修士論文 Fabry-Perot 共振器のアラインメント制御
Contents
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9. Fabry
10. 3 2 4 1 21
11. e d End Mirror yaw e e End Mirror pitch e
12. 5 2 3 00000 FP Cavity Front Mirror End Mirror Im 5 10 End Mirror Rae Front Mirror ar d R R Ra sin 7 5 5 wo Front Mirro
13. Bode 1 Unity Gain Frequency 180 PD H w 1 7 2 27 w gt wy 180 openloop y H w G w Unity Gain Frequency 180 Appendix 24 5kHz Unity Gain Frequency PZT loop 1k
14. Front Mirror 1 0 100mV 20mV End Mirror 1 0 45mV 55mV error signal Front Mirror End Mirror 2 2 1 End Mirror 2 1 loop error signal 0 20mV FP Cavity DC loop error signal 5 12 e a error sg 0 e b Front Mirror yaw e c Front Mirror pitch 00000000000
15. da d JAYE 122 102 42 2 1 5 3 2 513 0000000000060 Photo Detector PD Gauss 1 e w z 2 5 4 17 320um 15cm 240um 5 1 402um 1 5 1 4 Pound Drever 0 Cavity FP Cavity 5 5 FT EOM 15MHz PBS 8 2 4 Cavity 2 4 PBS 2 Photo Detector 15MHz error signal FP Cavity PZT 515 error signal PZT
16. At 2 1 f gt h t dt i wy 2 At Wo S 2 7 2 en y la ds dt 1 h t dy 0 Wo 5 h t dt Jk t wo f h t dt 2 8 i 2 h t Fourier h t 19 h w e du
17. E Wo em FY 4 3 Cavity p 1 riroer 278 on r2 l p Te u on S 1 7172 0 8 S1 6 carrier 6 r 1 279 r f 1 riroer 278 r 1 p t re 4 4 1 r ra 1 7172 r 1 p ti E Ep m rl p 27 BOK 2 sin wmt 1 Mr 1 7172 1 SIN wmt 14 8JoJ
18. 56 loop openloop DC DC error signal G r D DC G 0 2 Gpc 5 4 Gpc DC mV error signal mV Front Mirror pitch 50 40 yaw 50 55 End Mirror pitch 100 60 yaw 100 60 flat Differential Amp flat openloop F v F v G v 2 F v Gpc Flv 5 4 F v Gpc 5 5 5 5 loop Unity Gain Frequency Front Mirror pitch 45mHz yaw 20mHz End Mirror pitch 25mHz yaw 10mHz loop Unity Gain Frequency loop 17 UGF 4 16 4 17 FP Cavity ro 0 re
19. 2 1 Suv 2 45 z dz ds ds Ju da da ct y 2 Juv Einstein 1 87G Ruy Tw 2 1 G Tuy ore ore Be o da Oa E TT po E Viol ip R g Ry 9g 4 4 Ho gv pv po De g Bg OWE Christoffel Ricci Ricci Tu 0 2 1 1 du 0 Tuv 1 2 2 0 1 2 1 Juv huv Juv Tluv huy hu Minkowski juod Aw 1 9 00 A Oh 9 ah 82 h 0 2 3 522 H ortorv P 2 3
20. RppM Eins Ram Rrpm 1 0 RM a 0 T 0 exp 2jn lo Te 0 RppM la lt lt a 0 5 0 Tel Recycling Cavity Fins_0 E t 1 0 1 gi 1 rreo 1 rra eio 0 1 rroo 0 iet gt KA 3 59 3 59 Einsl t 1 rreo Recycling Factor G FPM FP Cavity Factor Eins Ugo FP Cavity G 3 60 L rreo Recycling Cavity Fins 3 45 3 58 1 f f9 LEE Tie 2 10 ern fe ra G g I r 0 1 J f 1 Fhein J g Ta G
21. 9 2 z Um y 2 exp 31 2 I m 1 n z 3 2 2 1 1 3 a k U H j 3 3 pe m 5 A 45 8 3 T w z wo4 1 i 3 4 20 2 2 Moy s 3 5 z 2 n arctan E GuoyPhase 3 7 20 2 3 8 kwo 3 8 H Hermite 2 y 2 Uis s 2 y z Um y z exp jl k 2 m 1 n 72 3 9 U x z Uf x 2 Un 2 9 2 Ura x 2 3 10 Hermite Gaussian Mode Fabry Perot Cavity Hermite Gaussian Mode 2 z 2x H2 x 4x 2
