POF Handbook - Optical Short Range Transmission Systems

POF Handbook Second edition

Olaf Ziemann · Jürgen Krauser Peter E. Zamzow · Werner Daum

POF Handbook Optical Short Range Transmission Systems Second edition

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Professor Dr.-Ing. Olaf Ziemann Georg-Simon-Ohm-Fachhochschule Nürnberg Wassertorstr. 10 90489 Nürnberg Germany [email protected]

Dipl.-Ing. Peter E. Zamzow R & D Cable Systems Erlen-Str. 5b 44795 Bochum Germany [email protected]

Professor Dr. Jürgen Krauser Deutsche Telekom Leipzig FB Optische Nachrichtentechnik Gustav-Freytag-Str. 43–45 04277 Leipzig Germany [email protected]

Professor Dr.-Ing. Werner Daum Bundesanstalt für Materialforschung und -prüfung (BAM) Unter den Eichen 87 12205 Berlin Germany [email protected]

ISBN 978-3-540-76628-5

e-ISBN 978-3-540-76629-2

DOI 10.1007/978-3-540-76629-2 Library of Congress Control Number: 2007943247 © 2008, 2001 Springer-Verlag Berlin Heidelberg This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilm or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer. Violations are liable for prosecution under the German Copyright Law. The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. Cover design: deblik, Berlin Printed on acid-free paper 987654321 springer.com

Preface

In almost all areas of daily life the demands on the communications infrastructure increased dramatically. With regard to the volume of data that has to be transmitted, no matter whether we are dealing with public or private networks, industrial fields or automobiles, needs will continue to rise. Consequently, the demands on the bandwidth of communications systems will continue to increase since more and more video data streams with high picture quality (IP TV), in addition to telephone and data circuits, will be transmitted. More data streams are coming about through the connection of an increasing number of Wi-Fi hotspots with high capacities. All these services require a basic infrastructure with high capacities which only optic technologies can offer. The expansion of the DSL network will bring glass fibers closer to the end customer and will generate a demand for easy-toinstall, efficient and favorably priced cabling solutions in buildings. In such a case polymer optical fibers are a veritable alternative. After POF demonstrated its performance capabilities in industrial use and in automotive engineering, nothing more stands in the way for employing these optical solutions within buildings. The use of inexpensive visible LEDs, simple plug connectors and insensitive cables and lines, allows for favorably priced systems which any private user can even install himself whenever required. In contrast to Wi-Fi or Powerline, POF is immune to interference and always guarantees high capacity in point-to-point connections. In combination with new electronic solutions and coding scheems it is possible today to bridge distances of over 100 m at a data rate of 100 Mbit/s using standard step index POF. Thus the technical basis is laid for large-scale use in building cabling. It now remains the task of the component manufacturers to make such systems available to the market as an economical alternative. The main emphasis of polymer fiber applications for data transmission lies in Japan as well as in Germany, Spain and Italy. Germany plays a leading role in many of these applications. The Polymer Optical Fiber Application Center (POF-AC) at the Nuremberg University of Applied Sciences has developed over the last few years into a European Competence Center for POF. The POF AC and Leoni have cooperated closely and successfully for years. For many years, the Leoni AG has been one of the leading manufacturers of POF and fiber glass cables for use in mobile networks (cars, trains, airplanes), in automation technology and in sensor technology.

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Preface

Leoni has also recently gone into the manufacture of glass fibers and the requisite preforms. Therein lies a particular main focus on the production of multimode and special fibers as described in this book. The areas of application range from building networks to medical technical applications used in spectrometric systems. Furthermore, Leoni’s developers have presented at conferences held over the last few years new solutions for optical pressure-sensitive sensors based on special plastic fibers. In all these areas of activity Leoni has aimed at combining its experience with optical waveguides from the field of telecommunications with the knowledge and the solutions from the market for special and POF fibers, thus making available new practical solutions to users in the most diverse fields. In 1997, Andreas Weinert, working today with colleagues at Leoni Fiber Optics, published one of the first comprehensive POF books. The book “POF - Optical Polymer Fibers for Data Communication” published in 2001 provided an overview of POF technologies and in the meantime is out of print. This new edition is now a handbook which, in addition to describing POF and thick core glass fibers, can also be used for short-distance communication. This specialized reference book is intended to help users and developers to obtain information themselves quickly and comprehensively about the state-ofthe-art development of POF fibers and to become acquainted with their performance capabilities. In a summarized form it conveys a number of experimental results along with new trends in development and is a valuable adviser for developers of POF systems. The physical fundamentals as well as practical applications are presented in a simple and understandable manner.

Nuremberg, May 2007 Dr. Klaus Probst CEO/Leoni AG

Editor’s Preface

In the past few years polymer optical fibers (POF) and their applications have continued to develop at a dizzying pace. This was the decisive factor in 2005 to decide on completely revising the book, „POF - Optical Polymer Fibers for Data Communication“, which appeared in German in 2001 and in English in 2002. Before you now lie the results of two years of work - almost double the number of pages of the First Edition. One essential reason for the new edition is the diverse results which have been obtained at the Polymer Optical Fiber Application Center at the Nuremberg University of Applied Sciences (POF-AC) since its inception in 2001. The scientific director of the POF-AC has written the majority of the sections in this book. Dr. Christian-Alexander Bunge from the Technical University of Berlin has contributed two sections (Microstructured Polymer Fibers and the Simulation of Optical Fibers). The organization and layout of the new book are essentially based on the following considerations: ¾All parts of the first edition have been taken over in order to provide the many newcomers in the field with the opportunity to completely understand the contents, without having to buy the first volume - which in the meantime is out of print. ¾In addition to the optical polymer fibers many details on other thick-core fibers, e.g. glass fiber bundles and plastic-coated glass fiber, have been added. Many of these fibers not only have the same applications, but also similar characteristics and place similar demands on measurement techniques. ¾Whereas the first edition mostly summarized the results from technical literature, the new edition now presents the POF-AC’s own measurement results on practically all fibers. Consequently, this new book presents and documents the first five years of our institute. ¾The individual chapters correspond to the subject matter of the first edition. The organization and sequence, however, have been adapted to the changed points of emphasis. For example, the waveguides are now dealt with in a separate chapter. The chapters on Fibers (No. 2) and on Systems (No. 6) are among the predominantly new sections. Together these two parts form the core contents of the book and document the progress of technology. Unfortunately, however, these new parts will also become obsolete most quickly since many new solutions will be found in the next few years. ¾The English edition is completely identical with the German one, including all page numbers. No new content has been included.

VIII Editor's Preface

At the time when the first edition of this book appeared POF applications were still exotic. Only in the fields of automation and lighting engineering had this medium already been established. In the meantime, millions of vehicles drive throughout Europe with polymer fiber on-board networks and the next generation is right in front of the door. Many telecommunications companies are working on solutions for transmitting ever higher bit rates via POF within apartments. The Deutsche Telekom, for example, offers its customers a complete set for fast Ethernet. Other large-scale applications for POF in multimedia applications will be introduced into the market in the near future. The authors are therefore very optimistic that this book will accompany the development of polymer fibers from a niche existence to an important basis for data and communications technology. In addition to use in telecommunications, sensor technology and multi parallel data connections above all promise to be wide and interesting fields for their use. A separate section is devoted to each of these areas in Chapter 8. POF are not necessarily a rival of the established technologies such as data transmission on symmetrical copper wires or radio. Different sections of the book show how the diverse technologies can be combined in an optimal fashion in order to achieve the best solutions technically and economically. We have done our best to represent the scientific results and the products available on the market as completely and as impartially as possible. Nevertheless, we are aware of the fact that this goal can only approximately be attained. Should a manufacturer or an institute mentioned in the book not feel being sufficiently represented - this was not intended. The POF-AC gladly offers all interested parties support in gaining access to the growing „POF community“. The POF-AC offers scientific activities such as the ITG Sub Committee 5.4.1 „Polymer Optical Fibers“ as well as technical information such as the „POF-Atlas“ as a German POF product catalog. As editor of the Second Edition I would like to express my thanks to all colleagues at the POF-AC Nuremberg, the Nuremberg University of Applied Sciences and not least my family for their support during the last two years and their giving up so many hours that I actually should have spent with them. A special thank to Prof. Economides (Berlin), who is the translator, and the Prof.’s Poisel and Hartl for their assistance during the correction phase. I wish all readers much pleasure when reading this volume. The aim and intention of this book is to provide you with some help, support, information and food for thought in your work. Please excuse the unavoidable errors and mistakes and do feel free to pass on your reservations, criticisms and ideas to us.

Olaf Ziemann Scientific Director of the POF-AC Nürnberg Chairman of the ITG Sub Committee 5.4.1 „Polymer Optical Fibers“ Member of the „International Cooperative of Polymer Optical Fibers“ as the responsible editor of the second edition, November 2007

Content

1. 1.1 1.1.1 1.1.2 1.1.3 1.1.4 1.1.5 1.1.6 1.1.7 1.2 1.2.1 1.2.1.1 1.2.1.2 1.2.1.3 1.2.1.4 1.2.2 1.2.3 1.2.4 1.2.5 1.3 1.3.1 1.3.2 1.3.3 1.3.3.1 1.3.3.2 1.3.3.3 1.3.3.4 1.3.3.5 1.3.3.6

Abbreviations and Symbols Basics of Optical Data Communication Light Propagation in Optical Fibers and Waveguides Wave and Quantum Nature of Light Electromagnetic Spectrum Refraction and Total Reflection Waveguides and Optical Fibers Singlemode and Multimode Waveguides Overview of Optical Fibers Designations of Optical Fibers Digital and Analog Optical Signal Transmission Digital Optical Signal Transmission Analog and Digital Signals Transmission Quality of Analog and Digital Signals Bit Error Probability and Error Correction Noise in Optical Systems Amplitude, Frequency, and Phase Modulation Modulating a Carrier Frequency Specific Transmission Methods in Optical Communications Modulating a Subcarrier Network Architectures Active and Passive Networks Network Structures Multiple Access Methods Time Division Multiplex Frequency Division Multiplex Code Division Multiplex Wavelength Division Multiplex The Special Features of Optical Multiplexing Bi-directional Transmission

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2. 2.1 2.1.1 2.1.2 2.1.3 2.1.4

Optical Fibers Fundamentals of Optical Fibers Refractive Index Profiles Numerical Aperture Ray Trajectory in Optical Fibers Modes in Optical Fibers

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37 37 37 39 40 42

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2.1.4.1 2.1.4.2 2.1.5 2.1.5.1 2.1.5.2 2.1.5.3 2.1.5.4 2.1.5.5 2.1.5.6 2.1.5.7 2.1.5.8 2.1.5.9 2.2 2.2.1 2.2.2 2.2.3 2.2.4 2.2.5 2.2.6 2.2.7 2.2.8 2.2.9 2.3 2.3.1 2.3.2 2.3.3 2.3.4 2.3.5 2.4 2.4.1 2.4.2 2.4.3 2.4.3.1 2.4.3.2 2.5 2.5.1 2.5.2 2.5.3 2.5.3.1 2.5.3.2 2.5.3.3 2.5.3.4 2.5.3.5 2.5.3.6 2.5.4 2.5.5

The Mode Concept Mode Propagation in Real Fibers Parameters for Describing Real Fibers and Waveguides Attenuation Mode-Dependent Attenuation Mode Coupling Mode Conversion Mode Coupling Lengths Leaky Modes Dispersion in Optical Fibers Mode Dispersion Chromatic Dispersion Index Profiles and Types of Fibers Step Index Profile Fibers (SI) The Step Index Fiber with Reduced NA (low-NA) The Double-Step Index Optical Fiber (DSI) The Multicore Step Index Optical Fiber (MC) The Double Step Index Multicore Fiber (DSI-MC) The Graded Index Optical Fiber (GI) The Multi-Step Index Optical Fiber (MSI) The Semi-Graded Index Profile Fibers (Semi-GI) An Overview of Index Profiles The Development of Polymer Optical Fibers Looking back Step Index Polymer Fibers Double Step Index Profile Polymer Fibers Multi-Core Polymer Fibers Multi-Step Index Profile and Graded Index Profile Fibers Glass Fibers for Short-Range Data Transmission 200 μm Glass Fibers with Polymer Cladding Semi-Graded Index Glass Fibers Glass Fiber Bundles Quartz Glass Fiber Bundles Glass Fiber Bundles Bandwidth of Optical Fibers Definition of Bandwidth Experimental Determination of Bandwidth Experimental Bandwidth Measurements Bandwidth of SI-POF Bandwidth Measurements on SI-POF Bandwidth Measurements on MC- and MSI-POF Bandwidth Measurements with GI-POF Bandwidth Measurements on MC-GOF and PCS Comparison of Bandwidth Measurements and Calculations Chromatic Dispersion in Polymer Optical Fibers Methods for Increasing Bandwidth

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Content

2.5.6 2.6 2.6.1 2.6.2 2.6.3 2.6.4 2.7 2.7.1 2.7.2 2.7.2.1 2.7.2.2 2.7.2.3 2.7.2.4 2.7.2.5 2.7.3 2.7.4 2.7.5 2.7.6 2.8 2.8.1 2.8.2 2.8.2.1 2.8.2.2 2.8.2.3 2.8.2.4 2.8.2.5 2.8.2.6 2.8.2.7 2.8.2.8 2.8.2.9 2.8.3 2.8.3.1 2.8.3.2 2.8.3.3 2.8.3.4 2.8.3.5 2.9 2.9.1 2.9.1.1 2.9.1.2 2.9.1.3 2.9.1.4 2.9.2 2.9.2.1 2.9.2.2 2.9.2.3

Bit Rates and Penalty Bending Properties of Optical fibers Bending Losses in SI-POF Bending Losses in GI Fibers Change of Bandwidth by Bends Bends on PCS, Multicore Fibers and thin POF Materials used for POF PMMA POF for Higher Temperatures Cross-Linked PMMA Polycarbonate POF Elastomer POF Cyclic Polyolefines Comparison of High-Temperature POFs Polystyrene-Polymer Fibers Deuterated Polymers Fluorinated Polymers Overview over Polymers for POF Jackets Fiber and Cable Production Production Processes for POF Production of Graded Index Profiles Interfacial Gel Polymerization Technique Creating the Index Profiles by Centrifuging Combined Diffusion and Rotation Photochemical Generation of the Index Profile Extrusion of Many Layers Production of Semi-GI-PCS Polymerization in a Centrifuge Continuous Production at Chromis Fiberoptics GI-POF with Additional Cladding Cable Manufacturing Cable Construction with SI-POF Elements Non-Stranded SI-POF Cables Stranded SI-POF Cables Principles of Stranding Corrugated Micro Tube Cables Microstructured Fibers Kinds of Wave Guiding Effective Refractive Index Photonic Band Gaps Bragg Fibers Hole-Assisted Fibers Production Methods Microstructured Glass Fibers Microstructured Polymer Fibers (MPOF) End Surface Preparation

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2.9.3 Applications for Microstructured Fibers 2.9.3.1 Dispersion Compensation 2.9.3.2 Endlessly Singlemode 2.9.3.3 Birefringence 2.9.3.4 Highly Nonlinear Fibers 2.9.3.5 Control of the Effective Area 2.9.3.6 Filters 2.9.3.7 Sensor Technology, Tunable Elements 2.9.3.8 Double-Core and Multi-Core Fibers 2.9.3.9 Imaging 2.9.3.10 Multimode Graded Index Fibers

p. 225 p. 225 p. 225 p. 226 p. 227 p. 227 p. 228 p. 228 p. 229 p. 229 p. 230

3. 3.1 3.1.1 3.1.2 3.1.2.1 3.1.2.2 3.1.2.3 3.1.2.4 3.1.3 3.1.3.1 3.1.3.2 3.1.3.3 3.1.3.4 3.1.3.5 3.1.3.6 3.1.3.7 3.1.3.8 3.1.4 3.1.5 3.2 3.2.1 3.2.2 3.2.3 3.2.4 3.2.5 3.2.6 3.2.7 3.2.8 3.2.9 3.3 3.3.1 3.3.2 3.3.2.1 3.3.2.2

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Passive Components for Optical Fibers Connection Technology for Optical Fibers Connectors for Polymer Optical Fibers Surface Preparation of POF Connectors POF Preparation by Cutting and Polishing Hot Plate Surface Preparation POF Press-Cut Procedure POF Preparation by Milling Overview of Connector Systems The V-Pin Connector System FSMA Connector The DNP System F05 and F07 ST and SC Connectors Connectors for Future In-House Networks Connectors for Vehicle Networks Other Connectors Processing Tools for POF Connectors Connectors for Glass Fibers Basis for Calculating Connector Losses Calculation of Connector Losses with Uniform Mode Distribution Differences in Core Diameter Differences in Numerical Aperture Lateral Offset of the Fibers Losses due to Rough Surfaces Losses through Angles between the Fiber Axis Losses through Fresnel Reflection Losses through Axial Distance of the Fibers Losses due to Different Causes POF Couplers Construction of POF Couplers Commercial Couplers Polished Coupler from DieMount Moulded Couplers from IMM

Content

XIII

3.3.2.3 3.4 3.4.1 3.4.2 3.5 3.6 3.6.1 3.6.2 3.6.3 3.6.4 3.6.5

Waveguide Couplers from the University of Sendai Filters and Attenuators for POF Filters Attenuators Mode Mixers and Converters Optical Slip Rings and Rotary Optical Connectors Rotary Optical Connectors The Micro-rotation Project POF Slip Rings Prism Coupler Slip Ring The Mirror Groove Slip Ring

p. 275 p. 276 p. 276 p. 277 p. 282 p. 285 p. 285 p. 286 p. 288 p. 290 p. 292

4. 4.1 4.1.1 4.1.2 4.1.3 4.1.3.1 4.1.3.2 4.1.3.3 4.1.3.4 4.1.3.5 4.2 4.2.1 4.2.2 4.2.3 4.2.4 4.2.5 4.2.5.1 4.2.5.2 4.2.5.3 4.2.6 4.2.7 4.3 4.4 4.4.1 4.4.2 4.4.3 4.4.4 4.4.5 4.4.6 4.5 4.5.1 4.5.2 4.5.2.1 4.5.2.2

Active Components for Optical Systems Emitters and Receivers The Principle of Light Generation in Semiconductors Structuring Semiconductor Components Structures of Semiconductor Transmitters Luminescence Emitting Diode Laser and Super Luminescence Diodes Surface Emitting Laser Resonant Cavity LED Non Resonant Cavity LED Transmitting Diodes for Data Communication Red LEDs and SLEDs Red Laser Diodes Blue and Green LEDs Green Laser Diodes Vertical Laser Diodes and RC-LED Red RC-LED Red VCSELs VCSEL in the IR Region Non Resonant Cavity LED Pyramid LEDs Wavelengths for POF Sources Receivers Efficiency and Sensitivity Photodiode Structures Junction Capacity and Bandwidth Overview of Receivers Commercial Products Improvement in Sensitivity Transceivers Components before 2000 Fast Ethernet Transceiver POF Solutions from DieMount in Wernigerode Optical Clamps from Ratioplast

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4.5.2.3 4.5.2.4 4.5.2.5 4.5.3 4.5.3.1 4.5.3.2 4.5.3.3 4.5.3.4 4.5.3.5

Transceiver Family from Avago Home Installation by RDM POF Transceivers from Infineon/Siemens Other Systems Comoss IEEE 1394, MOST and Fast Ethernet from Firecomms Japanese Manufacturers Fast Ethernet, Ethernet and Video from Luceat DSL Modem with POF

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5. 5.1 5.2 5.3 5.4 5.5 5.5.1 5.5.2 5.5.3 5.5.4 5.6 5.6.1 5.6.2 5.6.3 5.6.4 5.6.5

Planar Waveguides Materials for Waveguide Structures Production of Polymer Waveguides Singlemode Waveguides Multimode Waveguides Functional Components as Waveguides Thermo-Optical Switches Modulators Coupling Components Waveguide Gratings Waveguides as Interconnection Solutions Optical Backplane Systems from DaimlerChrysler Systems from the University of Ulm Electro-optical PCB from the University of Siegen IBM Research Center Zurich /ETH Zurich Results of the NeGIT Project

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6. 6.1 6.1.1 6.1.2 6.1.3 6.1.3.1 6.1.3.2 6.1.3.3 6.1.3.4 6.1.3.5 6.1.4 6.1.4.1 6.1.4.2 6.1.4.3 6.1.4.4 6.1.4.5 6.1.5 6.1.5.1 6.1.5.2

System Design Link Power Budget of Optical Transmission Systems Changes of the Transmitted Power Sensitivity of the Receiver Attenuation of the Fiber Link Coupling Losses from the Transmitter into the POF Losses in the Fiber Link Connector Losses Passive Component Losses Coupling Losses between POF and Receiver The Link Power Budget of the ATM Forum Specification Loss Analysis by the ATM Forum Changes in the Transmission Power Attenuation of the Polymer Optical Fiber Link Connector Losses Additional Losses through External Influences Choice of Wavelength for POF Systems LED as Transmitters for POF Systems Selection of the Type of Source

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Content

6.1.5.3 6.1.5.4 6.1.5.5 6.1.6 6.2 6.2.1 6.2.2 6.2.3 6.2.4 6.2.5 6.2.5.1 6.2.5.2 6.3 6.3.1 6.3.1.1 6.3.1.2 6.3.1.3 6.3.1.4 6.3.2 6.3.2.1 6.3.2.2 6.3.2.3 6.3.2.4 6.3.3 6.3.3.1 6.3.3.2 6.3.3.3 6.3.4 6.3.4.1 6.3.4.2 6.3.4.3 6.3.5 6.3.5.1 6.3.5.2 6.3.5.3 6.3.6 6.3.6.1 6.3.6.2 6.3.6.3 6.3.7 6.3.7.1 6.3.7.2 6.3.7.3 6.3.7.4 6.3.7.5 6.4

Typical Losses for LED Sources Lasers for POF Systems VCSEL and RC-LED for POF Systems Definition of new LED Parameters Examples of Link Power Budgets ATM Forum Specification IEEE1394b D2B and MOST ISDN over POF Link Power Budget for Bi-Directional Transmission Asymmetrical Couplers Symmetrical Couplers Overview of POF Systems Step Index Profile POF Systems at 650 nm The first SI POF Systems SI POF Systems with over 500 Mbit/s SI-POF Systems with more than 500 Mbit/s SI-POF Systems at the POF-AC Nürnberg Systems with PMMA SI POF at Wavelengths below 600 nm Systems with AIII BV Semiconductor LEDs Systems with GaN LEDs Commercial Developments POF-AC Systems Systems with SI-POF at Wavelengths in the Near Infrared Range PMMA Fiber Systems for Infrared PC Fiber Systems in Infrared System Experiments at the POF-AC Systems with PMMA GI-POF, MSI-POF and MC-POF PMMA GI-POF System Experiments before 2000 Recent PMMA GI-POF Systems System Experiments by Telekom and POF-AC Systems with Fluorinated POF First Systems with PF-GI-POF Experiments at the Technical University of Eindhoven Data Rates over 5 Gbit/s with GI-POF POF Multiplex Wavelength Multiplex Systems with PMMA POF Wavelength Multiplex Systems with PF-GI-POF Bi-Directional Systems with POF Special Systems, for Example, with Analog Signals Video Transmission with POF Transmission of Analog Modulated Digital Signals Radio over Fiber Mode Multiplex Fiber Ribbon Systems Other Optical Transmission Systems with Fibers

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6.4.1 6.4.2 6.4.3 6.4.4 6.5

Data Transmission on High-Temperature POF Multi-Parallel POF Connections Systems with 200 μm PCS and Semi-GI-PCS Systems with Glass Fiber Bundles Overview and Comparison of Multiplex Techniques

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7. 7.1 7.1.1 7.1.2 7.1.3 7.2 7.2.1 7.2.2 7.2.3 7.2.4 7.2.5 7.2.6 7.2.7 7.2.8 7.2.9 7.2.10 7.3 7.3.1

Standards Standards for Polymer and Glass Fibers Polymer Fibers Plastic Clad Glass Fibers Fibers in General Application Standards ATM Forum (Asynchronous Transfer Mode) IEEE 1394b SERCOS (SErial Realtime COmmunication System) Profibus INTERBUS Industrial Ethernet over POF D2B (Domestic Digital Bus) MOST (Media Oriented System Transport) IDB 1394 EN 50173 Standards for Measurement Techniques The VDE / VDI Guideline 5570

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8. 8.1 8.1.1 8.1.1.1 8.1.1.2 8.1.1.3 8.1.1.4 8.1.1.5 8.1.1.6 8.1.1.7 8.1.1.8 8.1.2 8.1.2.1 8.1.2.2 8.1.2.3 8.1.2.4 8.1.2.5 8.1.3 8.1.3.1 8.1.3.2 8.2

Application of Polymer Optical and Glass Fibers Data Transmission with POF POF in the Automotive Field D2B MOST Byteflight IDB 1394 MOST with PCS Outlook for the Automobile Networks Corrugated Micro Tube POF Cable in the Car Optical Camera Links for Trucks Data Networks in Apartments and Buildings Use of POF in LAN Applications Use of POF in Private Networks POF and the Development of Broadband Networks POF and Wireless POF Topologies Interconnection Systems with POF Parallel Date Transmission with Glass Fibers Parallel Data Transmission with POF POF in Lighting Technology

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XVII

8.2.1 8.2.1.1 8.2.1.2 8.2.2 8.3 8.3.1 8.3.2 8.3.2.1 8.3.2.2 8.3.2.3 8.3.3 8.3.3.1 8.3.3.2 8.3.4 8.3.4.1 8.3.4.2 8.3.4.3 8.3.4.4 8.3.5 8.3.5.1 8.3.5.2 8.3.5.3 8.3.5.4 8.3.6

POF for Light Guiding POF for Advertising Pillar Illumination POF Starry Ceiling Lights Side-Lighting Fibers POF in Sensor Technology Remote Powered Sensors Transmission and Reflection Sensors POF as Distance Sensor POF Sensors for Concentration Deformation and Pressure Sensors Sensors with Fibers as Sensitive Elements The POF Scale POF Expansion Sensor Sensors with Surface-Modified Fibers Bending Sensors with Notched Fibers POF Evanescence Field Sensors Fill Level Sensors POF Bragg Grating Sensors Sensors for Chemical Materials Humidity Biosensors Liquids Corrosion Glass Fiber Sensors

p. 634 p. 636 p. 637 p. 639 p. 643 p. 644 p. 645 p. 645 p. 647 p. 647 p. 649 p. 649 p. 650 p. 652 p. 652 p. 654 p. 656 p. 657 p. 658 p. 659 p. 660 p. 661 p. 662 p. 662

9. 9.1 9.2 9.3 9.4 9.4.1 9.4.2 9.4.3 9.4.4 9.4.5 9.4.5.1 9.4.5.2 9.4.5.3 9.4.5.4 9.4.5.5 9.4.6 9.4.6.1 9.4.6.2 9.4.6.3 9.4.6.4 9.4.6.5

Optical Measuring Methods Overview Measuring Power Dependence on the Launch Conditions Measurement of the Optical Parameters Near Field Far Field Inverse Far Field Index Profile Attenuation Insertion and Substitution Methods Cut-Back Method Measuring Attenuation for Discrete Wavelengths Measuring Attenuation over a Larger Spectral Range Results of Measurements Optical Backscattering Method Principle of the ODTR Improvement in the Resolution by Deconvolution Commercial POF OTDR Experimental POF OTDR Measurement of the Connector Attenuation

p. 665 p. 665 p. 666 p. 670 p. 674 p. 675 p. 679 p. 684 p. 687 p. 688 p. 688 p. 690 p. 690 p. 692 p. 698 p. 704 p. 704 p. 708 p. 709 p. 711 p. 713

XVIII

Content

9.4.6.6 9.4.7 9.4.7.1 9.4.7.2 9.5 9.6 9.6.1 9.6.2 9.6.2.1 9.6.2.2 9.6.2.3 9.7 9.7.1 9.7.1.1 9.7.1.2 9.7.1.3 9.7.1.4 9.7.1.5 9.7.1.6 9.7.1.7 9.7.2 9.7.3 9.7.4 9.7.5 9.8

Bandwidth Measurements with OTDR Dispersion Time Based Measurement Frequency Based Measurement Connector Measurements The Reliability of POF Environmental Influences on Polymer Optical Fibers The Effect of Environmental Influences on Optical Transmission Attenuation Factors of Polymer Optical Fibers Detection by Measuring Optical Transmission Detection by Measuring Backscattering Investigation of Reliability under Various Environmental Influences Mechanical Stress Repeated Bending Flexing Torsion Tensile Strength Impact Strength Crushing Strength Vibration Stress due to Change in Climatic Conditions Aging due to the Stress of High Temperature and Humidity Resistance to Chemicals Stress Caused by Ultraviolet and High-Energy Radiation Standards and Specifications

10. Simulation of Optical Waveguides 10.1 Modeling of Polymer Optical Fibers 10.1.1 Types of Fibers 10.1.2 Modeling Approaches 10.1.2.1 Approaches with Wave Theory 10.1.2.2 Ray Tracing Procedure 10.1.3 Wave Theory Description 10.1.3.1 WKB Method 10.1.3.2 Step Index Profile Fiber 10.1.3.3 Graded Index Fibers with Power-Law Profile 10.1.3.4 Multi Step Index Fibers 10.1.3.5 Determining the Mode Power Distribution 10.1.3.6 Calculating the Transmission Function and the Output Signal 10.1.4 Ray-Tracing 10.1.4.1 Step Index Fibers 10.1.4.2 Graded Index Fibers 10.1.4.3 Multi Step Index Fibers 10.1.4.4 Bends 10.1.5 Mode-Dependent Attenuation 10.1.5.1 Additional Path-Dependent Attenuation of Higher Modes

p. 714 p. 716 p. 716 p. 718 p. 719 p. 722 p. 722 p. 724 p. 724 p. 725 p. 727 p. 729 p. 729 p. 729 p. 733 p. 735 p. 738 p. 741 p. 745 p. 746 p. 747 p. 749 p. 756 p. 759 p. 760 p. 763 p. 763 p. 765 p. 766 p. 766 p. 767 p. 768 p. 768 p. 769 p. 770 p. 771 p. 772 p. 772 p. 773 p. 774 p. 774 p. 775 p. 776 p. 776 p. 777

Content

XIX

10.1.5.2 Additional Losses of Higher Modes through Loss-Encumbered Reflections 10.1.5.3 Goos-Hänchen Effect 10.1.6 Mode Mixing 10.1.6.1 Coupled-Mode Theory 10.1.6.2 Diffusion Model 10.1.6.3 Application with the Aid of the Split-Step Algorithm 10.1.6.4 Phenomenological Approach 10.2 Examples for Simulation Results 10.2.1 Calculating the Bandwidth of SI Fibers 10.2.2 A Linear POF Propagation Model 10.3 Measurement and Simulation of Bandwidth of PF-GI-POF 10.4 Simulation of Optical Receivers and Large Area Photodiodes

p. 778 p. 779 p. 780 p. 781 p. 783 p. 784 p. 785 p. 786 p. 786 p. 790 p. 793 p. 797

