Fabrication and Characterisation of Low-noise Monolithic Mode-locked Lasers

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Author: Larsson David

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/ ( > $52 -(>$52.1 > " ' ( 2; ->'(2. "1

%

"#$

H " ' ->'. $! 5 2; -$52. 4 " 4 " 4 ! @JN= 0 9 ! RI<S - 0 4 . * "! 1 ! ! O ! !

! 0 * 9 ! ! 5 $52 4 ! ! ">3 ?? 0 $52 4 " 1 1 4 RI?S $52 A= * " 4 5 > " ' R?JS @A

@?N >3 ! =I"@< # " ! * ! 4 H * 4 " > " ' ->'. 41 * ! ! * 0 ! !! 0 * R?JS "

" 4 ! ! 'O 1 RIAS " $52 4 * $52 / 6 ! ! 2 " * ! 6 ! * 6 4 ! " ! 9 4 AJ

! ! 6

4 * ! ! 9 +,-,-,. !' /$ * 0 6 ! 0 * @ H? > * $52 >' 4 ! " 4 " 1 4 " * 4 ! ! " $521 ; 4 ; 4 " ! RIIS1 4 < =J " "

! ! ! ?"@= !!

!0 * 6 ; " ? Y 2" @= >3 " ; -∼H= Y. ! <= >3 " ! % - 9. ! -6 4 ( 9. * ! ; ! 4 RK@S1 ! 5 $52

! * 1 1 Δνrep 1

=?"A= Y 61 νrep 1 1 ΔL1 01 Δng 1

1 6 HA HH Δνrep =

∂ν ΔL Δng ∂ν c ΔL Δng ΔL + ( + + Δng = − ) = νrep ( ) ∂L ∂ng 2ng L L ng L ng Δνrep ΔL Δng + =( ) νrep L ng

-HA. -HH.

* ! 6 ! ( -! " . 8 6 " !"

H=

% H= '"! $ " ! 1 ! !! " % 5 !

5 1ΔλB 1 9" 0 1 Δnave 1 1 ΔΛ1 6 H<1 ΔλB =

∂λB ∂λB ΔΛ = 2Λ0 Δnave + 2nave ΔΛ Δnave + ∂nave ∂Λ

-H<.

+,-,-,- ( , /! * % >' 4 1 6 H? * @== ! ! RIHS * >' 0 0 91 % 0 - $52. 1 D E $52 @? RIKS ! 4 ##&& * >' 4 $52 4 ! F =

ng ng1 − ng2

-H?.

ng 0 ng1 and ng2 0 ( 6 * ! ! Δλ1/2 = 0.8

λ2c Ltot (ng1 − ng2 )

-HI.

λc Ltot * ! 0 9 1

9 ! 6 ?"@= #&& 0 9 ! =@J"=HN @ -=@"=A A . ( ! - 0 . * ! 1 9 " * 1 4 ! !1 6 0 - 0 RI@1 INS.

! * $521 " "6 " # <=">3 ##&& ! :1 /! O $52 8 41 0 9 1 ! 1 4 H? ! 0 9

H@

0 9 ! ==@ ! 0 9 * ! ( $52" 4 ! " ! ; * ; 0 9 - 6 K 0 .

H?/ ( - 0 . O# $52 0 9 . O# 0 91 LDBR = 145μm !. O# 9 0 9 - . / λB = 1550nm1 H ?= Y $52 ; ! *

! ! !" - ! . 0 ' >' 4 $52 ! ! 0 1 ! ! % * ! =@Y

RIJS1 ! Δλ ΔnDBR = λ0 nDBR

-HK.

λ0 5 61 ΔnDBR 0 nDBR 0 O $52 4 ! / @. 8 6 - 8 !. A. 4 ! " - . +,-,-,+ , /! $52 -4 HI!.1 RIH1 IKS 1 -4 HI.1 RK=S/ @. 0 1 A.

HA

! ! 0 - ! "9.1 H. ; ! 9 <. -. ! ! 0 * " 4 ! % 5 ! ! 5 RK@S 1 ! 6 " 1 ! ! <=">3 ##&& ! $52 ! R??1 KAS

1 ##&& $52 1 " A="@I= >31 ! R?A1 ?K1 II1 KHS * ! ! ! ! + ( > -(>.1 ! * ! (+ " * ! ! A1 ! (+ R?NS ##&& $52 MO ! (> R@N1 ?NS ! MO" $52 8 ! ! 1 ! 9 $52 ! 6 4 ( 9 R@NS M O 0 -MO. ! " ! 6 MO ! ! ; MO ! ! RK<S ! ! RK?S *

##&& $52 ! MO !

ACTIVE

ACTIVE &

PASSIVE

HI/ ( . $52 !. +,-,-,1 !$ , $ /! ) * * $52" 1 1 - ?="@== . 1 4 ##&&

! ! ! 1 R@N1 ?N1 IIS

HH

!1 ! ! 1 4 HK HN * * : ! 6 * ! * 4

! ( 1 ! 1 0

O 8 ! 0 9

4 0 1 5'5 -53 " ' 5 ' H=AA"HA1 . ( 0 9 ! ! " " 1 8 " ! O ! ! " 1 " $" $52 ! ! ! @JJK & ?== 1 4 ! ' 5 -'5. RKIS ! * *

- HA
CH /H2 "2 @ μm "6 RKKS1 ! 2% CH /H2 -K<= . < μm -! H μm ! 91 <AH. R?HS O "; ! ;1 0 ! ( 4 ( ! " $52 * ##&& $52 $" % * ! * A@A? *

! !

-- 3 %, * $52 0 ! * 4

5 1 λB * 0 0 1 1 -(1 ++. * 5 0 0 #! * #! 1 Λm = λB m/nave -λB 5 1

nave 9 0 .1 0 - 0 . 4 - @1 A H. * H<

HK/ $ 5 % - ! ! <. * * ! 4 " 0 1 5'5

HN/ - %./ * 0 ! 1 ! !

H?

! 1 - 6 @? 4 ?. * ;1 21 O# ! 1 λF W HM 1 4 4 HJ 2 λF W HM 4 1 0 9 ! ; ! 1 ! ! 0 9 * ; ! ! 6 HAA * ; ! ; ! * * ! 0 1 0 0 40 - ! 1 ! 40 . 8 ! ! 9 ! ; ! $: ! ! 1

--! , 5 ! 2 O -2O. " + 4 !

1 5 " * ! 6 1 ! $52" 5 @??= ' 0 9 - 0 .1 ! <@1 ! ! ! : 0 ! " * 40 ! 1 A@A? - ! . HJ ; ! 9 1 H== ! - <. 9 9 0 9 ( 4 H@= ' 4 @A= 0 ! 5 6 ? Y ; A !

! ! N= @
HJ/ O# @ 1 A1 H Δn = 0.008 1 : * 5 @??= 1 @= 1 0 0 H@JJ

! 1 ;

HK

H@=/ O# & " 9 0 @A= HI= 1 A? Y ?= Y * 1 HI= Δn2 = 0.0027 - @H== . Δn3 = 0.008 - @N== . 5 @??= @= 2; ! 3

H@@/ 2; 9 @
; - .

