P010010-00-R - LIGO - California Institute of Technology

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List of Figures x 1.1 Internal thermal noise for fused silica and sapphire. . . . . . . . . . . 9 2.1 RSE interferometer optical layout. . . . . . . . . . . . . . . . . . . . . 20 2.2 Equivalent three mirror coupled cavity for differential signals. . . . . 21 2.3 Tile plot for coupled cavity with an under-coupled signal cavity. . . . 23 2.4 Coupled cavity transmittance with an under-coupled signal cavity. . . 25 2.5 Peak frequency and bandwidth vs. detuning. . . . . . . . . . . . . . . 28 2.6 Tile plot for a coupled cavity with an over-coupled signal cavity. . . . 30 2.7 Coupled cavity transmittance with an over-coupled signal cavity. . . . 31 2.8 The effect of a field incident on a moving mirror. . . . . . . . . . . . . 31 2.9 Arm cavity power as a function of ITM transmittance. . . . . . . . . 37 2.10 The effect of losses in the signal cavity. . . . . . . . . . . . . . . . . . 40 2.11 Cavity reflectivity as a function of one mirror’s transmittance. . . . . 42 2.12 1 kHz narrowband optimization. . . . . . . . . . . . . . . . . . . . . . 47 2.13 1 kHz shot noise limited sensitivity . . . . . . . . . . . . . . . . . . . 48 2.14 bench.m optimization for neutron binary coalescence. . . . . . . . . . 51 3.1 Signal extraction in the inphase demodulation. . . . . . . . . . . . . . 61 3.2 Signal extraction in the quadrature demodulation. . . . . . . . . . . . 62 3.3 Generation of the signal phasors. . . . . . . . . . . . . . . . . . . . . 63 3.4 Unbalanced RF sidebands in the phasor picture. . . . . . . . . . . . . 64 3.5 Example configuration for Twiddle. . . . . . . . . . . . . . . . . . . . 65 3.6 The optical layout of the RSE interferometer. . . . . . . . . . . . . . 67 3.7 The Michelson “mirror.” . . . . . . . . . . . . . . . . . . . . . . . . . 68 3.8 The power/signal coupled cavity. . . . . . . . . . . . . . . . . . . . . 69 3.9 Power/signal coupled cavity transmittance as a function of asymmetry. 73 3.10 Power and signal cavity spectral schematics. . . . . . . . . . . . . . . 77
xi 3.11 Signal cavity spectral schematic for a detuned RSE interferometer. . . 78 3.12 A single cavity representation of the RSE interferometer. . . . . . . . 82 3.13 Variation of the frequency of peak sensitivity with demodulation phase for narrowband RSE. . . . . . . . . . . . . . . . . . . . . . . . . . . . 91 3.14 Variation of the frequency of peak sensitivity with demodulation phase for optimized broadband. . . . . . . . . . . . . . . . . . . . . . . . . . 92 4.1 Layout of the optical table for the RSE experiment. . . . . . . . . . . 105 4.2 Calibration of photodiode/mixer gain. . . . . . . . . . . . . . . . . . 111 4.3 Fast piezo mirror actuator. . . . . . . . . . . . . . . . . . . . . . . . . 113 4.4 Block diagram of the feedback electronics. . . . . . . . . . . . . . . . 115 4.5 Block diagram of the RF frequency generation board. . . . . . . . . 117 4.6 Mode matching as a function of cavity loss, given a measured visibility. 121 4.7 Experimental setup for the Φ+ and Φ− demodulation phase optimization.125 4.8 Experimental setup for transfer function measurements in the dual- recycled Michelson. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134 4.9 Dual-recycled Michelson transfer function measurements. . . . . . . . 135 4.10 RSE transfer function data for the minor degrees of freedom. . . . . . 138 4.11 RSE transfer function data at the pickoff 81 MHz port. . . . . . . . . 139 4.12 Raw data of the Φ− transfer function measurement of the Fabry-Perot Michelson. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141 4.13 Measurement of the RSE gravitational wave transfer function, relative to the same measurement in the FPM. . . . . . . . . . . . . . . . . . 142 4.14 RSE transfer function of Figure 4.13, as well as one with an offset added to the φs signal. . . . . . . . . . . . . . . . . . . . . . . . . . . 143 4.15 RSE transfer function sensitivity to demodulation phase. . . . . . . . 145 5.1 Phasor representation of gravitational wave signal generation. . . . . 149 5.2 Phasor representation of frequency noise generation. . . . . . . . . . . 149 5.3 Phasor representation of amplitude noise generation. . . . . . . . . . 150 5.4 Phasor representation of second order amplitude noise generation. . . 151
Page 1 and 2: Signal Extraction and Optical Desig
Page 3 and 4: Abstract iii The LIGO project is tw
Page 5 and 6: v Of course, one couldn’t last si
Page 7 and 8: vii 2.3.2 Optimized Broadband . . .
Page 9: ix 5.7.2 Narrowband RSE . . . . . .