22. Nd B Fe eddy current 16 Cavity Appendix FP Cavity 65cm 5 2 FP Cavity Front Mirror R 99 9 flat end mirror R 99 9 1m 0 65m 3140 230 8MHz 68 78MHz 36 75kHz Fabry Perot Cavity 5 2 5 1 2 000 00000 3 1 Cavity Cavity R d FP Cavity Front Mirror Vd R d 5 1 d 7 5 3 we d di w da dj cv T d f B w3 ibi 7 7 5 2 50
23. 99 4 9 x 1077 rad Recycling Factor 90 5 5 x 107 rad loss Recycling Factor 10 Recycling Mirror Wave Front Sensing FP Cavity 1 8 x 107 rad V Hz 8 6 x 107 m V Hz Project 6 6 x 107 rad V Hz 1 4 x 107 m V Hz Wave Front Sensing Cavity Photo Detector error signal error signal Unity Gain Frequency 10mHz 45mHz Wave Front Sensing 71 Wave Front Sens
24. h 1 rire 4r ra sin2 1 1 I V 1 2 14 I l rire 1 F F 4 2F es SHE Les 2 15 1 mra L L 1 wlfe WFSR _ 2 16 LII SA Hermite Gaussian Modes 5 PRU 1 m 7 d 1 j d 1 2 17 4 n lm 2 18 51 2 18 2 3 2 Fabry Perot Cavity Cavity Cavity Hrp w Front Mirror r End Mirror r2 t2 l FP Cavity giwot Er E t2 r5 ei r r et gt meivot l aym abs 2 19 1 EE 24 17 218 n 2 7 do 25 2 h t dt C 2 1 251
25. 51 Pound Drever D O00 0 Cavity 5 1 1 Set Up LIGHTWAVE Nd YAG Model 120 03A Nd YAG Monolithic Isolated Single mode End pumped Ring laser MISER Ring Cavity 809nm PZT Ring Cavity 5 1 1064nm 40 0mW 10mW PZT 1MHz V PZT 100kHz PZT 15V 5 1 40mW 10mW Fabry Perot Cavity 0 99 9 Front Mirror End Mirror 1m 5 l
26. 2 8 t wg ar h w ejst dw t 2t l 2 1 sin gt J dwh w ej 2 9 oo W W l wl e 1 2 1kHz 75km 75km Delay Line Fabry Perot 2 2 Delay Line Fabry Perot Delay Line Fabry Perot U 2 2 Fabry Perot Fabry Perot Michelson 2 3 Fabry Perot Cavity Fabry Perot Michelson Fabry Perot Cavity Front Mirror End Mirror 2
27. X cos Guoy Phase Guoy Phase n z arctan a 2 z const Uo a z Uo y z Ut z US 2 xy z UT z 4 3 Uoly z US y z dy 0 Photo Detector r 0 z 0 Photo Detector r 0 zez 0 2E ZE WioUio UuWiojdzdy EN ATE reo s lt cos n z 0 ag 4 11 a Pound Drever Photo Detector 0000 Pound Drever 00 000 9000000000000000000000000050000 rol 186
28. 95 300m Fabry Perot Michelson TAMA Project 3 13 TAMA Project 3 1 3 3 1 Project Front Mirror flat R 98 8 loss lt 50ppm End Mirror 450m 99 99 loss lt 50ppm Recycling Mirror 9km R 93 RM FM lo 5m Nd YAG Laser 1064nm 00 FP Cavity Peo Front Mirror r V Rr End Mirror Te r re 1 Pr 1 r re Teo r 1 235 1 rra e 205 6 ex en R 0 975329 0000
29. En Eyeivottim Sin um t Unie ee Jn m Bessel 1 m n 0 1 En J _ ef wo wm tyy Fo Jo m 27 sin uj t e carrier 7 Wm sideband carrier reo sideband Te0 s Tc0 s 40
30. aj a3 aj a3 d d2 1 reo Ta we Teo t re reo Jwa ren t Ta Jao j reo kl ipasi 1 az 3 5 3 aja Teo re 500 T t 200 reo Ta 2 2 reo Hu ess 3 44 1 RppM 41 01 02 02 5 Re d1 a1 R a3 03 Teo reo 58 reo 54 reo ren 22 Iren ra 12219202 reo 22 rai 22 d reo re1 z reo Ira re E G a a2 01 02 3 45 g a 2 01 2 07 05 3 4 0000000000 Ege 0 Photo Detector 82 Detector la EQ4 E2 2EF Escos i Imax Imin Imax Imin cos d1 e 2 2 2 Imax min C max 3 46 Imax T Imin 1 Imax Imin Imin FP Cavity 1 3 44 3 45 E mar Bau Emax Rrpm