H@A/ 2; " 1 @
HJ

H@H/ ' " 1 @
<=

# * " 0 1 " - 0 SiO .1 ! $52" ( $52" " " " ! 2 O -2O. 1 4 <@ +

$52 ! ! 2O " * 4 $52 " 0 '

<@/ $ 2 O

<@

)* '

* 0 ! ##&& $52" - ##&&(+H. 0" MO" ! 0 - . % - ('++I. * " 1 ! ! ! ! 1 RH=S * 0 - ! <A 7.1 1 " H@1 ! RHJ1 H=S * 6 ##&&(+H ('++I In1−x Gax Asy P1−y 1 1 3 O ##&&(+H 6 1 ('++I @1 A H * 4 9

" ! ##&&(+H" * "! " ! ! ! * ! ! ! #"+ P 0 -#+P1 #"+ ' P $ 1 #+'P$. * ##&&(+H" " ! & 1 * <<

##&&(+H ! " *! <@/ 0 $52"##&& -##&&(+H. & # -0. -. ( * , -Y. -μm. - . @< ==A? \@@N T @H > =?H = =@K? \@@N T @A > =IK =K@ = =@ \?@N T @@ =J \@?@N T @= =? J@K T J =< ?@K T N ==? K > =N? =HA === =A< I =. =@I =?H === ==@? < > =K@ =J= =J= ===K H - >. =@I =?H === ===? A > =N? =HA === =A< @ @ @?@N (

' !-4 & $ 4
*! <A/ 0 ('++I"H1 "H 6 M-λ) 6 > ! λ μm *

6 % M-@AJ. & # $ * - . -nm. @I > AK? @? /T 2 · 1018 J== @< /T 9 · 1017 ?== @H /T 5 · 1017 A== 17 @A /T 1 · 10 A== @@ M-@@./T @= @= <= J M-@=K. =N? A== N M-@AJ. @N K > 0W=?H=1 W=NI HK I > 0W=AIN1 W=NI KA0H ? > 0W=?H=1 W=NI KH0A < > 0W=?H=1 W=NI HK H M-@AJ. @N A M-@=K. A== @ /( 1.5 · 1018 @===

<A/ 5 ##&&(+H MO " ! 7"0/ "0/ P -=1=. N
<H/ 5 ('++I]A

<
##&&(+H"

<<

1 ! ! O ! * L ! 2

! / [ - . 5 ! ! 1 ! RKN1 KJS - <AH .

<?/ (4 * * 0 1 ! ! 2 * " ! * ; 0 ! * ! ; ! ! ! * ! ! * 0 ( 5 ! 1 ! " 1 4 <? 1 ! ! 1 - " . 1 1 " * * 1 1

! !

+ 2 &((( 2 "6 @H?I #3 * 4 ! # 2 " @H?I #3 - . * ; RN=S + 2" 0 ! 1 ! 2 " * 9 " 6 * % ' -'. ! ! 63

A= > * ! H * ! ! ! 1 ; ! - ! <AH. * "

- λ = 628 . * ; 0 !

! ; * ! ! 1 ! V" ! O 1 1 ; 1 0

! ! (+

!-- 5 0¾,6 * (+ ! 0 !

! ! 1 RKNS ! 0 1 ! ( * - . O ! ' - . + 1 0 - ! ' . * ! ! ! 1 T?A="1 VP" T?A=I -T?A@< 0 . * 4 ! RKNS e− + CHF3 → 3F + CH + e−

-<@.

4F + SiO2 → SiF4 + O2

-<A.

3 * > ! * * ! ! ! - ! .1 O

<= N= O1 4 <I1 ! HH= P

N= O

! ! @=="A== * 0 ! ! VP" - "! . * ! ! ! ! 0 / 0 1 0 ! ! 1 * 0 -! <H. *

! 63 *! <H/ ( ! ! (+ / (+A]I=A - ! << . ' L+ 2 " * P

-. -* . -O. - ') -P. @N-@ILA. @== I= A= H==

<I/ (+ ! "2 * ! !" ! " ; ! ! ! 4 ! - . + ! " / @== * 1 @ILA -' L+. A= '

*! <
* ! ! ! $ " ; ( ! " 0 ! " ; ( ! 9 1 1 1 * ! ! 9

h=190 nm

EHT=3.00kV Mag=63.7kX WD=7mm

<K/ (# (+

* ! ! 4 " ?= ?== ! * 1 4 <K1 ! !1 4 0

!--

0 ,6 784(7 ( * 4 ' L ! , " !^ @JN? RKJS ' − based 0 ! / 0 1 - " 1 @?="A== ' [email protected] ! - 0 . * !
!

/ 6 ! "

! * 6 - . ' - . - 0. ( ! ! ' L O 1 RNAS1 ! ! - 1 ; . RNH1 N<1 N?S !24 O ! 0 ' +

6 ->. 9 ! * 0 R=1 1, 1S" R=1 1, 1S" * 8 ! 1 ( ! RN=S1 RNA1 NIS1 " ! R?H1 ?<S +

! V

*

1 ! 5 H ! 2" -( 2"@=,2. 1 * 0 - :. " " 9 ! ; 1 4 *

R?H1 ?<S "; -J? Y ; @? 1 @H< . ! ! " F >1 > > ! !

> RKJS !

NK Y " - M-@H. >1 AK? .

grating

ridge active

<N/ ( "; * 0

<J

( ! ! #+2 , !^ RKJS (#"

CH 1 ! " -

. ! " 4 SiO - .1 @"I L * 4 ! O " - . ( ! 01 1 -P H . 1 P H P H #+2 @JNJ RNHS RN<S 5 ! 1 C Hy 1 0 K1 ! 0 @@ ! ! ! RN<S * C H5+ ! % " RN<S 1

0 = K? Y * ! ! 1

* ! ! 1 0" -7(. " -L" / =?"=K. ! * ! e− + CH4 → CH3 + H + e−

-<H.

3CH3 + In → In(CH3 )3 and 3C2 H5 + In → In(C2 H5 )3

-<<.

-<?. * 9 ! " / 1 1 1 ; 3H2 + 2P → 2P H3

#$ > 2 " ! " 1 - !. 5 RNH1 N?S ! 2 " 1 - 0 .1 4 <J

1 4 <J 4 <@=1

!

-@?= P RKJS1 A== P RN?S. 4 !

1 (#" H 9 I=1 N= @== O 2 " - !
! 5 @== O N= O ! 1 4 <J <@=

?=

<J/ ! 2 " N= * 1 ;
mask

ridge

etched surface

<@=/ (#" ?K= P ! ?@

# CH ) 5 *, ! ! * * *

-∼ H= Y . 1 ! - SiO . RNH1 N?S $ 1 ! & $ > ! " ; RNHS1 ! ! 1 ; " 1 τ 1 ! τ=

P ·V Q

-<I.

O 1 P ! M ; -M ! 0 * L. 1sccm = 1cm3 /min @ 760T orr = 0.3167T orr litre/s

RNHS -

! ; .

@= =<

J= * ?= * 1 0 ; - . AA HK O 61 ?= * ! ! *! <? & 0 ; ! ! * 1 ! <? 0 * 0 & 0 - . 1 * - 1 ! . 1

@=Y

@== ' RKJS 5 ;1 ! ! A= ' - A? '.

?A

*! <?/ , 9 * ! ∼K -H= . _ -* . M -. -. @ @==
1 ! ! 8 1 8 8 ! - 8 . ! RNA1 ?HS 6 ! ! * R?HS - ! .

SiO " ! RNKS1 ! , * <=="I== H? μm - A?="HN= AAμm. * ! H== - ! . - . * 6 H L * ! @ L 1 * 0 ! ! 6 # O ! 9 -@A= " HI= . * * ! !1 4 <@A ( ! ! ! -! @== * . * "" ! ! RKN1 JS1 kT λ= √ 2πd2 P

-<K.

λ ""1 5 38 1 * 1 πd2 " - 0 =< . !

