+EXP<-2.~Al~+2.+DCOSC2.+3.14159+Bl~ !

TAR-NUMTRIDENT TAI-NUMTI/DENT ! ! ! ! !

HERE WE CALCULATE THE REAL AND IMAGINARY PARTS OF THE IMPEDANC COMMON DENOMINATOR

DENZl-
APPENDIX B

483

! ! !

NUMlR=(ZNlR+ZC~TAR)+~ZC+ZNlR+TAR-ZNlI*TAI) NUM2R-(ZNlI+ZC*TAI)*(ZNlI~TAR+ZNlR~TAI) ! ! ! + 4

! ! !

! !

!

! !

!

TRAIMP(FR,RO,CO,Z2R,Z2I,Z3R,Z3I,THO,ZINR,ZINI~ ! ! ! ! ! ! ! !

! ! ! ! ! ! ! ! D O U B L EP R E C I S I O NF R , C O , R O , Z 2 R , Z 2 I , Z 3 R , Z 3 1 , T H O , Z I N I , X , Y , Z , W

! = !

X-(Z2R+Z3R)+DSIN(THORAD) Y=2.-2.+DCOS(THORAD)+~Z2I+Z3I)~DSIN(THORAD~ Z=(l.+Z2R+Z3R-Z2I*Z3I)+DSINCTHORAD)+ W=(Z2R+Z3I+Z3R*Z21)+DSIN(THORAD~! !

! ZINR-(X+Z+Y~W)/(RO+((FR+CO~~~2.)*((Z4+2.)+(W4+2.))) ! !

APPENDIX B !

ZINI=((Z~Y-W*X)/(RO+((FRrCO)rr2.)r(
( 1 ./CFR*CO) ! ! RETURN END !

! !

! SUBROUTINE C O N E F F ( R A , X A C O , R S E , R G , C L ) ! ! THISSUBROUTINECOLCULATESTHETRANSDUCERCONVERSION ! LOSS I N dB. RA I S THEREALPART OF THE TRANSDUCER IMPEDANCE ! XACO I S THE IMAGINARY PART, RSE I S THE CONNECTION SERIES ! R E S I S T A N C E , AND RG I S THE IMPEDANCE OF THE SOURCE. ! THERESULTRETURNSTO CL.

! D O U B L EP R E C I S I O N ! -RG+RSE+RA -A1 A2-XACO.XACO A3=4.+RA*RG O4-CA1 +A2)/A3 CL-lO.O*DLOGlO(A4) A3-0.0 ! RETURN END

Index

A (dimensionless modulator design parameter), Acoustic absorber,

Acoustic diffraction, Acoustic harmonics, Acoustic impedance,

Acoustic anisotropy, Acoustic attenuation,

Acoustic lobes, Acoustic matching, Acoustic mode, Acoustic mode conversion,

Acoustic attenuation constant, Acoustic near-field, Acoustic nonlinearities, Acoustic attenuation measurement, Acoustic beam folding, Acoustic beam spread, Acoustic collimation, Acoustic crosstalk measurement, Acoustic curvature, Acoustic echo testing,

Acoustic pattern, Acoustic phase vector, 55 Acoustic plane waves, Acoustic power, Acoustic power flow, Acoustic rotation, Acoustic slowness surface,

48.5

INDEX

Acoustic transit time, Acoustic transmission line model, Acoustic velocity, Acoustic wave vector, Acoustic wavelength,

Acousto-optic facet tracking, Acousto-optic figure of merit,

KM, M,,

M,, Acoustically induced strain, Acousto-optic bandshape,

Mza, M3,

anisotropic LiNb03, anisotropic phased array TeO,, anisotropic TeO,, isotropic Gap, phased array LiNb03, Acousto-optic bandwidth, testing, Acousto-optic deflectors,

Acousto-optic interaction geometry, anisotropic, optically active, anisotropic phased array, isotropic, phased array,

applications, computer-aided design, construction, design procedure, GaP device, operating characteristics, performance characteristics, testing, Acousto-optic device, housing, Acousto-optic device manufacturing steps, Acousto-optic effect, Acousto-optic efficiency,

Acousto-optic interaction strength, Acousto-optic materials,

AOTF, birefringent, cut, cutting, defects, density, growth, modulators, optically active, orientation, parameters,

487

INDEX [Acousto-optic materials] polishing, sawing, selection, transmission and reflection coefficients, Acousto-optic modulator diffraction characteristics, dynamic contrast ratio, electronics, intensity modulation, light efficiency, head, history, market, materials, performance requirements, risetime, static contrast ratio, temporal response, testing, transfer function, Acousto-optic nonlinearities, Acousto-optic properties, A 0 materials, Acousto-optic tunable filter (AOW angular aperture, aperture azimuthal, polar, beam extraction, beam separation, collinear, crystals,