31. 3 508 x 10 3 2 0 1666 1 3 68 3 a a 0 1000 H 5 99 Recycling Factor 1096 FP Cavity Front Mirror R dja End Mirror Qe Ra D 3 670 3 68 a 2x Ra R 4 48 24 A_max 20 R 450 m d 300 m 3 67 3 68 a 99 4 9 1077 rad 3 69 Recycling Factor 10 a 5 5 1077 rad 3 70 TAMA300 32 5 10 7 rad 3 5 FP Cavity OOO a m FP Cavity Cavit
32. 277 _ I rge poa tr 2jn 1 1 rrae ge rf 3 62 Recycling Cavity Eins Eins CooVoo C1oU10 Beam Splitter 1 1 Eins V2 41 Ugo Uim Coo 1 1 ti 2 3 61 3 62 3 63 S 3 63
33. g 92 2 13 2 0 9 do 2
34. Cavity Fabry Perot 84
35. Pound Drever Wave Front Sensing 4 1 Pound Drever 2 3 1 FP Cavity Pound Drever 9 wo m Wm wot msn wnt
36. 10 00000 FP 00000000000000000 000 000000000 190 SOA 4000000 0000000000000 51
37. 3 42 3 3 3 Fabry Perot Michelson 0 O0 Fabry Perot Michelson FPM 3 8 Beam Splitter BS FP Cavity FP Cavity BS 3 8 Recycling Factor FP Cavity FP e 2 FP e BS Front Mirror e BS 1 10 BS FPM a1 01 92 02 3 43 5 R a1 01 24
38. VFSR 3 X 107 Hz 210 1 4 0 x 10 Hz 2 18 an y 2 17 cos 14 1 4 27 R d R 1 5 3x 108 y ww 23x10 Hz 2l T 9000 2x5 n lo 0 3 66 e2in Wo Qo 3 8
39. Q 4 2 carreir sideband 00 10 Tel a rev Ugo 2 o a U 0 222229 u 2220 U L G U 2 00 i 10 JTe 04 24 00 La a gt tai Uio 4 7 o esideband sideband Ubo Uio 720 8 1 8 sideband H a H U00 T J reo s 8 ES Uio ag sideband Teg s Tel s 0 Te0 s Ugo sideband Front Mirror 2a 43 Um E
40. 2 2 2 t 1 2rr eo 1 2rr lo 1 x 1 rreo 1 rreo 1 rra wg Ag r reo 2 r reo ra a 2 4 1 rreo wo 4 1 rreo ao r reo ra 2 r reo re rreo 5 4 1 rra 40 4 1 rreo 1 rra Tag ra f la r reo 1 rra 1 ar 3 64 prey ws a 1 rra 1 rra Nao T Te Tel GL Ten O 10 T 1 rreo 1 rra 2 wo 2 21 2 treo a 3 65 Wo Qo 29 Recycling Factor G 2 2 2 t 1 Arr o ie 2rr ey lo 1 a2 1 rreo 1 rreo 1 rra4 Wo Ag 1 rr 9 2rr4 rreo 2rra gt rreo 4 1 rreo r reo ra perge 4 ln l 4 rr l lo TON Arreo 2rra 2r reor 1 at rr zara 3 66 L rroj 1 rra wo 36
41. Cavity Vol 25 7 99 9 0 10mW error signal 0 error signal Front Mirror End Mirror yaw 1 0 10mrad Front Mirror End Mirror yaw loop error signal 5 3 Front Mirror 5 3 Front Mirror error signal yaw End Mirror error signal yaw
42. TAMA aussian Modes Fabry Perot Cavity e Recycling Factor CMRR
43. 66 End Mirror tilt 2 Front Mirror tilt 2 D 5 2 Guoy Phase rad c O nN N 67 Intensity of Reflected Light time sec 5 12 Intensity of Reflected Light yun Aleliqle time sec 2 5 13 68 rror signal Front Mirror yaw sA DUNS RE arbitary unit Intensity of Reflected Light arbitary unit time sec 5 14 Error signal 69 Error Signal Front mirror yaw time sec d c b Error Signal pitch Front Mirror time sec Error signal loop pitch yaw 5 15 Front Mirror T0 Chapter 6 Fabry Perot Michelson