! ! =< @== * + ! ! ! 5 2 RNNS * 2 ! ! ?H

<@@/ (# 9 6 RNNS 1 1 1 = + R kR φR SR kI φI EI

-<N.

! ! 1 1 φR ";01 φI " ;01 ( !! ! O ;0 * ! ;0 ! 4 -<=="?== P.1 ! * ! -$. ! -$. ! & RNJS " ! ! ! ! 1 ! " " @H= P - $'"! ! ! @L< P . @= * @= 1 ?= * @H RNNS 1 2 6 O# $ ! - . * ! 2 1 ( ""1 ;0 ! ! 1 -4 <@A.1 ! ;0 * 2 9 ! 4 <@A ! ;0 !

9 * ;0

?<

- .1 ;0 ! * 9/ @= ! 1 ! ! * 6 9 0 9 ! 9 " 0 6 0 D0E $ ! 9 0 9

! ;1 *

9 8 ! 1 @=="A== 1 D!E ( 9 ! ! !

pillar trench

a3

a2

<@A/ $ ; * 3 2 !/ tan α2 = 180/2100, α3 = 9.8 1 tan α2 = 60/2100, α2 = 3.2 3

2

* 3 9 3rd

HI= ?=Y 2nd ! ! @A=

' ( )

* ' +)

<@H/ (# 9 O ! ! " ??

5 ;0 ! O ; !" # 1

!

! " ; !

- ! 1 ! 1 . 9 @== 0 ! ===< - 0 . RJ=S , !^ - .1 ! ! / " -! . ;0 * ; !

" ! 4 1 6 <J

-<J. 1 0 1 ' 01 1 & 9 ! 9 " " 1 8 D E ( 9 " ! 3 ( 9 9 , !^ 3 " 9 " * " D E - " 1 HE . " ! <I (

1 ! : 1 0 - . ! -. O ! 0 ! * I= - AE . O 1 ! 0 6" !

r(x) = rv + rl (x) ∝ Cv + Cl (x) = Cv + Kcosh(x/L)

* 9 " ' 1 A"H 1

?I

*! <I/ 0 " &((( #>H== , " 0 ( > > , " 2 -* . V -L. -Y. -. @ N=

AE N AN A A?

AE I @N H A?

" I AI < A? ? AE "A? @< ? A? < AE @A @? I A? < " H? A= ! ! RJ@S * 9 ! 1 9 ! ' " 5 " * ! *

" 9 - . @=="A==

! : ( (+ - . RJAS O @I L 2" @A L , 6 ! 0 O -&. (+ 1 4 <@<1 &" 9 ' &"

* 6 ! &" ( 6 - .1 6 !

+ !-0,6 * 4 #+2 ! ! - 2 " 1 @==O I= O. ?I= P
5 1

9 1 HN Y * A= Y A? Y O ! @J μm

@@=

* @A= 9 - I== . ! ( HI= ?K

<@
?N

@A= ! "! ! - HI= ! .

* HI=

?= Y 9 9 * ! H== A μm 1 4 <@H * N= * " N Y -0 .1 ! <I1 @K= A@A? * ! 9 4 ?= * A? * O ! 1 ; ! ! !

; * ! 2 " 5 9 * ! A== * ! 4 ! <K1 (# A? * 4 <@?

2073 nm

<@?/ $ * ! 1 9 *! <K/ '! - .1 ! 4 #+2 2 " ' L 5 2! -* . -. -Y. -P. -L. -O. -OL .
!-- & * 4 ! 1 4 ! 0 ' ?J

6 ##&&(+H"0 AA= 1 ?H= ! -T. 1 ?= Y "! * H== HI< 1 ! >"2 4 @@? - ; ! < 1 @== . * T" ?="A== - ". 4 * T VP" I== * 9 : VP" 1 ! 0 0 4 2 -@@ . * @K="A== * 0 9 D E @A -H= . 1 ! <N * A= 1 ! <K1 ! - ! . * 4 #+2 @A * 4 2250 ± 80 1 ! 4 @== 4 <@I *! <N/ '! ! 2 " ' L 5 -* . -. -Y. -P. -O. -OL . I=

=@J

N=

A?

<@I/

I=

!-- & ( ! #+2 * 0 > " " ! -! . - " . 9 #+21 " ! ! * 6 ! " * 1 ! ('++"01 * ##&&(+H" H== 9 * @=">3 ! ! * $52" ! / I== HI= 1 N Y

!-! * ! I * 1 ! ! ! <J " , " ( ! ! ! ?=" *! <J/ & ! $52 & &" &DBR L

-μm. -μm. -μm. $52 @
IA

*

- . 1 ! * $52" -@ < . ! !1 4 ?@ * $52 - $52. ( $52 ! A? @= Y 1 0 8 ; * !! 0 !

! 1 <HA * @=
?@/ &" 1 @ < & $

- -

0& !0 $ (+ K - ; . 2" 1 -2∼@= . ; ("1 ! ! * ; ; ( 0 ; ! 8 ! 2" +

!" ( ! + ! RJHS1 " ! * ; " IH

HAY * ! ! / @. A. 6 ! ! - . RH=S * ! 9 1 A < 1 2" ; + ! ! *
?A/ 2 ; " '7?H! ?= -& AA @
* -! ?@. &" -4 <@<.1 6 * $52" -< @? .1 ! 9 01 - !

I<

! . < =H 1 @= < ! 0 ! *! ?@/ O $52" - . 9

* 1 0 $52" -Λm = λB m/nave . $52" RS RS RS @ <H @??@ @?K?"@?N= A <H @??H @?I?"@?K= H @ @??@ @??? < < @??H @?I?"@?K= ? AA @??? @?I?

?H/ ( 9 ! ! < 2" $52" -'(?I!. > N= μm 3

"

1 $52" 2" - 8 $52" . ?< A ! 2" I?

,

&$

?
??/ ' 'O " $52"##&&1 5*3.

II

" * " 9 #&& , " !" $52" " 1 ! " ! $52 ' " - 1 ! ! . ! " 0 !

O " ! ! ! 0 0 "AA P ?? $52" ! ! " ! ! ! * " $52" - 9 !. ! ! " !

$52" ! 2 /! &# * &" $52 4 ?I * " ? Y 2" 1 0 - H@ " HA"H? $52 1 A= '. * ! 4 ?I1 <= ?K 1 ! * ! ?= ' * 2" ! ! !

!

-A? '. +

--

5& & .8 (9 /! " 4! $52" * 4! 1 ! H 5 'O" * 4! ! ? O H= @=">3 $52"##&& R@NS H 5 4! @= @=">3 R?NS * $52" 6 > ! 1 " ! " * "

4 <= 5 -4 ??. - O#. ! =? @= * H"I 1 8 ! * $52" 1 0 ! ! ∼<== (# - IN L. * 4 ?K ?N * ! ? 4 > IK

?I/ &" @=">3 $52 ##&&(+H" * A= ' !" * " 1 4 ?J 0 " 0 " ! ! $52 ! 2 " 3 -2( (#2<=.1 4 <"@= >3 4 -'0 '5#=<@==H=H=1 H= 51 @ 5/ H= 51 , I 5. @ 5 4 ; , 2 " ! "N 5 * ! 4 H= 5 "N 5 O ! 0 ! ! AN 5 1 ! ; -(@@

@= >3 <= Y ; . * ! ! ! !