11. 11.1 11.2 11.3 11.4

p. 803 p. 803 p. 804 p. 807

11.5 11.6 11.7 11.8 11.9 11.10

POF Clubs The Japanese POF Consortium HSPN and PAVNET The French POF Club The Information Technology Society (ITG) sub committee (FG) 5.4.1 “Polymer Optical Fibers” The Polymer Optical Fiber Application Center (POF-AC) at the University of Applied Sciences Nürnberg VDI Working Group „Testing of Polymer Optical Fibers“ Product Directory POF-Atlas The POF-ALL Project The Korean POF Club Worldwide Overview

p. 807 p. 811 p. 815 p. 815 p. 816 p. 820 p. 822

References

p. 823

Translator

P. 874

Index of Key terms

p. 875

List of Advertisers

p. 883

Biographies

p. 885

List of Abbreviations and Symbols

Symbol

Explanation

D

Angle (here in an optical dense medium relative to the axis of incidence) Attenuation (coefficient) in dB/km Maximum propagation angle in the fiber Effective loss Excess loss Loss by cross area mismatch Linear expansion coefficient of HDPE POF attenuation for LED Loss by NA mismatch Linear expansion coefficient of PMMA, PA6 Complete attenuation Attenuation coefficient in km-1 Attenuation coefficient due to Rayleigh scattering Critical angle of total reflection Angle at the grating Propagation constant Non linear refractive index Propagation angle of a ray (see Fig. 2.3) Maximum propagation angle of a ray (see Fig. 2.3) Relative refractive index difference Spectral width Frequency difference Absolute refractive index difference Time difference generally Propagation time difference due to mode dispersion Propagation time difference due to profile dispersion Propagation time difference due to material dispersion Slit width Angle difference of the fiber axis Angle of a ray in the fiber relative to the cladding Non linear parameter Maximum angle of a ray in the fiber relative to the cladding

D Dmax Deff Dexcess DFl DHDPE DLED DNA DPMMA ,DPA6 Ds D‘ D`s DT E E F3 G Gmax ' 'O 'f 'n 't 'tmod 'tprof 'tmat 'x H J J Jmax

XXII

Abbreviations and Symbols

4´ 4max 2 4max Tmax1, Tmax2 Wgr Wm \ Z :1, :2 6z dE/dZ dR/dt

Reciprocal coupling length Coupling efficiency Frequency of the mode group m on the total power Exponent for pulse broadening Wavelength Source wavelength Various wavelengths Blaze wavelength Angle (here in the optical thinner medium, relative to the axis of incident) Angle of a reflected beam Acceptance angle Aperture angle of a fiber Various acceptance angles Group propagation time Propagation time of the mode group m Angle of skew rays relative to tangential plane Circular frequency Various solid angles Summarized number of elements Noise current density Group propagation time Reaction rate

a a a aT aT,L A AN AN Launch AN min, AN max AN1, AN2 A, B A 1, A 2 A/D ADSL AM APD ASK ATM AWG AZ

Fiber core radius Attenuation value Acceleration Acceleration factor Acceleration factor relevant to durability Attenuation Numerical aperture Launch NA Minimum and maximum numerical aperture Various numerical apertures Constants Fiber cross areas Analog/Digital Asymmetrical Digital Subscriber Line Amplitude Modulation Avalange Photo Diode Amplitude Shift Keying Asynchronous Transfer Mode Arrayed Waveguide Grating Active layer

Jf KEl Km N O Osource O1, O2, O3, O4 OB 4

Abbreviations and Symbols

XXIII

B BAM BB BBP BER BK BPSK BR BzMA

Bandwidth (generally) Federal Institute for Material Research and Testing Bromobenzene Benzyl n-Butyl-Phtalate Bit Error Ratio Broadbanf cable (Breitbandkabel) Binary Phase Shift Keying Bit Rate Benzyl Methacrylate

c cm cv C Cmn CPD CAN CCD CCP CD CDC CDM CDMA CMT CNR CSO CTB CYTOP“

Velocity of light Velocity of light in a medium Velocity of light in vacuum (2.99792458 · 108 m/s) Constant value (generally) Coupling coefficient between the modes m and n Capacity of the photo diode Controller Area Network Charged Coupled Device Customer Convenience Port Compact Disk Compact Disk Changer Code Division Multiplex Code Division Multiple Access Corrugated Metallic Tube Carrier to Noise Ratio Composite Second Order Composite Triple Beat Cyclic Transparent Optical Polymer (Asahi Glass Comp.)

d d d d 1, d 2 dGM(4) dm dmin, dmax dray D D D D DA DK Dm Drec D2B

Fiber diameter Diameter of the cable lay unit (Chapter 4.2) Reciprocal grating constant Various diameters Field penetration depth, dependent on the angle of incident 4 Cladding thickness Minimum and maximum diameter Beam diameter Wire diameter Distance generally Diffusion constant Dispersion constant Diameter of the stranding basket Insertion loss Average diameter of the cable lay up layer Reciprocal dispersion Digital Domestic Bus (serial bus for automotives)

XXIV

Abbreviations and Symbols

DA DBR DC DEMUX DFB-LD DH DH-MQW DNP DPS DPSK DSI DVB DVD

Wire pair (Doppelader) Distributed Bragg Reflector Direct Current Demultiplexer Distributed Feedback Laser Diode Double Heterostructure Double Heterostructure Multi Quantum Well Dry Non Polish (connector system from AMP) Diphenyl-Sulfide Differential Phase Shift Keying Double Step Index Digital Video Broadcasting Digital Versatile Disk

e/o E EEl ECOC EL ELED EN EMD EOF ETFE EVA

Electro/optical Receiver (Empfänger) Electrical field of the modes European Conference on Optical Communication Effective Laser Launch Edge emitting LED European standard Equilibrium Mode Distribution Elastomer Optical Fiber Tefzel® Ethylen-Vinylacetat-Copolymere

f f f f0 f3dB fa fgr F Fmax FDM FDMA FEC FEP FET FM FOP FP-LD FSK FTTB, FTTH FWHM

Frequency generally (Hz) Extension factor (chapter 4.2) Focal length Reference frequency Bandwidth at 3 dB below maximum Sampling frequency Cut off frequency Force generally Maximum force Frequency Division Multiplex Frequency Division Multiple Access Forward Error Correction Tetrafluoroethylen-Hexafluoropropylene Field Effect Transistor Frequency Modulation French Plastic Optical Fibre Fabry-Perot Laser diode Frequency Shift Keying Fiber To The Building, Fiber To The Home Full Width at Half Maximum

Abbreviations and Symbols

g g(t) GI GI-MPOF GI-PCS GOF GRIN

Index coefficient Pulse response Graded Index Graded Index profile multimode MPOF Graded Index Plastic Clad Silica Glass Optical Fiber Graded Index (continuously index ....)

h h(t) H(f) H0 HAVi HC-MPOF HCS HDMI HDTV HEC HFC HFIP 2-FA HL Homeplanet HPCF HSPN

Planck´s constant (6.629 · 10-34 Js) Impuls response Frequency response Thermal value Home Audio Video Hollow Core MPOF Hard Clad Polymer High Definition Multimedia Interface High Definition Televison Hydroxylethylenzellulose Hybrid Fiber Coax Hexafluoroisopropyle 2-Fluoroacrylate Semiconductor (in German: Halbleiter) Home Plastic Fiber Networks based on HAVi Hard Plastic Clad Fiber High Speed Plastic Network

I Iph IRMS Ith IDB IGPT IR ISDN ISM ITG

Current generally Photo current Noise current (root mean square) Threshold current Intelligent Data Bus Interfacial Gel Polymerization Technique Infrared Integrated Services Digital Network Industrial, Scientific, and Medical Band Informationstechnische Gesellschaft (Information Technology Society)

Jl(u) JIS

Bessel function Japanese Industrial Standard

k Kl (v) kr KF KIST KPCF

Boltzmann´s constant Bessel function Radial component of the propagation vector Correction factor Kwangju Instuitute of Science and Technology Korea POF Communication Forum

XXV

XXVI

Abbreviations and Symbols

l L L1, L2 Lc LAN LD LED Low-NA LWL

Peripheral order Length Lengths of different optical path’s Coupling length Local Area Network Laser Diode Light Emitting Diode Reduced Numerical Aperture Optical waveguide (in German: Lichtwellenleiter)

m M M M ('z) M1, M2 MC MC-GOF MCVD MFC MGDM MIMO MMA MM-GOF MOST MPOF MP3 MP-P MP-MP MPEG MQW MSI MUX

Order of refraction Material dispersion parameter Highest group number Mode coupling matrix Various monomers Multi Core Multi Core Glass Optical Fiber Modified Chemical Vapor Deposition Mode Field Converter Mode Group Division Multiplex Multiple Input - Multiple Output Methylmethacrylat Multimode Glass Optical Fiber Media Oriented System Transport (serial bus in automotives) Microstructured POF Compression method for music Multipoint to Point Multipoint to Multipoint Motion Picture Expert Group (data compression standard) Multi Quantum Well Multi Step Index Multiplexer

n n n0 n1 n2 n1, n2, n3 nair ncladding ncore ncore, max nPMMA N NA

Refractive index Number of layer (chapter 2.8.3) Refractive index of air (approx. 1) Rotational speed of stranding basket (chapter 2.8.3) Rotational direction and speed of the capstan gear (chap. 2.8.3) Refractive index in various media Refractive index of air Refractive index of the cladding Refractive index of the core Maximum refractive index of the core in GI fibers Refractive index of PMMA Number of guided modes Numerical Aperture

Abbreviations and Symbols

NEXT NRC-LED NRZ NTBA NTC

Near End Crosstalk Non Resonant Cavity LED Non Return to Zero (modulation format) Network Termination - Basic Access Negative Temperature Coefficient

o/e OIIC OTDR OVAL

Optical/electrical Optical Interconnected Integrated Circuits Optical Time Domain Reflectometer Optical Video/Audio-Link

p P P P0 P0x, P1x Peff Pelectr, Pel PL PL1, PL2 Popt Pout Pr Preceiv P(f) PA, PA-6 PAM PAVNET PC PC PC(AF) PCS PE PE-FRNC PE HD PE LD; MD PFA PFM PFM PF-POF PhMA pin-PD PLC P-LED PLL PNA

Impulse Profile dispersion Power generally Output power Power for measurements of connector losses Effective power Electrical power Power at the length L Power at fiber outputs Optical power Output power Backscattered power Received power Power at the frequency f Polyamide, Polyamide 6 Phase Amplitude Modulation Plastic Fiber and VCSEL Network Personal Computer Polycarbonate Partially fluorinated polycarbonate Plastic Clad Silica Polyethylene Polyethylene flame-retardant/halogenated Polyethylene (high density) Polyethylene (low density; medium density) Tetrafluoroethylen-Perfluoroalkylvinyl-Ether Preform method Pulse Frequency Modulation Perfluorinated POF Phenyl-Methacrylate Photo diode with p-i-n-semiconductor structure Power Line Communication Polymer LED Phase Locked Loop Phone Network Association

XXVII

XXVIII

Abbreviations and Symbols

PMMA PMMA-d8 PMT POF POF-AC

POFTO PP P-MP P-P PS PRBS PSK PTC PTFE PUR PVC, PVC 90° PVC flame ret.

Polymethylmethacrylate Complete deuterinated PMMA Photo Multiplier Tube Polymer Optical Fiber Polymer Optical Fiber Application Center at the University of Applied Sciences Nürnberg Paving the Optical Future with Affordable Lightning-Fast Links (EU project: www.ist-pof-all.org) POF Trade Organization Polypropylene Point to Multipoint Point to Point Polystyrole Pseudorandom Bit Sequence Phase Shift Keying Positive Temperature Coefficient Polytetrafluoroethylene Polyurethan (thermoplastic) Polyvinylchloride, Polyvinylchloride 90°C Polyvinylchloride flame retardant

QAM QWGext

Quadrature Amplitude Modulation External quantum efficiency

r rk R, ƒ R R R RH R RC-LED RIE RML

Radius generally Radius, which is not remained by helical rays (Fig. 2.7) Responsivity Electrical resistance Bending radius Radius vector Relative Humidity Radius of MC fibers Resonant Cavity LED Reactive Ion Etching Restricted Mode Launch

s s sH S S S Sin, Sout SC SCM SDM

Pitch length Axial distance of fibers Produced pitch length Transmitter (German: Sender) Backscattering coefficient Safety coefficient Modulation signal at input and output Strain Compressed Subcarrier Multiplex Space Division Multiplex

POF-ALL

Abbreviations and Symbols

Semi-GI SERCOS SI Si-PD SLED SM-GOF SNR SOA SQW SP1, SP2 ... St.-NA

Semi graded index profile Serial Real-time Communication System Step index Silicon photo diode Super luminescent diode Single Mode Glass Optical Fiber Signal to Noise Ratio Semiconductor Optical Amplifier Single Quantum Well Reference points Standard NA (typ. 0.50)

t t1, t2, t3 ta, tb tf ti tin, tout tr tA tL T T Tmin, Tmax TG TS T-DSL TDM TDMA TTP

Time Different propagation times Efficiency parameter (in Tab. 3.3) Fall time Length of the launched impulse Pulse width at input and output Rise time Aging time Life time (durability) Transmitter Temperature generally Minimum and maximum temperature Glass transition temperature Reference temperature Telekom ADSL Time Division Multiplex Time Division Multiple Access Time Triggered Protocol

u U UI UKW UMTS USB UMD UV UWB

Normalized propagation constant Voltage generally Unit Interval Ultra short wave (Ultrakurzwelle) Universal Mobile Telecommunications System Universal Serial Bus Uniform Mode Distribution Ultra violet Ultra Wide Band

v v vm v, x, y, z V

Group velocity Normalized propagation constant Draw velocity Variables for the calculation of SNR (chapter 1.3.3) Fiber parameter for the calculation of the mode number

XXIX

XXX

Abbreviations and Symbols

V VB VCSEL VDE

VDI VPAc VPE V-pin

Stranding number (chapter 2.3.8) Vinyl Benzoat Vertical Cavity Surface Emitting Laser Association for Electrical, Electronic & Information Technologies (Verband der Elektrotechnik, Elektronik und Informationstechnik) Association of German Engineers (Verein Deutscher Ingenieure) Vinyl-Phenylazetate Crosslinked polyethylene Versatile Link connector from Hewlett Packard

W W WG WG1, WG2 WDM WDMA WigWam WiMax WLF WPAN

Thermal activation energy Photon energy Band gap energy Band gaps of various semiconductors Wavelength Division Multiplex Wavelength Division Multiple Access Wireless Gigabit With Advanced Multimedia Support Worldwide Interoperability for Microwave Access Williams-Landel-Ferry Wireless Personal Area Network

x x, y y, z z z z

Lateral fiber displacement Fractions in quaternary semiconductors Different path lengths Variable value generally Number of layers (chapter 2.8.3) Fiber position

1. Basics of Optical Data Communication

1.1 Light Propagation in Optical Fibers and Waveguides 1.1.1 Wave and Quantum Nature of Light Many of the properties of light such as interference, refraction, and polarization can be explained with the wave model. Others, such as the photo effect, show that light does not always behave like a continuous type of radiation, but is rather made up of very small particles called photons. These photons are elementary quanta and cannot be divided any further. The energy of a photon is expressed by the following equation: W = h · f , where W = the energy in Joule [J], h is Planck's constant = 6.626 · 10-34 Js and f is the frequency of the light in [Hz]. The frequency of the radiation is calculated from c/O, whereby c is the speed of light in vacuum = 2.99792458 · 108 m/s and O is the wavelength of light in [m]. If the energy is expressed in eV, the conversion is 1 eV = 1.602 · 10-19 As · 1 V = 1.602 · 10-19 J, 1 J = 6.25 · 1018 eV. The particle character of light becomes even more prominent, the shorter the wavelength is or the higher the frequency is. 1.1.2 Electromagnetic Spectrum Figure 1.1 shows an overview of the electromagnetic spectrum. The zone of optical waves includes the ultraviolet, visible, and infrared ranges.

frequency [Hz] 1019 1018 1017 1016 1015 1014 1013 1012 1011 1010 109 108 107 106 105 104 103 102 10 10-11 10-10 10-9 10-8 10-7 10-6 10-5 10-4 10-3 10-2 10-1

1

10

102 103

1

104 105 106 107 108 wavelength [m]

Fig. 1.1: Overview of the electromagnetic spectrum

2

1.1 Light Propagation in Optical Fibers and Waveguides

The interesting ranges as far as optical transmission is concerned are the near infrared range between 850 nm and 1,600 nm for SiO2 fibers (glass optical fiber, GOF) and the visible range between 520 nm and 650 nm for polymer optical fibers (POF) because these show the least attenuation. A detailed overview of the optical range is offered in Fig. 1.2; the white line qualitatively represents the attenuation behavior of PMMA-POF.

10-14

10-12

300

10-10

400

10-8

10-6

10-4

500

10-2

800

1

wavelength [nm] 2000

1000

P O F 5

4

UV range

3

102 104 wavelength [m]

G O F

2

1

visible range

energy [eV]

IR range

Fig. 1.2: UV-, IR- and visible range of the electromagnetic spectrum (POF: Polymer Optical Fiber, GOF: Glass Optical Fiber)

1.1.3 Refraction and Total Reflection When light propagates in a medium such as a polymer, the speed of this light is reduced. The ratio of the vacuum light speed cv to the speed in the medium cm is referred to as the medium's refractive index n, which is expressed as follows: n

cv cm

Apart from the speed, the wavelength O of light passing through a medium is also altered, while the frequency f and thus the energy W remain constant. In Fig. 1.3 we see a light ray entering the optically denser medium at an angle 4 and being refracted at an angle D to the axis of incidence. A part of the light is reflected. Refraction is expressed with: sin 4 sin D

n2 . n1

By reversing the light path (transition from an optically denser medium to an optically thinner one, figure at the right), the ray is refracted away from the axis of incidence. If in this case angle D is continuously increased, the light ray stops

1.1 Light Propagation in Optical Fibers and Waveguides

3

being transferred to the other medium when angle D reaches a critical value; instead, it is completely reflected. For the boundary case of total reflection, i.e. when 4 = 90q, the following applies: n1 n2

sin D T axis of incidence n1 4 4‘

axis of incidence optically thin

4

n1 < n2

n2

D

DT

optically dense

D‘ D

Fig. 1.3: Light refraction and total reflection

1.1.4 Waveguides and Optical Fibers An optical fiber consists of a highly transparent core having a refractive index ncore and a surrounding transparent cladding having a refractive index ncladding. To ensure that a light ray that has entered the fiber can be guided along it, the following must hold true: ncore > ncladding (Fig. 1.4), so that below a certain angle 4max total reflection takes place at the interface between the core and the cladding. The surrounding medium is air with the refractive index n0 | 1.

n0

ncladding

cladding

ncore

J Dmax

core

4 max refractive index n Fig. 1.4: Wave guiding within the optical fiber

Rays that strike the end face of the fiber at an angle greater than 4max are no longer completely reflected at the core/cladding interface; instead they are partly refracted into the cladding so that they are no longer completely available for

4

1.1 Light Propagation in Optical Fibers and Waveguides

transmitting a signal. The following example illustrates how even small differences here can have great effects: with a core refractive index of 1.56 and a cladding refractive index of 1.49 the critical angle of total reflection is 72.77º. Thus, light rays with a maximum angle of Įmax = 17.23º with respect to the fiber axis, can propagate. Should the propagation angle exceed this value by only 0.001º, then the reflection coefficient is reduced from 100% to 95%. With this angle 310 reflections per meter will result in a fiber with a diameter of 1 mm. The remaining light output power would then be 0.95310 = 1.2 · 10-7 which corresponds to a loss of 69 dB. The shape of the waveguide can vary greatly as the three examples in Fig. 1.5 demonstrate. On the left is a singlemode glass fiber which is almost exclusively used today in the field of telecommunications. A planar waveguide can be seen in the middle and on the right a semiconductor laser in cross-section with which an optical waveguide is also formed.

singlemode fiber

n = 1.466

planar waveguide

n = 1.55

n = 3.55

n = 1.47

Ø: 10 μm

laser diode

n = 1.60

5 u 5 μm

n = 3.60

2 u 0.5 μm

Fig. 1.5: Examples for optical waveguides

Should the waveguide have very small dimensions in the light wave length ranges, then the ray optics description is not sufficient. As can be read in standard works, e.g. [Vog02], the number of possible propagation angles (modes) diminishes with decreasing diameter. An extreme case thereby is the singlemode waveguide which will be introduced in the next section. 1.1.5 Singlemode and Multimode Waveguides The number of modes in an optical waveguide is determined by the so-called V-parameter. The parameters thereby are the core radius a, the light wavelength Ȝ and the numerical aperture AN. V

2˜S˜a ˜ AN O

As long as V is smaller than 2.405, only one mode can propagate; otherwise it is a multimode fiber. The number of modes results approximately thus:

1.1 Light Propagation in Optical Fibers and Waveguides

N | V2 2 N|V

2

4

5

(step index profile) (graded index profile)

Strictly speaking, there are also two propagation states in a singlemode fiber, namely the two orthogonal polarization directions. As long as the waveguide is exactly rotationally symmetrical, or also square, and the material is completely homogenous, then both polarization directions propagate at the same speed. The number of modes always depends on the wavelength. A fiber is thus a singlemode fiber as of a certain wavelength (cut-off wavelength). The fibers dealt with in this book always have a large number of modes as shown in Table 1.1. (See Chap. 2 for a more detailed description of the fiber types.) Furthermore, you must keep in mind that in spectrally wide sources each wavelength occurring has its own modes. In a POF system with LEDs you not only have to keep the several million fiber modes in mind, but also all emitted wavelengths (a source can be considered ideally monochromatic when the coherence time is large in relation to the differences in propagation time which arise). Table 1.1: Number of modes in optical fibers Fiber type

Profile NA

Radius Otransmitter a [μm] [nm]

V

Number of Modes

Standard-POF

SI

0.50

490

650

2,368 2,804,369

Optimedia-POF

GI

0.37

450

650

1.609

647,592

MC37-POF (single core)

SI

0.50

65

650

314

49,348

PCS

SI

0.37

100

850

274

37,402

MC-GOF (single core)

SI

0.50

27

650

130

8,515

MC613-POF (single core)

SI

0.50

18.5

650

89

3,997

Lucina GI-POF

GI

0.22

60

1,200

69

1,194

GI-GOF (Europe)

GI

0.17

25

850

31

247

®

1.1.6 Overview of Optical Fibers The different types of optical fibers are described in detail in this chapter; an overview of the standards can be found in Chap. 7.2. The two following pictures show an overview of the different refractive index profiles. It can easily be seen that not only the index profiles, but also the refractive index differences - which determine the numerical aperture - and the core diameter vary considerably. The fibers with the greatest core diameter used in data transmission can be seen in Fig. 1.6. Standard SI-POF has an approx. diameter of 1 mm at a NA of 0.50. GI-POF with this diameter, but with a somewhat smaller NA, has also been available for a short time ([Yoo04]).

6

1.1 Light Propagation in Optical Fibers and Waveguides

refractive index difference 0.09 0.08 0.07 0.06 0.05

PMMAgraded index fiber AN = 0.39

standard step index polymer fiber AN = 0.50

0.04 0.03 ‡core = 900 μm

0.02 0.01

‡core = 980 μm

0.00

Fig. 1.6: Index profiles of different polymer optical fibers

The index profiles of different glass and polymer fibers can be seen in the next fig. 1.7. A hybrid is the so-called PCS - polymer clad silica - i.e. a silica glass fiber with a polymer cladding. The singlemode glass fibers have the smallest core diameters. For use in the 1300 nm to 1600 nm range these fibers only have a core diameter of about 10 μm. Special fibers, e.g. for erbium-doped fiber amplifiers or for fibers with non-linear properties, can even lie in the range of only 2 μm for the core diameter. These fibers are not the subject of this book. We can recommend [Vog02] as a work with an excellent overview for this area. refractive index difference 0.040 0.035 0.030 0.025 0.020

PF-GI-POF AN = 0.20

MM-GOF MM-GOF (US) (Europe) AN=0.275 AN=0.20

PCS AN=0.37 semi-GI PCS AN=0.4

0.015 0.010

SM-GOF AN=0.10

0.005 0.000 ‡core=120μm

‡core=200μm

‡core=200μm

Fig. 1.7: Index profiles of different glass optical fibers

‡core= 62μm

‡core= 50μm

‡core= 10μm

1.1 Light Propagation in Optical Fibers and Waveguides

7

1.1.7 Designations of Optical Fibers There are no general international guidelines for the designation of optical fibers. Due to the enormous variations in the different parameters it is hardly possible to give all fibers clear-cut designations since these would otherwise be much too long. The following list of parameters could be used for providing names. Table 1.2: Parameters in fiber names with possible versions Parameter

Description and Variants

Example

number of modes

mostly it is distinguished between single- and multimode (with V > 2.405)

singlemode fiber (SMF)

core material

General there are the variants glass, SiO2 or polymers

polymer optical fiber (POF)

special core material

primarily special polymers are marked

polycarbonate fibers (PC-POF, PMMA-POF etc.)

cladding material

Special hybrid fibers, for example SiO2-fibers with polymer cladding

polymer clad silica fiber (PCS)

index profile

The index profiles of GOF and POF can have very different variants: ¾Step index profile ¾Double step index profile ¾Graded index profile ¾Multi step index profile ¾Semi-graded index profile

SI-POF DSI-POF GI-POF MSI-POF semi-GI-PCS

number of cores

In GOF and POF there are variants of fibers with many cores

multicore fiber (MC-POF)

polarization behavior

(only in singlemode fibers) special fibers maintain the state of polarization or only one state of polarization can propagate

polarization maintaining fiber (PMF)

chromatic dispersion

(only in singlemode fibers) ¾dispersion shifted fibers ¾fibers with flattened dispersion ¾dispersion compensating fibers

Numerical Aperture

for single and multimode-fibers high NA fiber (HNA) (e.g. high NA for small bending radii)

microstructure

Bragg fibers are built by holes, or the effective refractive index is changed

bending losses fibers optimized for minimal bending losses (by high NA or micro structuring)

DSF DFF DCF

photonic crystal fiber (PCF); microstructured fiber; photonic band gap fiber bend insensitive fibers (BIF)

8

1.2 Digital and Analog Signal Transmission

standard

many fibers are accurately described in ITU-Standards e. g. singlemode fibers in ITU-G.652 G.656

standard-SMF (G.652 B1.1)

application

use in special applications, e.g. mobile networks

MOST-POF

In addition, there are numerous differences in diameter, in the numerical aperture, fiber qualities, kind, thickness, and construction of the primary coating, etc. In order to include all these parameters in fiber names it would be necessary, for example, to say: 500 μm PMMA GI-POF with NA 0.30 and black PE cladding, 1.5 mm. Some of the most common fibers are: ¾standard glass fiber (singlemode, Øcore = 10 μm, NA: 0.10) ¾standard POF (PMMA, Øcore = 980 μm, NA: 0.50) ¾PCS (SiO2 core, Øcore = 200 μm, NA: 0.37) ¾multimode fiber (MMF, GI profile, Øcore = 50 μm, NA: 0.17)

1.2 Digital and Analog Optical Signal Transmission For the communications engineer there is no doubt that, apart from spectral attenuation, the most important parameter of an optical fiber is its bandwidth. In waveguides there are usually different optical paths possible (with the exception of the very thin singlemode waveguides). The different lengths of travel along these different light paths lead to different time delays for an optical pulse, as illustrated schematically in Fig. 1.8. propagation length = fiber length/cos(D)

propagation length = fiber length

D

P

t input pulse Fig. 1.8: Different time delay due to different propagation paths

output pulse

1.2 Digital and Analog Signal Transmission

9

For a standard POF it is valid e.g.: core refractive index: cladding refractive index: maximum propagation angle: different flight times:

ncore = 1.49 ncladding = 1.42 Dmax = 17.6° 4.9 %

Only two light paths have been shown in this illustration. However, in a real experiment there are always many rays paths so that the individual pulses overlie each other to form one more or less broadened overall pulse. Figure 1.9 shows the effects of such a pulse broadening on a digital signal.

1 0 0 1 1 1 0 0 1 1 0 1 0 0 1 0 a) fiber length

b) c) d) e)

Fig. 1.9: Influence of mode dispersion to data transmission

An optical signal is launched into the fiber and is switched on and off at the respective bit rate (curve a). With the increase in pulse broadening, the bit edges get more and more fuzzy (signal sequence with downwards increasing transmission length). As long as the amount of broadening is clearly less than the bit time, the signal will remain easily identifiable (curves b and c). If the width of the edges exceeds the bit time, the signal can no longer be detected (curves d and e). The process of pulse broadening is called dispersion. The difference between different light paths described here is called mode dispersion (any possible condition of the propagation of light in a waveguide is called a mode). Apart from mode dispersion there is also the phenomenon of chromatic dispersion (different time delays for different wavelengths) and polarization mode dispersion; however, we will not be dealing with these two phenomena at this stage. The second important quantity which determines signal quality is the signal-tonoise ratio (SNR). In POF systems the optical receiver alone is almost always responsible for the noise. Under certain circumstances you have to pay attention to mode distribution noise within thin multimode glass fibers. In modern singlemode glass fiber systems there are even many more sources of noise, e.g. fiber amplifiers. The following sections provide a short insight into the fundamentals of analog and digital transmission methods, especially in regard to the various sources of interference. The effects which are important for short-range communication are particularly elucidated.

10

1.2 Digital and Analog Signal Transmission

1.2.1 Digital Optical Signal Transmission 1.2.1.1 Analog and Digital Signals For readers less familiar with the fundamentals of signal theory, a brief explanation of the various basic terms is provided here for a better understanding of the requirements of the different methods for the components. Generally speaking, transmission systems are classified according to the signal values to be transmitted, i.e. whether they have discrete or random values. In nature, information can be expected to be fully analog (see Fig. 1.10). We will assume that the signal of interest (for example, an acoustic signal) is to be converted into electrical voltage U(t) with the help of an electronic measuring instrument (in this case a microphone).

U(t)

t Fig. 1.10: Analog signal

Here, analog has two meanings. First, the signal is measured at any random time t. Furthermore, U(t) can take on any value. When a signal is digitized, two things usually happen. While the signal is being sampled, the values are not read in continuously but rather at discrete points (Fig. 1.11).

U(t)

sampling points t Fig. 1.11: Sampling an analog signal

11

1.2 Digital and Analog Signal Transmission

The second step is that the voltage U must not take any random value but only particular or discrete ones (quantization, Fig. 1.12).

U(t) sampling points quantization steps t Fig. 1.12: Quantization of a signal

Figure 1.12 shows that the values no longer lie exactly on the actual curve but always at the next quantization level. The digitalization of a signal always distorts the original one. Initially, the range of the recorded frequencies is limited by the choice of the sampling rate (sampling points per second). According to the Sampling Theorem, only signals whose upper limit frequency ful is equal or smaller than the half of the sampling rate fs (ful d fs/2) are fully transformed into the digital signal. Figure 1.13 graphically illustrates this problem.

U(t)

U(t)

t

t sufficient sampling rate

sampling rate is too low

Fig. 1.13: Choice of sampling rate

In the left figure, the sampling points are spaced sufficiently close to each other. In the right figure, the signal also changes very quickly between the sampling points (higher frequencies are present). The original signal cannot be reconstructed from the points that are too far away from each other. Quantization also distorts the signal. The difference between the actual value and the quantization level can be interpreted as added noise (Fig. 1.14).