44. 15MHz SN LC RF Detector 1 LC 15MHz Detector RF Phase Shifter RF Detector A 2 Phase Shifter loop filter 5 1 5 loop filter AB loop filter 5 1 5 loop filter Ad 5 1 5 24 5kHz loop A 5 loop loop MISER PZT 266 7kHz loop loop R C LF356 HA 5002 A 6 6 73 error signal Front Mirror yaw loop filter 5 2 4 loop filter 8
45. 272 J 20 8 1 wo 5 2046 Glimit 2 reo re reo s Sin Zz wol Photo Detector 414 4 15 4 16 4 17 Project Project 10W FP Cavity 1 2 0 6 yaw pitch 1 1 E l 5 x3 x 10 x 0 006 1 5 x 107 W m 0 5 Photo Detector enpp hwoll 0 3 A W 6 6 x 10 19 Glimit 14 10710 rad v Hz m V Hz
46. Wave Front Sensing Project Recycling Factor Fabry Perot Cavity
47. 0 2 3fa a Tel E T reco Udo 2 Nag ao 2 a fa reo 2 2 reo 3 41 ao ao Cavity Cavity R a a Teo reo Ey reo ra z reo na 5 ra 5 reo re1 Ta lt ay reo 3ra 5 2j reo re 7
48. otemt ioe mi VT EotJo m 2jJ1 m sin t el Uga 4 6 carrier Eg Jo m ej Ugg sideband 2j Eo J m sin wy te ecarrier 4 2 U im 42 a 0 Uso 5 00 EC Im Front Mirror End Mirror
49. Recycling Factor 4 Bed pA 4 it dd b eee e d ET BRE Ga an 4 1 4 2 5 1 2 UE xe edd Wave Front Sensing zu e Bann DAE dala ARRA eder abdo 5 2 241 oas fade deque E p iE srt ded die de di e 4 2 2 beam displacement 252 9 optat Ep rer ee De E qe dod R Pound Drever TE raa Ye 5 1 1 Set ul p everest ut ees TU 51 2 BEER e pes t ts mi dere 12 13 16 16 17 19 20 22 22 23 24 25 27 30 40 40 41 42 45 45 5 9
50. 00 331 00000000000 3 5 7 Ujm 2 2 7 x 2 2 y lo lo Um y lo exp j klo m 1 n Io 3 32 z Um 2 exp j 2klo 2 1 1 n lo 3 33 x y z x y 2 e 2a e x lo sin 2loa 7 lo 1 cos 2a 2loa amp y 2 Uim y z 202 1 2a 2loa 20 2 y z Uoo 41 eem 2 Wo 2 Nap Wo ao T 1 2 1 2a 2l 2 2 Wo 2 wo ao 710 3 20 3 2loa2 2 2l 2 r V a 2 u Uoo exp j 2klo 4n l0 2 Wo 2 wo ao wo ao 3 35 aUgo b 10 dU ioe R Ra 2 2 4 4 Tr 2 2 a i 8 2 3 2 es u zje 27n l 0 p 2jn lo exp 2jklg 3 36 0 exp 4jn lo Re R 22 3 3 2 Fabry Perot Cavity 000000000
51. 49
52. 2 Imax gt Imin Ge uc Imax ur I min 2 2 2 2 1 2 2 1 d 1 23 3 57 2 Peo w 2 Peo 3 5 Recycling Factor shot noise Photo Detector iq in 2 A V Hz shot noise FPM Power Recycling Rycycling FPM 3 10 FPM FPM FPM FPM Recycling Mirror 3 10 FPM 2 FPM FPM Front Mirror z 0 Front Mirror Recycling Mirror lo 3 11 1 Ei Ugo Recycling Cavity Eins Eins thi Eins Eins Eins I RM NM EM 3 12 Recycling Mirror r gt 0 Recycling Cavity Recycling Mirror Front Mirror 2610 2n lo 2n 1 r Recycling Mirror a RRM ld SER a 2 21 22 1 22 i 2 ba 2a j aexp 2jn lo r 2 Gs EEE E Bho nno 1 F a 2jn Ce o m 3 58 zw 27
53. js TW ZnSe Az 2 gt w z TWO ag __ ag TWO P d P dz d z 558 Az M Az P 2 1 1 23 arctan 25 12 Demi Az 2 arctan 3 Guoy Phase Gaussian Beam P z V Wo In 4 14 u au Y y 2 2 h P z 2 2 l i 06840 g h Hermite Hm sac n Hermite O 0000000000000 Ho x 1 14 Guoy Phase i 1 2 Hermite Gaussian Modes