! "?"-"I. P - AN 5 " " @?J P ?= Y ! ! ! ! ! ! a"< P. O 1 ! ! ! H? - <== (# . * ! " ! 9 4 6 > 2+> ! 4 4 ?@= ?@@ * O# *5 =H<1 * ! " IN

?K/ ( " $52"##&& > @<= ! ! ! "H= P

?N/ " $52"##&& > " @<= ! ! ! "H= P

IJ

?J/ ( " "##&& ! $52"##&& , 9 > N= ! ! "AK P

Retrived spectrum

0

10

10

8

6 −1

10

2 −2

10

0

Timeshift / ps

Optical spectrum

4

−2

−4 −3

10

−6

−8 −4

10

1542

1544

1546

1548

1550

1552

1554

1556

1558

1560

1562

−10

Wavelength / nm

?@=/ ( ! " $52"#&&&1 2+>" K=

Retrived field

0

10

10

8

6 −1

10

Intensity

2 −2

10

0

−2

Wavelength difference / nm

4

−4 −3

10

−6

−8 −4

10 −15

−10

−5

0

5

10

−10 15

time / ps

?@@/ ! " $52"#&&&1 2+>"

, 2+> !

$ " - 1 $52. ! 1 4 ?@A1 9

1 * - . 1 A@ 4 ! 1 ! ! -('++I. " R<JS * $52" 2 " 1 % 2, ! ?AA 18 (9 : :% * M$ MO -('++I]@. ! 9 O <=">3 MO" -4 ?@H. ! @=">3 " - " .1 M$" -4 ?@<. 9 ! > ! H * ! " 1 ! MO" 6 0 4 ! 4!

--

;,-,-,. ' ) * ! " " - . *

K@

?@A/ ( ! " @=>3 "##&&

?@H/ # " @ MO " ∼<=>3

KA

?@3 > K? ! ! ! "?I P 8 " 1 ! 8 1 8 : ! &' )!& 9* ! ! 6 AK - . " μ = 01 !! 1 * !! 2 , -2,. R
* 2, AA >31 K==== & 3 * ;,-,-,- ' ) <

* * 1 " " * ! 1 ! " 61 0 ! * - . 9 % * % - 9 ! . * 4 ! % - .1 : ! A== 1 % " "" * ! 6 ! *

KH

! ! 2 " # " ! 1 ,1

1 T = N · TR 1 A * " % ! 6 0 @L<* ∞ 3 ! RJ<S σpp =

2 2 σXC − σAC

-?A.

2 2 σXC " σAC * 6 % ! - 6. " 1 L(T ) = c/ng N · TR @=">3 @=== ! H= 1 ! ! * !

4! * !

0 4!

! AH % ! ! ! " " 4 * % " ! ! flow = 1/4N TR - 0 @=">3 H= flow = 2.5M Hz ( 1 @=== 4!1 ! ! RJ<S ! ! " ! % - . 1 % ! " ! ! 1 RAK1 <@S 6 - 0 .

&' ) * * " " 4 ! & @JNI R<=S ; - AA . * 6 6 1 ! 1 ;

- . * % ! ! ! 6 RHJS * " ( 3 -(. " 4 ?@? * ; -%. A1 AA * ! 1 1

K<

! 6 1 6 AK * ! " @= >3 <= >3 1 1 % ! 6 * 10/40 GHz synthesizer

Laser

22/50 GHz Spectrum Analyzer

?@?/ ! - . " " ( 3/ * ( 6 * ! 3 ! ! O ! ! 1 aA 5 ! RJ?S 1 2 " " ! 0 1 S F 1 1 S J ( 6 1 1 ( " ! -((5. " L(f )1 4 " - " ! φ = ωt1 Δφ = ωΔt. @ 31 Pn (f )(1Hz) 1 Pc 9 6 f L(f ) =

Pn (f )(1Hz) Pc

-?H.

* 2 1 SJ = 2πf L(f ) fr ! 6 * 2#( % ! - 6 AJ . R

1 σrms (flow , fhigh ) = 2πfR

K?

fhigh

flow

(L(f )l + L(f )u )df

-?<.

! 1 Lu 1 1 Ll 1 ! 1 ! R<@1

+ ! ! 6 - ! .1

! 6 % ! / @. 8 ! 61 A. " L'2" % ! " 6 % ,6 6 RA?S # % " ! * V >NA?@

*! ?A/ *V"* % 4 '2 RHNS 2 3 #0 @=">3 <= >31

% ! < & 2 = 2 @ 2 A 2 H @= >3 XA= A= "N=# <#"N=# N=#"?> <= >3 XA= A= "HA=# @I#"HA=# HA=#"A=> ;,-,-,+ .8 (9 :% $ = $

& " ! % 0" 1 ! R3 <A? * 0 -('++I1 H. 0 MO * ! " ! ! ! !1 4 NIKH' 3 * AA >3 & K==== & 31 ( - ?@?.

KI

* " " 4 ?@I + 2" A"MO @"MO 2" -2" ? Y . 3 6 @ #3 ! 3 1 ;

#3 ! 6 0 - H. @"MO 0! A"MO % 4 @= >3 -A= "N=#.1 % N@ 2" @"MO @@= A"MO , 1 1 % ! : !

" 4 -A"MO/ "@A? 5L31 @MO/ "@H= 5L3. 0" 1 0 * 0" "@AH 5L3 RJKS /! &# .8 (9 * " ! 1 0 3 2 [( 3 (#2<=1 NIKH' ! * 3 1 % ! 1 ! "6 ! ! 4 ?@K 3 ! "6 % * ! % $52" A?= % @NK " " 6 ! - . "@A= 5L3 1 $52"1 @3 $52 ##&& @??= 6 ! * 4 " $52 ! RI?S * 6 N@ >3 "

KK

?@I/ ( " ! ! % @= >3 " * ((5 3

KN

?@K/ ! 2#( % $52"1 " 3 -2[( (#2<=.

KJ

A= , 1 * O! R?NS JJ? >3 *5 =< - " . * ! N @ O 1 + R@NS ! I@ " *5 =HN 4!" =@N O * % ! =H ! * ! % R@NS1 - . 1 ! R?NS R@NS

6 ! HAA $52 ' 8 !

?@N/ ' 2, " $52"##&& "##&& 5 ! 0 : :% 18 (9 M ( 4 " " H ( 9 ! ! 1 & " + ! ! !1 ! 4 6 4 ( 9 -M'(.1 ! ! * 9 " 9 -2" .

N=

?@J/ 2, ! " @=">3 $52 ! ! " * M'( ! <= >3 M$" <= >3 MO" 5 ! @ " ! ! * MO" ('++I 0 - H. * M$" >"! # 5 0 * " >1−x M$ > #$ >#%$ * ∼@AN= 5 9 1

5 2" " 91 " * ! ! @== μm ! * ! * M$" H= ! 1 " MO" K 5 M$" H -I μm. 6 -H?= ?== L . 0 ! ! ! ! , !

+ 6" "

2 " - . ?A= " 2 " M$ @"MO 1 ! ?H 8 M$" @"MO &

((5"1 ?A@1 4 ! 9 A= 5L 1 R<@S1 A= 5 9 M$ ;

- M$ ! . N@

?A=/ (" " <=">3 M$" @"MO * " ! ! M$" 7 5 *V"*"4 ! @I"HA= #3 - ! ?A. % A@J M$ 1 ! I @H MO" * % M$ ;

@== #3 M$ ! ! " * 0 - .1 M$" MO" * MO" - ! A= O MO" K O M$".1 ! M$" H ! MO" * 9 4 !! ! M$" * ! ! ! 6 : !

> " : * : ! ! M$"(+ ! ! ! V ! 8 !