[Acousto-optic tunable filter (AOTFII design, fabrication, materials, noncollinear, passband, resolution, sidelobes, testing, tuning relation, Ag, Silver Akhieser loss, Al, Aluminum AIN, Alpha-quartz, Aluminum, Aluminum oxide, Amplified spontaneous emission, Amplitude modulation AOTF, Angular acceptance window, Angular aperture test, Anisotropic factor, Anisotropic interaction, Antireflection coating, AOTF optical bandwidth testing, AOTF spectral resolution testing, AOTF tuning relation testing, Apodization, Ar, see Argon Argon, Array pattern, Au, Gold

488

Back electrode layer, 290 Bandwidth, 14, 18-20, 71-75, 83, 85, 103, 116, 445 testing of, 413, 445-447 Bandwidth-efficiency product, 15, 34 Beam propagation method (BPM), 173 Beam walkoff, 410 Bessel function, 9, 12 Bevel, 396 Birefringent interaction, 16-24 Birefringent bandshape, 22-24 Birefringent reflection, 244 Blackbody radiation, 274 Bond wire, 294-296, 392, 395-396 Bonding, 236, 302-306, 376-385, 405 Bonding-transducer, 236, 376-385,405 adhesive, 377-378 bonding layer materials, 301-306, 379 cold vacuum compression, 381-382, 384 optical contact, 383-385 parameters, 302-306 temperature, 380 thermocompression, 378-382 thermocompression ultrasonic, 380-381, 383 thickness, 302-306, 377-378 Born scattering integralapproximation, 171 Bragg angle, 10, 71, 76, 103-104, 109, 116 Bragg diffraction, 10-12, 70, 78, 83 Bragg regime, 9-10, 70, 139, 169, 171

INDEX Bridgman growth technique, 343 Broadband transducer design, 298-300, 309-314, 315-316,319-321 CaF,, 257 CaMo04, 218, 242, 243, 246, 260 Carborundum grit,385 Cavity dumper, 397 CdS, 353, 359 Center frequency, 71, 73, 103-104, 109-110, 385 Cerium fluoride, 349 CH4,261 Characteristic impedance transmission line, 290-294 Chemical polishing, 387 Chromium, 303, 304, 379, 381, 384 Circular dichroism, 258 Clamped capacitance, 289 CO, 251,254 C02,251 CO2 absorption, 452 Coherence detection, 271-276 Collinear birefringent interaction, 22 Color analysis, 249 Combustion analysis, 251 Communications, 267-271 Computer-aided transducer design, 306-321,479-484 Conversation of momentum, 70-71 Contrast ratio dynamic, 154-156 static, 146-149 Contrast ratio testing, 447-448 Conversion loss, 74, 295-297

INDEX

489

Convolution integral response model, Cooling of AOTF, Copper,

Dynamic contrast ratio,

Coupled mode analysis, Coupled-wave equation,

Elastic anisotropy, Elastic IMPs, Elastic strain, Elastic stiffness constants,

Cr, see Chromium Crosstalk, Crystal classes, Crystal symmetry, Cu, see Copper Czochralski growth, technique,

Dynamic IMPs, Dynamic range,

Elasto-optic effect, Electric impedance matching,

Deflector bandwidth testing,

Electric input impedance, piezoelectric transducer, Electrical crosstalk measurement, Electrical impedancetesting,

Deflector TBWP, Deflector TBWP testing,

Electrical resistivity, Electro-acoustic response,

Derivative detection,

Electro-optic coefficients, Electrode, materials, Electrode layers,

DESIGN.FOR (See Appendix B) Detector sampling effects,

Diffraction efficiency testing,

Electromechanical coupling constant, Element pattern, Energy exchange, EOTF, Epoxy, Equivalent electric impedance acoustic impedance, Etendue, Evaporation techniques,

Diffraction orders, Doppler shift,

Fabry-Perot filter, Feynman diagram,

Diamond grit, Dielectric constant, Diffraction collinear, Diffraction efficiency,

INDEX Fiber spatial filter, Flue gases absorption by, Flurometer, Fourier transform, Fraunhofer region, Frequency constant, piezoelectric material, Frequency modulation AOTF, Frequency resolution, Fresnel region, Fused quartz, Fused silica,

High-frequency matching network, Hooke’s Law, Imaging AOTF, IR, scene shift, smear, spectral, Impedance load, Impedance matching network, In, Indium Index ellipsoid, Index of refraction,