54. Fabry Perot Cavity 10 Anderson Wave Front Sensing 4 2 1 beam tilt 13 14 4 1 error signal FP Cavity Pound Drever 00
55. 74 15 33H 0 1 HA 5002 220P 4 7K 2 2k 7T PD JN 19 25 241 gt C 20 5 1 20 3 3 DC LF356 0 1u A 1 RF Detector 5002 1k 220p HA 5002 4 7k 3 3k 1k HA 5002 47 AD841 or HA2541 00 2 Phase Shifter 76 0 01H 47k 50k LF356 0 014 0 022 u 680 15k LF356 0 014 10k 1k 10k 1k LF356 O LF356 loop filter 77 0 01u LF356 loop 18 LF356 filter HA 5002 2 1k 15k For PZT loop 266 7kHz 6 100 Buffer A 5002 se ss sms For Mass loop 24 5kHz R 6 4k C 1000p OP LF356 4 ss 79 AD707 5562275 Coil Driver 100u 0 33u Coil Driver SS 25A985 80 2 5k 1k V K Ik 100k ING 10 p 2 i 56 lk LF356 5002 Sg forAlignment 00k Control 777 3 3k O 3k Coil Driv
56. Recycling Factor 3 1 Hermite Gaussian Modes k 22 1 u t y z 0 u exp jwot Y w y 2 2 6 82 2jk 0 art ae ta Gauss
57. 0 2 0 4 0 6 0 8 MISERU D m loop ebrio ec is gt Z 2 5 5 Pound Drever Cavity 61 1 0 1 0 1 04 1 0 Frequency Hz Phase degree Frequency Hz 5 6 Cavity openloop 62 7 Filter a 09 Differential Quadrant PD Amp lens Front Mirror N 000000 loop 5 7 Wave Front Sensing 63 0000000000 00000 5 8 Photo Detector I 25 ZA ZZA ZAN 2 PSS ERE A o w 5 9 Photo Detector I End Mirror tilt Cavity axis Front Mirrortlt 5 10 Cavity
58. 46 Intensity arbitary unit 0 2 4 3 2 0 2 2 2 const profile 47 FP Cavity Fabry Perot Cavity Chapter 5 Wave Front Sensing 65cm FP Cavity Pound Drever FP Cavity Wave Front Sensing error signal
59. 2 huv 18 _ 0 2 2 3 ha 0 2 4 Einstein Minkowski huy Ay exp j amp z 2 5 2 0 kuk 0 TT gauge 0 hi zu hu 0 0 0 0 0 h h 0 huv 1 2 6 0 hx 0 0 0 0 0 h4 hx 2 2 Michelson U 2 1 7 X l At ds dt 1 h t de 0 E z 50 audi 21000000000 00000 gt Transverse Traceless gauge 11111 Mirror2 Photo Detector al
60. 3 4 XZ a U 3 4 XZ x 2 z 1 cos a sin a x z sin a cos a 2 Uoo z z 2o z sin x sina exp j kz sina 7 2 sin a 3 19 al 2 1 v6 2 Uoo y z 20 Uo x y 0 Une 0 ADD 0 1 1 a ew 4 2 oc v6 2 0 0 877 0 rp Uvo x y 0 lt a Uo z 1 0 Up a y 0 202 4 vola y 32 g 0 gg Umm y 0 8 32 32 2 2 1 a 3 2 v2 Z 1 3 Us x y 0 ERA 6 V6 3 3 5 Uao x y 0 V a la 0 et 3 20 19 10 1 a 2 42 Uio z y z 2o o y 0 ja 2 i _ 0 0 a 2 6 7 Uta 0 A y 0 3 3 2 3 2 3 6 gt 28 Uio a y 0 4 16 8 JEZ 0 a Ua z 0 0 64 L aad RE 1 0 G Bos 3 U y 0 217 0 205 16 J 32 2 32 an 20 47 JE 4 30 4 15 gt 42 up Uso z y 0 zx 0 ap Urol y 2 3 21
61. ag 3 996 x 10 rad TWO 50ppm0 000 31 Recycling Factor G 4 5 wo lo 5 pA _ _ a 16 27 4 982 x 107 w ag wo ao 2 2 1 02502 4 619 x 1072 0 9812 3 apa 5 064 x 107 aya Wo ao 000