6 $ ! 6 ! NA

?A@/ ! % " <=">3 M$" @"MO

*! ?H/ + " M$" @"MO" & -. P -P. λ -. Δλ -. & -O. M$ K? "?I @AKN @A ∼1 @"MO @K? "AK @?H@ AA J

NH

! " ! ! ! * " ! 2#( % 4 ?AA % *V"* 4 A -A= 3"HA=#3. " @A< " 8 " 3 MO 1 !!

; ! M$" ! ! " ! MO" * ! ! *

! % M$" 0 ! 0 ! " ! ! ! ) 18 (9* # 4 " <= >3 ! 6 ! HJ <= >3 2 % ! " % 3 1 * 4 8 " - %. ! 6 ! 3 6 " 1 " 2 "

* 9 ! ! , ! ! ! : 9 - 9 3 ! . * 9 61 ! @ #3 - 4 ?AA. ! " ! 6 2 " R

3 5 4 ;

3 ! ! - . !! 1 4 $' - !". + -. !! 1 ! ! ! - 0 5 ! . ! 6 91 " f -4 ?AH. 1 1

N<

?AA/ ! % ! " <=">3 M$" @"MO ! ?H

N?

?AH/ ' @"MO - 0 . 6 -X@#3.1 ! !

31 9 6 -\@== #3 .1 3 1 "@A? 5-@3. ! ! I?N? (

NI

! 2 " ! ! '2"1 A1 ! % '2 ( 1 ! ! 1 ! ! " " RJK1 JN1 3

" % ( R
! 61 ! 4 ! 0 5

" 1 ! ";

<= >3 : 6 - "6 . - 0. 0 ! <= >3 6 <= >3 ! A= >3 $' O ! <= >3 " M"! 0 HH ?= >3 -@K >3 ! .1 ! Vabs 50-GHz photodiode

Igain 40-GHz synthesizer High power RF amp

Q-band LNA

laser microwave delay LO RF Spectrum Analyzer

RF Q-band mixer IF

V LNA Bias-T

?A
NK

?= " ; -==N 5L>3 5O' \?= >3. 6 1 5 2 " 0 4 A< 5 &+" 0 ! ! ! 1 ! 6 - . 0 -$'"@K >3. 4 ! ! !"1 "

% ! 6 6 -A= 3"@? >3. ! ! 4 -' / H= 3L@A >3. ! ( 3 0 " ! 6 6 &+1 ±ωLO - . &+"6 !! 1 4 6 $'" 2 " ! 1 vRF (t) = VRF cos(ω0 t + φ(t))1 ω0 6 φ(t) = (ω(t) − ω0 )t - 6

6 . ! %! 1 vLO (t) = VLO cos(ω0 t + θ) O θ = π/21 1 - " 4 . vif (t) = vRF (t) · vLO (t) =

α α VLO V RF sin φ(t) ≈ VLO VRF φ(t) 2 2

-??.

α 01 " 0 O 2#( vif (1 1 α2 VLO VRF - ! " 0 5.1 Sφ Sφ ! ! " - ! ! ! 6. ((5 ! 1 L(f ) = Sφ (f )/2 R
1 ! ! 0 5 4 ! 4 41 , ? 5 A< 51 ;

"@IJ 5L3 " ! " "@IN 5L3 <? 5 -A $'".1 0 8 0 ;

; ! % 3

3 61 ! % 9 6 3 f = 1/4Δt1 Δt 9 RAKS 3 !

@. 6 ! - 4! !. A. " 3 + ! 4! A NA

NN

3 ! ! ! ! 6 -HN 5 .1 4 ?AN 0 ;

;

% ;

? ! " 5", # R
!" " @1 A H MO1 0 ('++I ! H 2" ! ! - <<A. A= ' 0 H"MO @N ' $ " / @. " 1 A. ! ! ! 0 2

! ! H. O

! ! ! ! " 1 40 0 2 "6 <. O 6 2, "! ?A? 2, 2 "6 -A"MO . 40 ?AI %

- $./

' $./

?A?/ 2, 2, 3 6 P NJ

?AI/ 2#( % 3 6 P

?AK "! -((5. " " - AA.1 6 ?I1 " 9 Lf gs (f ) =

2π TM

2

PASE 2τ 2 1 2 2 2 1 + 0.16ω τ T S (ω) relosc R 2 A A20 (2πf ) + (2γ0 )2 4π A0

-?I. RAKS 4 " 1 P 1 " 1 A20

! A H ! " 1 ! - .1 1 4 H Z & 3 " 9 " 2 2 τ /4TR 1 ! 4 1 61 γ0 = MAM ωM 1 M 1 1 τ 1 61 ωM 1 " 1 TR 3 0 ! 6 R3 6 ?I " 9 ! A= 5 ! 1 % J=

?AK/ 2 ! - ! $ ! ! ! ! H 5. @1 A H MO 0 ;

J@

# RHIS - AA . ( 6 2,"1 4 ?AK ! " 4 4 1 S 6 ?I1 & 3 0 6 RAK1 0 5S ! ! 4 6 0 6 ! 9 f 4 ! 6 -XH= 3. ! 6 H >3 ;

?AN 2#( % ! A= >3 ! 6 ! " 4 % ;

6 ! A= >3 @= >3 " 9 ! RHI1 AKS1 % -@= 3"A= >3. @"MO << ! ! " 6

JA

?AN/ . ( 4 !. % A= >3 5 A= @= >3 % @= >3 ;

2," 4 ?AJ " "

0 1 6" 0 6

9 ;

6 - "@?A 5L3. @"MO ! 6 @ 5 - 6 A@K ! A@. 0 2, 0 ! 1 ! A= >3 2#( ! 6 JH

! ?
4 _MO P ( ( λ Δt Δλ 5 & -. -P. - 5. ->3. -. -. -. -O. @ @J@ "AK AI HJKN @?H@ @@ AAA =HN JA A @J= "HN AI HJ?N @?
@== #3 >3 2, ! @= 5 @"MO 2#( -2," . = 3 A= >3 A"MO =IH L

J<

+ ! ! " > ! 1 ! ! 6 "1 0 " ; 2" ! @Y1 ! @KY ! ! ! A 9 0 9 ===N1 ! ===A - 0 . % " ! ! 1 0 < ! ! 6 ; - ! . & ; ?= μm ; K? Y1 ! A< Y ! " ! " " ! " " 1 % 6 8 % % @=">3 " " % 0 1 ! ! RH=S " " 4 " 5 ! ! @=">3 5 " $521 ! 1 ! ! + " !1 $521 0 ! ; $52 &1 " " <=">3 9 ! " "" ! 4 " <=">3 ! O ! ! % @"MO 4 ! " M$" <= >3

! @"MO M$" 0 " 1 !

J?

"

" " 5 "! !"Q ! / " 1 " $ 6

4 " 1

! 1 *

9 ! 0 # 9 ! ! ! ;

9 ! ! ! " !