Gap, Indium, collimating shear mode, longitudinal mode, Gaussian beam profile, Ge, Germanium Germanium, Gold, Goniometer, Half-wave frequency, Heat sink, Hg2Br2, Hg2C12, Hg2C12-LiNb0, design example, m2127

Input impedance, InSb, Intensity modulation, Integrated optics, Interaction length, effective, Interferometer, Intermodulation products, third order testing, Ion-milling, Ion sputtering, diode, magnetron, cylindrical, magnetron gun, planar,

INDEX [Ion sputtering] substrateharget geometry, 366-367 triode, 359 Isolation interchannel, 436 Isotropic A 0 interaction, 4-16 Isotropic Bragg diffraction, 11-12 k-loading, 309 Klein-Cook parameter, 9, 78 KRS-5, 25, 26, 28, 46-47, 49-50, 60 KRS-6, 25, 26, 59-61 Laser cavity tuning, 241 COz, 244 DFB, 268 dye, 242 GaAs, 268 Nd-YAG, 243 semiconductor, 267 Laser heterodyne metrology, 131-132 Laser scanning systems, 127-129 Lead, 303,305,311, 315 LiNbO,, 23, 25, 28-29, 40, 42, 52, 71, 82, 109, 112, 116, 201, 202, 235-237, 269, 280, 301-302, 307, 344, 350, 351, 353-357, 359, 370-377,380-382, 385-388, 390, 411, 414, 430-432 growth, 374 longitudinal mode, 112, 116 orientation, 374

[LiNbO,] physical properties, 373 piezoelectric coupling coefficient, 372-374,376-377 longitudinal mode, 374, 376-377 shear mode, 374-375, 376-377 platelet transducer, 301-302, 308, 314, 318, 376, 378 reduction, 300-301, 385-386, 388 sawing, 374 shear mode, 109 thickness, 375, 385 LiNbO, device, phased array, 40,42 LiNbO, device TBWP testing, 430 LiNbO,-LiNbO, design example, 318-321 MI, 15, 144 M*, 13,76-77, 89, 103-104, 109, 116, 144, 224, 424 Ma, 18 M,, 15, 82, 145 Magnesium fluoride, 315,349 Magnetron sputtering, 349, 364 Mason equivalent circuit, 288, 296 Matching network, 321-335 Mean free path, 366 Mechanical impedance, 290-294 Mechanical input impedance, 290-292 Mechanical stress, 354, 358 internal, 354, 370-371 thermal, 354

INDEX Melting temperature, Mercurous halides, Mg2F2, Misorientation angle, Modulated beam profile distortion, Modulation of AOTF, Modulation bandwidth testing, Modulation transfer function (MTF), testing, Modulator contrast ratio testing, Modulator design strategy, Momentum conservation of, mismatch, Momentum-matching condition,

Multiple-beam scanning, Multiple diffraction orders, 8 Multiplexing wavelength division, N (dimensionless design parameter), NaBiMoO,, N~B~(MOO~)~, Network analyzer, Ni, see Nickel Nickel, Normalized impedance,

Oil vapor, Optical activity, Optical bandwidth testing, Optical beam deflection angle,

Multichannel Bragg cell,

Optical beam divergence angle,

Multichannel Bragg cell testing,

Optical illumination angle,

Multichannel crosstalk, Multichannel deflector testing, Multichannel isolation, Multichannel modulators, Multichannel performance uniformity, Multichannel phasehime nonuniformity, Multichannel power delivery, Multiple beam modulation,

anisotropic, optically active, isotropic, phased array, phased array anisotropic, Optical normal surface, Optical polishing machine, Optical properties, A 0 materials, Optical time-domain reflectometry (OTDR), Optical wavelength,

INDEX Optical window, antireflection coating, material growth, material orientation, polishing, sawing, Out-of-band transmission testing, Parasitic acoustic lobe, Parasitic diffraction loss, Parasitics Passband ripple Pb, Lead PbMoO,, PbMoO, device, PbS, Phase grating, Phase mismatch, Phase-time-uniformity, Phased array transducers, Phased array transducer geometry, Phenyl compounds, Photoelastic coefficients, Photoelastic effect, Photolithography, Photodphonon interaction,

493

Piezoelectric resonant frequency, Piezoelectric tester, Piezoelectric transducer, bonding, bonding layer, bottom electrode, fabrication, platelet, thin-film, length, platelet, performance, reduction, structure, thickness, thin film, top electode, width, Planar phased array, Planck radiation law, Platinum, Polarization rejection ratio, Polycrystalline film, Poynting vector, Pt, Platinum Pulse echo,