12

1.2 Digital and Analog Signal Transmission

U(t)

quantized signal quantization noise (deviation from the original signal)

t Fig. 1.14: Generation of the quantization noise

The signal of a CD player is a good example of a digital signal. The human ear can detect frequencies up to 15 kHz to 18 kHz. Music is stored on a CD with 44,200 values per second. Thus, signal frequencies up to 22.1 kHz can be recorded. Each of these sampling values is divided into 65,536 amplitude steps (216). The original continuous signal is thus broken into 44,200 numbers per second, for example, 23,546; 22,125; 19,714; 13,120 etc.

The errors that occur as a result of this quantization are negligible. If the available levels are equally distributed to positive and negative voltages, for example to the range between +1 V and -1 V, the deviation of the real value to the next quantization level can be at most 15 μV. This is a difference of approximately 96 dB. This is the equivalent of the difference between a whisper and the sound of a loud airplane propeller 5 m away. In the world of digital signal processing, the numbers are represented with the symbols “1” and “0”. 65,536 values can be represented by 16 binary characters (16 Bit). As a binary number, the signal above would then look like this: 0101101111111010,0101011001101101,0100110100000010,0011001101000000

When the signal is transmitted, the commas are, of course, omitted. Both symbols are characterized by various signal states, for example, -1 V for the “0” and +1 V for the “1” or also “light off” for the “0” and “light on” for the “1”. Figure 1.15 illustrates the difference between the original analog signal and the binary signal generated by means of digitalization.

U(t)

analog signal t

U(t)

digital signal t

Fig. 1.15: Analog and digital signal

1.2 Digital and Analog Signal Transmission

13

The figure shows that the digital signal changes much faster than the analog signal. This is easier to see if you consider that music at a maximum frequency of approximately 20 kHz must transfer 44,20 × 16 = 707,200 bit/s. Why digital signal processing still has many advantages over analog processing is explained in the next paragraph. 1.2.1.2 Transmission Quality of Analog and Digital Signals The analog signal from Fig. 1.10 will again serve as our starting point. A data cable will be used for data transmission. In reference to the signal, the transmission link represents an obstacle replete with many interference effects. At first, an amplifier is needed at the transmitter to create the required voltage level. He can be limited in his bandwidth and consequently distort the signal through nonlinearity. Similarly, the actual transmission line has a limited bandwidth. Other influences can also distort the signal such as a nearby source of radio interference. The receiver too will only have a limited bandwidth. The signal was attenuated while on the transmission line and thus only has a weak signal level. This is why inherent receiver noise is often the most conspicuous source of interference. Figure 1.16 summarizes the most important sources of interference. U(t) t

transmitter

fg input signal

f

distortion bandwidth limitation

transmission line

fg

f

attenuation external perturbations

receiver

fg

f

noise bandwidth limitation

output signal

Fig. 1.16: Influences on an analog signal transmission

Even though some of the sources of interference have been somewhat exaggerated, they are intended to show the problems involved in transmitting analog signals. Each element involved in the transmission can distort the original signal. These forms of interference can only be eliminated in exceptional cases and are also relevant to digital transmission, as Fig. 1.17 illustrates.

14

1.2 Digital and Analog Signal Transmission

U(t) t

transmitter

fg

transmission line

f

fg

receiver

fg

f

f

input distortion attenuation noise signal bandwidth limitation ext. perturbations bandwidth limitation

output signal

Fig. 1.17: Influences on a digital signal transmission

The signal behind the receiver appears to be strongly distorted; but this is where the digital „trick” sets in. The receiver knows that the signal can only have one of two levels and that the signal was transferred with a specific bit rate. This knowledge is then used to reconstruct the signal free of error. The signal is at first filtered to eliminate as much noise as possible. A decision threshold is then defined. For binary signals, this is the border between “0” and “1”. At the sampling points that correspond precisely to the bit raster, the signal is compared with the threshold and then reconstructed. This procedure is shown schematically in Fig. 1.18. U(t) 010011 t received signal

filtering

decide threshold

sampling

reconstructed signal

clock recovery Fig. 1.18: Signal reconstruction in digital transmission systems

Although the signal was clearly distorted, the complete reconstruction of the original bit sequence is possible. This is what users recognize as “CD quality”. The question still remains as to how the analog signal, i.e. the music, is restored. A digital analog converter is used for this purpose. In the example shown, the converter uses 16 bits in the 65,536 intervals between -1 V and +1 V. The signal is then subsequently filtered to eliminate the resulting harmonic waves and then is ready for use (for example, to be fed into a loudspeaker). This step is not needed for communication between the digital devices.

15

1.2 Digital and Analog Signal Transmission

1.2.1.3 Bit Error Probability and Error Correction An analog signal can usually be described quite accurately with the Signal to Noise Ratio (SNR). This is done by comparing the average signal power to the average noise power. Since there is noise in every system, the SNR is always finite. As we have seen earlier, this value is not sufficient for digital systems, since the signal is reconstructed at the receiver. To be sure, a complete error-free transmission is also not possible for digital systems. The cause for this is to be found in the statistical character of many noise processes. Only thermal noise will be discussed here. Due to the particle like structure of the electrons, every flow of current is irregular which leads to voltage fluctuations at resistors. This represents a physical bottom limit for the noise power of each system. If you apply the probability of a particular voltage deviation occurrence, this will give you a Gaussian function. In Fig. 1.19, it is assumed that the binary symbols are transmitted in an ideal system by -1 V and +1 V and that both symbols are being distorted through noise.

rel. probability density 1.2 “1” ideal

“0” ideal

1.0 0.8

“1” with noise

“0” with noise

0.6 0.4 0.2 0.0 -2.0

-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

2.0

voltage [V] Fig. 1.19: Influence of noise on ideal, digital signals

As you can see in Fig. 1.19, the levels +1 and -1 are the most likely ones but there are also other levels. In the case at hand, the decision threshold is 0 V. It appears that it is still possible to clearly differentiate between the two symbols despites the noise. However, the Gaussian curve never drops completely to 0. This is shown in Fig. 1.20 in which the same curve is scaled logarithmically.

16

1.2 Digital and Analog Signal Transmission

relative probability density 10 0 10 -1 Symbol “0” with noise

10 -2

Symbol “1” with noise

10 -3 10 -4 10

optimal decision threshold

-5

10 -6 10 -7 10 -8 -2.0

area of bit errors voltage [V] -1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

2.0

Fig. 1.20: Generation of bit errors in digital transmission systems due to noise

Here you can see that the curves for “0” and “1” overlap. This means that at times a “0” can be distorted to such a degree that it is detected as a “1” or vice versa. The hatched area represents exactly the bit error provided that the decision threshold is actually 0. Integrating this area and putting them into relationship with the integrals of the probabilities for “0” and “1”, yields the bit error probability (Bit Error Ratio BER). In this case the result would be  ˜ 10-7 . Returning to the CD example, this would mean one error every 10,000,000 bits or, on the average, one error every 14 s. For normal use, this would not pose a major problem. However for data transmission, this would be entirely inadequate. If saved as a file, this book would consist of about 109 bits. At this error rate, 100 bit would be faulty. At best, this would result in incorrect characters or errors in the illustrations. A more likely scenario would be, however, that many of the errors would cause the system to crash and make the file unusable. Considering all the time we authors have invested in this documentation, this would be anything but a welcome course of action. Hence, data connections should be considerably more reliable (for example, BER < 10-15). The characteristics of noise anticipate the conclusion that error-free data transmission is nothing more than an illusion. But this is where we can call on statistics for help. If the voltage levels are increased to ±2 V, the error probability drops to approximately  ˜ 10-25 for the same noise level. For our CD signal, this would mean one error in 9 billions years, i.e., this book could be transmitted several trillion times without error.

1.2 Digital and Analog Signal Transmission

17

However, there are other ways to reduce the error probability. Particular coding schemes make it possible to detect individual errors on the receiver end (FEC: Forward Error Correction). This is achieved by adding so-called „control bits” to the signal flow. The bit rate is usually increased by only a few percent. On the receiver end, practically all errors can be corrected. These procedures are often used in mobile communications where, for example, the less than ideal transmission channels cause an inordinate amount of errors. 1.2.1.4 Noise in Optical Systems As mentioned above, there is a large number of sources of noise in optical systems all of which could hardly be dealt with in a single book. There are entire books, e.g. [Pet88], just on noise in optical transmitters - which are usually laser diodes. In systems for short-range data communication, however, you only have to pay attention to a few noise processes which are dealt with briefly here. Laser Noise: Laser diodes and LEDs are normally very low noise and stable sources. Clean driving is especially important for signal quality. Edge emitting laser diodes in particular can show high noise if light is reflected back from the transmission link. This can hardly be avoided since about 4% of the light is already reflected at the very first frontal area of the fiber. All reflections which appear within the coherence length are disruptive. These can be on occasion many kilometers when using high quality laser diodes. In order to avoid fluctuations in laser performance caused by reflections, anti reflection coatings, optical insulators and special lowreflecting plug-in connections are used. The LEDs used in most POF systems have a coherence length of a few μm and are hardly influenced by reflections. Conventional LDs or VCSELs can be disturbed by reflections. One advantage of using multimode fibers is their greater diameter compared with the emitting surface of the laser. Even if much light is reflected, only a small fraction reaches the active surface of the laser (Fig. 1.21) so that the effect is negligible.

reflected light

VCSEL ‡active = 10 μm

Fig. 1.21: Influence of reflections in POF/PCS-systems

PCS ‡core = 200 μm

18

1.2 Digital and Analog Signal Transmission

Quantum Noise of the Light and the Diode Dark Current: Light and current have a basic quantum noise as they are quantized energy flows. Noise in light - called shot noise - is caused by the power and energy of the photons, i.e. by the wavelength. With reference to the photon flow, which is also determined by the responsivity, the following is true: quantum noise current: iQ2

2 ˜ e ˜ IPH ˜ B

2 ˜ e ˜R ˜P ˜B

with the quantities: B: e: IPH: P: R:

signal bandwidth (determined by bit rate) elementary charge photodiode current received power spectral sensitivity (mA photocurrent per mW optical power)

As an example, we shall consider a data transmission of 1.25 Gbit/s at a wavelength of 650 nm (R = 0.4 mA/mW). The received power is -24 dBm (4 μW). At a bandwidth of 700 MHz a medium shot noise current of 19 nA results. With reference to the signal photon current of 1.6 μA the result is a SNR of 38.5 dB, consequently, the noise is negligible. In fact, practically all optical transmission systems are limited by electronic receiver noise and not by shot noise. The dark current flowing in most photodiodes also generates quantum noise. The strength of this noise is: iD2

2 ˜ e ˜ ID ˜ B

ID is dark current and lies in the nA range with normal pin-photodiodes so that the additional noise is also negligible. Receiver Noise: The most important source of noise for the systems under consideration in this book is receiver noise. In principle, every optical receiver can be described, at least in a rough comparison, as a combination of a photodiode, an ohmic input resistor and an amplifier (transistor or operational amplifier, Fig. 1.22).

POF

input resistance Fig. 1.22: Optical receivers’ principle

amplifier

1.2 Digital and Analog Signal Transmission

19

The photo current is converted into a voltage at the input resistor which then continues to be amplified. The greater the resistance, the higher the signal voltage. On the other hand, however, every resistor generates a thermal noise according to the following equations. 2 uth

with: k: T: B: R:

4 ˜ k ˜ T ˜ B ˜ R or:

2 ith

4 ˜k ˜ T ˜B R

Boltzmann constant (1.38 ˜ 10-23 Ws/K) absolute temperature system bandwidth ohmic resistor

In the example above, the input resistor could lie at 500 Ÿ. The thermal noise current would then be 152 nA, corresponding to a SNR of 20.4 dB. The following amplifier will never work ideally. The noise figure indicates how far the actual noise lies above the theoretical minimum. Depending on the components, values of 1 dB to 3 dB are typical. The SNR is diminished correspondingly. You can easily see that the signal voltage increases proportionally to the resistance R; the thermal noise current, however, only increases with the root of R. In principle, the SNR can be raised whenever you like by increasing R. However, there is a fundamental limit. Every photodiode possesses a junction capacitance which, together with the input resistor of the circuit, forms a RC low pass filter which restricts the speed of the receiver. Therefore, you can only select a resistance as high as allowed by the diode capacitance and the bit rate. With a RC low-pass bandwidth of: f3 dB

1 2˜ S ˜R ˜C

and a minimum bandwidth of the receiver - which corresponds to one half the bit rate - the maximum input resistance may amount to:

R

1 bit rate ˜ S ˜ C

With a diode capacitance of 0.5 pF a R of about 500 Ÿ, as indicated above, results. This calculation is only a very rough approximation, but it does show the principle problem involved. Diodes intended for use in singlemode fiber systems only have to be a little bit larger than the core diameter of the fiber. A typical size for photodiodes is from 30 μm to 50 μm. Their capacitance only lies at some 10 pF, but they do allow large input resistances with high data rates and thus have good sensitivity. For thick polymer fibers and PCS, however, photodiodes with very much larger surface will be needed. Their capacitance lies at some nF or some tenths nF. With high data rates the input resistance must correspondingly be reduced and thus the sensitivity. This is the only indirect influence of the fiber diameter on the possible bit rate with thick optical fibers.

20

1.2 Digital and Analog Signal Transmission

Modal Noise: A special kind of noise only appears in multimode fibers: mode distribution noise. In multimode fibers light propagates in different specific modes, whereby each one possesses its own distribution of power over the fiber cross-section. The kind of power distribution between the modes changes with tiny changes in the exterior conditions, e.g. temperature, wavelength of the transmitter or also vibrations of the fiber, but the overall power remains constant. Figure 1.23 shows examples of power distribution of modes (multimode GOF/POF at 650 nm, laser excitation).

Fig. 1.23 Examples for energy distribution of modes in multimode fibers (left: 50 μm GI-GOF, right: 1 mm SI-POF with much higher mode number)

Steadily fluctuating power distributions only become problematical when the overall output power is not transmitted at coupling points. Random exchanges of power occur between the transmitted and the decoupled share which in the end generates additional noise (schematic depiction in Fig. 1.24). opt. power lost power

coupled power in the second fiber

fiber with fluctuating power distribution

cross section of the second fiber

Fig. 1.24: Origin of modal noise

time

21

1.2 Digital and Analog Signal Transmission

The intensity of the modal noise depends on the number of the power maxima on the cross-section (in the order of magnitude of the number of modes) and the differences in power. For 50 μm multimode glass fibers the mode distribution noise is typically only a good 20 dB below the overall transmitted level ([Vog02]). This is insignificant for digital transmission, but makes analog transmission impossible. In order to avoid modal noise, transmission must take place either with singlemode or with very many modes since this effect is inversely proportional (statistical effect) to the root of the number of modes. Polymer fibers with several million modes are therefore of interest for analog data transmission and are much better suited than GI glass fibers. 1.2.2 Amplitude, Frequency, and Phase Modulation Whenever digital and analog signals are transmitted, there is virtually always an electrical voltage U(t) present at the beginning and at the end of the transmission path. To cover the distance, other physical parameters can also be used. The changing of these parameters is referred to as modulation. As we will see, when we want to transmit signals with light, there are a number of problems to consider. In general, the desired parameters can be modulated analog, i.e. with varying strength, or with only a small number of discrete steps. Below we will show some examples of binary, digital modulation procedures. We shall start with the electrical transmission procedure depicted in Fig. 1.25:

U(t)

U(t) t

transmitter

t receiver

Fig. 1.25: Most simple electrical signal transmission system

On the transmitter end, the signal is the voltage difference between two conductors (for example, the wires of a twisted data cable or the core and shielding of a coaxial cable). If we neglect such factors as attenuation and band limitation, the signal is tapped again directly at the output end of the cable. This method is, of course, the easiest but, experts know, also the one most susceptible to interference.

22

1.2 Digital and Analog Signal Transmission

1.2.3 Modulating a Carrier Frequency A simple but reliable transmission method is to use a carrier frequency that is significantly higher than the cut-off frequency of the signal to be transferred (Fig. 1.26). U(t)

transmitter

Ucarrier(t)

t

t

receiver

source for carrier frequency Fig. 1.26: Signal transmission with carrier frequency

The carrier wave can be described with three parameters: amplitude, frequency, and phase. All three parameters can be used for modulation. For binary signals these are: ASK: FSK: PSK:

Amplitude Shift Keying; Amplitude Modulation Frequency Shift Keying; Frequency Modulation Phase Shift Keying; Phase Modulation

The principle is shown in Fig. 1.27. signal

ASK

FSK

PSK

Fig. 1.27: Signal transmission with ASK, FSK or PSK

In addition, there are a number of other procedures such as DPSK (Differential Phase Shift Keying), in which only the phase difference between 2 sequential bits is of significance or multilevel procedures such as QAM (Quadrature Amplitude Modulation) or combinations of several modulated parameters (PAM, Phase Amplitude Modulation). An in-depth description of these procedures can be found in many standard works on communication technology, for example [Lüke90], [Kreß89] or [Hulz96] or as a very simple introduction, in [Eng86]. Each individual modulation procedure requires special receivers that can recover the original signal. A distinction is made between procedures that measure the power of the carrier and those that operate synchronously to the carrier frequency (for example, PLL tuners for FM radio).

23

1.2 Digital and Analog Signal Transmission

1.2.4 Specific Transmission Methods in Optical Communications The advantages of optical communications are undisputed and have been know for some time. The reader will undoubtedly be familiar with many of them. With the low attenuation characteristics of modern singlemode fiber optic cables, many hundreds of kilometers can be bridged with high data rates. If fiber amplifiers are used, transcontinental communication is even possible. Particularly systems with polymer optical fibers are well suited for short distances due to their insensitivity to interference. Light is an electromagnetic wave with a particular frequency. At 500 nm, i.e. green light, this is 6 · 1014 Hz. No electronic component is able to process this frequency. Photodiodes only measure the optical power of a light signal. Furthermore, optical sources cannot maintain their frequencies nearly as accurately as electric oscillators. Directly modulating the parameters frequency or phase (and polarization in particular) of light is only possible with so-called heterodyne receivers. This involves modulating an extremely frequency-stabilized laser on the transmitter end and heterodyning it on the receiver end with a second laser that is just as stabilized. A mixed frequency is produced at the photodiode (the difference between the both laser frequencies), which can be further processed by the subsequent electronic components. Heterodyne systems offer, at least in theory, the best frequency economy of all optical systems. Nevertheless they have not gained acceptance due to the many technical problems involved. For further information, see [Fra88] and [Ziem95]. Therefore, the only parameter left for modulation is amplitude. A photodiode measures the optical power that is converted into a proportional photo current. Since the electrical power, measured at a resistor, is proportional to the square of the current, the following relationship holds true: Pelectr ~ Iph² ~ Popt² Although the electric field of the transmitted light can take on positive and negative values, the actual measured parameter is always positive. This is a significant difference compared to electrical communication systems. Let us take a simple binary signal transmission as an example. In the electrical stage, the bits are switched between -1 V and +1 V at the transmitter. The decision threshold is set to 0 V. The levels 2 mW and 0 mW should be selected for an optical signal. The decision threshold should be at 1 mW (see Fig. 1.28).

Popt(t)

U(t) +1 V 0V -1 V

t

2 mW 1 mW 0 mW

Fig. 1.28: Electrical and optical, digital signal transmission

t

24

1.2 Digital and Analog Signal Transmission

Initially, both systems appear similar. In the Fig. 1.29 below, additional attenuation is inserted, for example by increasing the temperature or aging the transmitter. The level drops to 40 %.

U(t)

Popt(t)

+1 V

t

0V -1 V

2 mW 1 mW

t

0 mW

Fig. 1.29: Electrical and optical, digital signal transmission with attenuation

In the electrical system, both symbol levels are equally decreased. If the noise is not too large, it will still function flawlessly. In an optical system, the zero level will, of course, remain unchanged while the “1” level falls below the threshold. The system then no longer functions. This problem, of cause, can be solved. Capacitive couplings or decision threshold controls are used, or the decision level is set initially so low that the threshold is always above the noise level of the “0” symbol (Fig. 1.30 to 1.32). optical signal

photodiode capacitve coupling

+1 V

2 mW 1 mW 0 mW

electrical signal

0V

t

t

-1 V

Fig. 1.30: Receiver with capacitive coupling optical signal

photodiode, threshold control

2 mW 1 mW 0 mW

electrical signal +2 V

t

+1 V 0V

t

Fig. 1.31: Receiver with threshold control optical signal 2 mW 1 mW 0 mW

electrical signal photodiode, threshold optimized +2 V for minimal level t

Fig. 1.32: Receiver with minimal threshold

+1 V 0V

t

25

1.2 Digital and Analog Signal Transmission

All of the methods discussed have their advantages and disadvantages which, however, will not be elaborated further here. Various commercial systems for POF use the third method. 1.2.5 Modulating a Subcarrier To be able to use the many possibilities of carrier frequency technology in optical communications, a subcarrier can be used. Hence, light is modulated in its intensity as a sine wave. The signal is then modulated onto this carrier, whereby ASK, FSK, PSK or other methods can again be used. The receiver only needs to process the range around the carrier, i.e., it will always be coupled in a capacitive manner. Figure 1.33 illustrates the method using the subcarrier FSK as an example.

Popt(t) 2 mW 1 mW

t

0 mW Fig. 1.33: Optical signal transmission with a frequency modulated subcarrier

It should be noted that the optical power curve still represents a much higher optical frequency. One advantage of the method shown is that the average optical output power remains unchanged from the succession of the “0” and “1” symbols. Laser diodes are particularly well-suited for this type of modulation.

5 Popt(I) /mW

output signal bias current

4 3 2 1 0 0

10

20

30

40

50 ILD /mA modulation current

Fig. 1.34: Subcarrier modulation of a laser diode

26

1.3 Network Architectures

As described above, lasers are best operated with a bias current. In direct power modulation, this would be slightly below the threshold. In subcarrier modulation, the bias current is set higher than the laser threshold so that the laser is always operated above the threshold current as shown in Fig. 1.34. Thus the tools for transmitting analog and digital signals are now also available in optical communications. Apart from modulation, coding is of great importance. We would like to refer the reader to the relevant technical literature, as this would go beyond the scope of this introduction.

1.3 Network Architectures The next section of the introduction deals with various network architectures. Here too, attention will be drawn to the unique features of optical communications. The first topic is that of Point-to-Point transmission and distributed systems. The Point-To-Point system (P-P) is the simplest form of data communication, involving only one transmitter and one receiver. The second case deals with connecting several devices to each other. In this case, there can be one transmitter and several receivers (Point-to-Multipoint, P-MP), several transmitters and one receiver (MP-P) or also several transmitters and several receivers (MP-MP, see Fig. 1.35). P-P

P - MP

MP - P

MP - MP

Fig. 1.35: Possible network topologies

It should be noted that it is often necessary to send data in both directions (upstream and downstream). For example, a network can be P-MP in one direction and MP-P in the other. When more than two stations are to be connected to each other, several solutions are conceivable. These are discussed in the sections below. First we will briefly discuss active and passive networks. Then a network structure or topology must be selected, for example, a tree-shaped network or bus structure. Finally, a multi-access method must be selected. 1.3.1 Active and Passive Networks A P-MP case will serve as an example of the difference between an active and passive network. Figure 1.36 illustrates both possible solutions for this connection.

1.3 Network Architectures

P - MP passive

27

P - MP active

Fig. 1.36: Active and passive P-MP connections

Passive means in this case that the receivers are physically connected to the same medium. As a result, every receiver receives the complete signal, even if it is intended for other receivers. This is an ideal situation for distribution services such as broadcast radio. With active networks, there is an interfacing device between transmitter and receivers that has the function of distributing the signal to the proper receivers. In principle, this interface functions as a switch, which is the reason why they are called exactly that: switches. If you take a closer look at this architecture, you can see that it actually consists of several P-P connections. Since the aim of this book is only to describe transmission technology, all other active networks can be regarded as some form of a Point-to-Point solution. You can say that every architecture can be made active by inserting the right number of switches at the branch points. The functionality of the active points can be formed in many different ways. The active points, for instance, could be used solely as an amplifier. This means that the signals are forwarded without regard to their destinations. Address and access control must be performed by other elements. A multiplex function means that the signals are routed according to their destinations and, in a MP-P structure, are combined. Some form of access control must be available also in this case to prevent collisions. A complete switch also takes on the access control functions. This can be made by rejecting non-processable data or by serving as a data buffer. 1.3.2 Network Structures The network structure describes the topology of the data connections. It can refer to the physical structure i.e. the way the cables are arranged as well as to the logical structure, i.e. the flow of the data streams. Figure 1.37 illustrates the most widely known structures. All modern data networks are designed as active star-type structures. The bestknown examples are Switched Ethernet and the ATM network (Asynchronous Transfer Mode). Tree networks play an important role for television distributing networks. Here it is crucial that each receiver receives the complete transmission signals. Data networks for residential areas, such as USB or IEEE 1394 function

28

1.3 Network Architectures

logically as tree-shaped networks; however, they are physically set up as P-P connections. This means that several other devices can be connected to one device. Each device then forwards the complete data.

star

tree

ring

bus

Fig. 1.37: Typical network structures

In all passive networks, one problem becomes apparent, in particular when you examine the direction to the central element. Several transmitters can access the same medium. To prevent mutual blocking, this form of access must be controlled. This will be the subject of the next section. 1.3.3 Multiple Access Methods The goal of all multiple access methods is the administration of a shared channel (shared medium). The various parameters of the channel which can be used are time, frequency or amplitude. 1.3.3.1 Time Division Multiplex With Time Division Multiplex (TDM), each user is assigned a particular time. In the P-MP direction this is known as multiplexing since the transmitter simply has to split its capacity. The opposite MP-P direction is known as multiple access (TDMA) since each transmitter is only allowed to send data at the proper time. Figure 1.38 illustrates the principle. It is easy to see that the division of time does not have to be steady or continuous. The critical aspect of allotting time slots in TDMA is that data packets sent from two transmitters do not arrive at the receiver simultaneously. In principal, there are two methods for the TDMA. First the central node can be assigned with the task of permitting the transmitters to use the time slots. Obviously, all elements must be synchronized in the network. In addition, each transmitter must at least be given a temporary connection in order to inform the center that further time slots are needed.

1.3 Network Architectures

P - MP TDM

29

MP - P TDMA

„1“

„1“

„2“

„2“

„3“

„3“

t

t t t

Fig. 1.38: TDM and TDMA

Another possibility is to initially permit every transmitter to randomly access the connection. If a collision takes place, the transmitters must be able to detect it, discontinue the transmission and retry it after a set time. As long as the required transmission capacity is small in relationship to the available capacity, this method works quite well since the probability of collision is relatively low. This is all the more true if delays occurring occasionally due to the wait for free time slots can be accepted. This is the method used for Ethernet. The advantage is that no centralized capacity administration is required. The disadvantage is that transmissions requiring continuous data rates and constant delay times (for example, video) are quite unreliable. This is a good time to address a widely-spread misconception concerning access control and the question of using an active or passive network. Both network types require the same overhead for access control. The only advantage of an active network is that the physical access can be separated from management of the data streams. In the figure above, this means that the identical TDMA method can be selected or that a buffer in the active node can prevent collisions (see Fig. 1.39). In passive networks, the malfunctioning of a single component can lead to a complete failure of the network. If a station sends signals uninterruptedly, all other stations will be affected. In an active network, the incorrect working station can simply be ignored. On the other hand, there are additional components in the active network, i.e., the transmitter and receiver in the distribution point and the central switch. All of these elements can fail and result in a total loss of the network. The question as to what type offers the better reliability cannot be answered conclusively. The particular requirements must always be taken into account.

30

1.3 Network Architectures

t

t „1“

„1“

„2“

„2“

„3“

„3“

buffer memory

t

t

t

t

t

t

Fig. 1.39: TDMA in active networks

1.3.3.2 Frequency Division Multiplex In frequency multiplex or multiple access (FDM/FDMA), the signals of each station are modulated on a separate carrier. All stations are allowed to transmit simultaneously. The signals are divided using band pass filters, as shown in Fig. 1.40 (Fig. 1.41 illustrates multiple access).

f1

P - MP, FDM band pass 1

f2

band pass 2

f3

band pass 3

Fig. 1.40: FDM in star networks

f1

MP - P, FDMA

band pass 1

f2

band pass 2

f3

band pass 3

Fig. 1.41: FDMA in star networks

The advantage over TDM is that selection of the band pass filters determines the synchronization. If these are permanently built in, there is practically no interference from other stations. But unfortunately it is then no longer possible to dynamically allocate the capacity. This is why the frequency channels are often assigned by the central node temporally on demand.

1.3 Network Architectures

31

1.3.3.3 Code Division Multiplex For code division multiplex/multi-access (CDM/CDMA), all stations transmit simultaneously in the same frequency range. Instead of individual bits, special sequences (codes) are sent. These must be known to the receiver. Using special receivers that are often very costly, the signals of the various transmitters can be divided. The immense costs for CDMA systems is often worth it for poor quality channels such as in mobile telephone communications since CDMA is highly immune to many sources of interference. In optical communications this method is rather insignificant. 1.3.3.4 Wavelength Division Multiplex A special feature in optical communications is the possibility of using various optical frequencies in a single network. Generally speaking, we are talking about different carrier frequencies. However, they are so great, just like the distances between them, that they cannot be processed by electrical components. For example, processing, combining, separating or filtering the various wavelengths is done exclusively by optical components. In singlemode glass fiber technology, a number of components have been developed over the last few years such as arrayed wave guides (AWG), Fiber-Bragg gratings and wide band tunable lasers. They have made WDM the key technology for optical communications (see, for example, [Hulz96]). Soon many hundred optical channels will be transferred over glass fibers that will be forwarded transparently over hundreds of kilometers in optical nodes. Wavelength division multiplexing also plays an increasing role for polymer optical fibers, as we shall see later. In principle, the access methods introduced here can be combined in any way. A complete time division multiplex channel can, for example, be inserted into a wavelength channel. 1.3.3.5 The Special Features of Optical Multiplexing The special features of optical signal transmission have already been mentioned earlier. Another difference to electrical systems requires some explanation. The level of an electrical signal is defined by the voltage at a resistor. This makes it possible to split a signal into several points, as is done, for example, in bus systems by selecting suitable resistors shown in Fig. 1.42.

U(t) 50 : 15 k: 15 k: 15 k: 15 k: 15 k: 15 k: Fig. 1.42: Distribution of an electrical signal

32

1.3 Network Architectures

The low-ohmic-transmitter supplies a data line with 50 :of characteristic impedance. The line is also terminated with 50 :. The various stations access the line with high-value resistor connections (these lines should be short). Thus, the signal is only loaded to a small degree. The same level is detected at practically all stations (disregarding the attenuation of the data line). For very broadband signals, for example, for broadcast television, the receivers must all have the same impedance, i.e. 75 :. Splitters are available that can divide up the output with nearly no loss. With two receivers, each receiver detects a level that is 3 dB lower, that is to say, approximately 70% of the transmitting voltage. Unfortunately in optics, a “high-ohmic resistance” access is not possible. Ideally, the optical transmitting power can be distributed to all connected stations. With 2 receivers, the received power is one half of the transmitting power. This results in one half of the photo current at the receiver and consequently 6 dB less electrical power. We encounter the same problem when trying to join optical signals. If you assume uniform mode distribution in optical fibers, then couplers will have losses during distribution as well as when joining that correspond to the number of optical branches. Figure 1.43 shows typical components.