@=">3 $52

@=">3 6

/ " ! 1 " 4 ! 1 " ! " $52 ! HI 1 4!" ? O % A?= -A= 3"N=#3. ;

<=">3 2" @== # 6 ! 1 6 1 <= >31 ! ! " " $9 ! ! 0 / 4 1 0 " ! JI

9 6 9 %

<< A= >3 @= 3 @"MO "

! " ! $" %1 ! ! 1 ! / @. @= >3 ! ! ! A. "

! H. 5 + ! ! 4 ! % '

! ! ! ! R?AS O ; 1 <=">3 $52 ! " " 6 $52 4 " / "1 1 ! 4 " ! % "; 0 ! ! " 2" ! 4 1 4 4 40 0 6 0 " 6 " <=">3 " ! ! 3 0 > 61 ! ! : $'" 0 M$ MO 1 M$

JK

% R@S >^1 D5 ! 1E M " 1 > , 5 ! 1 , / ' ! V 1 @JI<1 @@@H"@@@J RAS 1 D# "& 1E 1 ( M 1 P I1 , I1 , !L$! A=== RHS 5 1 # 1 #1 ( O ' 31 D # "& ( &1E M 1 P A?1 , I1 @JNJ R<S $ 1 D ! ! " 1E 1 P <<1 , H1 @JKN R?S , 1 M 1 P N1 , AJ1 @JKA RIS '1 # ' O1 !" 1 2 & 1 # '1 D(!" " " 6 1E & ?N [email protected] A? # @JJ@ RKS > 1 D !"+ ' (1E O ( #" + 1 ! ' 1 ((5, ="!L 1E & 1 @<-@=./AH<<"AH?A1 + ! @JJI RJS ( 1 1 V1 ( 1 # 1 DH !L -@I=>!LU@J. +$#LO$# 01 + ' 1 $@"@1 +(1 ( $ 1 V(1 @JJJ R@=S $ 51 1 D' ,2T" 2T" <=">!L $# "4! 1E &1 P J1 , H1 # @JJK R@@S '1 1 & +0 1 ( 1 ( 1 1 D 6 +$# 1E A==H &+( # ' R@AS # 1 D9 ' "+ "$ $0 V , ! ( ( 1E M 1 P H=1 , @A $ @JJ< JN

R@HS & +0 1 '+#"$V1 1 " R@<S & +0 1 D" " +$# 1E '+' A==< R@?S + 1 (31 1

1 D+ 0 @=>!L ! " 1E + ' 8J?1 " $ 1 1 ANN"J1 @JJ? R@IS # (1 1 1 1

1 D+" " " 1E + ' A==@ R@KS + 1 ( 1 (31 1 1 D<=">3 @I= >!L " 1E + ' A==A R@NS + 1 1 ( 1

1 D " 6 " " " " 1E + M HH1 K=J"KA?1 A==@ R@JS ( 1 ( ( 1 !1 + 1 D"+ @I= >!L ' 0 O # "& & $ # 1E &1 P @I1 , I1 A==< RA=S + 1 ( 1 2 1 1 1 1 D @I=">3 (" # "& & $ + ' 2 1E A==? RA@S + 1 1 1 (31

1 D" "+ > V (! ! ! # "& & $ 1E &1 P @=1 , <1 @JJN RAAS 1 1 + 1

1 "+ H2 2 ! + ' 2 # "& &$1E '+' 1 @JJJ RAHS 1 # & 1 D# " > 3 " / ' 1 01 1E "+ 1 P @
1 D

$52 # "& & #"O !"2 (1E & 1 P @N1 , @1 A=== RA?S O 1 ' 1 > 51 1 2 $ 1 & O1 +8$ 1 > 21 2 ' O 1 D+ ( " "$ ' 1E # 61 P <J1 , @=1 + ! A==@ JJ

RAIS 1 2 &1 ( > 1 2 5 1 2 1 #1 ' 1 ( 1 2 O 1 D " " $ ' / ( M3 @== >L1E # 61 P ?H1 , @1 A==? RAKS & 1 DV ", # &1E $"1 #1 # A==A RANS O 1 ' * 1 9 & O1 > 51 2 ' O 1 D# " % ! " 1E + &1 P AI1 , ?1 # @1 A==@ RAJS 5!1 ( 31 D' V E ! , $ 1 '! V @JJ? (5, = ?A@ 1E M 1 P AJ1 , A1 ! @JJH RHAS O $& 1 2 ! 1 [ O O1 D 6"

" 1E +( 5 P @@ -@@. @JJ< RHHS 2 ! 1 D 2+> # V 1E !1 (5, @"<=A="K=II"K1 A=== RH<S $1 D' V E ! , $ 1 '! V @JJ? (5, = ?A@ 1 1 1 D, " 1E ( * M 1 K-A./@?J@IK1 #L A==@ RHIS $> % 2 # 1 # " & &1 M AN1 I1 @?J< -@JJA. RHKS & 1 1

1 D( " ! 1E + ! ' 2 A1 @"H@ -A==?. RHNS >NA?@ D % - .1E 2 >NA?@1 V"1 , ! A==@ RHJS 1 $ & 1 & '1 ' 1 & +0 1 # 1 $ 5 1 ! 1 D& "% " <=">3 " # "& &1E & 1 P @I1 , @@1 , A==< R<=S $ P & 1 D' " 1E 5 HJ1 A=@1 @JNI @==

R<@S # 331 D, # "& &1E M 1 P AJ1 , H1 # @JJH R31E &1 P HK1 , AA1 @HHN"@HHJ1 A==@ R '1 D" ' "2 ' ! + "& &

-+&&.1E ' & + A==?1 1 D5 2 " +$# ( 5 # > 1E & 1 P @N1 , @@1 , ! A=== R 1 + 1 D(" !

41E M 1 P A?1 , @@1 AAJK"AH=I1 @JNJ R3 " " 1E P <=1 , @A1 @= A==< R?=S $ & 1 1 # 1 DO "5 2 ", #" <=">3 # # "& &1E & P @K1 , @@1 , A==? R?@S 5 1 2 1 # 1 ' (!1 > 1 " 1 D+ <= >3 ! " $52 1E + # $ + ' 1 (1 P I=A=1 A==? R?AS ( 1 1 1 1 # 1 D 6 2 0 # "& & ! # V ' > 1E ( M 1 P H1 , A1 @JJK R?HS # # 2%1 O 1 ( * 1 ( 1 ! ( 1 D "2; L53 ! 5 2; # >L &1E P <=1 AAIJ"AAKK1 -A==@. @=@

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

4 ?K" 1 & I= -AI.1 AJ @JJA RIHS " 2 1 ( , 1 5 ! 1 1 O1 5 ( 1 5 1 5 ( 31 @@<" " ! 5 ; 1 &1 K1 IJK"IJJ1 @JJ? RI<S 1 $ ! 2 O $0 1 D ! 1E & P HK1 , H1 @JN= RI?S 1 > 2! 1 V 1 5 #1 # 1 # '1 ' 51 2 1 D??" & > # 0 "' & 5 "2; # "& 1E & P <1 , H1 # @JJA @=A

RIIS ( 1 1 1 # 1 D # "& ( "> #6"O & ! " # $! 5 2; 1E ( M 1 P A1 , H1 (! @JJI RIKS $ 1 ( ( 1 > !1 5 2 1 5 1 D5"% $52 @? ! #+P 1E &" 1 P H@1 , @?1 A= @JJ? RINS " 1 > 1 & ' 1 ( $51 D$

> P > " ' ' 2 ' ' : $! 1E & P+& J1 ,+ K1 V& @JJK RIJS ' ' ' 31 D$ & '1E O1 @JJ? (5, =""1E & [email protected] @N @JNN RK@S $ $1 2 1 + 33 # '1 DP " ! 1E & P HA1 , A1 A< + ! @JJI RKAS 2 1 5 ^1 1 ( 1 O 2!1 ( 1 2 (31 O !1 > (1 D*! # # "& &