Piezoelectric coupling coefficient,

Q, Q (dimensionless design parameter), Q-switched lasers, Quarter wave matching,

Piezoelectric material properties,

Quartz,

INDEX Quartz device, folded acoustic beam,

Scattering measurementsystem, Schaefer-Bergmann pattern,

R (dimensionless modulator design parameter), Radiation resistance, Raman-Nath diffraction,

Schlieren imaging,

Raman-Nath equation,

Scrolling spatial light modulation, Self-collimation, Sellmeier equations, Si, see Silicon Sidelobe suppression, Sidelobes, Silicon, Silicon dioxide, Silicon oil, Silver,

Raman-Nath regime, Rayleigh criteria, Reduction, ion milling, mechanical lapping, Reflection coefficient, Refractive index, Resist, Resolution spatial, of AOTF, spectral, of AOTF, Resolution criteria, optical, Resolvable spots, Resolving power, Resonance condition, Response time, RF matching network,

RF power, delivery, dependence of transmission, Risetime, testing, Rocking curve, Scanner systems, Scattering,

testing, Scophony scanner,

Slowness curve, Smith chart, Sn, see Tin Snell’s Law, Source internal resistance, Spatial resolution, Spatial separation of orders testing, Spectral resolution test, Spectrometer grating, prism, Spectrometry, Spectrophotometry astronomical, Spectropolarimetry, Spectroscopy correlation, differential absorption, fluorescence, Spinel,

ZNDEX Sputter etching, Star coupler, Stepped phased array, Static contrast ratio, testing, Steering angle, Steering error, Stopcock grease, Strain, Tangential birefringent interaction, Tangential phase matching,

Third-order intermodulation products, testing, Ti, see Titanium Time-aperture, Time-bandwidth product, Time-bandwidth product testing, Tin, Ti02, Titanium,

TEM, laser mode, Temporal point modulation,

TI~AsS~,

Temporal response model,

Tl3AsS4-LiNbO3 designexample, T13AsSe3, (TAS),

Te02,

Top electrode thickness, Transducer, acoustically rotated, anisotropic A 0 interaction, elastic constants, optically rotated, slow shear mode, 106, Texture ratio, Thermal coefficient of linear expansion, Thermal gradients, Thickness mode piezoelectric transducer,

analysis, AOTF, apodization, bonding, construction, conversion loss, cylindrical, design evaluation criteria,

INDEX [Transducer] equivalent ciruit 287-297 fabrication, 235 height, 72, 76-79, 83, 95, 103-104, 107, 109, 111 length, 72, 76-78, 83, 103-104, 107-109, 111 anisotropic, isotropic, 85-86 phased array, 92 risetime dependence, 165- 167 materials, 300-302 multichannel, 97-98 phased array, 90, 91 center-to-center spacing, 92, 94, 116, 119-120 element width, 92-93, 95, 116,119-120 length, 92, 94, 116, 119-120 number of elements, 92, 94, 116, 119-120 platelet, 340 bonding, 236, 302-306, 376-385, 405 reduction, 385-391 power handling, 302 thin film, 340 growth speed, 360, 364 wideband considerations, 298-300 Transducer design example for Hg,Cl,, 314-318 Transducer design example for LiNb03, 318-321 Transducer design example for Tl3AsS4, 308-314 Transducer frequency response, 298-300 Transducer loss, 294 Transfer function, 140-141

Transit time, 442 Transmission line network, 330, 327,335 Transmittance of AOTF, 202 Travelling wave, 5 Tuning AOTF relation, 201, 207 of laser cavity of AOTF, 241 Two-element matching network, 322-323

Ultrasonic delay lines, 339, 388

Vacuum compression bonding, 236-237 Vacuum deposition, 358, 361, 380-381 Varnish, 377 Voltage reflection coefficient, see VSWR VSWR, 297, 321-322,404, 411, 413 Wave equation, 4 Wave equation solutions, 9, 12, 17-18 Wave vector, 6, 200 Wave vector diagram, 10-11, 14-17,22-23 Waveguide optical, 269 Wire bonding, 395-396 thermocompression, 396 ultrasonic, 396

X-ray, 346, 349

INDEX Zinc, 303, 305 Zn, see Zinc ZnO, 235, 301, 353-354, 357-359, 362-371 boundary growth speed, 364, 365 c-axis, 362, 365, 368, 371 deposition technology, 359-361 film characteristics, 361, 364, 366-367

497

P01 film growth speed, 364-366 vs. texture ratio, 364-365 piezoelectric coupling constant, 362, 372 longitudinal mode, 363, 368 shear mode, 363,368,371 vs. orientation angle, 363 polycrystalline, 362 rocking curves, 368-370, 372-375