X-splitter 3 dB loss

Y-splitter 3 dB loss

Y-coupler 3 dB loss

1 : 4-splitter 6 dB loss

Fig. 1.43: Losses at different optical couplers

The minimum loss of 3 dB (half of the optical power) is easy to see for the X-coupler as for the Y-divider. Because of the reversibility of the light path, this also applies to the Y-coupler. If the divider at the far right is used as a coupler, its attenuation will also be at least 6 dB. With polymer fibers, additionally the losses that are unavoidable for multimode fibers must be taken into account. There is a „trick”, however, for coupling and splitting light waves without losses for singlemode fibers. If the light segments to be separated or combined differ in wavelength or polarization, the proper WDM couplers (or polarization couplers) can be used. Otherwise WDM systems would not be feasible with over 100 channels. For polymer optical fibers, the appropriate WDM components are relative complex, as indicated below. The special features of optical communications are adverse for particular multiplex methods. If, for example, you want to use time division multiplexing with two transmitters and two receivers that are located at two different sites, they must be arranged as shown in Fig. 1.44.

1.3 Network Architectures

transmitter 1

33

receiver 1

transmitter 2 coupler

splitter

receiver 2

Fig. 1.44: Example for an optical network

The TDMA method ensures collision-free use of the shared transmission link. The optical components yield a minimal loss of 3 dB + 3 dB = 6 dB. If the signals could be combined before the optical transmitter and split behind the receiver, this loss could be prevented. This would, for example, also increase the range. When designing an optical transmission system, careful consideration should always be given to the question as to which functions can be implemented better optically and which ones better electrically. 1.3.3.6 Bi-directional Transmission Bi-directional transmission on one channel plays a special role in multiplex methods. Only two directions have to access the channel. Classic multiplex methods are applicable particularly in optical signal transmissions. While we have only been discussing ideal systems, at least one interference factor will be explained here that poses restrictions on bi-directional systems. This is near end crosstalk (NEXT). Figure 1.45 illustrates how a receiver can interfere with its own transmitter if there are reflections on the line.

transmitter 1 x dBm

disturbance, depressed by v dB

transmitter 2 y dBm

channel attenuation z dB receiver 1

receiver 2

Fig. 1.45: Near end cross-talk in optical systems

Transmitters 1 and 2 operate simultaneously on both sides of the channel. Since it cannot be assumed that we always have the same power, let us just assume levels x and y. The signal of the remote transmitter 2 therefore arrives attenuated with (y-z) dBm at receiver 1. At points of interference in the channel, for example a plug-in connection, a part of the light emitted from transmitter 1 may directly fall onto its own receiver. We will call the attenuation of transmitter 1 to recei-

34

1.3 Network Architectures

ver 1 as v. The value of v should be as large as possible. Thus, the interference level through NEXT is x - y. If you assume that a particular SNR is required for error free operation, the following inequality holds true: v > (x-y) + SNR + z Let us look at a practical example: The difference between the transmitting powers is max. 6 dB, i.e. at worst (x - y) = 6 dB. The SNR should be at least 16 dB and the path attenuation is z = 18 dB. The following then applies: v > 6 dB + 16 dB + 18 dB = 40 dB. This value is very difficult to maintain with POF components. Additional measures for NEXT suppression are required. They will be introduced below. First, a system with time division multiplex will be shown (Fig. 1.46). On the fiber medium, the required data transfer rate is more than twice as fast as the individual data streams on both sides since less than half the time is available due to the run times that occur for each direction. It is common to divide up data streams into larger packets that are then transmitted alternately. The larger the blocks are, the less influence the run time has on the line. However, an increasing delay is generated through the required buffering of a complete packet. buffer memory with bit rate adaption transmitter 1

buffer memory with bit rate adaption transmitter 2 in

in fiber line

out

out receiver 1

receiver 2

transceiver 1 transceiver 2 transport:

1Ÿ2

time 2Ÿ1

1Ÿ2

2Ÿ1

Fig. 1.46: Bi-directional transmission with time multiplex

These types of solutions are very good, particularly for systems with low and medium data rates and short distances, for which the POF is also used, and can be implemented at low cost since the entire data processing is performed in integrated circuits. A second possibility is frequency division multiplex, by which the data of both directions are modulated upon different carrier frequencies (Fig. 1.47).

35

1.3 Network Architectures

source 1

mixer

source 2

mixer in

in transmission link

out filter

receiver 1

out receiver 2

filter

isolation filter transport from 1 to 2

transport from 2 to 1

frequency

Fig. 1.47: Bi-directional transmission with frequency multiplex

The bandwidth requirements of this system are relatively high, because a carrier frequency modulation needs typically twice the bandwidth as a direct NRZ modulation (Non Return to Zero, switching between one and zero at the end of each bit). Furthermore, a certain „guard band” is also required between the bands. On the other hand, subcarrier methods are very immune to interference and allow continuous simultaneous operation in both directions. The NEXT suppression is very good since filtering in the electrical domain of the receiver can function very efficiently. Especially for low data rates, this method is very well suited. Signals can be easily processed with a small number of analog components or else completely with a signal processor. For wavelength division multiplexing, every transmission direction is assigned to a separate wavelength, as can be seen in Fig. 1.48. source O1

source O2 Y-splitter

Y-splitter

in

in out receiver

out

transmission link WDM-filter

WDM-filter

receiver

Fig. 1.48: Bi-directional transmission with wavelength multiplex

This procedure has the big advantage that the full capacity of the fiber medium is available for each direction. Continuous operation without additional delays is possible. The NEXT suppression is performed by optical filters placed before the receivers. Signal processing is not necessary. A disadvantage is that two different transceivers are always required on one link. However, this is a question concerning the system concept. WDM is particularly interesting for fast data transmission, such as IEEE 1394. WDM also provides efficient solutions for systems with asymmetric data rates.

2. Optical Fibers

2.1 Fundamentals of Optical Fibers The term optical fibers indicates special forms of optical waveguides, the most important special features of which are: ¾rotationally symmetrical cross-section ¾flexible ¾can be produced in great lengths The characteristics of optical fibers are determined by a multitude of possible constructive details. For example, the material selected primarily determines the attenuation and the thermal stability. On the other hand, the optical bandwidth, in essence the transmission capacity, is determined by the refractive index profile. This is most likely the reason why most optical fibers are named after their index profile. All current variations will be presented in the following sections. 2.1.1 Refractive Index Profiles The properties of wave guiding through a fiber are governed largely by the profile of the refractive index of the core and cladding. In a step index profile fiber the refractive index is constant across the entire cross section of the core and cladding (Fig. 2.1) while the light rays propagate along straight lines in the core and are completely reflected at the core/cladding interface.

r a refractive index n(r)

-a Fig. 2.1: Refractive index profile in a step index profile fiber

38

2.1 Fundamentals of Optical Fibers

The profile of the refractive index in the core and in the cladding is expressed as follows: n(r )

ncore

for r d a

n(r )

ncladding

for r ! a

where a is the core radius. The individual rays cover different distances, so that there are considerable differences in their respective transit times. Choosing a fiber with a graded-index profile can minimize these differences. Fibers with a graded-index profile are made up of a core having a radius-dependent refractive index and a cladding with a constant refractive index (Fig. 2.2): n(r )² n(r )

where

g § §r· · ncore, max ² ˜ ¨1  ' ˜ ¨ ¸ ¸ for r d a ¨ © a ¹ ¸¹ © ncladding for r ! a

g is the profile exponent and ' is the relative refractive index difference: '

a

ncore 2  ncladding 2 2 ˜ ncore 2

r

-a refractive index n(r) Fig. 2.2: Principle of a fiber with a graded-index profile

Those rays propagating in the center travel a shorter distance, but because of the higher refractive index there, they travel at a lower speed. On the other hand, the smaller refractive index near the cladding causes the rays traveling there to have a higher velocity, but they have a longer distance to travel. By choosing a suitable profile exponent it is possible to compensate for these differences in transit time. For negligible chromatic dispersion the ideal profile exponent is 2. One then speaks of a parabolic index profile.

2.1 Fundamentals of Optical Fibers

39

2.1.2 Numerical Aperture When light enters the fiber's input face at an angle 4max, it is refracted at an angle Dmax (Fig. 2.3). Applying the law of refraction we have: n0 ˜ sin4max

ncore ˜ sinD max

ncore ˜ sin(90 - J max )

n0 ˜ sin4max

ncore ˜ cos J max

n0 ˜ sin4max

ncore ˜ 1 - sin2 J max , with ncladding ncore

n0 ˜ sin4max

ncore ˜ 1 - ncladding ncore





sin2 J max

2

ncore 2  ncladding 2 , for n0

n0 ˜ sin 4max

2

1 follows

ncore 2  ncladdimg 2

sin 4max

The sine of the maximum incident-ray angle 4max is defined as the numerical aperture AN (Fig. 2.3). The angle 4max is referred to as the acceptance angle, and twice the acceptance angle is referred to as the aperture angle. Using the relative refractive index difference ', the value for AN is obtained as: AN

sin 4max

ncore ˜ 2 ˜ '

n0 4max

Jmax Dmax

Fig. 2.3: Definition of the acceptance angle

Thus, the value of the numerical aperture (NA) is solely dependent on the difference in the refractive indices of the core/cladding material. Example:

The refractive indices of a standard PMMA fiber are ncore = 1.49 and ncladding = 1.40; we thus obtain AN = 0.50 and 4max = 30q.

Whereas the numerical aperture of the step-index profile fiber remains constant over the entire core, the graded-index profile fiber exhibits a decreasing acceptance angle from the center of the core to the cladding (Fig. 2.4).

40

2.1 Fundamentals of Optical Fibers

Fig. 2.4: Acceptance angle of a graded-index profile fiber

Compared with other fiber types (Fig. 2.5), POF has the largest numerical aperture and the largest core diameter. This is one of the most important advantages of POF, since the connection technology that can be used for POF is more economical to apply than that used for glass fibers.

10/ 125 μm

singlemode glass fiber

multimode glass fiber 50/ 125 μm

multimode glass fiber

62.5/ 125 μm

polymer fiber 980/ 1000 μm

(plastic clad) 200/ 230 μm 100/ 140 μm

0 mm

0.5 mm

1.0 mm

Fig. 2.5: Aperture angle and core diameter of glass fibers and polymer fibers

2.1.3 Ray Trajectory in Optical Fibers In the step index profile fiber, light propagates along a zigzag path, being totally reflected at the core/cladding interface; in the graded-index profile fiber, light propagates on a sinusoidal trajectory that is created within the graded-index profile through refraction. If the incident light rays lie within one and the same plane through which the fiber axis runs, meridional rays are formed. In all other cases, skew rays are formed. Figure 2.6 shows the projection onto the fiber's incident face. Step and graded-index profile fibers show the same behavior. The specification of the numerical aperture always refers to the meridional rays.

2.1 Fundamentals of Optical Fibers

D’

41

D’ D’ D’

Fig. 2.6: Meridional rays

Skew rays form an angle of \ < 90q with the tangential plane at the core/cladding interface (Fig. 2.7). They never cross the fiber axis and propagate along screw-like paths. For step index profile fibers, the projection onto the crosssectional area resembles a polygonal line so that these rays do not cross a circleshaped area having a radius rk around of the axis.

\ rk

\

Fig. 2.7: Skew rays in step index profile fibers

In graded-index fibers with a parabolic profile, ellipses are formed in the projection (Fig. 2.8 left) that may under certain circumstances form circles; these rays are called helical rays (Fig. 2.8 right). Their distance from the fiber axis is always constant.

Fig. 2.8: Helical rays (left) and skew rays (right) in graded-index profile fibers

42

2.1 Fundamentals of Optical Fibers

2.1.4 Modes in Optical Fibers 2.1.4.1 The Mode Concept The phenomena of refraction and reflection discussed so far can be graphically explained with the help of geometrical optics, whereby the size of the wavelength and the diameter of the finite ray are not considered (O and dray= 0). However, to obtain a complete description of the wave guiding phenomenon, the wave properties of light must also be considered. The goal is to calculate the electric field and intensity distribution of the light in the optical fiber. The Eigenvalue equation is derived and solved on the basis of the Maxwell equations. Ref. [Blu98] provides a detailed description. The solutions to the Eigenvalue equations are a finite number of field distributions within the light waveguide. These field distributions are referred to as modes of the waveguide. If we apply this concept to the ray model, this means that apparently not all incidental rays for which 4 < 4max is true can propagate, but rather only those rays that have a particular angle. Figure 2.9 illustrates this situation: in order for light to propagate in a particular direction, a wave must constructively overlap itself with its own reflecting wave in such a way that the phase position is repeated after double reflection. The black lines perpendicular to the direction of propagation identify the planes with the same phase angle. The spacing is O/ncore. transverse direction

O/ncore

d

electrical field Fig. 2.9: Formation of the mode structure within the waveguide

Whereas the zigzag paths would lead to intensity distributions within the rayoptical model that would change depending on the length of the fibers, the wave model provides a constant light-dark distribution that is independent of the length across the waveguide's cross-section. The number N of the guided modes is approximately described by: N|

1 g ˜ ˜ V2 2 g2

where V = 2S ˜ a ˜ AN/O, a is the radius and g is the profile exponent (see also Section 1.1.5). For step-index profiles g o f. This results in a value of N | ½ · V² for the number of modes. For parabolic profiles g = 2 and thus N | ¼ · V². A polymer op-

2.1 Fundamentals of Optical Fibers

43

tical fiber with AN = 0.5, a core radius of 0.5 mm and a wavelength of O = 650 nm can carry 2.9 million modes. If the angle of total reflection is exceeded, radiation modes are created and the light is radiated into the cladding. If the refractive index of the cladding is higher than the surrounding medium (air, for example), cladding modes may be formed. In the POF, the optical cladding is encased in an absorbing jacket so that no cladding modes can form. In contrast to guided modes, it is not possible to count radiation modes. They do not take part in signal transmission. (Fig. 2.10 special conditions for POF are explained below). Higher modes propagate under a larger angle, lower modes under a smaller one. Under certain circumstances skew rays may turn into so-called leaky waves, which, on the one hand, are guided in the Z-direction and, on the other hand, transfer energy to the cladding. Under certain conditions they can still be detected in POF even after several 10s of meters. Hence, they can influence both the transmission process as well as the measuring techniques used.

radiation mode

higher mode

lower mode cladding mode

Fig. 2.10: Guided, cladding and radiation modes

The following equation describes the relationship between the angles D, \ and G in Fig. 2.11 ([Sny83]): cos D

sin G ˜ sin ȥ

D is the angle of the incident and reflected ray relative to the surface normal of the tangential plane in P. \ describes the angle between the reflection plane and the tangent plane, and G is the angle between the projection of the skew ray on the cross-sectional plane and the direction of propagation (parallel to the fiber axis). Figure 2.12 summarizes the various ray types according to the respective angles derived from the above equation ([Bun99a]). For guided rays holds G < Gmax and D > Dmax. The leaky waves are shown in the subsequent rectangle while the ray modes are shown above the line D = Dmax. For meridional rays D = 90q - G because \ = 90q, i.e. they lie on the blue line.

44

2.1 Fundamentals of Optical Fibers

D \

D

G

P Fig. 2.11: Designation of the angles of a skew ray; the right diagram shows the angle G, which is obtained by projecting the skew ray on to the cross-sectional plane

0

\ q

inside this triangle there are the radiation rays

D[°]

10 20

\ q

inside this triangle there are the guided rays

30 40

\ q

50 meridional 60 rays 70

\ q

Dmax

80

inside this rectangle there are the leaky modes

Gmax

90 0

10

20

30

40

50

60

70

G[°] 80

90

Fig. 2.12: The different types of rays

2.1.4.2 Mode Propagation in Real Fibers Several chapters of this book discuss the special characteristics of light propagation in POF. Here now, the processes that need to be considered will be looked at as a whole. The function of fibers as a waveguide for passing on light by means of total reflection at the core/cladding interface has already been discussed. If the ray model were applied consistently, then a light ray launched into an ideal fiber would always propagate at the same angle relative to the fiber axis. With a divergent light source, the far field would always remain constant along the length of the fiber. This would not be true for the near field, as Fig. 2.13 illustrates: depending on the course of the ray, different locations along the fiber would

2.1 Fundamentals of Optical Fibers

45

generate different near fields in the form of point structures. However, this contradicts the results obtained through experiments: there a continuous distribution of intensity is obtained, and from a certain length onwards the intensity does not change at all. Although the ray model is very illustrative, its practical application is limited as the example above shows. In order to be able to describe experimental results it is thus necessary to move on to the mode concept. In this respect it is important to keep in mind that many optical simulation programs work on the basis of discrete light rays. In order to obtain truly realistic results, a sufficient number of rays has to be simulated. only a few launched discrete modes

nearfield (very schematically) Fig. 2.13: Near fields under conditions of the ray model with only a few discrete light paths (in practice very difficult to measure and visible only on very short lengths)

2.1.5 Parameters for Describing Real Fibers and Waveguides In order to describe the characteristics of real fibers and waveguides different parameters are defined which vary in importance depending on their respective application. All of these parameters are influenced by the propagation conditions of the different modes. In the case of multimode fibers most characteristics depend typically on the mode distribution. This means that a fiber initially allows the propagation of light in different paths (modes). Depending on the light sources at the front end of the fiber, not all these modes are launched, at least not with a uniform power distribution. Since each mode has different characteristics, an altered behavior of the fiber is on average the result. In addition, the problem becomes more complicated since an exchange of energy between the modes can occur over the length. Typical fiber characteristics will be defined and explained in the following sections. Uniform Mode Distribution (UMD) and Equilibrium Mode Distribution (EMD) are the usual standard measuring conditions.

46

2.1 Fundamentals of Optical Fibers

2.1.5.1 Attenuation The most important process encountered by light as it passes through a fiber is attenuation. When passing through an optical fiber of the length L, the power of the light decreases (Fig. 2.14). The following equation applies to the optical power: PL

P0 ˜ e Dc˜L

where PL and P0 are the power of the light after passage through a fiber of length L in km and at the front end of the fiber, respectively; D´ is the value of the attenuation coefficient in km-1.

PL

P0 L Fig. 2.14: Definition of attenuation

To make it easier to work with the numbers involved here, it is usual to express attenuation logarithmically. Thus, the attenuation coefficient is expressed as D in dB/km. D

10 P ˜ log 0 L PL

4,343 ˜ Dc

Attenuation value a is the non-dimensional variable (given as a number or in dB) obtained from the product D · L. Figure 1.19 illustrates the relationship between the attenuation value and the change in power as a percentage.

attenuation factor a [dB] 30

0.1

25

20

1

15

10

5

10 power ratio PL/P0 [%]

0

100

Fig. 2.15: Conversion of the power ratio PL/P0 in % into the dB value

Very often there is not a clear differentiation in the technical literature between attenuation per unit length D and attenuation factor a. One often speaks simply of the attenuation of the fiber. The addition “spectral” refers to the wavelength dependence. A mistake is avoided, however, when the unit is indicated. We still have to mention that attenuation and attenuation per unit length are practically always indicated as positive numbers.

2.1 Fundamentals of Optical Fibers

Quantity

Symbol

Unit

Formula

attenuation coefficient, lin.

D´

km-1

{ln (P0/PL)}/L

attenuation coefficient, log.

D

dB/km

attenuation

a

dB

47

{10˜log (P0/PL)}/L 10˜log (P0/PL)

Especially in the area of optical short-range communication, indicating the fiber attenuations in dB is much more practical than, for example, representing the absolute transmission. POFs are being used more and more in the near infrared range for quite short transmission lengths. Finally, PMMA can also be used for waveguide structures in the mm range. Fig. 2.16 shows the attenuation curve of a PMMA-POF according to [Hess04].

100,000

attenuation [dB/km]

30,000 10,000 3,000 1,000 300

theory measured

100 30 wavelength [nm] 10 500

600

700

800

900

1000

Fig. 2.16: Attenuation spectrum of the PMMA-POF (theory and measured by [Hess04])

Nevertheless, the representation comprises approximately 3 decades, i.e. a factor of 1,000 which cannot be overlooked on a linear scale. 2.1.5.2 Mode-Dependent Attenuation When talking about glass fibers, it is often assumed that the attenuation of all light rays is identical. For practical purposes, this assumption is sufficiently accurate. With POF, the path difference between the rays parallel to the axis and the propagation directions close to the critical angle of total reflection can become quite large. For the standard NA-POF with AN = 0.50 this difference is about 6%. For polycarbonate fibers with AN = 0.90, the difference is even 21%. For this reason alone, there is a considerably greater level of attenuation where large propagation

48

2.1 Fundamentals of Optical Fibers

angles are involved. In 100 m of POF, a light ray of this type will travel 6 m farther which results in an additional loss of more than 1 dB when the attenuation level is 200 dB/km. At 1,000 dB/km for polycarbonate fiber, this would result in an additional loss of 4 dB after 20 m of travel (less than 50% of the launched power reach the fiber output). The second, more significant cause for mode-dependent attenuation is the attenuation resulting from the cladding material. Fluorinated polymers are used as optical cladding for PMMA fibers; these claddings may have an attenuation of several 10,000 dB/km [Paar92]. Locking more exactly on the propagation of a plane wave at the interface, we find that, even if total reflection results, the electrical field escapes into the optically thinner medium by a distance in the order of magnitude of the wavelength. This process is also known as the Goos-Hänchen Shift ([Bun99a]) and the model explains this as resulting from a shift of the reflection plane into the optically thinner medium. The reflected ray is hence slightly displaced on the interface surface, as can be seen in Fig. 2.17. In this model, the additional light path would be subjected to the higher attenuation of the cladding material.

cladding core area of higher attenuation Fig. 2.17: Goos-Hänchen shift

Although the light path in the cladding is only in the Pm range for each reflection, it still plays a significant role because of the much higher attenuation encountered there. This effect is particularly striking when the core diameters are reduced in size. Theoretically speaking, attenuation and bandwidth should not be dependent on the core diameter. Nevertheless, thin cores such as those used in multicore fibers have indeed considerably larger bandwidths [Tesh98], a slightly increased attenuation and narrower far-field widths. These effects are explained quite well in [Bun99b] and [Ziem99c]. This effect also occurs in glass fibers. Silica glass fibers with a polymer cladding (PCS) have losses in the core below 10 dB/km (wavelength range from 650 nm to 1,300 nm), whereas the polymer cladding has an attenuation of several 100 to 1,000 dB/km. Attenuation values of 180 dB/km for the core and 9,000 dB/km for the cladding are indicated in [Ebb03] for step index profile glass-glass fibers (used in fiber bundles). Reasonably priced conventional glasses - albeit much purer than in window glass - are used in these fibers and not silica glass. In singlemode and graded-index profile silica fibers there are no mentionable differences in attenuation between the core and the cladding since both consist of

2.1 Fundamentals of Optical Fibers

49

Si02. The germanium dopant in the core does not have any great influence. An important consequence of the mode-dependent attenuation is, as will be discussed later on, a significantly narrower far field after greater fiber lengths than one would expect from the fiber NA. 2.1.5.3 Mode Coupling The term mode coupling refers to the process by which energy from one direction of propagation is transferred to several others. This can happen, for example at scattering centers. Since the light scattering in a PMMA-POF makes up a considerable part of the attenuation, this process is always present. Figure 2.18 clarifies the procedure (still in the ray model).

scattering center

Fig. 2.18: Mode coupling at a scattering center

Many experimental results clearly indicate that mode coupling occurs predominately at the core/cladding interface (Fig. 2.19). This can be explained by the fact that is it not possible to create an ideal surface in the sub-nanometer range when very large polymer molecules are involved. Thus, mode coupling is also dependent on the angle of propagation. cladding

core

scattering center

Fig. 2.19: Mode coupling at the core/cladding interface

Mode coupling alters the bandwidth of a fiber. When collimated light is launched, energy is gradually transferred to the higher angle ranges so that mode dispersion increases and bandwidth decreases. If light is introduced in all angle ranges, so that maximum differential delays occur, energy is exchanged between the angles so that the initially slower rays become “faster” and vice versa. Accor-

50

2.1 Fundamentals of Optical Fibers

ding to the laws of statistics, the differential delay (or more precisely, the standard deviation) does not increase in a linear relationship to the length but approximately only proportional to the square root of the length. This applies to lengths in excess of a characteristic coupling length, which for PMMA-POF is generally several 10 m. Mode coupling always results in additional attenuation. Whenever there are changes in the light propagation, energy is coupled into those angle ranges in which there is no longer any light guiding. The shorter the coupling length, the larger the additional attenuation will be. If the observed behavior of the POF, namely the filling up of the near field after a few 10 cm of fiber, could be explained exclusively because of the mode coupling, then additional attenuations in the range of 1000 dB/km would result - which indeed does not occur. Figure 2.20 shows an electron microscope picture of the core-cladding interface layer (photo ZWL, 2003). The marked smooth part running from the top left to the bottom right is the surface of the core with the cladding removed. At the top right you can see the cracked core. The step is the 10 μm thick optical cladding. Further theoretical considerations on the problems of scattering can be found in [Kru06a] and [Kru06b].

Fig. 2.20: Photo of the core-cladding interface of SI-POF taken by electron microscope (ZWL Lauf)

2.1.5.4 Mode Conversion The definition of propagation angles or of modes actually applies only to waveguides that are straight. It takes just one bend to make a different approach necessary. The most precise method would be to recalculate the modes for the system of the now bent fiber; however, this is theoretically and practically much too complex a process. It is more appropriate to consider the zone before and after the bend as a straight waveguide and, at the bend, to perform a transformation onto the new reference axis. Formally, light is thus transmitted from one propagation direction to another, as Fig. 2.21 demonstrates.

2.1 Fundamentals of Optical Fibers

fiber axis in front of a bend

51

fiber axis behind a bend

new propagation angle

Fig. 2.21: Mode conversion at a bend

Strictly speaking, mode conversion can be described as a special case of mode coupling. The difference is that the number of modes or the propagation directions is not increased. In the POF mode conversion most likely occurs at the core/cladding interface surface, for example at micro bends or at fluctuations in the refractive index difference. The question of the influence of mode conversion and coupling on the additional attenuation depends essentially on the angle dependency of the processes. The more the direction of the light is altered, the more losses occur. A quantitative analysis of these processes for POF is extremely difficult and is yet to be carried out. However, for the physical processes assumed, mode coupling should have a larger angle-independent contribution (scattering on larger inhomogenities).

Fig. 2.22: Far fields of different POF (product A/B at the top/bottom); left/right after 20 m/50 m of fiber, launch with collimated light (AN Launch < 0.016)

52

2.1 Fundamentals of Optical Fibers

An impressive experiment that confirmed this statement was shown in [Poi00]. If collimated light is launched into a SI-POF, a ring-shaped far field can be generated at the output even after 50 m of fiber, for which purpose the fiber might be properly bent. This experiment can only be explained under the assumption that mode conversion predominates. However, the different fibers made by different manufacturers show considerable differences in their behavior which do not necessarily have an effect on attenuation. It is easy to see here that the mode field is not completely filled even after 20 m to 50 m (Fig. 2.22). 2.1.5.5 Mode Coupling Lengths The length of a fiber in which a state of equilibrium arises through mode conversion and coupling is described as coupling length whereby different definitions exist. The best known is the description with the aid of a length-dependent bandwidth. Here the coupling length is the point at which the linear decrease in the bandwidth turns to a root dependency (see Fig. 2.36). In practice this point is difficult to measure, but other parameters such as far field width and attenuation, change with fiber length. For example, values for the kilometric attenuation with different launch conditions are shown In Figures 2.23 and 2.24.

400

D [dB/km]

fiber “A”

350

source “I” source “II” source “III” source “IV”

300 250 200 150 100

lPOF [m] 50

1

2

5

10

20

50

100

Fig. 2.23: Attenuation of a SI fiber under different excitation (acc. to [Lub02b])

Both diagrams show very clearly that the different launch conditions (source I emits very widely, source IV nearly collimated) lead to extremely different attenuation values. After some ten meters, however, the differences disappear for the most part through mode coupling. Evidently, there are great differences among the fiber types.

2.1 Fundamentals of Optical Fibers

53

D [dB/km]

400

fiber “B” 350

source “I” source “II” source “III” source “IV”

300 250 200 150 100

lPOF [m] 50

1

2

5

10

20

50

100

Fig. 2.24: Attenuation of another SI-fiber at different launch conditions

The next two figures 2.25 and 2.26 show measurements of far field widths for a POF and a PCS each with altered launch conditions. Once again it can clearly be seen how the differences caused by the different coupling conditions are evened out after some 10 to 100 m.

32 30 28 26 24 22 20 18 16 14 12 10

far field width [°]

NALaunch:

0.64 0.48

0.33 0.19

0.09 0.05

PMMA SI-POF POF length [m] 5

20

50

100

Fig. 2.25: Launch dependent far field widths of a PMMA SI-POF

In the 200 μm thick PCS it takes considerably longer to establish the equilibrium mode distribution especially when the length is related to the fiber diameter. The values of the NA (calculated from the 5% far field width) are represented for lengths up to 500 m.

54

2.1 Fundamentals of Optical Fibers

0.40

measured NA

0.35 0.30

AN = 0.02 AN = 0.09 AN = 0.17 AN = 0.26 AN = 0.34 AN = 0.48

0.25 0.20 0.15

fiber length [m]

0.10 1

10

100

1000

Fig. 2.26: Excitation dependent far field width of a 200 μm-PCS

In general, the mode coupling length is characterized as the distance in which a parameter has come closer by 1/e to the state of equilibrium. For example, this corresponds to the charging time constants of a capacitor. One cannot therefore say that EMD conditions exist after one coupling length. Depending on how large the tolerated deviations are, several coupling lengths have to be considered. Figure 2.27 shows the theoretical curve of a parameter.

mode dependent fiber parameter [a.u.] 600 500 characteristic at Lc = 100 m

400 parameter deviation for short fibers

300

parameter deviation for 1, 2 und 3 u Lc

200 equilibrium mode value

100 10

20

50

100

200

500 1000 fiber lenght [m]

Fig. 2.27: Approximation of an optical parameter to the equilibrium value by mode coupling (schematically)

2.1 Fundamentals of Optical Fibers

55

2.1.5.6 Leaky Modes The significance of leaky modes has already been touched upon earlier. For the sake of completeness, it should be noted here again that light rays that lie above the critical angle of the total reflection do not entirely vanish but still contribute significantly to light propagation even after several 10s of meters. Not until we examine the interaction of attenuation, mode-dependent attenuation, mode coupling and mode conversion and take leak modes into account, can we establish a model for the light propagation of SI polymer fibers that can at least qualitatively describe the experimentally observed behavior. In principle, the same processes take place in GI-POF; however there are basic differences: ¾ ¾ ¾

With GI-POF, there is no core/cladding transition to serve as an essential cause for mode coupling, mode conversion, and mode-dependent attenuation. Fluorinated GI-POF are used in wavelength ranges in which Rayleigh scattering is less significant. To form the index profile, various zones of the fiber, as seen from the axis, are provided with varying concentrations of a dopant or a copolymer so that the attenuation usually gets a gradient. This is probably the most significant cause of mode-dependent attenuation in GI-POF.

