Isola d’Elba, Italy 2006
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Isola d’Elba, Italy 2006GWADW-VESF meeting
Diagonalizing sensing matrix of RSE interferometer
Shuichi Sato
TAMA projectNational Astronomical Observatory of Japan
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IntroductionBackgroundOverview of RSE interferometerHistorical review
Signal extraction scheme(1)Modulation arrangementSignal sensing matrix
Signal extraction scheme(2)“Delocation”Signal sensing matrix
Summary
Contents
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BackgroundLCGT : (exact) broadband RSE
3km longUndergroundCryogenic
No specific R&D for broadband RSERSE
GoalDevelop length sensing scheme
Points(Sufficiently) Diagonal sensing matrixRobust sensing schemeScheme less sensitive to various noisesEasy to acquire lock
Introduction
Tokyo
Kamioka
~250 km
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Additional mirror (SEM) at dark portLCGT: (exact) broadband RSE
Length degrees of freedomCommon-arm: Lp = (L1+L2 )/2Differential-arm: Lm = (L1-L2 )/2Power-recycling cavity: lp = (l1+l2)/2Michelson : lm = (l1-l2 )/2Signal-extraction cavity: ls = (l3+l4 )/2
Signal portsBright (reflection)PickoffDark (GW-readout)
RSE interferometer
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Idea of RSEMPQ
Jun MizunoSeveral schemes and experiments (past)
MPQGerhard Heinzel et al.
CaltechJames Mason et al.
Australian National UniversityDaniel Shaddock et al.
University of FloridaGuido Müller et al.
NAOJ (Suspended w/o PRM as a part of full-RSE)Osamu Miyakawa, Kentaro Somiya
Several schemes and experiments (on-going)40m@Caltech : Suspended, detuned (broadband)
LIGO 40m team4m@NAOJ (full-RSE this time!) : Suspended, Broadband
Fumiko Kawazoe, Volker Leonhardt et al.Tabletop@ANU : Fixed, detuned
David Rabeling et al.
Historical review
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Readout schemeRF readoutDC readout is still under consideration
Modulation schemeDouble modulation (producing balanced sidebands)Double demodulationParallel EOM modulation (to avoid sub-sidebands)
Modulation arrangementCarrierPhase modulationAmplitude modulation
Signal extractionArm control signals from CR x PMSignals for central part of RSE from PM x AM
Base line
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CarrierCirculates inside arms and PRC
Phase modulation (f1) circulates inside PRC+SEC
Amplitude modulation (f2) circulates inside PRC
No longer coupled cavityFor both modulation side bandsPM: Michelson as a steering mirrorAM: Michelson as an ideal reflection mirror
Modulation design (1)
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Michelson interferometer (MI) is a kind of “mirror” rMI, tMI are functions of lsch and Ωm
rMI = cos(lsch Ωm/c)tMI = i sin(lsch Ωm/c)
Point 1MI is transparent to PM
rMIPM = cos(lsch ΩPM/c) = 0, lsch ΩPM/c = 0+nπ
Point 2MI is opaque to AM
rMIAM = cos(lsch ΩAM/c) = 1, lsch ΩAM/c = π/2+mπ
Example:lsch = 7.5 mΩPM = 10 MHzΩAM = 60 MHz (2ΩPM = 20MHz, 4ΩPM = 40MHz does not work)
Modulation design (2)
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L-signalsFrom CR x PMAlmost diagonal due to carrier enhancement in arms
l-signals (central part of RSE)From PM x AMOrthogonal (instead of diagonal)
LCGT base line
Signal extraction matrix
Black: Analytic resultsRed: Numerical simulation using “FINESSE”
lplp
lslsdiagonal orthogonal
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Same modulation arrangementsPM: circulates inside PRC+SECAM: circulates inside PRC
The ideaMake use of slight “off-resonance”
→ Causes rotation of sideband fieldsDifferent demodulation phasesTwo diagonal signals from one port
“Delocation”
0 1 2 3 4 5 6- 1
- 0.5
0
0.5
1
0 1 2 3 4 5 6- 1
- 0.5
0
0.5
1
lp lpls
ls
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Almost diagonal!Perfect separation for lp and ls (in principle)
Some effect on Signal strengthOff-diagonals
Sensing matrix
DMPort RF1 RF2
1 0
1 0
1 0
1 0
1 0
Phase Degrees of freedomLp Lm lp lm ls
Bright CRPM -1.3 - 0 0.00356 0 0.002561 0 -0.0026 -0.000062 -0.0013
Dark CRPM 90 - 0 0 0.001 00 1 0 0.0013 0
Bright AMPM -1.3 14.4 0.001 0 0 0-0.0017 0 1 0 0
Dark AMPM 90 -14.4 0 0.001 0 00 -0.0017 0 1 0
Pickoff AMPM -1.3 42.4 0.001 -0.001 0 010.00088 0 0 0
Black: Analytic resultsRed: Numerical simulation using “FINESSE”
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Base line signal sensing scheme for LCGT
Simple arrangement of modulations PM: inside PRC+SECAM: inside PRC
Delocation enables diagonal signal sensing
Still need to verifyLock acquisitionNoise issueRobustness
Summary
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