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

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ii c○ 2001 James E. Mason All Rights Reserved
Abstract iii The LIGO project is two 4 km baseline interferometers which are currently being constructed in the quest to directly detect gravitational radiation. Concurrent with this effort is research aimed at increasing the strain sensitivity of the initial interferometers to 2.5 × 10 −23 / √ Hz. The optical configuration, which defines the detector gain and bandwidth, is one such area of research. Resonant sideband extraction (RSE) is the configuration which is proposed for advanced LIGO. RSE allows for much more freedom in the optimization of the detector response compared to the initial configuration. The principle of RSE is examined in the context of a three mirror coupled cavity. The effect of optical losses on the design of an RSE interferometer is discussed. Two model optimizations of the interferometer design are done: one for binary inspiral sources and one for periodic sources at 1 kHz. An optical heterodyne signal extraction scheme is proposed to sense the deviation of the mirrors away from their nominal positions, and to read out the gravitational wave signal. The scheme is applied to the two model interferometers previously designed, and its performance is analyzed for each case. Allowable residual deviations of the common mode degrees of freedom are also derived. A tabletop prototype of an RSE interferometer has been constructed to demon- strate both the viability of the proposed signal extraction scheme and the tunability of the RSE interferometer. Good agreement on both counts is found between the measured experimental data and the modeled predictions. The coupling of laser frequency and amplitude noise into the gravitational wave readout port is analyzed for the RSE configuration assuming the proposed gravitational wave signal readout scheme. Specifications for the allowable laser frequency and amplitude noise, as well as allowable residual deviations of the differential mode degrees of freedom, are derived for the two model interferometers.
Page 1: Signal Extraction and Optical Desig
Page 5 and 6: v Of course, one couldn’t last si
Page 7 and 8: vii 2.3.2 Optimized Broadband . . .
Page 9 and 10: ix 5.7.2 Narrowband RSE . . . . . .
Page 11 and 12: xi 3.11 Signal cavity spectral sche
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
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38 mirror is calculated based on th
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40 This is not the transmissivity o
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Cavity reflectivity 1 0.9 0.8 0.7 0
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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
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228 [19] Yuk Tung Liu and Kip S. Th
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230 [38] T.T. Lyons, M.W. Regehr, a
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232 [60] J.E. Mason. Noise coupling
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