Yabre and Zubia made comprehensive observations on mode propagation in GI-POF [Yab00a], [Yab00b], [Arr99], [Arr00]. The problem of mode coupling and mode conversion is sure to be very interesting for multi step index fibers. Bandwidths could result that are larger than what is theoretically expected. Some different theoretical investigations were made in cooperation between the POF-AC and the University of Bilbao (Spain). More details will be given in the fiber simulation chapter. As the example of the multi-core fibers shows, mode-dependent attenuation can be used to exchange attenuation for bandwidth. Less attenuating cladding would reduce the overall attenuation of the POF, but more than likely also reduce the bandwidth (always assuming equilibrium mode distribution). The future will decide which parameter is of greater significance for users. If the transmission budget is sufficiently large, it would be possible to increase the bit rate though multi-level coding or by electrically compensating the dispersion so that a reduction in attenuation is the minimum goal to be targeted in this field. 2.1.5.7 Dispersion in Optical Fibers Dispersion refers initially to all processes that result in a difference in the transit times of various modes. One mode is thereby always a propagation condition of the light that is uniquely defined by the wavelength, polarization, and propagation path. Differential delays between the various light components lead to a reduction in the modulation amplitude of higher frequencies. This makes the fiber a low-pass filter.

56

2.1 Fundamentals of Optical Fibers

The bandwidth of a fiber communication transmission system is usually considered to be the frequency for which the optical level of a sine-modulated signal has dropped by 3 dB. Strictly speaking this approach only applies to a Gaussian low-pass filter. This means that a pulse of insignificant width will correspond to the Gauss function after it has traveled the length of the fiber: P( f ) P0 ( f ) ˜ e



- f 2 f02



where P(f) is the power of a random frequency f at the end of the measuring path, P0(f) is the launched power and f0 is a constant that describes the bandwidth. Figure 2.28 illustrates the process schematically.

a) P0(f)

b)

pulse response

c)

d)

e) P(f) time t Fig. 2.28: Effect of dispersion on a sine-wave signal

Curve 'a' shows the sine-modulated source optical signal (it must be noted that optical power can only take positive values). Figure 'b' shows how a single pulse approaching a Gaussian function after traveling through the fiber. This is a theoretical borderline case because the Gaussian function extends from -f to +f, but the output pulse cannot begin before the input pulse has started. To measure the shape of the complete output signal, the input signal can be split into a series of pulses, as shown in Fig. 'c'. After traveling through the fiber, every pulse forms a Gaussian function of the respective height (Fig. 'd'). These have to be brought together again to achieve the result in curve 'e' (mathematically speaking, this is a convolution of the input pulse with the so-called pulse response of the transmission link).

2.1 Fundamentals of Optical Fibers

57

It is easy to see that the amplitude of the signal has decreased. Attenuation of the light has not been taken into consideration. A short light pulse is briefly broadened when it travels the length of a fiber (Fig. 2.29) and this in turn reduces the transmission bandwidth.

optical input power

optical output power

100 % 100 %

50 %

optical fiber

50 %

time

time

tin

tout

Fig. 2.29: Pulse broadening by passing an optical fiber

If Gaussian-shaped pulses are assumed, the result of the pulse broadening 't is the square root of the difference of the squares of the input and output pulse width (FWHM full width at half maximum): 't

2 2 t out  t in

The consequence of this broadening is that the time gap between the bits becomes smaller, that the pulses finally overlap and that the receiver can no longer differentiate between the two. The transmission bandwidth is limited as the light waveguide functions as a low-pass filter. The product of bandwidth and length characterizes the transmission capacity of a fiber. [Gla97] applies to Gaussianshaped pulses: B ˜L |

0.44 ˜L 't

Pulse broadening is caused by mode dispersion and chromatic dispersion. For multimode fibers it is necessary to consider the factors of material, modes and profile dispersion (in graded index fibers). Waveguide dispersion additionally occurs in singlemode fibers, whereas profile dispersion and mode dispersion do not. All the kinds of dispersion appearing in optical fibers are summarized in Fig. 2.30. The mechanisms dependent on the propagation paths are marked in yellow, whereas the wavelength-dependent processes are marked in green.

58

2.1 Fundamentals of Optical Fibers

dispersion modal dispersion

chromatic dispersion

(multimode fibers)

(multimode and singlemode fibers)

profile dispersion

material dispersion (multimode and singlemode fibers)

(multimode fibers)

polarization mode dispersion

waveguide dispersion

(singlemode fibers)

(singlemode fibers)

Fig. 2.30: Dispersion mechanisms in optical fibers

In regard to the fibers and applications dealt with in this book only mode and chromatic (material) dispersion play a role so that the following sections deal solely with these two effects. 2.1.5.8 Mode Dispersion Since the light paths have different lengths, the pulses that have started simultaneously arrive at different times at the fiber's output, a fact that leads to pulse broadening. Figure 1.29 shows the 'fastest' (D = 0) and the 'slowest' (D = Dmax) rays.

ncladding

Jmax

L2

a

Dmax

2

1 L1 ncore

Fig. 2.31: Deriving the difference in the transit time

2.1 Fundamentals of Optical Fibers

59

The propagation times of the two different propagation paths are determined purely geometrically for: t1

n L1 ˜ core c

t2

n L 2 ˜ core c

' t mod

t 2  t1

L1 ˜ ncore 1 ˜ c sin J max

2 L1 ncore ˜ c ncladding

§ ncore  ncladding · n ¸ L1 ˜ core ˜ ¨ ¸ ¨ c n cladding ¹ ©

L1 2 L1 ˜ ncore ˜ AN | ˜' c 2 ˜ c ˜ ncladding

Figure 2.32 shows the dependence of the bandwidth on the numerical aperture with which the light is launched. The assumption is that the far field, i.e. the angular distribution of the light in the fiber, will remain constant over the entire length of the sample (no modal coupling or conversion). For a PMMA standard fiber with an AN = 0.50, a differential delay of 't | 25 ns for 100 m is produced. The transit time is proportional to the square of the NA. From the above-mentioned expression B | 0.44/'tmod, a value of 15 MHz results for the bandwidth. theoretical bandwidth [MHz] 1,000 500

200

fiberlength:

100

10 m

50 25 m 20

50 m

75 m 100 m 10 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50 0.55 0.60 numerical aperture Fig. 2.32: Bandwidth calculated as a function of the launch NA

60

2.1 Fundamentals of Optical Fibers

The critical angle Jmax of total reflection is determined by the ratio of both refractive indices (example, 1.492 for the core and 1.456 for the cladding): 1.456 = arcsin 0.976 = 77.4q 1.492 (max. angle to axis : Dmax 12.6q) J = arcsin

Thus, the relationship between both paths y and z is: z = y/sin (D) = y ˜ 1.0247 The NA of this fiber is determined by: AN = (ncore2 - ncladding2)

0.5

= (1.4922 -1.4562)

0.5

= 0.32

The pulse broadening for a fiber length L is derived as follows: Transit time of the parallel-axis modes: Transit time of the modes with max. angle: Differential delay: For example for 100 m, n = 1.492: With the approximation B · 't = 0.44

t1 = L · n/c0 t2 = L · n/c0 · 1.0247 't = L · n/c0 · 0.0247 't = 12.3 ns B = 33 MHz

Different NA lead to different bandwidths, whereby a doubling of the NA reduces the bandwidth to a quarter: Theoretical bandwidth:

AN = 0.60: AN = 0.50: AN = 0.40: AN = 0.30: AN = 0.25: AN = 0.19:

10 MHz ˜ 100 m 14 MHz ˜ 100 m 22 MHz ˜ 100 m 40 MHz ˜ 100 m 57 MHz ˜ 100 m 97 MHz ˜ 100 m

To correctly calculate the theoretical bandwidth, it is just not sufficient to consider the two possible ray paths selected here. A very comprehensive description of mode propagation in POF is provided in [Bun99a]. In the ray model, each possible propagation direction is described by the two angles D and G (for an explanation of these angles, please refer to Fig. 2.11). As far as transit time is concerned, only angle G is of relevance. Figure 2.33 is an illustration from [Bun99a] of the zone of the guided rays and the leaky rays which themselves are again subdivided. Regardless of the size of \, angle G cannot exceed a particular maximum value so that a maximum possible differential delay is the consequence. Only the marked triangle contains not attenuated rays that are capable of propagation. If one assumes that all possible propagation paths have the same energy (UMD - uniform mode distribution), it can be seen that paths having a larger propagation angle are more probable than rays traveling parallel to the axis.

2.1 Fundamentals of Optical Fibers

D>q@

70

61

\ q \ q meridional rays

75

\ q \ q

80

Gmax

85 guided rays

90 0

5

15

10

20

G>q@

Fig. 2.33: Possible rays in an optical fiber

As measurements of the far field (that is the power as a function of the angle to the fiber axis, measured in a sufficient large distance) of a POF shows, this is also reflected in the greater power obtained with larger angles. If the power is expressed in relation to the solid angle element, a constant power density is found because larger angles cover a correspondingly larger arc. This is shown schematically in Fig. 2.34. 1.0

rel. power/solid angle UMD

0.8 0.6 0.4 0.2 0.0 -30

-20

-10

0

10

20

angle to the 30 fiber axis [°]

Fig. 2.34: Power distribution with UMD

The differential delay increases approximately by the square of the angle relative to the fiber axis. If a short pulse having a mode distribution that corresponding to UMD is launched into the fiber input, an approximately rectangular pulse is generated at the output of the length of which corresponds to the approximate values shown above for the maximum differential delay. Figure 2.35 demonstrates the precise results for an assumed attenuation-free standard NA POF for the pulse form obtained after 10 m, 20 m, 50 m, and 100 m of ideal POF (from [Bun99a]).

62

2.1 Fundamentals of Optical Fibers

100%

norm. signal

80% 60%

10 m 20 m

50 m

100 m

40% 20% time [ns] 0%

0

5

10

15

20

25

30

35

Fig. 2.35: Output pulses of a POF under UMD conditions ([Bun99a])

Real SI-POF provide considerably higher bandwidths. The main reason for this is the presence of mode-dependent attenuation in conjunction with mode mixing, as will be shown in the next chapter. The differential delay 't increases proportionally to a particular length Lc (coupling length); for longer lengths, the increase is sub-linear (Fig. 2.36). The following holds true: 't v L

for L  L c

't v LN

for L ! L c

with

N 1

whereby the exponent N must be determined for each fiber. It is typically between 0.5 and 0.7. The coupling length Lc ranges between 30 m and 40 m for standard SI-POF. 2.5

pulse broadening [a.U.]

W a —l

2.0

Wal

1.5

in reality

1.0 0.5

Lc length [m]

0.0 0

20

40

60

80

100 120 140 160 180

200

Fig. 2.36: Schematically representation of the pulse broadening reflecting mode coupling effects

2.1 Fundamentals of Optical Fibers

63

The impulse response of a 50 m long standard POF can be seen in Fig. 2.37. The half-value width of the impulse amounts to about 50 ns, i.e. only about 30% of the expected value. Furthermore, it is noticeable that the rear pulse edge drops more slowly. It is in this range that the higher modes lie which are attenuated very greatly by the mode-dependent losses. The dropping off of the rising edge can be explained by the effect of modal mixing.

0.7 U [V]

theoretical pulse shape 'W = 16 ns

0.6 0.5 0.4

'W = 5 ns

0.3 0.2 0.1 0.0 0

5

10

15

20

25

30

35

40 t [ns]

Fig. 2.37: Real pulse shape for 50 m St.-NA-POF

Calculating the bandwidth of graded-index fibers is clearly more complex. Current studies in this field can be found in [Yab00a], [Yab00b] and [Arr99]. Profile dispersion occurs in graded-index profile fibers. It is the remainder of the mode dispersion that can no longer be compensated for and it depends on the relative refractive index difference ', which in turn is wavelength-dependent. An optimization of the profile exponent can be accomplished for a certain wavelength for which d'/dO = 0. A profile exponent of g | 2 causes a temporal broadening of: 't prof

L1 ˜ ncore '2 ˜ , c 2

in other words, a factor '/2-reduced broadening of the pulse as compared with step index POF; for a typical graded-index POF this means a reduction by approximately 2 orders of magnitude [Blu98]. Mode dispersion or profile dispersion can only be avoided by using singlemode fibers. As explained later on, due to the combination with the chromatic dispersion, certain polymer fibers, have some advantages as opposed to silica glass fibers.

64

2.1 Fundamentals of Optical Fibers

2.1.5.9 Chromatic Dispersion Chromatic dispersion describes the influence of the spectral width of a transmitter on a temporal broadening of the input pulse. This includes the material-dispersion and waveguide-dispersion types of dispersion. Both effects also occur in singlemode fibers. Waveguide dispersion is caused by the fact that light waves penetrate into the fiber cladding to various depths, depending on the wavelength of the light wave. Thus, the different speeds of the core and cladding parts result in pulse broadening. Since only a small portion of the light wave in higher modes of large diameter fibers spreads into the cladding, this effect is only considered for singlemode fibers. However, even if only one mode is allowed to propagate, pulse broadening occurs due to material dispersion. Every light source has a spectral width 'O > 0. The following applies for the pulse broadening 'tmax due to material dispersion: ' t mat

where

'O n(O): M(O):

L ˜ 'O ˜

O d² nO c d O²

L ˜ 'O ˜ MO

is the spectral width of the transmitter wavelength-dependent refractive index, material dispersion parameters usually given in ps/km˜nm

Figure 2.38 shows the influence of material dispersion on pulse broadening, using polymer fibers as an example. Corresponding to the material dispersion, the longer wavelengths (red) propagate with a greater velocity than the shorter ones (blue). output pulse 't

input pulse

time

length 'O

wavelength

Fig. 2.38: Temporal broadening as a result of material dispersion

The real influence of the chromatic dispersion from different polymer optical fibers to the system bandwidth will be shown in the next chapter which will contain detailed descriptions of the materials and fiber types.

2.2 Index Profiles and Types of Fibers

65

2.2 Index Profiles and Types of Fibers After the theoretical descriptions on the properties of optical fibers in the section on the fundamentals of light propagation and the observations indicated above on mode propagation and the essential characteristics of fibers this following section will deal with concrete, available fibers. First, the different index profiles, as briefly mentioned in 1.1.6, will be introduced using examples. The next section shows the historical development especially in regard to the different POF variants. Thereafter the important characteristics attenuation and bandwidth will be shown in a series of experimental results. Three parameters are basically responsible for the actual properties of optical fibers. The core and cladding materials used determine the attenuation and chromatic dispersion. The refractive index profile determines the mode dispersion and the core diameter is also responsible for the number of modes. Especially the core material and the index profile are at least recognizable from the name of the fiber, a designation method widely used in this book. In the following section the historical development of the different polymer fibers is summarized. The POFs are dealt with in regard to their index profiles. Thereafter, different hybrid and glass fibers for short-range data transmission will also be introduced. The following chapter deals especially with the bandwidth of thick optical fibers since this characteristic is particularly important and also it makes the greatest demands on measurement techniques. 2.2.1 Step Index Profile Fibers (SI) As was the case with silica glass fibers, the first polymer optical fibers were pure step index profile fibers (SI-POF). This means that a simple optical cladding surrounds a homogenous core. For this reason a protective material is always included in the cable. Figure 2.39 schematically represents the refractive index curve. As already shown above, the refractive index step determines the numerical aperture (NA) and thus the acceptance angle. Some typical values are shown in Table 2.1. The refractive index of the core was always taken as 1.5, whereas the cladding has a correspondingly smaller refractive index. The last line is valid for wave guiding against air (n = 1). Here an acceptance angle of 90° is valid since the NA exceeds the value of 1. ncore ncladd jacket optical cladding

core

jacket optical cladding

Fig. 2.39: Structure of a step index profile fiber

66

2.2 Index Profiles and Types of Fibers

Table 2.1: Relationship between relative refractive index difference and numerical aperture (core refractive index = 1.50) Relative RefractiveIndex-Difference

Refractive Index of the Cladding

Numerical Aperture

Acceptance Angle of the Fiber

0.22 %

1.497

0.10

6°

0.4 %

1.494

0.13

8°

0.8 %

1.488

0.19

11°

1.0 %

1.485

0.21

12°

1.5 %

1.478

0.26

15°

2.0 %

1.470

0.30

17°

2.7 %

1.460

0.35

20°

4.0 %

1.440

0.42

25°

5.8 %

1.413

0.50

30°

8.0 %

1.380

0.59

36°

12.0 %

1.320

0.71

45°

20.0 %

1.200

0.90

64°

33.3 %

1.000

1.12

90°

A larger acceptance angle of the fiber simplifies the launching of light, e.g. from a semi-conductor source. In addition, a high NA reduces the losses associated with fiber bending, as schematically illustrated in Fig. 2.40.

rays, exceeding the critical angle of total reflection behind the bend

launched light rays

bend radius

Fig. 2.40: Loss at fiber bends

rays, guided behind the bend

2.2 Index Profiles and Types of Fibers

67

Due to the effects of bending, the propagation direction of each individual ray is changed relative to the axis of the fiber. In the case of multi-mode fibers, a part of the rays is always extracted because the rays exceed the angle of total reflection at the interface between core and cladding. For fibers with a large NA, the effect of a change in angle for a certain amount of bending is not so significant so that the bending losses diminish. Likewise, when coupling fibers to each other (at connectors) the loss due to angle errors is less significant when there is a large numerical aperture. A disadvantage of fibers with a large NA is the greater difference in time delay between the different light paths, and this in turn leads to a greater level of mode dispersion. This limits the bandwidth. In addition, the loss at coupling points increases if there is a gap between the abutting faces. Some advantages of larger or smaller numerical apertures are listed in Table 2.2. Table 2.2: Influence of higher NA to various fiber parameters Property of the Fiber bending sensitivity fiber coupled power connecting loss for fiber angular mismatch connecting loss for axial fiber gap connecting loss for fiber axis lateral gap bandwidth

Behavior with increasing NA becomes smaller becomes higher becomes smaller becomes higher becomes higher becomes smaller

Silica glass multi-mode fibers usually have an NA of approximately 0.20. Silica glass fibers with polymer cladding have an NA in the range of 0.30 to 0.40 (sometimes 0.65). The large refractive index difference between the materials that are used for the core and the cladding of polymer fibers allows significantly higher NA values. The majority of the initially produced SI-POF had an NA of 0.50 (e.g. [Asa96], [Esk97], [LC95]). SI-POF with an NA around this value are nowadays generally called standard NA-POF or standard POF for short. The bandwidth of such fibers is approximately 40 MHz for a 100 m long link (quoted as the bandwidth-length product 40 MHz · 100 m). For many years this was a completely satisfactory solution for most applications. 2.2.2 The Step Index Fiber with Reduced NA (low-NA) However, when it became necessary to replace copper cables with polymer optical fiber to accomplish the transmission of ATM data rates of 155 Mbit/s (ATM: asynchronous transfer mode) over a distance of 50 m, a higher bandwidth was required for the POF. In the mid-nineties all three important manufacturers developed the so-called low-NA POF. POF with a reduced numerical aperture (low-NA POF) feature a bandwidth increased to approximately 100 MHz · 100 m because the NA has been reduced to approximately 0.30. The first low-NA POF was presented in 1995 by Mitsubishi

68

2.2 Index Profiles and Types of Fibers

Rayon ([Koi98]). Figure 2.41 shows that the fiber construction corresponds to the standard POF, the distinction being that the refractive index difference is smaller (approximately 2 %). Usually the same core material is used, but the cladding material has a modified composition.

ncore ncladding jacket optical cladding

core

jacket optical cladding

Fig. 2.41: Structure of a low-NA step index profile fiber

Unfortunately, practical testing showed that although this fiber met the requirements of the ATM forum ([ATM96b]) with respect to bandwidth, it did not meet the requirements with respect to bending sensitivity. These requirements specify that for a 50 m long POF link the losses resulting from a maximum of ten 90° bends having a minimum bending radius of 25 mm should not exceed 0.5 dB. In order to meet both these requirements at the same time it became necessary to find a new structure. 2.2.3 The Double-Step Index Optical Fiber (DSI) The double-step index POF features two claddings around the core, each with a decreasing refractive index (Fig. 2.42). In the case of straight installed links, light guiding is achieved essentially through the total reflection at the interface surface between the core and the inner cladding. This index difference results in an NA of around 0.30, similar to the value of the original low-NA POF.

ncore ncladding1 ncladding2 jacket

core

outer / inner optical cladding Fig. 2.42: Structure of a double step index profile fiber

jacket inner / outer optical cladding

2.2 Index Profiles and Types of Fibers

69

When fibers are bent, part of the light will no longer be guided by this inner interface. However, it is possible to reflect back part of the decoupled light in the direction of the core at the second interface between the inner and the outer cladding. At further bends, this light can again be redirected so that it enters the acceptance range of the inner cladding. The inner cladding has a significantly higher attenuation than the core. Light propagating over long distances within the inner cladding will be attenuated so strongly that it will no longer contribute to pulse propagation. Over shorter links the light can propagate through the inner cladding without resulting in too large a dispersion. A schematic illustration is shown in Fig. 2.43. launched light rays

4 rays behind the bend

1 rays, guided only by

3

the inner cladding

1

2 rays, guided by the outer cladding behind the bend

3 rays, guided by the outer cladding over a limited distance

bend radius

2 1 2

4 not guided rays behind the bend Fig. 2.43: Operation of a bent double step index profile fiber

The first generation of DSI-POF primarily served the purpose of increasing the bandwidth of 1 mm fibers from 40 MHz · 100 m to 100 MHz · 100 m with an unchanged minimum bending radius of 25 mm. The respective applications are to be found in LANs and home networks. The fiber producers offer these fibers under the same type names as the original “real” low-NA fibers. It has since become standard procedure to call the fibers low-NA and to indicate DSI as the index profile. Currently, another goal is being pursued: the bandwidth of standard POF is sufficient for applications in vehicle networks, but the bending radius should be reduced. Presently being discussed are POFs, the index steps of which correspond to a NA of 0.50 or 0.65 respectively to the inner and outer cladding. The bending radius can thus almost be halved.

70

2.2 Index Profiles and Types of Fibers

2.2.4 The Multi-Core Step Index Optical Fiber (MC) As described above, the requirements of high bandwidth and low sensitivity to bending are difficult to accomplish together within one and the same fiber having a diameter of 1 mm. Fibers with a smaller core diameter can solve this problem since the ratio to the fiber radius is larger for the same absolute bending radius. However, this contradicts the requirements for easy handling and light launching. A PCS with a core diameter of 200 ȝm and an AN = 0.37 permits, for example, a bending radius of 5 mm with very low bending losses. As a compromise, Asahi developed a multi-core fiber (MC-POF, see [Mun94], [Mun96] and [Koi96c]). In this fiber many cores (19 to over 200) are put together in production in such a way that together they fill a round cross-section of 1 mm diameter. First, the individual fibers are all perfectly round and each has its own optical cladding. Only a certain share of the total cross-section of the bundle enters the cores guiding the light, since the cladding areas and the spaces between the fibers have to be accounted for. Figure 2.44 shows the parameters which mark the percentage of the filled-in area. The number N here indicates how many fibers lie next to each other over a diameter while n indicates the entire number of fibers.

R

R dm

dm r N=5

N=1

n = 19

Fig. 2.44: Schematically arrangement of cores in a MC-POF

In the figure, R denotes the radius of the complete fiber (typically 0.5 mm) and d the thickness of the optical cladding (e.g. 5 μm). Let us assume first of all that the individual cores are arranged in a hexagonal shape with N = 2z + 1 cores positioned next to each other. The next Fig. 2.45 shows how the arrangement for fibers is changed for z = 1 to 5. While these sketches can give a clear definition of the number of fibers that can be arranged within a circular shape, for smaller and smaller individual cores the possibilities are more complex. The arrangement at the bottom right shows one possible deviation. For the first five arrangements the number of individual fibers is calculated as follows: n = 3z2 + 3z + 1.

2.2 Index Profiles and Types of Fibers

71

It follows that the individual radius r is: r = R/N = R/(2z + 1). N=3

N=5

N=7

N=9

N=11

N´=11

Fig. 2.45: Possible circular arrangements of cores in a MC-POF

In Table 2.3, the degree of coverage of the circle area is calculated for the cases shown. First, the number of individual cores is calculated from z. The radius r results from the overall radius of the fiber (here always 500 μm). Parameter ta indicates what percentage of the total circular area is covered by the individual circles (for the hexagonal arrangement of an infinite number of circles a maximum of 90.69 % of the area can be covered). When calculating parameter tb, the fact that part of the cross-section is lost to the optical claddings (all uniformly 5 μm thick) is taken into account. Table 2.3: Core cross area degree of coverage for MC fibers (ideal) z:

N:

n:

r:

ta:

tb:

0 1 2 3 4 5

1 3 5 7 9 11 11´ 13 15 17 29 -

1 7 19 37 61 91 85 127 169 217 631 -

500 μm 167 μm 100 μm 71.4 μm 55.6 μm 45.5 μm 49.3 μm 38.5 μm 33.3 μm 29.4 μm 17.2 μm -

100.00 % 77.78 % 76.00 % 75.51 % 75.31 % 75.21 % 82.47 % 75.15 % 75.11 % 75.09 % 75.03 % 90.69 %

98.01 % 73.18 % 68.59 % 65.31 % 62.36 % 59.57 % 66.57 % 56.88 % 54.27 % 51.73 % 37.82 % -

6 7 8 14 f

72

2.2 Index Profiles and Types of Fibers

Figure 2.46 shows the proportion of core area tb as depending on the number of cores for four different thickness’ of the optical cladding. use of the total cross area tb 100% 80%

dm = 5 μm

dm = 20 μm

dm = 10 μm

dm = 30 μm

60% 40% 20% 0% 1

7

19

37

61

91

127

169

217

number of single cores

Fig. 2.46: Proportion of core area for different cladding thickness

As can be expected, the proportion of the overall covered area decreases with an increasing number of cores because the proportion of cladding area will become larger and larger. A certain minimum thickness of cladding is necessary for it to be able to fulfill its function and still be technologically feasible. The four individual data points show the case of the optimized fiber arrangement with 85 individual cores in accordance with Fig. 2.45. Given a minimum thickness of the optical cladding between 5 μm and 10 μm, these considerations indicate that a maximum number of some 100 single cores should be used, in which case the proportion of useable area will hardly exceed 70 %. It is easy to conclude that a smaller proportion of useable core area would lead to an increase in the losses encountered when connecting transmitters to, and fibers between each other.

Fig. 2.47: 37 core POF with deformed single cores (schematically)

2.2 Index Profiles and Types of Fibers

73

Practical experience shows that a better utilization of the area can be achieved. During the manufacturing process the fibers are placed together at higher temperatures which means that they change their shape and thus reduce the gaps between the fibers. Apparently, the resulting deviations from the ideal round shape do not play a significant role in light propagation (the causes for this are not yet completely understood; some points worth discussing can be found in the chapter on light propagation in POF). Figure 2.47 shows a schematic illustration of the cross-section of a fiber with 37 cores, such as e.g. in [Tesh98]. Data of available MC-POF and -GOF are grouped together later. Figure 2.48 shows the refractive index profile of a MC-POF, shown as a crosssection through the diameter of the fiber. The index steps correspond to those of a standard POF.

ncore ncladding jacket

jacket

cores

optical cladding

optical cladding

Fig. 2.48: Structure of a step index multi core fiber

Since the bandwidth only depends on the NA for SI fibers, it should be possible to measure values comparable to the standard POF. However, the fact is that the measured values are actually significantly higher, which has been explained in the chapter 2.1.5.2 discussing mode-selective attenuation mechanisms. Glass fibers are also produced for use in many areas as fiber bundles. In lighting technology fiber glass bundles with a large NA are widely spread. (The lighting of the headlight outer ring at BMW via such a fiber bundle is wellknown.) In the meantime, such fibers are also available for data communication ([Lub04b]). 2.2.5 The Double Step Index Multi-Core Fiber (DSI-MC) In the MC-POF, too, an increase in bandwidth was achieved by reducing the index difference. Due to the smaller core diameters it was still possible to avoid an increase in bending sensitivity. Even better values were achieved with individual cores having a two-step optical cladding such as illustrated in Fig. 2.49. The principle is the same as in the double-step index POF with an individual core. In this case a bundle with single cladding is completely surrounded by a second cladding material (“sea/islands” structure).

74

2.2 Index Profiles and Types of Fibers

ncore ncladding1 ncladding2 cores

jacket

jacket

outer / inner optical cladding Fig. 2.49: Structure of a double step index profile multi core POF

2.2.6 The Graded Index Optical Fiber (GI) When using graded index profiles (GI) an even greater bandwidth becomes possible. In these profiles, the refractive index continually decreases (as a gradient), starting from the fiber axis and moving outwards to the cladding. Of particular interest are profiles that follow a power law (remember chapter 1.4.1). refractive index

n=n

fiber axis

g ª § distance to fiber axis · º ˜ «1- ' ˜ ¨ ¸ » core radius «¬ © ¹ »¼

The parameter g - often also Į - is characterized as the profile exponent. When g = 2 one speaks of a parabolic profile. The borderline case of the step index profile fibers corresponds to g = ’. The parameter ǻ states the relative refractive index difference between the maximum core and the cladding refractive index. Figure 2.50 shows a parabolic index profile.

ncore ncladding core jacket optical cladding

jacket optical cladding

Fig. 2.50: Structure of a graded index profile fiber

Due to the continually changing refractive index, the light rays in a GI fiber do not propagate in a straight line but are constantly refracted towards the fiber axis. Light rays that are launched at the center of the fiber and do not exceed a certain angle are completely prevented from leaving the core area without any reflections occurring at the interface surface. This behavior is illustrated schematically in Fig. 2.51. The geometric path of the rays running on a parallel to the axis is still significantly smaller than the path of rays that are launched at a greater angle. However, as can be seen, the index is smaller in the regions distant from the core. This means a greater propagation speed. In an ideal combination of parameters the different path lengths and different propagation speeds may cancel each

2.2 Index Profiles and Types of Fibers

75

other out completely so that mode dispersion disappears. In reality, this is only possible in approximation. It is possible, however, to increase bandwidths by two to three orders of magnitude compared with the SI fiber. graded index profile fiber

step index profile fiber

n

n

Fig. 2.51: Comparison of step and graded index profile (see also chapter 2.1.1)

When considering not only the pure mode dispersion but also chromatic dispersion, i.e. the dependence of the refractive index on the wavelength and spectral width of the source, an optimum index coefficient 'g' deviating from 2 is achieved. This has been the subject of comprehensive investigations by the research group around Prof. Koike ([Koi96a], [Koi96b], [Ish00], [Koi97a], [Koi96c], [Koi98] and [Ish98]). In [Ish00] and [Koi00] the significance of this effect is particularly pronounced (see also Chapter 2). Due to the smaller chromatic dispersion of fluorinated polymer compared with silica, the bandwidth of GI-POF theoretically achievable is significantly higher than that of multi-mode GI silica glass fibers. In particular, this bandwidth can be realized over a significantly greater range of wavelengths. This makes the PF-GI-POF interesting for wavelength multiplex systems. However, in this case the index profile must be maintained very accurately, a requirement for which no technical solution has as yet been provided. Another factor involved in the bandwidth of GI-POF is the high level of modedependent attenuation ([Yab00a]) compared to silica glass fibers. In this case modes with a large propagation angle are suppressed resulting in a greater bandwidth. An example is the simulation that was carried out in [Yab00a]: the bandwidth of a 200 m long PMMA-GI-POF increases from 1 GHz to over 4 GHz, taking into account the attenuation of higher modes. This is also confirmed in practical trials. Mode coupling is less significant for GI fibers than it is for SI fibers since the reflections at the core-cladding interface do not occur. 2.2.7 The Multi-Step Index Optical Fiber (MSI) Following the many technological problems experienced in the production of graded index fibers having an optimum index profile that remains stable for the duration of its service life, an attempt was made to approach the desired characteristics with the multi-step index profile fiber (MSI-POF). In this case the core consists of many layers (e.g. four to seven) that approach the required parabolic curve in a series of steps. Here a “merging” of these steps during the manufacturing process may even be desirable. A diagram of the structure is shown in Fig. 2.52.