62. ee GE 51 5 1 4 Pound Drever 51 5 1 55 EV EM ru RR aa a x kt u S 4 51 5 2 Wave Front Sensing 52 5 2 1 bw ce A Q ee Sih 02341 sh si 52 5 2 2 Photo Detector 72 3 4 5 MAME RES VENTER 52 5 2 9 EME ee des riorem dep tr geo eoi nid 53 524 EHEN EINE ute teh DL DR De d 53 gAs E a GA OKA ea ARG 53 71 73 Chapter 1 Introduction Einstein 1 2 LIGO 3 VIRGO 4 300m Michelson Fabry Per
63. 2 JoJ1 rzorco s Peo sos Voor Uso 5 J 2 1 reo re U 10 reo rea reo sUgoU10 s n 0 Peo s Teo rai ros co ra Guoy Phase Uo 000 2 2 00 x sinn 2 a reo Te 2 sin n z 0 ya 423 mmm Wave Front Sensing shot noise 4 1 4 2
64. ra rf t 221 99 J h w e Hpp w dw IDEE FP Cavity t ra Wo ja 44 1 Hrp w 1 er sin gt w ri ra r w 1 r rge se aei sin 2 22 w cC J l riroe 7 1 8 20 BR 2 23 24 7175 w 10 Ts 2 23 w Low Pass Filter Jeut oft 11 NT 2 24 Chapter 3 Beam axis Well aligned 3 1
65. Uoo z y 2 zr 0 4 1 2 wo 3 4 0 z Uoo z y 0 3 23 1 Uio z y 11 35 92 3 24 1 3 24 Uoo z z lar 0 E wo 3 25 page 221 2 m Ag wg 1 lt N 0 7 S Ujo a y 0 3 26 2 25 Uoo z J PS Uoo 2 21 0 2 ag 3 5 0 si zu e y 0 3 27 41 J m 117 2 2 z Uime a X Um Z ez Ugo 2 y 2 zr 0 x 2 j U o z 0 GI 3 28 41 2 Z e ag X wp B 3 29 lec buta 3 29 2 952 0 mU ag Wo 1 a 0 T E Uio z y 0 3 30 J Uoo a Uoo 2 Yo 2 Ag a 3 31 2 VESS E moyo 2 Upgo z y z izo 2 Ag 21 3 3 00000000000000
66. 2 2 2 62 a 2 7 62 3 TAMA 2 5 2 wy d 1 185 x 10 m T wo 8 476 x 10 3 m 2 ao 3 996 x 107 rad kwo 0 wo lt 1 Ya Ya 4 ava 3 996 x 10 5 ZA 1 a 2 ay 8 2 6 263 x 10 a gt 107 rad aga a 107 rad 4 5 10 00 10 l m gt 2 0 9 0 lt 1000000000 20
67. Ein Eo Jo m e _ 4 3 e oo temi DC lo IrcoJoP Fco_5J1 reos I 16 12040 IN 45 4 12 4 13 Photo Detector tpc enpp Ic ipo wo shot noise M 2eipc 8 npplo r2J2 2r2 _ J hwo A VHz 4 11 K 2 2 rep 2 PA l Jo Ji reo reo s 2 cos n z 0 1 rod al Qlimit 23 0 5 cos 2
68. 00000000000000 0 00000 elwotn t gjwota giwa t 281 22 2 1 221 Er jwot ti jwot 3 y jwy 22 l jwot jwa zul 740 h t dt 2 20 re e P r c 6 T r 5 r n l gt n l ina h t Fourier h t h w e du 2nl Ia ti Y yenit T 21 A wo gt 21 1 1796 709 67908 A wo m dw ie A wo A wo e vot 1 er M aks e E tirage l rir 1 mie je tire jel gt e e2sin 1 rir3 1 rir e je E PNE 1 p amp 2 dw h w e 2 ei 2 2sin 2 1 rir 20 1 rir3 1 rare 76 e 24 42 12 1 1 15 rir r ro r Jo
69. 00000 0 1000 j rzg reo x B 00000000000 44 4 2 2 beam displacement U 4 4 Doo Uis _ pr U 0 Wo carrier a reoUoo reo Uio wo sideband Front Mirror Poo s Ung carrier sideband sin W yt
70. a DE E Eget 7 ratte ra ZU 23 J1 snontra Uf 0 SIN 2 f ok H 2EgJoJ1 07 0 000 Voo H H 2 me reo rei Uio reo ra oss 10 sin wy 4 8 0 1 2 3 a Teo Pro res S real ony Ugo Hermite Gaussian Mode zt z z Um y 2 31 2 1 m 1 n z 4 9 24 9 e A RZE neas zs m 5 eS Ut 2 0 2 2 00 2 2
71. 2 a a a a Imax Teo reo Te Aw reo re Aa 2 2 Q J reo ra re gt Teo Tel a Teo Tel a 0 0 2 we 0 2 a Teo Tel Tel A 3 55 2 2 a w dun a 2 3 j reo 5 Teo Tel a Teo Tel a S 22 3 56 2 w 2 a 26