& 1E &1 P @?1 , ?1 # A==H RKHS + 1 ( 1 2 1 1 1 1 D@I=">3 # "& ( & + ' 2 1E & ( 2 & 1 P HH1 A1 A==? RK<S ( 1 ( 5 1 ( $!1 & ' " 1 D M"O"0 O " " '1E ( M 1 P N1 , <1 V&LV>V(* A==A RK?S #1 ' #&1 > & 1 ' 51 2 # $ & 21 #1 ' ' 5 1 D# >"> #"M"O ( V & 0 1E M 1 P HH1 , @1 @JJK RKIS 2 # &1 # 1 ' 1 ( 1 ( $ 2 1 1 ' 1 D>" 2 "O $52 & "+ ( > ! V '51E " &1 P J1 , @@1 , !! @JJK RKKS # 1 5 $ 1 7 &1 5 1 5 ' M1 M1 ' 1 ( $ #$ 1 + 1 ' 51 2 # $ & 21 #1 D# ! 5 ; @? μm ! 1E + # @< -A===. @JH"@JI @=H

RKNS $ 1 # $ $ 5 >:1 D( P&( 1E A===1 (5, ="@H"=N?=HK"H RKJS V , !^ 1 # 1 > >1 D " 1 ' 2 ' 1 3 1 1 @JN? RN=S >1 D + ' # > $0 >L1E $" , @A=JH1 @JJK RN@S ( ' #,1 D' > ! / " ' 1E P ( 51 P <1 , ?1 @A@I"@AAI1 @JNI RNAS 2 > 1 P 31 + ( 1 P P1 D "! "

"6 1E P ( 5 @J-?.1 (L+ A==@ RNHS 2 1 # $!1 # 1 O ' "(1 & !

1 D2 ' *!1 D; 0

'<"A E1 P ( 5 @?-?.1 (L+ @JJK RN?S 1 ' ' 1 5 > 1 > !1 D '<"A 0 ! 1E P ( @I-H.1 #L @JJN ',2(1 [ [ RNIS 51 D # & " + # 1E $"1 V 1 A==< RNKS 5" &1 2 1 # 1 2 1 ( 1 1 D(+ 'L1E & P IH1 , I1 $! @JJH RNNS 1 # 5 1 2 O 1 , 1 ( 1 ' , 1 # 1 D2 &> , > ('* 2+ 2,' ',> + (&'+,1E # H?1 1 ( 1 D ! ! 1E P IN1 , N1 + ! @JJ= RJ=S V , !^ 1 D " '
RJAS ( +1 D, 2" M "! " 1E '+ @JJ? RJHS 2 & D0 V !G ^ , 1E $"1 VG 51 @JJH RJ<S & 1 ( O 1 # >1 1 D# O + ' ' 1E M P HN , N1 A==A RJ?S 5 1 ( ,@?=1 " @JNJ RJIS 1 $ & 1 & '1 & +0 1 " # 1 # 1 ! 1 D$ " !1E " ( -(5,/ =N @J"1 1 ' #, 1 ( 1

1 DM" " 1E + & P AK1 , @1 <J"?@1 A==A RJNS $ $ 1 #1 5 1 D2 ! % " 1E & P AI1 , A<1 @JJ= RJJS 31 ' # $1 $1 1 5 !1 D# " ! " 0 1E + &1 P AK1 , @=1 # A==A R@==S #"' 51 D*! $ &1E 1 ,

1 #1 @JJN1 (5, ="NJ==I"JIH"N R@=@S T"# ' & ' 1 D$ O *! ( " & V > " ' "' 1E M 1 P AJ1 , <1 @JJH R@=AS 1 51 D 1E 2 HA/JK1 @JAN R@=HS ,61 1 D 1 D 2 HA/@@=1 @JAN R@=<S 1 1 D+ 1E +0 V" 1 @JJK1 (5, ="@J"?@=IAI"@ -. R@=?S T+,27 /LL 3 %

2

@=?

T?A=

P@=A

#A==@1

& &

,

0 ! ! < # ! 0!

R@==1 IJS ' ! 4 ! R@=@S ! 4 ! 9 ! 1 ! 9 1 Δβ 3 9 ! -@. 4 9 ! 9 ! Δβ(λ) = β1 (λ) − β2 (λ)

2π κ λc -Δβ = 0.

Δβ = β1 − β2 −

-A.

41 ! 1 Λ1 9 9 0 ! / -H. 1 ! ! 0 9 ( λc = 1.55 μm λc = Λ · (n1 − n2 )

Δn = 0.05 → Λ = 31.90μm Δn = 0.10 → Λ = 15.95μm

! 4 ! &" 1 9 0 (ng1 − ng2 ) R@==1 @=@S @=I

Δλ1/2 = 0.8

λ2C Ltot (ng1 − ng2 )

-<.

&" ! ! 3 ! " -! ! ?"@= - <.. ! 1 1 & 1 1 κ Ltot = xLc = x

π = NΛ 2κ

-?.

0 " 4 0 !

! !1 ! @ κ ! ! 0 &" -&" ! % 4 ! . ! κ ! : ! 0 9 4 κ 0 9 - 6 . RIJ1 AKNS

(- - 2 O ( ! 1 0 9 ! !

! ! ! 1 ! " -( ++. < -##&&(+H. 0 9 ! ! 8 0 9 9 0 4 ! <"@= ! ' ! A - ! <= >3 1 ! @ . 4 !

@= - !! . 6 < Δng > 0.096 4 0 9 =@J 0 0 9 ! " ==@ 0 >'"4 !

! @/ , 0 " " " " @ 2 @ 2 A Δnmax Λ Δng 5O & -μm2 ) -μm2 ) -. - . -. -. @I0=@ AA0A@ ==@I @== "==@ KN? JI A===

@=K

2.2

1.6

InP

BCB

BCB

@/ >'"4

& - % +. (-- 69 2 9 0 9 ! 0 ; 4 $52 1 6 I"K + 0 9 -?="@== . 1 R@==S 0 9 1 0 9 4 H 0 - .1 ! 0 1 4 " 0 -5'5. ! 0 " 0 1 0 ; -X=<.1 ; ! 0 ! RIJS |R| = 2mr

sin(δLg ) δLg

, (mr < 0.2)

-I.

O ! ; -A . δ 5 6 & ;

0 9 Lg 2mr = Λk

Δn n ¯

-K.

O Λk 1 Δn 9 0 9 n¯ 9 0 5 1 λDBR @=N

Λk = k

λDBR 2n

-N.

9 0 9 " ! A$ 1 ++ ( 0 4 # #

,

A/ # 4 ( AA μm @N μm ( 1 0 9 ++ #! 0 ; ! 0 9 ! 4 < 0 0 " 8 9 0 9 5 0 01 W H
(-- 1 2 2; ! -(. -. RIJS ("0 0 :1 "0

4 0 0 ! 1 (! (! 0 !"Q 0 1 0 0 + 1 0 4 0 1 t2 = 1 − r2 6 ; ! " 1 r1 = r2 = r1 " 0 ! RIJS @=J

H/ 9 0 9 1 -##&&"(+H. 9 0

0.12

reflectivity [a.u.]

0.1

0.08

0.06

0.04

0.02

0 1544

1546

1548

1550 1552 wavelength [nm]

1554

1556

@@=

TF P =

1 1−r

−(re−jφ1 − rejφ1 ) ejφ1 − r2 e−jφ1 jφ1 −jφ1 −(re − re ) e−jφ1 − r2 ejφ1

-J.

O 0 !

Ttrl =

ejφ2 0

0

-@=.

e−jφ2

! -@@. O ) 9 0 α " 0 ! φk = bk l = (2πf /c0 · nk − iα/2) · lk

, k = 1, 2

-@A.

M = M1 · M2 · ... · Mn

5 -@H.