76

2.2 Index Profiles and Types of Fibers

ncore ncladding core jacket optical cladding

jacket optical cladding

Fig. 2.52: Structure of a multi step index profile fiber

In this case light rays do not propagate along continually curved paths as in the GI-POF, but on multiple diffracted paths as demonstrated in Fig. 2.53. However, given a sufficient number of steps, the difference to the ideal GI profile is relatively small so that large bandwidths can nevertheless be achieved. MSI-POF were presented in 1999 by a Russian institute (Tver near Moscow [Lev99]) and by Mitsubishi (ESKA-MIU, see [Shi99]). In the meantime, other companies are producing such fibers which are often called GI fibers. These GI and MSI fibers are classified in the same class of standards, e.g. A4e.

n Fig. 2.53: Light propagation in the MSI-POF

2.2.8 The Semi-Graded Index Profile Fibers (Semi-GI) A relatively new version of index profiles are fibers which have a gradient with a slightly varying index above the core cross section, but do have an optical cladding with a great index step as shown in Fig. 2.54 ([Sum00], [Sum03], [Ziem05f] and [Ziem06i]).

ncore ncladding jacket optical cladding

core

jacket optical cladding

Fig. 2.54: Structure of a semi-graded index profile fiber

2.2 Index Profiles and Types of Fibers

77

At first sight this variety of fiber has enormous advantages. Light which propagates within the gradient is only subject to very little mode dispersion. If a ray of light has a greater propagation angle, e.g. after being bent, then it continues to be led to the core-cladding interface layer through total reflection. However, these rays do have a very much higher mode dispersion. Figure 2.55 shows how light spreads theoretically and what consequences this has for the pulse response.

input

output „GI“-modes „SI“-modes

t

Fig. 2.55: Light propagation in semi-graded-index profile fibers theoretically

In principle, two different groups of modes can be seen in the picture. The paths designated as GI modes do not touch the cladding and only show a very slight difference in propagation times. The shares designated as SI modes are completely reflected at the core-cladding interface layer. These light paths are also bent in the core, but the light path, now very much longer, can no longer be compensated for in the outer areas by the lower refractive index. With very high data rates the second mode group is drawn out so widely that it is presented solely as a kind of DC offset in the eye diagram. At the POF-AC a data rate of 1 Gbit/s was transmitted over 500 m of a GI PCS fiber with a PRBS signal ([Vin05a]). Data rates up to 3 Gbit/s could be attained with a small surface APD receiver ([Kos95]). In order to do justice to the complex behavior of the semi-GI POF, corresponding modulation formats should be selected. 2.2.9 An Overview of Index Profiles Figures 2.56 through 2.58 again show all index profiles described in an overview. Due to the wide range of possibilities offered in polymer chemistry further developments are certainly to be expected. For example, multi-core graded fibers, fibers with special cladding for a reduction of the losses at the core/cladding interface or to increase the bandwidth or even multi-core fibers with different individual cores are all conceivable. In the following figures POF variants are shown with typical parameters.

78

2.2 Index Profiles and Types of Fibers

SI-POF AN = 0.50 40 MHz˜100 m

Low-NA-POF AN = 0.30 100 MHz˜100 m

DSI-POF AN = 0.30 100 MHz˜100 m

Fig. 2.56: POF with single core and step index profile

Single-core fibers with diameters between 125 μm and 3 mm are available from different manufacturers at a reasonable price and in robust quality. Most of the polymer optical fibers used in practical applications are of these types.

MC-SI-POF e.g. 200 cores AN = 0.30 100 MHz˜100 m

MC-DSI-POF e.g. 37 cores AN = 0.19 400 MHz˜100 m

Fig. 2.57: POF with multiple cores and step index profile

MC fibers are available from various manufacturers. They are deployed in applications ranging from high data rates transmission systems through to optical image guides. Because of the short lengths produced, the prices are still significantly above expectations. However, further developments in this field can be expected in the future.

GI-POF AN = 0.20 2 GHz˜100 m

MSI-POF AN = 0.30 500 MHz˜100 m

Fig. 2.58: Polymer fibers with graded index and multi step index profile

Graded index as well as multi-step index profile POF are commercially available today. Laboratory experiments and a series of practical installations in Japan and Europe, (e.g. [Mös04]) show the great potential in regard to the bit rates possible. Asahi Glass introduced them into the market around 2001. Lucent Technologies, later called OFS and trading under the name of Chromis Fiberoptics as of 2004 ([Whi04], [Park05a]), also announced the possibility of producing large amounts of GI POF in case of demand.

2.3 The Development of POF

79

In Europe, fibers by Nexans are manufactured in Lyon ([Gou04]). All three fibers will consist of the fluorinated polymer material CYTOP®. The core diameter of the LucinaTM Fiber by Asahi Glass is 120 μm with an AN = 0.28. A protective cladding made from PMMA and measuring 500 μm is placed around an area of fluorinated polymer outside the core profile. The duplex cable has external dimensions of approximately 3 by 5 mm. The lowest attenuation achieved to date is approx. 15 dB/km for a wavelength of 1,300 nm. The specified value is < 50 dB/km for 700 nm - 1,300 nm. There has also been significant progress in the manufacture of GI or MSI-POF respectively on a PMMA basis (see Section 2.3.4).

2.3 The Development of Polymer Optical Fibers The following sections will describe the polymer fibers presented so far, whereby particular attention will be paid to the chronological sequence of the developments. Section 2.4 supplements these observations with some types of multimode glass fibers which were not discussed in the first edition. 2.3.1 Looking back The first POF were manufactured by DuPont as early as the late sixties. Due to the incomplete purification of the monomer materials used, attenuation was still in the vicinity of 1,000 dB/km. During the seventies it became possible to reduce losses nearly to the theoretical limit of approximately 125 dB/km at a wavelength of 650 nm. At that point in time glass fibers with losses significantly below 1 dB/km at 1,300 nm/1,550 nm were already available in large quantities and at low prices. Digital transmission systems with a high bit rate were then almost exclusively used in telecommunications for long-range transmissions. The field of local computer networks was dominated by copper cables (either twisted-pair or coaxial) that were completely satisfactory for the typical data rates of up to 10 Mbit/s commonly used then. There was hardly any demand for an optical medium for high data rates and small distances so that the development of the polymer optical fiber was slowed down for many years. A significant indicator for this is the fact that at the beginning of the nineties the company Höchst stopped manufacturing polymer fibers altogether. During the nineties, after data communication for long-haul transmission had become completely digitalized, the development of digital systems for private users was commenced on a massive scale. In many spheres of life we are being increasingly confronted with digital end user equipment. The CD player has largely replaced analog sound carriers (vinyl records and cassettes). The MP3 format is leading to a revolution in music recording and distribution. The DVD (Digital Video Disc) and large hard disk drives could lead to the replacement of the analog video recorder within a few years. Even today more digital television programs

80

2.3 The Development of POF

are available than analog programs. Decoder boxes have become standardized (MPEG2 format) and will be integrated into television sets in the future. More and more households are using powerful PC and digital telephone connections (ISDN). With offers such as T-DSL (ADSL technology provided by Deutsche Telekom AG) as well as fast internet access via satellite or broadband digital services on the broadband cable network, private users are being offered access to additional digital applications even before the start of the new millennium. Likewise, in the automotive field the step towards digitalization has long been made. CD changers, navigation systems, distance-keeping radar and complex control functions are increasingly part of the standard equipment being provided in all classes of vehicles. The development of electronic outside mirrors, fast network connections even from within an automobile as well as automatic traffic guidance systems will ensure a further increase in the range of digital applications for the motor vehicle. All these examples demonstrate that completely new markets for digital transmission systems are being developed for short-range applications. Polymer optical fibers can meet many of these requirements to an optimum degree and are therefore increasingly of interest. A significant indicator for this development is the history of the International Conference for Polymer Optical Fibers and Applications which has been taking place annually since 1992 and represents the most significant scientific event in this specialized field. Many of the developments described below were presented for the first time at these conferences. 2.3.2 Step Index Polymer Fibers The SI-POF is the oldest variant of all polymer fibers. Its development goes back to the beginning of the 1960’s, i.e. in a period when silica glass fibers were being developed. Today the SI-POF is by far the most common POF variant. In Table 2.4 data from different publications on this fiber type are summarized - without claiming to be complete. Table 2.4: Published data of SI-POF Ref.

Year Producer Product

[Min94] [Koi97a] [Koi96c] [Sai92] [Min94] [Koi95] [Sai92] [Sai92] [Koi95] [Min94]

1963 1964 1968 1976 1978 1982 1983 1983 1983 1984

Du Pont Du Pont Du Pont Mitsubishi Mitsubishi NTT Mitsubishi Mitsubishi Mitsubishi Mitsubishi

CROFON

Eska Super Eska Eska Extra Eska Extra Eska Extra

Øcore Attenuation at O μm dB/km nm 1.000 650 500 650 500 650 300 650 300 650 55 568 124 650 65 570 1000 110 570 150 650

NA Remarks st. st. st. st. st. st. st. st. st. st.

first POF first SI-POF

4 MHz˜km

2.3 The Development of POF

81

Table 2.4: Published data of SI-POF (continued) Øcore Attenuation at O NA Remarks μm dB/km nm Asahi 80 570 st. Mitsubishi Eska Extra 125 650 st. up tp 85°C Mitsubishi Eska Extra 65 570 st. Hoechst 1000 130 650 st. Asahi Luminous-F 175 660 0.50 310 MHz˜10m AN, LED=0.50, 105°C Asahi X-1 0.37 540 MHz˜10m AN, LED = 0.50 Asahi X-2 0.28 >1.000 MHz˜10m AN, LED = 0.50 Höchst EP51 970 190 650 st. 90 MHz˜100 m with 650 nm LED Mitsubishi Eska Premier 1000 135 650 0.51 up to 85°C Sveton MNCIS 200- 150 650 0.45 up to 70°C Series, Grade U 600 Sveton MFCIS 200- 120 650 0.48 up to 70°C Series, Grade U 1000 Sumitomo n. a. 480 150 650 0.51 200 MHz˜50m 'n=0.055 Mitsubishi n. a. 1000 110 650 0.47 80 MHz˜100 m Dig. Optr. n. a. 1000 0.50 2003 announced Luvantix SI type 1000 160 650 0.40 200 MHz bandwidth Nuvitech Nuvilight 1000 250 650 0.38 for illumination Luceat SI-Type 1000 150 650 0.46 30 MHz˜100 m Nanoptics A-POF 1000 100 650 - conception Huiyuan SI-POF 1000 300 650 - coextrusion Luceat SI-POF 1000 135 650 0.50 from preform 65 520

Ref.

Year Producer Product

[Koi95] [Sai92] [Sai92] [Koi95] [Tesh92]

1985 1991 1991 1991 1992

[Tesh92] 1992 [Tesh92] 1992 [Eng96] 1992 [Kit92] 1992 [Lev93] 1993 [Lev93] 1993 [Non94] 1994 [Koe98] [Mye02] [Luv03] [Nuv04] [Luc05] [Wal05] [Hai05] [Zie06h]

1998 2002 2003 2004 2005 2005 2005 2006

5,000 attenuation [dB/km] 2,000 1,000 500 200 100 50 400

wavelength [nm] 450

500

550

600

650

700

750

800

Fig. 2.59: Attenuation of different standard-NA SI-POF (measurement by POF-AC)

82

2.3 The Development of POF

It was not until about 1980 that technology made possible the production of POF which came relatively close to the theoretical attenuation minima. Initial problems with the service life and with certain mechanical loads were quickly solved with on-going developments. In Fig. 2.59 the spectral attenuation curves of three SI-POFs are shown (data sheet information). All three fibers from Japanese manufacturers are close together. The visible differences may possibly be due to different methods of measurement. Most manufacturers offer SI-POFs in different diameters. In [Zub01b] and [Nuv04] the properties of these fibers are compared (Table 2.5). Table 2.5: Attenuation of POF with different diameter diameter [μm] Mitsubishi Toray Asahi Chem. BOF Optectron Nuvitech

Attenuation [dB/km] 500 750 < 190 < 180 < 180 < 150 < 180 < 180 < 150 < 150 < 150 < 150 < 250 < 250

250 < 700 < 300 n. a. < 150 < 150 < 350

1.000 < 160 < 150 < 125 < 150 < 150 < 250

For Toray fibers, the losses of fibers with different diameters are listed in the data sheet and are shown in Fig. 2.60.

10000

attenuation [dB/km]

3000 1000 300

‡core t 750 μm ‡core = 500 μm ‡core = 250 μm

100 30 400

wavelength [nm] 500

600

700

800

900

Fig. 2.60: Attenuation of different PMMA-SI-POF by Toray

With a few exceptions the losses for all fiber diameters are similar. Some reasons for the increase in attenuation with thinner fibers could be that either the high attenuation of the optical cladding plays a greater role or that more stress is exerted on the thin fiber during manufacture. A fiber with a ¼ mm core diameter

2.3 The Development of POF

83

has only one sixth the thermal capacitance. When the cladding and opaque jacket are applied this fiber is necessarily warmer. The process temperatures during manufacture can indeed lie clearly above the glass transition temperature. The youngest manufacturer of PMMA SI-POF is the Italian company Luceat. Here fibers for diverse applications, mainly in mechanical engineering, are produced. The highest quality is still in the developmental stage. A comparison of the measured values of Luceat fibers (POF-AC 2006, [Ziem06h]) with the values from [Wei98], more or less the POF reference curve up until now, is shown in Fig. 2.61. 500 attenuation [dB/km] 300 200 Luceat

100 80 [Wei98] 60 50 400

450

500

550

600

650 700 wavelength [nm]

Fig. 2.61: Attenuation of SI-POF by Luceat (2006)

In the area of 520 nm this fiber is even somewhat better that the data of the best fibers so far. Thanks to the availability of reasonably priced and fast green LEDs this advantage can be assessed very highly. As part of the European POF project POF-ALL (see www.ist-pof-all.org) the transmission of a 10 Mbit/s data stream was able to be demonstrated over 425 m (see System Chapter). 2.3.3 Double Step Index Profile Polymer Fibers We have already discussed the principle idea of a double step index profile POF. All three important Japanese manufacturers presented such fiber types around 1995. After the expectations that ATM would become the dominating network technology in the home were not fulfilled, these fibers have more or less become niche products today, albeit at relatively high prices. Today in many areas there is a demand for data rates which require the use of these fibers instead of the normal SI-POFs. Technically, DSI-POFs are on a comparable level and would hardly be more expensive than SI-POFs when produced in high volumes.

84

2.3 The Development of POF

Table 2.6 compares the properties of DSI-POFs of the three manufacturers ([Mit01], [Nich03], [LC00b]). Table 2.6: Overview of DSI-POF

diameter attenuation (650 nm) numerical aperture bandwidth temperature range bend radius

[μm] [dB/km] MHz ˜ km [°C] [mm]

Mitsubishi Toray MH4001 PMU-CD1001 980 1000 ± 45 160 170 0.30 0.32 10 >10 -55 .. +75 -20 .. +70 25 -

Asahi AC1000(I) 1000 ± 60 160 0.25 15 -40 .. +70 25

We would like to point out once again that the DSI-POFs are usually offered now as before as low NA POF. In the first few years manufacturers did not provide any information at all about the double cladding structure. In [Eng98b] the double cladding structure was proven quite early on the basis of measurements of the far field and with optical microscopy. In Fig. 2.62 you can see the far field distributions for different fiber lengths measured with the inverse far field method at the FH Gießen/Friedberg. 1.0

Popt

1m 10 m 50 m 90 m

0.8 O= 594 nm

0.6 0.4 0.2 0.0 -30

-20

-10

0

10

20

30

4 [°]

Fig. 2.62: Inverse far field measurement of a DSI-POF

You can clearly see that after short distances much light from the interface layer between inner and outer cladding is still guided. After 50 m these shares have disappeared and the angle distribution corresponds to a true low NA POF. Figure 2.63 shows two microscope photos of DSI-POF (Univ. of Ulm). Both optical claddings can be easily recognized. At the 2003 POF Conference Mitsubishi was the first manufacturer to present the actual structure. The effect of suppressing higher modes by high attenuation of the inner cladding was also confirmed theoretically and experimentally. For example, Asahi gives a value of 6000 dB/km at 650 nm for the losses in the inner cladding.

2.3 The Development of POF

85

Fig. 2.63: Double cladding structure of a POF

2.3.4 Multi-Core Polymer Fibers Since 1994, polymer fibers as multi-core fibers have been introduced, e.g. in [Tesh98], [Mun94], [Asa97] and [Tesh98]. Table 2.7 shows a few parameters from these publications. Table 2.7: Multi-core POF (Asahi Chemical) Type

Ref.

NMC-1000 PMC-1000 MCS-1000 NMC-1000 PMC-1000 -

POF´94 Data´96 Data´97 POF´98 POF´98 POF´98 Data´98 Data´98 POF´98 POF´98

No. of Structure NA Attenuation Bandwidth Cores at 650 nm 19 SI 0.25 125 dB/km 170 MHz˜100 m 217 SI 0.15 270 dB/km n. a. 217 SI 320 dB/km n. a. 37 DSI 0.19 155 dB/km 700 MHz˜50 m 37 DSI 0.25 160 dB/km n. a. 37 DSI 0.33 160 dB/km n. a. 37 DSI 0.25 160 dB/km 500 MHz˜50 m 37 DSI 0.19 160 dB/km n. a. 217 SI 0.50 160 dB/km n. a. 217 SI 0.33 160 dB/km n. a.

The MC-POF features a noticeably reduced sensitivity to bending and only insignificantly increased attenuation as well as a significantly increased bandwidth compared to single core fibers, this being due to the possibility of smaller numerical apertures. Whether these fibers can be produced at the same price is still an open question. Should this be possible, data rates of 500 Mbit/s up to 1 Gbit/s over 50 m can easily be achieved in commercial applications. At the POF-AC a data rate of over 1 Gbit/s over 100 m MC-POF has already been achieved. At present, only Asahi chemical offers MC-POF for data communication while other manufacturers offer this kind of fiber for lighting purposes or also as image guiding fiber. The following photos show the cross-sections of the three, presently available MC-POFs with 37, 217 and 631 cores (the 19 core variant is no longer available).

86

2.3 The Development of POF

Fig. 2.64: Photo by microscope of MC-POF, 37, 217 respectively 631 cores

An overview of the technical data of the four different MC-POFs is summarized in the following Table 2.8 (Nichimen data sheets). The PMC 1000 permits the highest data rates on the basis of experiments conducted so far since it possesses a DSI structure. Table 2.8: Data of MC-POF Unit Parameter number of cores μm ‡single core core material cladding material 2nd cladding material NA mm ‡fiber core mm ‡cable jacket attenuation1) dB/km bit rate (50 m) Mbit/s temperature °C bend loss2) dB 1) 2) 3)

MCQ-1000 MCS-1000 NMC-1000 PMC-1000 613 217 37 60 PMMA PMMA fluoro polymer 0.50 0.5 r 0.05 1.0 r 0.06 1.0 r 0.06 2.2 r 0.07 2.2 r 0.10 PE PE (black) <200 320 n. a. n. a. -40 .. +60 -40 .. +60 <0.1 <0.23)

Cut back 12 - 2 m, at 650 nm R = 3 mm, 180°, no stress R = 3 mm, 360°, Launch-NA: 0.2

4) 5)

19 37 200 130 PMMA PMMA FMA-copolymer VDF-copolymer 0.25 0.19 1.0 r 0.06 1.0 r 0.06 2.2 r 0.10 2.2 r 0.10 PE (black) PE (black) 1634) 1634) 5) 350 5005) -40 .. +70 -40 .. +70 <0.13) <0.13)

650 nm monochromatic light 650 nm LD, BER = 10-12

We do have to point out one special feature of these four MC POFs: the fibers are tightly bound in the cable as opposed to the individual fibers in a fiber glass bundle or other MC POFs used in lighting technology. The share of the core surface is not only enlarged, but it is considerably easier to work the fibers. These strands can be mounted like quite normal 1 mm SI-POFs. The two enormous advantages of MC-POF, namely the high band width and the low bending losses, have in the meantime been somewhat qualified since considerably cheaper GI-POFs on a PMMA basis have become available. The latter will be treated in the next paragraph.

2.3 The Development of POF

87

2.3.5 Multi-Step Index Profile and Graded Index Profile Fibers The greatest bandwidths of all fibers - with the exception of the singlemode fibers - are shown by graded index profile fibers. They have been used extensively for some time in the field of silica glass fibers and are a standard. In the USA, predominately fibers with a core diameter of 62.5 μm are used, whereas in Europe and most other countries fibers with a core diameter of 50 μm are used. This diameter is nevertheless 5 to 6 times greater than with singlemode fibers whereby the plug costs are greatly reduced and the coupling of lasers is also easier. The bandwidthlength product (BLP) of these multimode glass fibers lies in the range of 200 to 500 MHz · km. For the transmission of 10 Gbit/s a new fiber specification with a BLP of 2,000 MHz · km at a wavelength of 850 nm is even being developed (for example, see [Oeh02] and [Geo01]). The advantages of the large core diameter and high bandwidth would be an optimal combination with POFs. Furthermore, numerous problems with the corecladding interface area would cease to exist with GI fibers since the light guiding would take place exclusively in the core. Glass GI fibers are produced by applying many layers of a SiO2-GeO2 mixture with different compositions to a quartz glass pipe. Finally, the fiber is drawn (several 100 km) out of such a preform. Unfortunately, this is not possible with POFs. The different methods and combinations of materials with which attempts have been made to produce GI-POF will be described further on. Since GI fibers are difficult to produce - as we shall describe later on - a series of multi step index profile POFs have been introduced. These MSI-POFs also offer high bandwidth depending on the number of steps. For now, the optical characteristics are summarized here. Table 2.9 shows an overview of the values for PMMA-based GI, MC and MSI fibers. To the best knowledge of the author, all PMMA-GI-POF published to date are produced by doping, whereas only MSI-POF are produced in a co-polymerization process. Table 2.9: Published data of PMMA-GI-, MSI- and MC-POF (IGPT: interfacial gel polymerization technique; PFM: preform method) Ref.

Year Producer Material

Øcore μm

[Koe98] [Koi95] [Koi96c] [Koi95] [Koi90] [Koi90] [Koi92] [Koi92] [Non94] [Shi95]

1998 1982 1990 1990 1990 1990 1992 1992 1994 1995

1 Keio Univ. Keio Univ. Keio Univ. Keio Univ. Keio Univ. Keio Univ. Keio Univ. Sumitomo BOF

MMAco VPAc PMMA

MMA co VB MMA-VB

MMA-VPAc PMMA PMMA PMMA PMMA

200-1500 200-1500 400 600

Attenuation

dB/km

at O nm

NA Remarks

11 1070 130 134 143 113 90 160 300

670 650 652 652 650 570 650 650

0.26 0.19

8 ˜100 m first GI-POF 670 nm: 300 MHz˜km IGPT, 260 MHz˜1 km IGPT,125 MHz 1˜km IGPT, 1,000 MHz˜km 'n=0.014, 8GHz˜50m 3 GHz˜100 m

88

2.3 The Development of POF

Table 2.9: Published data of PMMA-GI-, MSI- and MC-POF, continued Ref.

Year Producer Material

[Ish95] [Koi97b] [Tak98] [Tak98] [Tak98] [Tak98] [Mye02] [Shin02] [Liu02a] [Luv03] [Fuj04] [Rich04] [Yoo04] [Nuv05] [Nuv05] [Fuj06]

1995 1997 1998 1998 1998 1998 2002 2002 2002 2003 2004 2004 2004 2005 2005 2004

Keio Univ. Keio Univ. Kurabe Kurabe Kurabe Kurabe Dig. Optr. KIST Korea Huiyuan Luvantix Lumistar Optimedia Optimedia Nuvitech Nuvitech

Attenuation

Øcore μm

dB/km

at O nm

NA Remarks

150 132 145 159 329 350 120 160

650 650 650 650 650 685 650 650

0.20 0.26 0.33

200 200 180 180 100

650 650 650 650 850

0.40 0.40 0.25 0.30 ?

PMMA-DPS 500-1000

PMMA PMMA PMMA PMMA PMMA Polymer PMMA PMMA PMMA PMMA PMMA PMMA PMMA PMMA Lumistar-X new low loss

[Shi99] 1997 Mitsubishi PMMA

500 500 500 500 180 1000 ? 500 900 675 500 900 120 MSI-POF 700 210

650

585 MHz˜km 2 GHz˜100 m 2 GHz˜100m, PFM 2 GHz˜90m, PFM 680 MHz˜50m, PFM PFM no samples available g=2.4; 3.45 GHz˜100m since 2001 3.5 GHz bandwidth 3 Gbps˜50m commercially available commercially available 3 Gbps˜50m 3 Gbps˜50m 10 GHz˜50m

0.30 500 MHz˜50m, 4-7 layers (?)

(Eska-Miu)

[Lev99] 1999 RPC Tver PMMA/ 4FFA

800

400

650

7 layers, 310 MHz˜100 m

From the beginning of the 90s, it became possible to produce PMMA-GI-POF having an attenuation at 650 nm that is similar in quality to that of SI-POF. In doing so, it was possible to attain bandwidths up to 50 times larger which are adequate for transmitting several Gbit/s across distances up to 200 m. Likewise, multi-core and multi-step index POF achieve similar values for attenuation and allow data rates up to 1 Gbit/s across distances of 50 m, e.g. for applications in compliance with IEEE1394 (up to S800). The core diameter of all these fibers typically lies between 0.5 mm and 1 mm which means that existing reasonably priced connectors can be used. Multi-step index profile fibers - the last lines in the table - have been described in [She99] and [Lev99]. In the group headed by Prof. Levin, different materials were used for the production of layers with different refractive indices (P(MMA/4FFA), P(MMA/4FMA) and PMMA-naphthalene). The best results were obtained with the mixture PMMA/4FFA which has an attenuation of approximately 400 dB/km (at 650 nm) and a bandwidth of 310 MHz·100 m. The total number of 7 steps in the fiber with a core diameter of approximately 800 μm were produced in a preform and subsequently drawn. The ESKA-MIU has a core/cladding diameter of 700 μm/750 μm and also has several layers (probably between 4 and 7) which are produced by co-polymerization. Originally, 4 to 7 layers were presumably being aimed at but in the end this

2.3 The Development of POF

89

fiber with 3 layers was achieved as a product. It is said to be produced in a continuous drawing process. The bandwidth in [Shi99] is stated to be larger than 500 MHz ˜ 50 m. In several publications this fiber is called a GI-POF ([Sak98], [Num99]). The difference between this design and “genuine” GI fibers is primarily the larger core diameter. In [Num99] the attenuation of the fiber is stated as being 210 dB/km with an AN = 0.30, i.e. values that are comparable with the DSIPOF. Materials and measurements of the index profile will be discussed in the Section Production and Materials. Institutes and companies from South Korea have been very successful in producing PMMA GI-POF. In the past few years publications have come from: ¾ Department of Materials Science and Engineering, Kwangju Institute of Science and Technology (KIST), Kwangju ¾ Center for Advanced Functional Polymer, Department of Chemical Engineering, KAIST, Taejon, Korea ¾ E-Polymer Laboratory, SAIT, Taejon, Korea ¾ Optics Laboratory, Seoul, Korea ¾ Optimedia, Korea ¾ Nuvitech, Korea ¾ Luvantix, Korea The production method for GI POF is described in [Shin03]. A MMA-BzMA mixture is poured into a rotating cylinder. The purpose of the rotation is simply to form even concentric layers. The polymerization takes place thermally and the concentration of BzMA is continuously increased to 15%. This emerging preform is then drawn into a fiber. Figure 2.65 shows the pulse broadening for a 66 m long fiber which corresponds to a BLP of 3.45 GHz · 100 m. The smallest measured attenuation of the fiber is given at 120.6 dB/km. 1.2

Intensity [a.u.]

1.0 1m

66 m

0.8 0.6

99.5 ps

129.5 ps

0.4 0.2 0.0 t [ps] -0.2 0

200

400

600

800

1000 1200 1400 1600

Fig. 2.65: Pulse broadening in PMMA-GI-POF ([Shin03])

90

2.3 The Development of POF

Since 2004, a new GI-POF on a PMMA basis has been available on the market. The OM-Giga (see [Rich04] and [Yoo04]) has a core diameter of 900 μm or 675 μm respectively and a nearly parabolic profile. It is produced through polymerization of several layers, although the steps are almost completely smoothed through thermal treatment. According to the data sheets available in the Internet the fibers have the following parameters (Table 2.10). Table 2.10: Parameter of GI-POF OM-Giga Property core diameter diameter variations tensile strength bend radius temperature range attenuation bandwidth

Unit μm % N mm °C dB/km GHz

B-075 750 (675) ±5 > 35 25 -30 .. +60 < 200 > 1.5

B-100 1,000 (900) ±5 > 65 25 -30 .. +60 < 200 > 1.5

Remarks (GI-region) at break

at 650 nm for 100 m

The fact that this fiber possesses thermal stability comparable to a standard POF, different from GI-POF with doping, must be rated as a particularly great step. Even after 5,000 hours of operation at 80°C no change in the bandwidth could be determined. The cross-section of a 1 mm OM-Giga is shown in Fig. 2.66 (microscope photograph shown in wrong colors). The approx. 10 index steps can still be seen quite well.

Fig. 2.66: Cross section of an OM-Giga (POF-AC) and a MSI (Tver, [Ald05])

In Fig. 2.67 the change in the refractive index profile of a doped PMMA GI-POF is shown after accelerated aging (122 hours at +109°C, from [Bly98a] and [Bly98b]). You can see quite well that the index profile is still parabolic at the beginning of the aging process. The share of the dopants is the greatest in the center of the fiber which is why the glass transition temperature has sunk the most.

2.3 The Development of POF

91

The dopant diffuses outwardly. Consequently, the concentration increases outwardly, Tg also drops there and the diffusion process continues until the profile has almost become rectangular. The attenuation of the fiber will hardly increase, but the bandwidth drops dramatically. Decisive for the application temperature of the fiber is the dopant concentration in the axis.

Fig. 2.67: Change of the refractive index profile of a GI-POF by ageing

Measurements on OM-Giga at the POF-AC will subsequently be introduced. The results of a long-term temperature test are shown in Fig. 2.68. The bandwidth was measured for over 5,000 hours on a 50 m long sample in order to be able to determine changes in the index profile. 2500

measured bandwidth [MHz]

2000 1500 1000 500 70°C

80°C time [h]

0 0

400

800

1200

Fig. 2.68: Long-term behavior of OM-Giga

1600

2000

2400

92

2.3 The Development of POF

The frequency range of the network analyzer extended to 1.3 GHz. The values represented were determined through extrapolation and thus burdened with a relatively large error. A clear deviation from the parabolic index profile would in any event have caused a very strong decrease in the bandwidth. The stable bandwidth proves that co-polymerization is obviously a suitable means to produce thermally stable and thus long-life PMMA GI-POF. A comparison of the measured attenuation of ESKA-MIU and OM-Giga is shown in Fig. 2.69. The attenuation of the OM Giga is somewhat higher at 650 nm than that of the Mitsubishi fiber and also of the SI-POF. However, it clearly shows the greatest bandwidth.