Page 13 and 14: xiii D.7 Michelson compensation boa
Page 15 and 16: xv 4.2 Effective response of the mi
Page 17 and 18: 2 into which a stone has been dropp
Page 19 and 20: 4 but no smoke). These tricks have
Page 21 and 22: 6 At the heart of passive technique
Page 23 and 24: 8 The various terms are defined as
Page 25 and 26: Pendulum Thermal Noise 10 The test
Page 27 and 28: 12 back-action force on the inciden
Page 29 and 30: 14 Scatter and absorption of coatin
Page 31 and 32: 16 Another feature of signal tuned
Page 33 and 34: 18 A scheme for controlling the fiv
Page 35 and 36: Laser PD1 PD2 ¦¡¦ ¥¡¥ PRM +
Page 37 and 38: 22 known as the detuning phase. The
Page 39 and 40: 24 cavity induces a phase shift upo
Page 41 and 42: 26 of the first cavity, then for a
Page 43 and 44: Frequency (Hz) 5000 4000 3000 2000
Page 45 and 46: 0.8 0.6 0.4 0.2 0 −4 φ sec 1 6 5
Page 47 and 48: the mirror is 32 i2k(l+δl/2 cos(ω
Page 49 and 50: The shot noise current spectral den
Page 51 and 52: 36 depends on the choice of ITM, up
Page 53 and 54: 38 mirror is calculated based on th
Page 55 and 56: 40 This is not the transmissivity o
Page 57 and 58: Cavity reflectivity 1 0.9 0.8 0.7 0
Page 59 and 60: 44 For high frequency response, bot
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46 Although this is a tiny signal,
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Strain sensitivity (h(f)/rtHz) 10
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50 sources the interferometer would
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Chapter 3 Signal Extraction 52 The
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photodiode is proportional to 54 |E
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56 The demodulation phase β = 0 is
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58 to the difference in the rates o
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60 out of the amplitude of the audi
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62 is non-zero. This is the basic f
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64 further to generate the second o
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The source amplitude is set by the
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68 of their sum and difference, or
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however, is given by 70 φ− = Ω
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72 transmittance is then higher tha
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74 resonance, for both upper and lo
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76 due to the fluctuating length of
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78 the hash marks corresponding to
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sensitive to differential signals,
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Laser �§�� §� rp
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compound mirror. The derivatives of
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freedom. 86 N ′ = 1 ∂rc −irc
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88 The φs degree of freedom is qui
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care must be applied to this questi
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92 The magnitude likewise doesn’t
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94 Φ+ Φ− φ+ φ− φs Refl 81
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96 10 more than this. With a transm
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98 factor to Φ+, which was ∼ 500
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100 Degree of freedom Residual leng
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3.5 Conclusions 102 Designing the R
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Chapter 4 104 The RSE Tabletop Prot
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106 Two input test masses (ITM) and
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108 a CVI W1-1064 window, AR coated
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110 order diffracted beam. Although
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112 Reflected 81 Reflected 54 Picko
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114 combination of the PRM and SM1
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116 from ETM2 and SM5. A box of ele
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118 output roughly +18 dBm, while t
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120 The reflected powers are used t
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122 Waist size (mm) Waist position
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124 characterized mirrors, alignmen
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126 completely different mixer, and
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128 on with minimal gain and using
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130 for the φ− servo, hand tunin
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132 matrix to imperfections in thes
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RF photodiodes L.O. BLP-5 5 MHz low
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136 modeled matrix are the demodula
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138 the dual-recycled Michelson. Th
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140 4.5.3 Gravitational Wave Transf
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Relative Magnitude Relative Phase (
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144 an offset can be estimated. The
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146 Many aspects of the process of
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148 the detuned case is more compli
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150 different, and these terms do n
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152 where there (ideally) is no car
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154 equivalent to shot noise, isign
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156 The laser field can be expanded
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Φ+ = φ3 + φ4 Φ− = φ3 − φ4
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160 Eq. (5.15) will then be evaluat
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DC Carrier Term 162 It’s useful t
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164 of interest, then, the noise si
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166 transmissivity terms. Eq. (5.15
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168 match the detuning phase for th
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170 A second subscript, I or Q, wil
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each noise source. 5.7 Analysis 172
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174 the demodulation phase. This is
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176 noise, the frequency noise spec
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Amplitude noise (arb. units) Freque
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180 ferential length RMS fluctuatio
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182 characterizes the fringe width
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A.1.1 Cavity Coupling 184 One of th
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186 A.1.2 Cavity Approximations The
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esonance. 188 rcanti−res. = rf +
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190 where the primed parameters ref
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Magnitude Phase (degrees) 10 0 10
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194 The magnitude of the transmitte
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196 Where As is 1 − Ls, or one mi
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198 The beamsplitter is typically v
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200 closed loop gain of the control
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202 Substitution and some algebra m
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204 Defining the phases for the RF
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Appendix C 206 Cross-Coupled 2 × 2
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208 the coupling due to the second
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to the disturbance at d1. 210 ⎛
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212 The measurement is also assumed
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214 is replaced with a 1 µF capaci
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216 Figure D.2: PZT compensation sc
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Page 235 and 236:
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Input Test In 1 kΩ 1 kΩ − + 1
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Figure D.10: RF frequency generatio
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Bibliography 226 [1] J. Weber. Dete
Page 243 and 244:
228 [19] Yuk Tung Liu and Kip S. Th
Page 245 and 246:
230 [38] T.T. Lyons, M.W. Regehr, a
Page 247:
232 [60] J.E. Mason. Noise coupling
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P010010-00-R - LIGO - California Institute of Technology

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