DAVID H. SHOEMAKER - LIGO - Caltech

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A tota,l path lclgth diEercnce of !.boui 2 !o ic obscwed whca both 90 beara delay
li!€! are rc..!tra.qt, iEplying a a€t EisEatch i! curyaturc of about 0,02 o for the
pr.!c[t Eirlot!.
Ia rdditioa, str.y Ught in thc dclay lincr (due for inctr.ucc to scattering frod
thc eiEor rurfacca) allowc irtcrfrrcace batwcca liglt breilg Eavclcd diEermt path
hagtb! [f6, f8li for lI = 90 bc!E! in tbc delay liac, thr charact.liltic diEercacr- i!
abou! 3 LiloEct€r!- fhc hig! nflrtivity of thc mirlol! dlow! liglifi.ca.Bt conrribuliolr
ey.E 6oE 'trappcdr ctr&f ligbt whicb has oadc a large lu.aber of roErd
ttip! of th. dclay liac (coacspoadilg to petl' difcrcaca sp to tbc o!de! of onc
hurdrcd kjloactcrc). The cnrrr,at ar.irrorr employcd slow a lcatlcti-og coc6cient
o (rclativc lrqplitudc of thr lcattered light which the! iaterfelg with thr Eain
beae) of about 10-{; givca th. cj:lor reflectivity of 0.99f, otlc fia& tlat rhe
[uctuatiol i! rpparc!.! path leagth :::e to tbi! cfect is of thc :a.Ee ordrr of oaglitud.
r! thar duc to the ltr,tic patjl lcngth difercrcr. Tbu!, thc coeEci.at thaf
relatc! frcqucncy loisc du to apparent rnirro! Eotioo i is about t. t0-u a/Ez.
Tbe ftequcncy ir rtabilizcd in two stepr (sec 6gure 1). h thr 6Jst step lul,
roec of thc ligbt lcaving thc larcr ir dirccrcd to I Fabrt-p.rot !!f.!!!cr cEvity uled
ir traslEilciod, coopa.rcd with a refercncr bcao' and an error :ignal ir foroed.
Suitnbly a,apliEed aod 6ltcrcd, ii i! applicd at low frcqucacier to a pilzo-elesrric
tsalsducer holdilg on. of ths lascr oJrrorc, ald at bigh frequcucicr to aa i[!racrvity
Pockels cell. Tte u.uity-gaia frequcocy of this scwo-loop i! about 4OO !.82,
liait€d by th. baadridth of thc clectronics.
Ia thc sccoad stcp {I21, a &actio!. of thc ligbt leavirg the i.s.t€rfelon.ter on tbr
iaput cidc of thc b€lslplitt.s i! blowlt to iarerfcrcocc with a fracliol of thc input
liglt. Tbc phs. dif.rcncc bctwca thcsr two beaor ir a fuqction of ihc avcragc
prth l.ogth i! tlc tsro arE alrd thc r.Eainitg hrquc'rcy loicc o!. thc bscr light.
Thc cttor rignal ir dcvctoped *ith a roodulrtioa-derlodul,*ioa rchcsc ris,ilar to
t!!! dc.ctibcd fot thc oaia signal peth, utiliziag Poctcb cell p3 a.sd photodiodc
D2. At &cquacie ia thc raage of a few Ecrtz, th€ rdcreacc Fr,bry-Fcror is t!,c
EolG ltablc sd.!.ncr, ead, tbc cror siglrl i! u!.d to p!€v.!t €oEoon-oodr lqorioq
of thq dclsy-linr Eirrors (i.c., thc iarcrfcrcocc patt.n otr D? ir hcld to a r,.ia;a',*
of iatcuity), At &cqucacir: hig"bcr ihaa 4 f.w t.!! of Ecrtr, th! lcogt! of lhc
dclay liar i! r $dct .rd Eorc lcaliliva leu$h refcre€c; thc cFo! liglal i.!, thi!
&cqucacy reagc ir fcd b.ct to th. hsct. Th. gaia porrible i.o thir rcrv+loop ir
pli.Earilf liFit.d, by th. tiBG dalay i! th. dclay lia.c; fot r llortgc tilqc of 9 ,4
(qoFspoadilg to tY = 9o beaor il thc dllay liBcl it i! about 60 LEz. A.l €timatc
of thc iaducucc oa th? i!t.rf.!oEetc! of thc rqaniling frcqucncy toirc ir showa
r! crrvc g il 6gr:rc 2. Ths rqoaancc lttsctuR. scca arouad IO &Er a.tr du. to
thcnrdly drivca notiorr ia tha cosltsuctiotr of tha rfermcc Fabry-pcrot.
Iluc!ur,!i2!r ;! th! b.aor gcoE.try cr.! ba tlalrlsted irto app.Jroi Eirros
aotioor [22]. Ia a :imple Michci.lon iatcrferooctcr, a oisaligaraeot of thc bcasrplittcr
lcadr to a !.Eitivity to chaager ia thc bca,m positiotr; a diE r.nc! i!
thc lcltth of thc two arqr lca& ro a scBitiviiy to b.aE djreclio[. Is additio!.
thcE rcauiu a scasitivity duc to irrrgslaritic! i! thc optical compoacn* (ojrron
aad Pockelc cclls ia particular) cvea whcn rhe iaterferooetcr ir wcll aliEacd and
ryEEctrized.