1000 attenuation [dB/km] 800 600

OM-Giga

400

217 dB/km

300 200 ESKA-MIU

100 400

450

500

161 dB/km

550

600

650 700 wavelength [nm]

Fig. 2.69: Spectral attenuation of ESKA-MIU and OM-Giga

The Korean manufacturer Luvantix offers preforms for PMMA GI-POF ([Luv03] and [Kim03]). The index profiles from both refernces - measured values and approximation of each - are shown in Fig. 2.70. The authors do not know what relations exist between Luvantix as preform manufacturer and Nuvitech and Optimedia as fiber producers as well the different research institutes. Overall, however, POF production in South Korea seems to enjoy greater attention and more progress in the field is foreseeable. Other announcements concerning the production of GI-POF came from the USA (Digital Optronics and Nanoptics, [Wal02], [Mye02] and from China [Liu02a]). Since no data or even fibers are known from these producers they will not be considered in greater detail. In Sections 2.5 and 2.6 data on bending behavior and bandwidth are summarized. The production methods are presented in Section 2.8.

2.4 Glass Fibers for Short-Range Data Transmission

1.512

refractive index

1.510 AN = 0.21

1.510

1.500

1.506

1.495

1.504

1.490

1.502

1.485

1.500

refractive index AN = 0.32

1.505

1.508

1.480

theory

1.498

theory

1.475 measured

1.496 1.494 1.492 0.0

0.2

0.4

measured

1.470

rel. radius (r/rc) 0.6

0.8

1.465

rel. radius (r/rc)

1.460

1.0

93

0.2

0.4

0.6

0.8

1.0

Fig. 2.70: PMMA GI-POF index profile (left: [Kim03], right: [Luv03])

2.4 Glass Fibers for Short-Range Data Transmission 2.4.1 200 μm Glass Fibers with Polymer Cladding Thanks to their simple production and great robustness silica glass fibers with polymer cladding have been used for a long time. Figure 2.71 shows the principle structure. A core (typically with a diameter of 200 μm) of homogeneous SiO2 is surrounded by a high-strength, transparent polymer with smaller refractive indices (about 15 μm thick). ‡ 500 μm inner jacket

‡ 2.3 mm outer jacket ‡ 230 μm polymer

‡ 200 μm SiO2-core

Fig. 2.71: Structure of a 200 μm PCS

Production is so easy because the core is drawn from a quartz glass cylinder. The polymer cladding is applied by extrusion after it has cooled off. First of all, all glass fibers are extremely sensitive to water and must be protected by a plastic coating as thick as possible. Furthermore, pure glass fibers do not have a great

94

2.4 Glass Fibers for Short-Range Data Transmission

mechanical load capability. The polymer cladding gives the fibers the capacity to bear extreme loads. The jacketed fiber can thus hardly be shattered. Pure glassglass fibers (glass core with an optical glass cladding) are always surrounded by similar protective layers, e.g. acrylates which, however, do not have any optical function. Because of its refractive index and attenuation the polymer cladding determines to a great extent the optical parameters of the PCS. In short wavelength ranges the attenuation nearly corresponds to pure SiO2 fibers. Above approx. 1,000 nm the losses in the polymers are so high that the effective PCS attenuation also rises rapidly. Silica glass can endure temperatures up to 1,000°C, but not the polymer cladding. Consequently, the primary coating material determines the thermal and chemical characteristics. Most PCSs available in the market have been specified for an application temperature of +70°C. Some more recent types have been dimensioned for use in automobile networks for temperatures up to +125°C. Information on such PCSs can be found for example in [Hub03] and [Schö03]. Fig 2.72 has been taken from the latter work. You can clearly recognize how strongly the attenuation spectra of different PCSs can depend on the cladding materials selected.

10,000 attenuation [dB/km] 1000 100 diff. PCS 10 1 theoretical limit 0.1 200

400

600

800

1,000 1,200 1,400 1,600 1,800 wavelength [nm]

Fig. 2.72: Attenuation of different 200 μm PCS according to [Schö03]

Just as with glass-glass fibers the absence of water plays an important role for PCS for keeping losses low especially in the long-wave ranges. So-called all-silica fibers in which the optical cladding consists of silica glass are used at high temperatures. These fibers are also employed for the transmission of very high light power (working with lasers) since it is very important that no light is absorbed at the core-cladding interface layer.

2.4 Glass Fibers for Short-Range Data Transmission

95

Table 2.11 lists some of the representative types taken from a number of different PCS variants which differ in cladding material, core diameter and NA (data from [Hub03] and [OFS02]). Table 2.11: Properties of different PCS Parameter producer core/ cladding

NA D (820 nm)

bandwidth

Unit

All Silica High OH OFS μm 200/240 365/400 550/600 940/1000 0.22 dB/km 10 10 10 10 n. a. MHz ˜ km

bend radius (long term)

mm

temperature

°C

14 47 94 118 -65..+135

All Silica Low OH OFS 200/240 365/400 550/600 940/1000 0.22 8 8 8 10 n. a.

HCS High NA OFS 200/230 400/430

HCS PCS Low OH [Hub03] OFS Polymicro 125/140 200/230 200/230 300/330 400/430 0.43 0.37 0.37 6 12 6 8 6 8 8 n. a. 20 20 20 15 13 14 16 15 16 47 47 16 94 24 118 47 -65..+135 -65..+125 -65..+125 -40..+125

PCS are generally used in lengths of up to a maximum of 200 m. The attenuation then only amounts to a few dB which can for the most part normally be disregarded. If a LED is used as a transmitter, considerably less light will be coupled into the fiber than into a 1 mm POF. On the other hand, the light can be coupled more effectively into the photodiode. Different manufacturers even offer transmission systems which can work with the same plug construction with POF as well as with 200 μm PCS, e.g. [HP01]. system with 1 mm POF Popt [dBm]

system with 200 μm PCS

-4 -6 -8 -10 -12 -14 -16 -18 -20 -22 -24 -26 -28 -30 LED-power range (launched into the fiber) receiver sensitivity range allowed path loss (with margin) Fig. 2.73: Link power budget for POF and PCS

96

2.4 Glass Fibers for Short-Range Data Transmission

Fig. 2.73 shows power budgets for both possibilities, each with the same transmitters and receivers (system for 125 Mbit/s). The result for PCS is a permissible fiber attenuation of at least 11 dB - taking the system margin into consideration - thanks to the greater input power. In this way at least 20 m of POF can be bridged. The guaranteed loss for PCSs is only 7 dB. However, at least 100 m of fiber can be bridged, limited here due to the bandwidth. 200

max. bit rate [Mbit/s]

max. bit rate [Mbit/s]

max. at +25°C

max. at +25°C

100 70 40 20 10 10

recommended application area with PCS

recommended application area with POF

fiber length [m]

fiber length [m] 20

30

40

60

80 100 10

20

50

100 200

500 1000

Fig. 2.74: System parameters of the HP-system with POF and PCS (according to [HP01])

The bandwidth for PCS indicated in the data sheets has to be viewed with a certain degree of skepticism. Measurements conducted at the POF-AC show that all PCSs investigated with An = 0.37 at full launch have a BLP in the range of 5-7 MHz · km. This lies clearly below the specified data of 10-20 MHz · km. This is not a contradiction, however, since none of the manufacturers as a precaution provided any information about the measurement conditions. One reason may be that the PCS was developed for relatively low data rates (10 Mbit/s and less). The fiber bandwidth therefore did not play any role whatsoever while the POF was also designed from the very beginning for higher data rates. Diverse information and publications on bandwidth exist for the different polymer fibers as summarized in Chapter 2.5. The most recent draft for the standardization of PCS is viewed by the IEC as having a bandwidth of 5 MHz · km for fibers with a NA of 0.40 ± 0.04. A specific problem with PCS in the past was that the temperature coefficients of glass and plastic did indeed deviate considerably from one another. In the case of some fibers this resulted in a refractive index difference - and NA, too - which dropped to zero at low temperatures. This effect is shown in Fig. 2.75 taken from [Dug88]. Far field distributions are represented in the picture after 2 m of fiber at different temperatures. They were measured with laser stimulation at altered angles. In this case the optical cladding was a silicone plastic. Modern PCSs no longer show this effect.

2.4 Glass Fibers for Short-Range Data Transmission

97

rel. power

1.0 0.9

+40°C -2°C -31°C -51°C -65°C -72°C -92°C -98°C

0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0

T [°] -5

0

5

10

15

20

25

30

35

Fig. 2.75: Temperature dependence of PCS-NA, presented as far field

2.4.2 Semi-Graded Index Glass Fibers Up until some time ago this class of fibers was only available as a product from the manufacturer Sumitomo ([Sum03]). Except for the gradients introduced this fiber corresponds to conventional PCS. The index variation is attained by adding germanium which is also usual for silica glass. Even with normal 50 μm GI fibers the germanium share represents a considerable cost factor. The semi-GI PCS, however, has a 16-fold cross-section. This type of fiber is still extremely expensive. It is still open how far the price can drop when manufacturing greater lengths. In the meantime, OFS has appeared as a second manufacturer ([Ziem06i]). 100 80 60

spectral attenuation [dB/km]

40

Sumitomo

30 20

OFS

10 8 6 wavelength [nm] 4 450 500 550 600 650 700 750 800 850 900 950 1000 Fig. 2.76: Spectral attenuation of the semi-GI-PCS

98

2.4 Glass Fibers for Short-Range Data Transmission

Figures 2.76 and 2.77 show the attenuation curve and the pulse response of the semi-GI-PCS based on measurements made at the POF-AC. The following table gives the parameters from the data sheet - the bending radius and the operating temperature are not specified. The bandwidth and maximum data rate measurements are dealt with in the corresponding sections.

opt. power [a.U.] 1.0

full mode launch 500 m PCS

0.8 FWHM: 6.8 ns | 32 MHz˜km

0.6 0.4 0.2 0.0

t [ns] 0

10

20

30

Fig. 2.77: Pulse response of Semi-GI-PCS Table 2.12: Parameters of Semi-GI-POF Parameter

Unit

core cladding core structure NA GI-NA D (820 nm) bandwidth

μm μm n. a. dB/km MHz ˜ km

HG-series Sumitomo 200 230 n. a. 0.40 n. a. 6 100

Semi-GI V2 OFS 200 230 VAD/MCVD GI 0.36 0.275 8 48 (overfilled)

2.4.3 Glass Fiber Bundles 2.4.3.1 Quartz Glass Fiber Bundles Glass fiber bundles are employed in the most diverse areas. Above all, it makes sense to use them when a large light-guiding cross-section is to be combined with high cable flexibility. In optical measurement techniques bundles of quartz glass fibers are employed which permit a continuous high transmission rate in the range between 380 nm and 2000 nm. If you lay out the fibers differently at both ends of

2.4 Glass Fibers for Short-Range Data Transmission

99

the cable, then they can also serve as cross-section converters, e.g. monochromators. The end surfaces are usually prepared: the bundle is glued in the plug and then polished. Figure 2.78 shows an example.

Fig. 2.78: Example for a quartz glass fiber bundle

The transmission of such a bundle is shown in Fig. 2.79 (acc. to [Ori01]). The greatest part of the 100% missing share is determined by the only about 60% part of the core surfaces and the Fresnel losses. The numerical aperture of the bundle shown is 0.22, the length is about 1 m, and the single fiber diameter is 200 μm. 70% transmission 60% 50% 40% 30% 20% 10% 0% 200

wavelength [nm] 400

600

800

1,000 1,200 1,400 1,600 1,800 2,000

Fig. 2.79: Transmission of a quartz glass fiber bundle [Ori01]

100

2.4 Glass Fibers for Short-Range Data Transmission

2.4.3.2 Glass Fiber Bundles Pure quartz glass is many times more expensive than normal polymers but also as conventional mineral optical glasses. Attenuations of some 100 dB/km is absolutely acceptable for many applications, e.g. in lighting technology. Schott has been producing bundles of thin glass-glass fibers for quite some time. The index difference can be varied in diverse areas by choosing a particular glass composition. The spectral attenuation of a typical glass fiber bundle compared with a PMMA POF is shown in Fig. 2.80. The glass has higher losses in the blue areas whereby the cable length is limited when guiding white light. The POF has greater losses in the near infrared range.

1,000

D[dB/km]

500

POF MC-GOF

200 100 50 500 550

O [nm] 500 550 600 650 700 750 800 850

Fig. 2.80: Spectral attenuation of glass fiber bundles and POF

An entirely new application for such glass fiber bundles has come about with the ever increasing use of optical networks in vehicles. The previous systems are specified with 1 mm POF. Two parameters especially limit the use: the temperature range is limited to a maximum of +85º and the relatively large bending radius. Both limitations can be reduced considerably with glass fiber bundles, whereby the usual optical characteristics are for the most part retained so that the identical active components can be used. Table 2.13 from [Lub04b] compares the parameters of a glass fiber bundle (MC-GOF) with those of a POF for vehicle networks. The construction of the plug is especially problematical. The usual method of cementing and polishing takes too much time for mass production and results in the core surface having too low a share with correspondingly high losses with the plug connections. Megomat TS AG, working together with Schott, has developed a new kind of assembly procedure ([War03]). The actual fiber bundle has a diameter of 1.2 mm. The plug has a metal ferrule with a corresponding opening. During production the fiber bundle is heated to such an temperature that the glass can be compressed. The fibers are pressed closely together when crimped so that the diameter of the bundle is lowered to 1 mm.

2.4 Glass Fibers for Short-Range Data Transmission

101

Table 2.13: Comparison MC-GOF and POF Parameter core diameter cladding thickness number of cores ncore/ncladding numerical aperture attenuation at 650 nm bandwidth (full launch) bend radius temperature

Unit

MC-GOF

MOST-POF

[μm] [μm] [dB/km] [MHz·20 m] [mm] [°C]

53 3 approx. 400 1.585 / 1.49 0.50 250 150 5 -40 .. 125

1,000 r 45 10 1 1.49 / 1.40 0.50 160 >50 (200 typ.) 25 -40 ..85

The core share of the plug end face then amounts to about 85%. After the crimping the bundle is broken off and polished. Figure 2.81 shows a photo of the plug end face.

Fig. 2.81: Photograph of a MC-GOF

The irregular arrangement of fibers in the bundle leads to different patterns when pressed together. Neighboring fibers mostly form regular hexagonal structures which can, however, also have big gaps. Every once in a while linear structures with pentagonal fibers are formed. The individual fibers are deformed at the edge of the bundle, something which happens quite irregularly.

102

2.4 Glass Fibers for Short-Range Data Transmission

Fig. 2.82: Details of MC-GOF connector end faces

Fig. 2.83: Details of MC-GOF connector end faces

Since the bundle consists of about 400 individual fibers this irregular deformation of individual fibers does not play any role overall. Since the deformations only arise over a few millimeters there is no significant additional attenuation. In conclusion, Fig. 2.84 shows an x-ray photo of the bundle within the cable. The individual fibers have to move freely within the cable. When there is a tight bend the change in length is distributed on the inside and outside for a long stretch so that the fibers are only subject to a slight load. That is why the bundle can take bending radii of only a few mm.

Fig. 2.84: X-ray picture of a bundle

2.5 Bandwidth of Optical Fibers

103

2.5 Bandwidth of Optical Fibers In order to be able to determine the bandwidth of an optical fiber, several different influencing factors need to be considered. Mode dispersion and chromatic dispersion are the most important factors involved in multimode fibers. Particularly in the case of POF, mode dispersion depends on various parameters such as wavelength, the light launching conditions, refractive index profile, fiber-laying conditions as well as the homogeneity of the fiber's characteristics. In the following sections we intend to show how the conclusions drawn from basic physical processes can be used to explain values that are measured in reality. 2.5.1 Definition of Bandwidth It is possible to define the term bandwidth in quite different ways. Essentially it describes the frequency range of a system within which the transmission of signals can be achieved with reasonable attenuation. In POF systems, the limiting factor is usually the bandwidth of the fiber itself, which is created by modal dispersion. As we will demonstrate later on, one can describe the SI-POF as being very close to a Gaussian low pass filter. In this book we will use the following definition of bandwidth: f3dB : Frequency at which the amplitude of a sinus modulated monochromatic signal has been reduced to ½ of the optical level (see Fig. 2.28). Figure 2.85 schematically illustrates this definition. rel. opt. amplitude at fiber output 1.0

frequency response

0.5 bandwidth f3dB 0.0

frequency f

Fig. 2.85: Definition of POF bandwidth

Nonetheless, knowledge of the bandwidth alone is not adequate for estimating what the actual capacity of the complete link will be. In order to determine this parameter, it is further necessary to know the actual transmission procedure as well as the complete transmission function. For example, it is possible to transmit signals of significantly broader bandwidth if an electrical compensation of the frequency response takes place, as illustrated schematically in Fig. 2.86.

104

2.5 Bandwidth of Optical Fibers

P(f)POF

P(f)compensating filter

P(f)resulting

1.0

0.5

0

1

2

f

f

f [a.U.] 0.0

0

1

2

0

1

2

Fig. 2.86: Compensation of the POF low pass characteristic

A high pass filter is used for compensation. In the case of low frequencies, the signal is attenuated - in the case of higher frequencies the signal is passed through without attenuation. The resulting function has a significantly higher bandwidth; however, due to the overall existing level of attenuation, a higher level of signal is necessary. In addition, the type of signal involved (digital or analogue) is also of significance and finally the required system reserves must be considered. The following general relationship can be used as a rule of thumb for digital systems: maximum bit rate [Mbit/s] = 2 u bandwidth [MHz]. We intend here to look at bandwidth as a function of fiber characteristics. For this reason, the effect of chromatic dispersion will be initially neglected because it is directly proportionally dependent on the spectral width of the source. In this section we will show experimental investigations on the bandwidth of SI-POF fibers. After explaining the measurement procedures, we will show to what extent bandwidth is particularly dependent on the launching conditions. 2.5.2 Experimental Determination of Bandwidth As a frequency response multimode fibers show an almost Gaussian-like behavior: P( f ) P0 ˜ e

f 2 / f02

As can be easily demonstrated, the amplitude of a Gaussian low pass filter (P(f) = P0 · exp (f²/f0²)) for f = 1.17741 · f0 has dropped to half the value that applies for f = 0. When using a spectrum analyzer to measure the frequency response of a fiber link, it is necessary to determine the electrical 6 dB width because the photodiode will convert the optical power proportionally into a current. Therefore the following applies:

2.5 Bandwidth of Optical Fibers

Pel

105

2 Popt

Figure 2.87 shows an example for such a bandwidth measurement for a 30 m standard NA-POF.

-3 electr. power [dBm]

measured

-6 15 m SI 650 nm 239 MHz NA: 0.34

-9 -12

Gaußian approx.

-15 -18 1

10

100 f [MHz]

1,000

Fig. 2.87: Bandwidth measurement at a SI-POF

Due to the limited dynamics of the measurement system, the frequency response can be measured only up to a certain distance. In this case a measurement of up to 200 MHz was easily possible. The 3 dB bandwidth is found simply by determining the point at which the electrically measured transmission function has dropped by 6 dB, here approximately 150 MHz. Apart from the values actually measured, an approximation with a Gaussian low pass function has been entered into the figure. By determining the frequency f0 it is then possible to determine the bandwidth even when the measurement is not possible because of the limited dynamics or bandwidth of the measuring system. Figure 2.88 shows the measured transmission functions for a SI-POF and a DSI-POF of 50 m length each. The optical 3 dB bandwidth for an SI-POF is approximately 67 MHz, corresponding to a bandwidth-length product of 33 MHz · 100 m, with the NA of the fiber being 0.52. It follows that the measured value is substantially greater than had been theoretically expected (approximately 14 MHz · 100 m, see Fig. 2.31). For DSI-POF (AN = 0.30) the measured value is 130 MHz, corresponding to 65 MHz · 100 m, with the theoretical value being 42 MHz · 100 m. The measurement was carried out with a 520 nm LED. The LED had a wide emission angle so that approximate equilibrium mode distribution can be assumed.

106

2.5 Bandwidth of Optical Fibers

0 rel. power [dB]

50 m DSI-POF

-3

-6 50 m St.-NA-POF

-9

frequency [MHz]

-12 1

10

100

1,000

Fig. 2.88: Bandwidth measurement for SI-POF and DSI-POF

When measuring bandwidth, a two to four ranging factor of deviation from the theoretical value of an ideal SI fiber can be generally expected, even when working in an EMD condition. The reason for this is the combination of mode dependent attenuation and mode coupling described in Chapter 1. As a result of the continuous energy exchange that takes place between the faster and slower modes, the delay does not rise in proportion to the length. The increased attenuation of those beams having a particularly large propagation angle - many reflections at the cladding - has the additional effect of reducing the pulse width. Figure 2.89 shows the bandwidth measurement of a standard NA-POF for 3 different wavelengths for samples between 20 m and 100 m in length. 1000

bandwidth [MHz]

bandwidth [MHz]

GH 4000, St.-NA

ACU 1000, Low-NA

300 100

525 nm 590 nm 650 nm

525 nm 590 nm 650 nm

30

fiber length [m]

fiber length [m] 10

10

20

50

100 10

20

Fig. 2.89: Bandwidth of a SI-POF and a DSI-POF at different wavelengths

50

100

2.5 Bandwidth of Optical Fibers

107

Once again, the measurements in Fig. 2.89 were carried out with an LED having an emission characteristic near to EMD (see [Gor98] and [Rit98]). The figure reveals 2 significant items of information: ¾ ¾

The bandwidth of the POF does not decrease in proportion to the length-1; its decrease is less than proportional. The bandwidth of the POF is nearly identical for the 3 attenuation windows.

2.5.3 Experimental Bandwidth Measurements The section on experimental bandwidth measurements first summarizes the results from earlier technical literature. As we shall see, determining the bandwidth is among the most difficult metrological challenges with thick-core fibers. A series of systematic measurements on the most diverse fibers is introduced as a supplement to the first edition (Alexander Bachmann is responsible for the bandwidth measurements at the POF-AC, cf. for example [Bun02a] and [Ziem04a]). Since there are still no standards for the definition and measurement of bandwidth, the following description will therefore not represent the definitive assessment. 2.5.3.1 Bandwidth of SI-POF After presenting some examples of our own measurements in the previous section we will now compare these with measurements carried out by other authors. Some of the first efforts made to systematically investigate the bandwidth of SI-POF were undertaken by [Tak91], [Tak93] and [Rit93]. As shown in Fig. 2.90, the bandwidth was measured for SI-POF having lengths between 20 m and 100 m. The fiber used was an EH4001 by Mitsubishi with an NA of 0.47. The bandwidth was measured through the pulse broadening of a 660 nm laser pulse (150 ps). Different launching devices were used to vary the NA between 0.10 and 0.65. The detector used consisted of a wide area photo multiplier. 2,000

bandwidth [MHz]

launch conditions

1,000 500

AN Launch = 0.10 AN Launch = 0.65 theory

200 100 50 20 10 10

fiber length [m] 20

50

100

Fig. 2.90: Bandwidth measurement according to [Tak91]

108

2.5 Bandwidth of Optical Fibers

The results allow three significant conclusions: ¾

¾ ¾

The bandwidth of a SI-POF is always significantly higher than the theoretical values for a SI-POF under theoretical UMD conditions, even with full launching in the acceptance area. The measured bandwidth is strongly dependent on the launching conditions. Although the bandwidth difference for measurements using different launching conditions decreases with the increasing length of fiber, it is still clearly in evidence even after 100 m.

Figure 2.91 shows measurements of bandwidths for different detector NA, also taken from [Tak91]. In principle, detection with a small NA means the same limitation in mode number as launching light at a small angle so that it is not surprising to find that the value curves are similar. 1,000

bandwidth [MHz]

receiver detection angle range

300

AN Det = 0.22 AN Det > 0.65

100

theory 30 fiber length [m]

10 10

20

50

100

Fig. 2.91: Bandwidth measurement according to [Tak91] with different receiver NA

Another measurement of bandwidth on standard NA-POF (1 mm) is presented in [Tak93] (Fig. 2.92). Again, the measurement was carried out using the pulse method at 650 nm. Apart from measuring the bandwidth, the half far field width following the corresponding sample length was also determined. The bandwidth was calculated from the far field width as follows: 't mod

2 A N, FF

2˜n˜c

and therefore : B ˜ z

C 't mod

(C const.)

whereby tmod is the modal pulse propagation and B · z is the product of bandwidth and length. Parameter C is a free selectable constant which depends on the coupling conditions. The speed of light is c. In the formula AN , FF is not the fiber parameter indicated, but the value measured depending on length. For a sample length of 10 m, the difference between the measured bandwidth for launching the light with AN = 0.10 and AN = 0.65 is more than one order of magnitude. For lengths up to 100 m this factor decreases to 2.

2.5 Bandwidth of Optical Fibers 10,000

109

launching conditions

bandwidth [MHz] 3,000 1,000

AN Launch = 0.10 AN Launch = 0.65

300

theory based on far field width

100 30 10

20

50

fiber length [m] 100

Fig. 2.92: Bandwidth according to [Tak93]

When launching light with a small NA, the bandwidth drops disproportionately, from approximately 80 MHz ˜ km to approximately 16 MHz ˜ km. This suggests an increasing filling out of modal field. By comparison, when launching with a large NA, the bandwidth is reduced somewhat more slowly than the length, from approx. 4 MHz ˜ km to approx. 5 MHz ˜ km. This is due to the effect of mode coupling and mode related attenuation. The bandwidth values determined by means of the far field width correlate very well with the results of the bandwidth measurements made by pulse propagation. This suggests that mode dependent attenuation and mode conversion are the determining processes because they affect the bandwidth by changing the mode distribution. In contrast, if mode coupling were more pronounced, the bandwidth would also change without affecting the far field. However, any estimated quantification based on these measured results alone would be questionable. In [Rit93] measured results for the bandwidth of standard NA-POF at launching conditions of AN = 0.10 and AN = 0.65 (Fig. 2.93) are also shown.

5,000

launching conditions

bandwidth [MHz]

2,000

AN Launch = 0.10 AN Launch = 0.65

1,000 500 200 100 50 20 10

30

100

300

fiber length [m] 1,000

Fig. 2.93: Measured bandwidth of a SI-POF according to [Rit93]

110

2.5 Bandwidth of Optical Fibers

Here too, the measured bandwidth for short lengths (20 m) differs by more than an order of magnitude. For large lengths the difference is reduced correspondingly. The authors calculate the bandwidth based on their own theory that follows the concept of the diffusion model. Instead of investigating separate modes, this model investigates modal groups that differ in their 2 angles of propagation (radial and azimuthally). The coupling between the modes is described by a diffusion constant that only takes into account the energy transfer in neighboring mode groups. The model also takes into account mode dependent attenuation. In this work the remaining deviation between theory and measured values is explained by means of the mechanism of mode coupling. In variance to the model, this is a factor that is not independent of the angle. Simulations provide good results if elongated scattering centers of 37 μm length and 2.5 μm diameter are assumed in the fiber with random distribution and orientation along the axis of the fiber (caused by the drawing process), as shown schematically in Fig. 2.94.

scattering centers

Fig. 2.94: Model for scattering centers in POF

An indication of a non-uniform inner structure of the PMMA fiber is the photo (from >Fei00@) of the surface of a cut POF taken by a scanning electron microscope and shown in Fig. 2.95. The fibril-like structures in the sub-Pm range can clearly be seen.

Fig. 2.95: Microscopic structure of a PMMA POF cut ([Fei00])

2.5 Bandwidth of Optical Fibers

111

Figure 2.96 shows further experimental results for the bandwidth of polymer optical fibers [Kar92]. In each case collimated light or light with an angle adapted to the fiber's NA (UMD) was launched into the POF. As was the case in the results previously shown, very large differences result for short lengths of fibers. The parameter shown in the figure here is the product of bandwidth and length. 50

bandwidth length product [MHz˜km]

launching conditions collimated 1.0 mm 0.5 mm

20 10

UMD 0.5 mm 1.0 mm

5 sample length [m] 2

5

10

20

50

100

200

500

Fig. 2.96: Measured POF bandwidth of a SI-POF according to [Kar92]

Apart from the effect of the launching NA, [Kar92] also investigates whether the bandwidth depends on the size of the launched beam. In fact, for UMD launching, a larger bandwidth was found as well as a smaller light spot, compared with complete illumination of the fiber cross-section; however, the differences are not as pronounced as when the launch angle is changed. For collimated light the relationship is reversed. Because all processes described up to this point are only dependent on the angle, it seems surprising to find that the size of the launching spot has an effect on the measured bandwidth of SI fibers. However, when considering the fact that mode conversion can cause deviations in location and deviations in angle after just a short length of the specimen (see schematic in Fig. 2.97), the result becomes understandable [Kar92].

bending deviation in location deviation in angle

Fig. 2.97: Conversion of spatial and angular distances

112

2.5 Bandwidth of Optical Fibers

In [Poi00] the results of [Kar92] are compared with current measurements on 2 standard NA-POF by Toray and Mitsubishi (Fig. 2.98). These measurements qualitatively confirm the previous results. For very short lengths of samples the differences between small and large launching angles are even greater.

30,000 bandwidth [MHz] Toray Mitsubishi [Kar92] Toray Mitsubishi [Kar92]

10,000

3,000

NALaunch: 0.09 0.09 collimated 0.64 0.64 UMD

1,000 theory 300 100 length [m]

30 1

3

10

30

100

300

Fig. 2.98: Measured bandwidth of different SI-POF according to [Poi00]

2.5.3.2 Bandwidth Measurements on SI-POF This section as well as the following four sections deals with bandwidth measurements conducted at the POF-AC Nürnberg. All measurements were carried out under uniform measurement conditions. Semiconductor diodes with a wavelength of 650 nm or 850 nm respectively served as transmitters. Both lasers can be modulated analogously up to 2 GHz. A singlemode glass fiber is mounted firmly to the laser diodes. Using a combination of different microscope lenses and optical apertures the coupling angle in the area AN Launch = 0.01 to 0.64 can be varied. The coupling spot is directly visible through a beam splitter. With the aid of adjustment screws the size as well as the position of the light spot can be changed. Figure 2.99 shows the complete setup of the measurement device. A commercial product on the basis of a 400 μm Si-PIN photodiode with an integrated preamplifier and about 1.5 GHz bandwidth was used as a receiver. In order to attain mode independence the receiver was connected to a 1 mm mixed glass fiber bundle with a large NA.