72. Hs x 823 12x 00000000 m e Hi z Hy dx 2 VY Tim 00000 15 3 2 Hermite Gaussian Modes 8 0000000 321 00000000 Y 34 X X Z 3 2 x 00 3 2 a 2 00 Uoo a y z 2 2 0 0 2 9 2 0 Ulz 6 27 o U x 6z 0 Uo y 0 16 zu 5 D cu 9 1 Ugo 2 2 Uoo
73. 1 rreo rra 76 rfge in rg rrea Je B rge rreof 1 rrea rG e rf g I Ramkrpm 1 1 rra rG e rf g 1 Ram 1 I RamkRrpPm U 2 rroo f 1 1 rreo rg Pra fet Hrrof rG re ra F G reo F I x 1 rrco 1 e237 1 A rr o 1 rra e t 1 t E S usd c pw 00 0 1 rra e pra rG e r 1 rreo 1 Eins Uoo 1 rreo r 1 of G iem 1 A rreo 1 rra e 28 rfg 292 3 61 t
74. 4 q 40 2 z 0 wo 2 TW qo i 4 w z R z
75. DUM 4 sin Wy 4 5 1 7179 SIN DC 6 error signal error signal Pound Drever Cavity en 0 Awly woAl error signal w l 4 2 Wave Front Sensing 4 1 FP Cavity 00 00 error signal e Anderson e Wave Front Sensing 41 om uec E e FP Cavity 000000 4 1
76. Perot Cavity FP Cavity FP Cavity Gaussian Beam FP Cavity Pound Drever e FP 3 6 FP Cavity 27 z Ujm t y 2 Ui z a y 2 a Cavity 00 2 1 zu Hs a Uio 2 wo FP Cavity 00 re0 10 Te Uio Uio x y z 2 1 a U 41 1 Uno 00 2 00 10 2 3 Uio f u Uoor 2 Wo 2 1 Peo 2 Ugo wy Ute 2 2 1 1 p ee bets Uoo U10 2 Wo 2 Wo a 3 fa 2 Pel Uyg 3 37 Wo 2 wo 2 2 Teo 2 2 reo Uio 3 38 10 2 ra esee ph e ra U 3 39 cl wo cO cl 10 wo 0 cl 00 e 3 7 FP Cavity 27 z a 23 2 a Ted 2 Ubo jra 10 0 0 2 a a gt 2 ra ro Ugo 2 ra reo U10 3 40 ao ao
77. f ON End Front Mirror yaw pitch 4 loop 400 loop OO 5 13 a ON 4 loop e b Front End Mirror yaw e Front End Mirror pitch e d OFF loop Front Mirror yaw loop error signal 5 14 e a yaw pitch e b ON 4 loop e c Front End Mirror yaw d Front End Mirror 0 pitch e OFF error signal 0 Front Mirror yaw loop pitch loop error signal error signal e a Front Mirror yaw pitch b ON 4 loop e loop 00 e d OFF yaw pitch error signal 0 pitch 0 yaw pitch yaw pitch 55
78. 0000000000000000000000000000000000000000000000 54
79. 1 003000000000 10300000000000
80. 3 2 z o 2 3 Fabry Perot Cavity 231 2 3 71 79 t ta l Fabry Perot Cavity wo Ei t Ejelt Er Er Er E ra tye rre n 0 _ none Te 240 Er 5 PP 22 n 0 Segas 2 11 ri t pj 1 6 l C Ei By Er Ti I FT 2 1 L E ri re 1 pi Ar ra 1 p sin 6 2 12 1 rire 4rirs sin 6 1 1242 124 213
81. Emin 1 Emax 0 J 25 gt gt 255 aita aite Teo reo re jui reo re 207 i nae 2 reo Te ren ta 3 47 1 Emin 0 2_ 2 2_ 2 A z reo ra y reo J reo Dae cue J reo raj J reo fu 3 48 Imax Imin Imax ai a aj a 7 Teo reo ra Em T reo re 33 ka a ka reo 2 gt eo T re ma 3 49 Imin Eis a a2 a az 2 reo re 5 2 reo Ta 3 2 a Qi reo ra pm 2 ra po 3 50 a1 02 01 02 a 0 04 0 a 3 51 gt 3 52 05 3 53 3 54 3 9 04 a_ a_ 3 51 3 54 3 49 3 50
82. H Ward Appl Opt 33 5041 1994 E Morrison B J Meers D I Robertson and H Ward Appl Opt 33 5037 1994 1992 K Tsubono A Araya K Kawabe S Moriwaki and N Mio Rev Sci Instrum 64 2240 1993 1992 83 Project Project