M1 = M2 = Mn = TF P · Ttrl

! 4

-@<. #! / 9 0 ) 1 0 g,k 1 1 - . 6 @?1 R@==S 4 < 4 ?1 ! A Mtot = M n

y=

O

Λhigh

Λhigh 1 sin(πk ) k Λ

0

-@?. Λhigh /Λ

! A/ + 5 @??= 9 0 H@J

-. -Y. -. @ A
1

0.9

0.8

Normalised grating strength

0.7

0.6

0.5

0.4

0.3

0.2

0.1

0

0

0.1

0.2

0.3

0.4

0.5 Duty cycle

0.6

0.7

0.8

0.9

1

?/ , - . 4 $52" ( / 1 $ / A

$ / H $ /
@@A

I/ ; O# @1 A [ H 9 0 9 ===N

@@H

' !

! 0 5 !

"! " " 1 ! " ' ;

!

/' #

5@ " " - %. ∼<=">3 3" - " . ! 1 ! ! ! "! ! " 6 -<= >3 . " 0 ! ! ! ! ! ! ! -$' . ! 5@/ 4 " $ $ &, & , 4 , 1 4 1 >1 $ " 1 H 5 , > ( ->3. - 5. - 5. - 5. VA $ $'"?= " " "? - . &,@ HH"?= ? A< @N - . #0 HH"?=1 ="@K K "K"-"N. @H -.1 ? - . 5"* ======?"@? =? "=? HH &,A =====H"@? I AII AH? - . & " 4 4 -, . ! - . -6 5@@. , 4 4 @@<

, 0 1 @= 5L V abs 50 - GHz photodiode

Igain 40 - GHz synthesizer

Q -band LNA

laser microwave delay

High power RF amp

LO

Q - waveguide Coax Opt fibre

RF Spectrum Analyzer

RF Q -band mixer IF

V LNA

5@/ ( " P 1 ! ! $' F 1 F 2 1 6 - .F &+1 F 1 " 6F P1

"% ! 1 !1 !! " ! ! ! 1 4 1 6 4 4 ! 1 6 1 ! ! 0 & + 1 4 " 1 4 0 !

! ! % ! 1 E 1

1 &+" &+"6 40 1 f +1 9 &+"6 1 f + ± f ! !! 01 vIF ! 9 61 f / vIF (t) =

α VLO VRF sin(2πf t) 2

-5@.

" 1 Kφ[BEAT ] = αVLO VRF @@?

Noise synthesizer

-60 - (-90) dBm

Att.

LO

28-30 dBm

40GHz

ESA

RF

30-50GHz

Reference oscillator

Pick-off Tee

12-13 dBm Variable phase shifter

5A/ '! " / 1 2 / 61 &+/

1 (/ ( 3 " 9 ! " ! " -4 5@. ( 4

1 1 , 1 31 2 - 3 ! .1 6 5A ! R
-5A.

5 ! 1 6 " - NHI?=1 @=#3" ?=>3. ! 1 -4 5H.1 ! ! 0 &+" 0 &+"31 4 5< - 0 @="@H 5 &+" . !6 ! &+" 1 VLO 4 0 (

9 6 @= 3 @= >3

" . 9 ! 0 3 1 ;

! " ! 0 ;

1 6 5H1 6

1

1 i0 = R · P0 R
5H/ D E 31 NHI?=1 " 6

5
@@K

5?/ 1 6 5K 4 ! ! R@=AS ,6 R@=HS @JAN1 ! ! 0 !

1 R@=<S

" ! "@K< 5L3 * 1 4 -, .1 5 ! 1 6 5@= 1 δishot 1 (dishot )2 R ! δishot

=

2qio B

(dishot )2 R

=

2qi0 BR

-5H. -5<.

-$2. " i0 i0 )2 = DR = ( √ 2qB 2qi0 B

-5?.

, @ 3 5 $2

-5I. A" i0 = 2mA 1 Pc = −12dBm Pshot = −12dBm − DR = DR(dB) = 155 + 10log[i0(mA)]

−12dBm − (155 + 3)dB = −170dBm/Hz

6 1 i2N,th(v) 1 - ! i2N,th(v) =

4hvΔv 4kT Δv ∼ = hv/kT R R(e − 1)

@@N

-5K.

-5N.

PN = kT B

! , kT = −174dBm/Hz

, T = 300K

N F = 10log[PN,actual/kT B]

-5J. -5@=.

! 5A/ , 4 " " ' , - 5. > - 5. &,@ ? A< #0 K "K &,A ?K?"I? A? 4 ! Fsyst = F1 +

F1 F2 F1 F2 ...Fn + ... + G1 G1 G2 ...Gn−1

-5@@.

4 4 > 8 4 - ( . 4 1 ! 5A1 ! 4 48 , -! . 6 5@@ ! ?@ 5 " ;

! ! -5@A. ! "@K= 5L3a -"@K< 5L3a?@ 5. 5L3 W " @II< 5L3 + " / "@II< 5L3" -"@A 5." H 5 W "@?K< 5L3 # ;

! !1 " 1 1 4! ! 6 - ( I= >31 <= 5. 5I ;

! 3 - (> NA
! " ;

6 A >3 ! 6 ;

! 1 " O ! 0 -a@H 5 " . ! !

1 ! H 5 @?= 1 ! ! 4 PN, tot = Pshot + Pthermal

@@J

5I/ # ;

(> NA
@A=

&

"!" ; ! " "

"

!- % )"0-

(+ #+2 - . ! " -≤@ L .1 !

' " 5 9 + ! #+2 (, RNIS1 1 , ' R?HS 9 ! (+ RNAS (+ (( -( (. ' P $ -'P$. ?N L (+ " 9 ! " (+ V VP" I== A μm ! 1 ! 4 @A="HI=

1 !

"! ! ! 0 % 0 "! 1 0 (+

" )% O T"?A= -T+,27 '.1 "! " 1 !

! R@=?S 2 ! ! ! L T @@Y 1 " @=== L A=== ?A="??= 1 <=== L @A@

I=== H@= "! @I= ' A "! &" 1

-<= . "! 0 +&"57JH== ( @== P - ! @= . ! - . AA= μC 0 T$",?= @ @= 1 1 ! ! "! @@= ' A

" !- 1 "2+3- +() "! ! <AA @== 1 ; @I ' A + 1 I= O - A= '. ! HA= P

0 AK L ! 1 -A? L . ! H"< 1 ! 6 -( # 2 @@I?. I= ' ! 4 -+0 . =A ! @== O ?

" 40 5 VP" ! ! ! @?= ' #$( T?A=I -T?A@< . ! I== ! J= ' J= 0 63 ? @ TH?@5/+ -@/?.1 ! J= '

! ! AA μm

" !- 1 "2+3- +() VP" 2 1

! 1 ! 1 1 $" @AA

"

( 1 "13- -

5 #+21 ! @A #+2 ! ! <AH 4 -$ . ! " ! M" 5 9 ! 0 @== 1 ( 1 1 (+ @ 0 @? !

"5 " 1 ! -! #$(. VP" T?A@< A μm 0

? μm 1 -∼@== . 8 1 0 @=Y (+ + -@/@. I= \A==

"6 " 53 ! -5'51 ' H= AA"HA . ! - . 1 A? 5'5 -H===. ! 5'5 ∼A μm1 5'5 A?= ' ? 5'5 0 5'5

"7 8 1 H===1 4 ! / J== &+2K5 -! ? @K= '. I== T?A=I -! J= J= '. 0 @= ? OL TH?@5/+ -@/?. I= "! A @A= ' -&+2K5. -TH?@5. ? 1 ! 41 " " 9 @AH

! " / /?==`LK?=`L/?===` ! " 9

" 9 : ! ! 0 ! + " ∼@@=

"

," -, N=1 > @==1 A?=.

@A<

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