2.5 Bandwidth of Optical Fibers

113

Fig. 2.99: Experimental setup of bandwidth measuring by POF-AC

The lengths and NA-dependent bandwidths were systematically measured for a series of different step index profile fibers. An overview can be found in [Bun02a]. The following Figs. 2.100 to 2.102 show the results for three types of fiber: ¾ 1 mm standard PMMA POF with AN = 0.46 ¾ 1 mm standard POF made of cross-linked PMMA with AN = 0.54 ¾ 1 mm polycarbonate POF with AN = 0.75 B3dB [MHz]

5,000

NAlaunch: 0.64 0.48

2,000 1,000

0.33

500

0.19

200

0.09 0.05

100 50 length [m]

20 5

10

20

50

100

Fig. 2.100: Bandwidth measurement of a 1 mm SI-PMMA-POF

114

2.5 Bandwidth of Optical Fibers

For a 1 mm PMMA POF (Toray PFU CD1000, see also [Ziem04a]) 3 dB bandwidths for lengths between 5 m and 100 m were measured. The coupling angle was changed for NA values between 0.05 and 0.65 with the unit described above. For short fiber lengths the bandwidths measured differ by almost a magnitude which demonstrates once again the importance of correct measurement conditions for correctly indicating the bandwidth values. After a 100 m test length there still is a factor of two between the values measured. The curves for under filled launch (small NA) fall more steeply than with length caused by a predominance of mode mixing. For overfilled launch (large NA) the curves run flatter. Here the modedependent attenuation dominates. The next figure shows the results with a 1 mm POF made of modified PMMA (Toray PHKS CD1001). The fiber is specified with a NA of 0.54. NAlaunch:

B3 dB [MHz]

3,000

AN = 0.05 AN = 0.09

1,000

AN = 0.19 AN = 0.33

300

AN = 0.48 AN = 0.64

100 30 5

10

20

100 length [m]

50

Fig. 2.101: Bandwidth measurement of a 1 mm SI-mod. PMMA-POF

Since the losses of this fiber lie at about 300 dB/km at 650 nm, test lengths of only up to 50 m could be measured. Incidentally, the measurement results are similar to a large degree to the results of the PMMA POF. 3.000

NAlaunch:

B3 dB [MHz]

AN = 0,05

1.000

AN = 0,09 AN = 0,19

300

AN = 0,33 AN = 0,48

100

AN = 0,64 length [m]

30 1

2

5

10

Fig. 2.102: Bandwidth measurement of a 1 mm SI-PC-POF

20

2.5 Bandwidth of Optical Fibers

115

The third fiber tested is the polycarbonate POF FH4001 from Mitsubishi. The NA of the fiber lies at 0.75, the attenuation amounts to 650 nm at about 800 dB/km, whereby the maximum measurement length remains limited to 20 m. Surprisingly, the bandwidth differences between the three types of fiber are only very slight although there were clear differences in the NA. One explanation for this could be the greater effects for mode mixing and above all for the modedependent attenuation which occurred in the fibers made of modified PMMA and polycarbonate. Figures 2.103 and 2.104 illustrate the far fields of the three fibers in comparison (cf. [Bun02a]). 3.000

B3 dB [MHz] PC PHKS PMMA

1.000 300 NALaunch = 0.33 100

length [m]

30 2

5

10

20

50

100

Fig. 2.103: Comparison of the bandwidths of different SI-POF 1000

power [a.U.] mod. PMMA

800 PC

600 PMMA 400 200

T [°] 0 -40

-30

-20

-10

0

10

20

30

40

Fig. 2.104: Comparison of the farfields of different SI-POF

The fibers of PMMA and PC - each after 10 m - have half-value widths of about 27°. The fibers of modified PMMA have only 17°. Here the share of modedependent attenuation predominates over the nominally larger NA.

116

2.5 Bandwidth of Optical Fibers

Fig. 2.105: Comparison of the far fields of different SI-POF (3-d representations)

As part of the European Project POF-ALL (www.ist-pof-all.org) other comprehensive measurements of both length and launch-dependent bandwidths of different fibers were carried out. The following Figures 2.106 and 2.107 show the measurement results for a 1 mm standard POF (Luceat, high quality fiber) and for a 500 μm standard POF. 10,000

B3 dB [MHz]

NALaunch 0.05

5,000

0.10

2,000

0.19 0.34

1,000

0.47

500

0.65

200 100 50 1

2

5

10

20

50 100 fiber length [m]

Fig. 2.106: Bandwidth measurements of a 1 mm SI-POF (Luceat, HQ)

Both fibers essentially show comparable results. Since the fibers also have very similar attenuation values they can be used in almost all the same applications. The advantages of the thinner fibers are primarily the smaller space needed, an important point with multiple cables, and the smaller bending radius. The argument that the fibers with a smaller core diameter would enable higher bit rates or better receiver sensitivity because of the smaller photodiodes has for the most part since been dropped because of technical developments.

2.5 Bandwidth of Optical Fibers

10,000

B3 dB [MHz]

117

NALaunch

5,000 0.05 0.10

2,000

0.19 1,000

0.34

500

0.47 0.65

200 100 50 1

2

5

10

20

50 100 fiber length [m]

Fig. 2.107: Bandwidth measurements of a 0.5 mm SI-POF

2.5.3.3 Bandwidth Measurements on MC- and MSI-POF Multicore and multistep index profile POFs allow significantly greater bandwidths than conventional step index profile fibers. In the case of MC-POFs the differences in propagation time between the different individual cores, in addition to mode dispersion, have to be added. The pure length differences, however, should hardly play a role. The pure path differences alone between the modes amount to about 6% at a maximum propagation angle of 20° in the fiber. Since the fibers lie well-ordered in the MC-POF the geometric differences in length lie at the most in the thousandth range. Of greater significance is the fact that the fibers in the MC-POF are deformed in different ways. For example, differences among the fibers in the middle and at the edge of the bundle can already be seen in the attenuation. These differences are also formed for the mode selective processes resulting in different average propagation speeds in the individual cores.

launching with magnified light spot: - medium fibers obtain small angles only - outer fibers obtain large angles

launching with mode field converter: - all fibers obtain around the same optical power and rays of all angles

Fig. 2.108: Optimal launching into multicore fibers

118

2.5 Bandwidth of Optical Fibers

In order to register these effects when making a measurement, a so-called mode field converter (MFC) is used. The coupling unit shines into a short piece of SI fiber with a large NA. The far field distribution remains intact as the light is distributed over the fiber cross-section. This ensures that the individual fibers receive approximately identical light intensity and comparable angle distributions. The difference between this arrangement as opposed to a simple widening of the light spot is depicted schematically in Fig. 2.108. As indicated above, there are in the meantime different MC-POFs. Here we wish to present the results of the bandwidth measurements of two 1 mm MC-POFs with 37 cores (Fig. 2.109) and 217 cores (Fig. 2.110, see also [Ziem02a]). 2,000 B3 dB [MHz]

launch NA: AN = 0.09

PMC 1000 37 cores

AN = 0.19 AN = 0.33 AN = 0.48 AN = 0.64

1,000 500

200 length [m] 100 20

30

40

60

80

100

Fig. 2.109: Bandwidth measurements of a 37-cores MC-POF (measured on single samples)

2,000 B3 dB [MHz]

MCS 1000 217 cores

launch NA: AN = 0.09 AN = 0.19 AN = 0.33

1,000

AN = 0.48 AN = 0.64

500

200

100 20

30

40

60

80 100 length [m]

Fig. 2.110: Bandwidth measurements of a 217-core MC-POF (measured on single samples)

2.5 Bandwidth of Optical Fibers

119

Both fiber types show considerably greater bandwidth values compared to standard SI-POF. The 37 core fiber above all shows hardly any drop in the bandwidth over great lengths, especially since the dependence on the coupling conditions is very small. The reason is the very great mode dependence of the attenuation. This fiber possesses a double step index structure. Using a laser coupling it has been possible to transmit 1 Gbit/s over this fiber for 100 m. Systematic investigations of the bandwidth have been carried out at the POF-AC on a 37 core POF sample with a relatively small diameter (400 μm). The results for the two different NA are shown in Fig. 2.111. The bandwidth of this fiber is almost independent of the launch conditions. The reason for this is the strong mode-dependent attenuation which, as described above, occurs intensively with very thin fibers and leads to a equilibrium mode distribution after very short lengths.

B3 dB [MHz] 10,000 NALaunch 0.05

5,000

0.65

2,000

1,000

500

200 0.1

0.3

1

3

10

30 100 fiber length [m]

Fig. 2.111: Bandwidth measurements of a MC-POF (measurements on a single fiber sample, cut-back method)

Multi step index fibers have already been introduced by different manufacturers. However, they are not yet ready to go into mass production. The youngest product so far is the ESKA MIU from Mitsubishi-Rayon, a fiber with three different layers. Using a sample length of 100 m of this fiber, a bandwidth of almost 300 MHz was ascertained. Figure 2.112 shows the frequency response.

120 3

2.5 Bandwidth of Optical Fibers

rel. level [dB] NA 0.10 NA 0.34 NA 0.64

0 -3 -6 -9 -12 -15 -18 -21 -24 10

20

50

100

200

500 1000 frequency [MHz]

Fig. 2.112: Frequency responses of a 100 m MSI-POF

2.5.3.4 Bandwidth Measurements on GI-POF The bandwidth measurements of graded index profile fibers are associated with a series of particular difficulties. First of all, the attenuation is relatively high with polymer fibers so that the sample lengths can not be very great because of the limited dynamics of the measuring system. For PMMA POF the maximum measuring lengths lie between 50 m to 100 m. For PF GI-POF lengths of some 100 m can be used. On the other hand, POFs have a relatively large core diameter. The detector must be relatively large in order to record most all modes and thus obtain a meaningful bandwidth measurement. Then again the size of the diode limits the bandwidth of the detector. The only commercially available measuring system that can be used for this special task is the optical oscilloscope from Hamamatsu (described in the Chapter on measurement techniques). However, only measurements in the time domain are possible. The bandwidths of PMMA GI-POF and PF-GI-POF have been measured at the POF-AC. The transmission functions for the PMMA GI-PF OM-Giga from Optimedia (see also [Yoo04], [Rich04]) and a PF-GI-POF (Nexans, see [Gou04]) are illustrated in Fig. 2.113 and 2.114. The optical bandwidth of the fiber at 1.504 MHz was ascertained by adapting the measuring curve to a Gaussian function. This value, however, can clearly fluctuate with slightly altered launch conditions. The measuring conditions lie close to the “worst case scenario”. When there is under-launching, e.g. with a VCSEL transmitter, even greater values can be attained.

2.5 Bandwidth of Optical Fibers

121

rel. electr. level [dB] 0 -1 -2 -3 50 m OM-Giga OLD = 650 nm ANLaunch = 0.34

-4

f3 dB opt. = 1,504 MHz -5 frequency [MHz] -6 10

20

50

100

200

500

1,000

Fig. 2.113: Frequency response of 50 m OM-Giga (AN = 0.34; 650 nm)

In order also to be able to measure bandwidths of several GHz with thick core fibers, an optical oscilloscope is a practicable device, whereby the widening of a short laser pulse (about 120 ps) is measured. In [Lwin06] the results for the OM-Giga are shown compared with the microstructured POF (with effective graded index profile). 350 pulse broadening [ps] 300 Optimedia 1,000 μm 250 200

MPOF: 500 μm

150 length [m] 100 15

25

35

45

55

65

Abb 2.114: Pulse broadening measurement of a MPOF and GI-POF

A pulse width of about 340 ps corresponds approximately to an optical bandwidth of 1.4 GHz. The value matches pretty much the measurements in the frequency range when taking the various problems of measurement techniques with such large frequencies into account.

122

2.5 Bandwidth of Optical Fibers

The next illustration shows the frequency response for a PF-GI-POF at the wavelengths 650 nm and 850 nm together with the fitted Gaussian functions.

rel. electr. level [dB]

+1

measurement 650 nm Gaussian fit 650 nm measurement 850 nm Gaussian fit 850 nm

0 -1 -2 -3 -4

300 m PF-GI-POF OLD = 650 nm/850 nm ANLaunch = 0.10

-5 -6 0

200

400

600

800

1000

1200

frequency [MHz] Fig. 2.115: Frequency response of a PF-GI-POF

The 3 dB bandwidths are around 1,600 MHz for both fibers. The bandwidthlength product is at about 500 MHz · km, somewhat in the range of conventional multimode graded index glass fibers (cf. further results in [Bach01]). 2.5.3.5 Bandwidth Measurements on MC-GOF and PCS

The bandwidth measurement of multimode glass fibers proceeds according to the same principles. First, the glass fiber bundles from the Schott manufacturing company are measured. The bundle consists of about 400 individual fibers each having a diameter of 53 μm. The fibers have been hot pressed into the plug so that the overall diameter is about 1 mm. In Fig. 2.116 the frequency response for various coupling conditions are shown. The NA of the fiber lies at 0.50. The fiber bandwidth does not recognizably change when coupling in at great angles. With full mode launch the measured bandwidth amounts to about 150 MHz · 20 m which is almost exactly the same value as for SI-POF with a comparable NA. Consequently, this fiber type can be used alternatively to the 1 mm St.-NA POF when either high temperatures or very tight bending radii are necessary ([Lub04b]).

2.5 Bandwidth of Optical Fibers

2

123

rel. electr. level [dB]

0 -2 20 m fiber at 650 nm

-4 -6

launch NA: -8

-14

AN = 0.10 AN = 0.34 AN = 0.46 AN = 0.60 AN = 0.64

-16 10

20

-10 -12

f [MHz] 50

100

200

500

1000

Fig. 2.116: Bandwidth measurement of 20 m MC-GOF

In another series of measurements the length dependence of the bandwidth of MC-GOF was investigated. Fig. 2.117 shows the results for 3 different launch conditions. The bandwidth decreases almost linearly with the length so that one can assume that the influence of mode mixing is relatively small. B3 dB [MHz] 1 mm MC-GOF 375 cores NAfiber: 0.50 O = 650nm

3,000

1,000 launch NA: AN = 0.64 AN = 0.34

300

AN = 0.10

length [m] 100 2

5

10

20

50

Fig. 2.117: Length- and NA-dependent bandwidth of MC-GOF

Finally, the bandwidth for different lengths was determined using a 650 nm laser. In order to be able to make measurements relatively independently of mode, a 1 m long SI-POF was used as an adapter fiber at both the transmitter and the receiver. Figure 2.118 shows the results.

124

2.5 Bandwidth of Optical Fibers

1000

B3 dB, opt. [MHz]

excitation by laser NAlaunch | 0.30 O = 650 nm

500

200 length [m] 100 10

20

30

40

50 60

Fig. 2.118: Bandwidth of a MC-GOF excited by a laser source

This type of fiber is suitable for the transmission of data rates in the Gbit/s range over lengths of 10 m to 20 m. Another glass fiber version which has gained increasing attention is the PCS, i.e. silica glass fibers with a polymer cladding. The typical NA lies around 0.37. However, there are versions available with a NA up to 0.48. Accordingly, the bandwidth of PCS should lie in the range of DSI-POF. At the POF-AC predominantly fibers with a core diameter of 200 μm - the most commonly used value were measured. In Fig. 2.119 the length and launch-dependent results for a typical PCS are represented. The fiber, 200/230 μm with a 500 μm primary coating, was laid out for this measurement as a loose bundle with a diameter of about 30 cm (see also [Ziem04a]). 2000

B3 dB [MHz] launch NA: 0.02 0.09 0.17

1000 500

0.26 0.34 0.46

200 100 50 20 10

200 μm PCS loose bundle 20

length [m] 50

100

200

500

Fig. 2.119: Bandwidth of a 200 μm PCS

This fiber was specified with a bandwidth of 100 MHz · 100 m. This value can be achieved for an under filled launch. For a full launch, however, you can only attain about 60 MHz · 100 m. The differences between the different launch condi-

2.5 Bandwidth of Optical Fibers

125

tions hardly decreases with fiber lengths up to 250 m. Mode mixing hardly occurs with this measurement. The measurement was repeated for the same type of fiber, whereby the fiber was wound around a spool. The results are shown in Fig. 2.120.

2000

bandwidth [MHz]

launch NA: 0.02 0.09 0.17

1000 500

0.26 0.34 0.46

200 100 200 μm PCS fiber on a spool

50 20 10

20

50

length [m] 100

200

500

Fig. 2.120: Bandwidth of a 200 μm PCS

The results pretty much agree for short fiber lengths. For longer lengths, however, the differences roughly disappear between the different launch conditions for the rolled up PCS. This can only be explained by a recognizable increase in the mode mixing. The bandwidths dependent on the coupling NA are compared for 250 m long samples in Fig. 2.121. 90

Bopt, 3 dB [MHz]

250 m PCS

80 70 60 50 40

fiber on a spool

30

loose bundle

20 10

launch NA

0 0.00

0.10

0.20

0.30

Fig. 2.121: Bandwidth comparison of 250 m PCS

0.40

0.50

126

2.5 Bandwidth of Optical Fibers

Examinations of the different types of 200 μm SI-PCS confirm the measurements mentioned above. The specified bandwidth-length products of 10 to 20 MHz · km could be attained for all fibers examined only with under filled launch. Unfortunately, none of the currently active manufacturers provided any data on measurement conditions for the bandwidths indicated. Even the corresponding standards are completely missing. Should PCS seriously advance into areas of application in which the available bandwidth is to be completely used, then a lot of work still has to be done in this area. A comparison between the launch-dependent bandwidths is represented in Fig. 2.122.

40

B˜L [MHz ˜ km]

30 20 15 10 8 6 4 0.0

0.1

0.2

0.3

0.4

0.5 launch NA

Fig. 2.122: Bandwidth dependence on launch conditions for 5 different PCS types

A number of publications, especially in regard to applications in the GigabitEthernet and 10Gigabit-Ethernet ranges, exist for a bandwidth of 50/125 μm GI glass fibers. Articles providing an overview include [Oeh02] and [Bun03a]. With GI glass fibers, too, keeping the exact parabolic index profile as well as the mode-selective coupling play the most important role in achieving large bandwidths. Originally, two different types of fibers were specified: ¾ customary in the USA: 62.5/125 μm fiber (AN = 0.275 ± 0.015) ¾ customary worldwide: 50/125 μm fiber (AN = 0.200 ± 0.015)

The typical bandwidth-length product is 160 MHz · km to 200 MHz · km (62.5 μm) when using an 850 nm LED as emitter. 500 MHz · km is attained with 1,300 nm laser emitters. The limiting factor is the refractive index dip in the middle of the fiber which is caused by the production technology.

2.5 Bandwidth of Optical Fibers

127

For fast Ethernet (125 Mbit/s) the bandwidths entirely suffice to bridge distances of up to 1 km. The first range limitations (maximum of 275 m at 850 nm emitters and 62.5 μm fiber) arise with Gigabit-Ethernet so that a new class of fibers (OM2) has been defined which generally guarantees a transmission range of 550 m. In the worst case a data rate of 10 Gbit/s could be transmitted on OM1 fibers over about only 30 m. OM2 fibers are also limited to about 80 m. In order to be able to transmit high data rates, three different procedures have been suggested: ¾ Splitting the data rate into 4 × 2.5 Gbit/s which are then transmitted by WDM on a fiber. ¾ Emitter with so-called Restricted Mode Launch (RML) or Effective Laser Launch (EL) respectively, whereby the power is coupled if possible within the annulus with a diameter of between 4.5 μm and 19 μm. Moreover, the NA of the emitter may not be too large. ¾ Use of the new OM3 fiber class which has been optimized for the employment of 850 nm VCSEL.

An overview of the specified characteristics of the different GI-GOFs is presented in Table 2.14. Specific products can on occasion clearly surpass these parameters. Table 2.14: Properties of MM-GI glass fibers OM1

OM2

OM3

OM3 550m

Fast Ethernet

Gigabit Ethernet

10Gbit Ethernet

10Gbit Ethernet

[μm]

50/62.5

50/62.5

50

50

D at 850 nm

[dB/km]

3.5

3.5

3.5

3.0

D at 1.300 nm

[dB/km]

1.5

1.5

1.5

1.0

BW 850 nm (OFL)

[MHz˜km]

200

500

1,500

3,500

BW 1.300 nm (OFL)

[MHz˜km]

500

500

500

500

BW 850 nm (LD)

[MHz˜km]

n.d.

n.d.

2,000

4,700

Class

Unit

typical applications core-‡

(OFL: Overfilled Launch)

Other less customary fiber types are, for example, GI-GOF with a core diameter of 100 μm and a cladding diameter of 140 μm. Fig. 2.123 shows the frequency response of a 500 m long sample with three different launch conditions. At 200 MHz · km the results lie in the range of the fiber specifications. The last fiber presented here is the semi-GI-PCS described above. The measurement conditions become extremely more noticeable here so that the measurement results shown may not be conclusively representative.

128

2.5 Bandwidth of Optical Fibers

1

rel. electr. level [dB]

0 -1

500 m fiber at 650 nm

-2 -3 -4

launch NA: AN = 0.10 AN = 0.34 AN = 0.64

-5 -6 -7 -8 1

10

100

f [MHz] 1000

Fig. 2.123: Frequency response of a 100 μm GI-GOF

Fig. 2.124 first shows the frequency response with a 500 m long sample for 6 different launch conditions measured at a wavelength of 650 nm.

rel. opt. power [dB] 0 AN Launch = 0.03 .. 0.64

-2 -4 -6

500 m Semi-GI-PCS

-8 -10 -12

1

3

10

30

100 300 frequency [MHz]

Fig. 2.124: Bandwidth of a Semi-GI-PCS

The bandwidth-length product of the fiber was determined as having values between 24 and 55 MHz · km which clearly lies above the specification of 100 MHz · km. Bandwidths with their length and launch dependence are also determined for this type of fiber. Fig. 2.125 summarizes the results.

2.5 Bandwidth of Optical Fibers

129

3000 B3 dB [MHz] launch NA: AN = 0.02 AN = 0.09 AN = 0.17 AN = 0.26 AN = 0.34 AN = 0.46

1000

300

100 length [m] 30 10

20

50

100

200

500

1000

Fig. 2.125: Bandwidth measurement of Semi-GI-PCS

What is striking is the low dependence of the bandwidth on the launch conditions with longer sample lengths. Evidently, there is a significant exchange of energy between the SI and GI modes in the fiber. The specified bandwidth value could only be determined in short fiber lengths with under filled launch. Bandwidth measurements on semi-GI PCS have also been published by [Aiba04] and [Aiba05], whereby a method was used in which a light pulse circulates in a 100 m long ring and passes an acousto-optic modulator after every pass. The numerical aperture of the coupling optics amounts to only 0.25 and SI modes are for the most part suppressed. The results for the frequency response, determined by Fourier transformation, are shown in Fig. 2.126. 0

rel. opt. power [dB] 1st circulation

-2

10th circulation

-4 -6 -8

f [GHz] -10 0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

Fig. 2.126: Frequency responses of a Semi-GI-PCS according to [Aiba04]

The bandwidths thus determined are shown in Fig. 2.127. The values lie higher by a factor of ten than the values measured with full launch on long fibers. This

130

2.5 Bandwidth of Optical Fibers

reveals impressively how important correct specifications of the measurement conditions are when indicating bandwidth values. The succinct statement in the Sumitomo data sheet that “the bandwidth can change under other measurement conditions” is of little help.

2.0

B3 dB, opt. [GHz] semi-GI -PCS

1.5 1.0 0.8 0.6 0.4 0.3 100

length [m] 200

400

600

1000

Fig. 2.127: Bandwidth of a Semi-GI-PCS according to [Aiba04]

2.5.3.6 Comparison of Bandwidth Measurements and Calculations

The diverse measurements of fiber bandwidths show that the same principles are essentially valid for thick glass and polymer fibers. Important effects are: ¾The bandwidth drops with the square of the numerical aperture by increasing the differences in propagation time among the individual modes. ¾The diameter of the fiber does not play any role in regard to the bandwidth. ¾Strong mode-dependent attenuation increases the bandwidth of fibers, but it also leads to a rise in transmission losses. ¾Multicore fibers and fiber bundles permit smaller NAs with the same bending radius and thus greater bandwidths. ¾The bandwidth of fibers greatly depends on the launch and detection conditions. The difference can be » 10 for short fiber lengths. When stating the bandwidth in data sheets, measurements should always be made with UMD (full launch) or EMD (equilibrium mode distribution). ¾Graded index profiles increase the bandwidth up to two magnitudes. However, the index profile must be as ideal as possible - it should be parabolic when the chromatic dispersion is disregarded. ¾In the case of a non-ideal GI profile a large bandwidth can still be attained through a selective launch. ¾In addition, the chromatic dispersion especially with glass GI fibers has to be taken into account (this will be discussed in the next paragraph). ¾It is technically easier to produce a multi-stepped index profile, with which the bandwidth can clearly be increased, than a GI profile.

2.5 Bandwidth of Optical Fibers

131

¾Semi-GI fibers have large bandwidths, above all over short lengths and when coupling into small angles. ¾The bandwidth of individual fibers - not yet placed in cables - under laboratory conditions can depend to a great extent on the external conditions, depending on the degree of induced mode coupling.

A comparison between POF and PCS is particularly interesting since both can be used alternatively in many applications. The length-dependent bandwidths of both types of fiber with full launch are illustrated in Fig. 2.128. B3 dB, opt. [MHz] 1.000 PCS, NALaunch = 0.48 POF, NALaunch = 0.64

300

100

30

length [m] 3

10

30

100

Fig. 2.128: Bandwidth comparison of POF (fiber-NA: 0.50) and PCS (NA: 0.37)

Theoretically, the PCS should show about 50% greater bandwidth because of its smaller NA - which has just about been confirmed by measurements. Both measurement curves run approximately parallel which suggests similar magnitudes in mode-dependent processes. The angle-dependent attenuation of a typical PCS fiber is illustrated in Fig. 2.129. 225 excess loss [dB/km] 200 175 150 125 100 75 50 25 0 -25 -20 -15 -10 -5

fiber length 50 m 100 m 200 m

T[°] 0

5

10

15

Fig. 2.129: Mode dependent loss of a PCS (at 650 nm)

20

25

132 400

2.5 Bandwidth of Optical Fibers

attenuation [dB/km] 50 m

300

200 100 m

100

11 dB/km 0 -30

-20

-10

0

T [°]

10

20

30

Fig. 2.130: Mode dependent loss of a Semi-GI-PCS (at 650 nm)

PCS does indeed show very large mode-dependent attenuation, the intensity of which is comparable to POF. This explains the similar behavior even if the core material itself has a very much lower attenuation. A schematic comparison of typical bandwidth values for the different multimode fibers described above are illustrated in Fig. 2.131. The values, as already mentioned several times, can clearly deviate for specific products or under different measurement conditions. Ø: 1000 μm Ø: 1000 μm

PC-POF MC-GOF St.-NA-POF

SI-MC-POF

Ø: 1000 μm Ø: 200 μm Ø: 1000 μm Ø: 1000 μm

Semi-GI-PCS

Ø: 200 μm

DSI-MC-POF

Ø: 1000 μm Ø: 750 μm

200 μm PCS DSI-POF

MSI-POF

GI-GOF OM2

Ø: 900 μm Ø: 62.5 μm Ø: 50 μm

PF-GI-POF

Ø: 120 μm

GI-GOF OM3

Ø:

50 μm

OM3 mit LD

Ø:

50 μm

OM-Giga GI-GOF OM1

1

10

100

1,000

10,000

bandwidth [MHz·km] Fig. 2.131: Bandwidth comparison of different optical fibers (typical values)

2.5 Bandwidth of Optical Fibers

133

The bandwidths of the fibers presented vary over more than 3 magnitudes. If singlemode fiber is used, however, then nowadays there is practically no longer any bandwidth limit. Mode dispersion no longer arises. Chromatic and polarization mode dispersion can be compensated for as one likes. The significance of chromatic dispersion will be discussed in the next section. 2.5.4 Chromatic Dispersion in Polymer Optical Fibers

In all optical media we can observe the effect that the speed of propagation of light of different wavelengths differs. When we differentiate the propagation constants according to wavelength, we obtain the so-called chromatic dispersion, usually expressed in ps/nm·km. This constant indicates by how much a signal's delay will vary with the wavelength. In the typical application range of optical fibers this value is negative which means that with increasing wavelength the delay becomes smaller (corresponding to greater speed). Figure 2.132 shows the chromatic dispersion for silica glass, PMMA and a typical fluorinated polymer (according to [Koi97a]). 200 dispersion [ps/(nm˜km)] 0 -200 -400 -600

PF-Polymer

-800

silica glass PMMA

-1,000 -1,200 400

500

600

700

800 900 1,000 1,200 1,400 1,600 wavelength [nm]

Fig. 2.132: Dispersion of different materials

Typical semiconductor sources feature certain spectral widths that range from some 10 nm for LED up to a few MHz for lasers (corresponding to some 10-5 nm). In addition, there is the fact that when a light source is modulated there is always a spectral broadening that cannot be less than a certain theoretical limit. This effect only plays a role, however, with spectral singlemode lasers and with very high data rates. Figure 2.133 shows a schematic illustration of the effect of chromatic dispersion on a light pulse that has a given spectral width. A pulse with a certain spec-

134

2.5 Bandwidth of Optical Fibers

trum of the width 'O is launched into the fiber. After passing through the fiber (length L) and experiencing a certain amount of dispersion D, the pulse has the width 'W = D · L · 'O, whereby the shorter wave components arrive first. (cf. Fig. 2.38 as well). spectral shape of the source 'O

O

't = D˜L˜'O

POF

t

length L

input pulse

t output pulse broadening by time

Fig. 2.133: Influence of chromatic dispersion

For silica singlemode fibers, the value for chromatic dispersion at 17 ps/nm·km lies within the range of the smallest fiber attenuation at 1,550 nm wavelength. Today, DFB-laser diodes are predominantly used for long-distance systems, the spectral width of which is a maximum of a few MHz. What matters here essentially is the broadening effect that is brought about by the data itself. In this case, 1 nm corresponds to approximately 125 GHz of spectral width. This means that for a data rate of 10 Gbit/s a spectrum in the range of one-tenth nm is generated. Where the permissible bit broadening is 0.05 ns, the fiber link may have a length of approximately 30 km. For 2.5 Gbit/s this value rapidly increases to approximately 500 km due to the narrower spectrum and the greater pulse broadening permitted. Conventional 2.5 Gbit/s systems can operate without specific actions against dispersion. However, all systems that have many inline fiber amplifiers or higher bit rates require devices to counteract chromatic dispersion. The most common method today is the use of dispersion compensating fibers with strong negative dispersion. Since these fibers utilize waveguide dispersion they can only be produced as singlemode fibers. The situation is significantly different for POF. The chromatic dispersion of PMMA-POF with over 300 ps/nm·km at 650 nm wavelength is over 20 times larger than of silica fibers at 1,550 nm wavelength. For POF it is also usual to use LED with a typical spectral width of 20 nm to 40 nm and not lasers that have just a few tenths of a nanometer of spectral width. On the other hand, there are the typically short distances of POF systems and the moderate bit rates. Table 2.15 lists some examples for the effect of chromatic dispersion in POF systems.

2.5 Bandwidth of Optical Fibers

135

Table 2.15: Influence of chromatic dispersion in POF systems Example

SI-POF ATMF DSI-POF ATMF DSI-POF IEEE1394 MC-POF STM16 PF-GI-POF

Bit Rate/ POF-Length 50 Mbit/s / 50 m 155 Mbit/s / 50 m 155 Mbit/s / 100 m 500 Mbit/s / 70 m 2,500 Mbit/s / 200 m

Wavelength/ Spectr. Width 650 nm LED 20 nm FWHM 650 nm LED 40 nm FWHM 525 nm LED 40 nm FWHM 525 nm LED 40 nm FWHM 650 nm LD 2 nm FWHM

Pulse Broadening/ rel. to the Bit Length 0.375 ns 2 % of the bit time 0.75 ns 12 % of the bit time 2.8 ns 43 % of the bit time 1.96 ns 98 % of the bit time 0.05 ns 12 % of the bit time

The first three examples are based on LED for transmitting data rates up to 155 Mbit/s over a maximum length of 100 m. Even in the unfavorable case of using green LED, pulse broadening is less than one ½ the bit length so that there is only a small effect on the system. In the fourth example, the intention is to transmit an IEEE1394 S400 data stream (with 500 Mbit/s physical data rate) over a distance of 70 m using a green LED. Here pulse broadening is nearly in the same range as the bit length. When this deteriorating effect due to