83. Hz Low Pass Filter PZT 266 7kHz 2 loop openloop openloop 5 6 5 2 Wave Front Sensing 0000000000000 FP Cavity 5 2 1 Set Up 5 70 Wave Front Sensing FP Cavity 2 4 PBS Beam Splitter Photo Detector Pound Drever 5 5 BS Photo Detector Detector yaw pitch Differential Amp yaw pitch error signal 00 5 2 2 Photo Detector Wave Front Sensing Photo Detector Photo Detector 0 0 54349 5 8 5 9 1064nm 1 0 52 Photo Detetor
84. LEID l Fabry Perot J II HH B HH BE 00000 0000000 00000 1996 10 UL 1 Introduction 2 1 2 2 2 3 Fabry Perot Cavity E e olka Ee hte E Hber ek 4 Rer turbet Rs ZANE NR ETC ERE 2 3 2 Fabry Perot Cavity LH HL BL DG 3 1 3 2 3 3 3 4 3 5 3 6 Hermite Gaussian Modes Hermite Gaussian 10000000 0 2 24 PLECH s o za 5 02094 39 92 EE Wa Du ee de pede 324 zer bada 6 6 bob 22 A a 33 4 4 0 ZEE 3 3 2 Fabry Perot Cavity D UU DU 000 ow 3 3 3 Fabry Perot Michelson
85. er for 1k Front Mirror Pitch control 10 and End Mirror Pitch Yaw control HA 5002 LF356 Sg for Cavity length control Y Sg for Alignment Control t gt gt i Coil Driver for Front Mirror Yaw control AT 81 gt AU m N UJ O 1M loop 1M lu LF356 filter Bibliography 1 A Einstein Sitzber Deut Akad Wiss Berlin kl Math Physik u Tech 1916 2 J H Taylor and J M Wenberg Astrophys J 345 434 1989 3 A Abramovici W E Althouse R W P Drever Y G sel S Kawamura F J Raab D Shoemaker 10 11 12 13 14 15 16 17 L Sievers R E Spero K S Thorne R E Vogt R Weiss S E Whitcomb and M E Zucker Science 256 325 1992 A Brillet el al VIRGO Final conceptual design 1992 H Kogelnik and T Li Proc of The IEEE 54 1312 1966 private communication M W Regehr F J Raab and S E Whitcomb Opt Lett 20 1507 1995 to be published R W P Drever J L Hall F V Kowalski J Hough Ford A J Muneley and H Ward Appl Phys B 31 97 1983 K Kawabe N Mio and K Tsubono Appl Opt 33 5498 1994 D Z Anderson Appl Opt 23 2944 1984 N M Sampas and D Z Anderson Appl Opt 29 394 1990 E Morrison B J Meers D I Robertson and
86. ing Photo Detector yaw pitch error signal Project 72 Appendix Detector
87. o s 1 10mW 1 4 2 5mW 5 9 Photo Detector enpp hwo 0 005 A W m 0 5 wy 4 02 x 107 m ag 8 43 104 rad Qlimit 1 8 x 107 rad V Hz 5 7 limit 8 6 x 1071 m v Hz 5 8 v 0 00 2 08 Reo 3 30 2 1 x 10 rad v Hz 5 9 dimit 2 5 x 10 m V Hz 5 10 100000000000000000000000000000000000000000 57 Magnet Mirror 7 Magnet 5 1 FP Cavity
88. ot Cavity Fabry Perot Michelson Wave Front Sensing Fabry Perot Cavity Chapter 2 UUUUUUUUUUUUUUU
89. pre modulation 0 0 00000000000000000 700 0000000000000000000 520000 30 0 999965 0 00425115 1 6 3 57 FP Cavity Recycling Mirror 3 57 a ya C 1 2 051 3 199x10 3 67 wo ag Recycling Factor G 3 66 no 0 wo w acr d wo 8 475 10 3 m n lo 3 7 lo n lo arctan 2 357 x 10 2 rad TW 0 0 n lo 0 Recycling Mirror Front Mirror
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