Abstract

We present a method by which the effect of laser field variations on the signal output of an interferometric gravitational wave detector is rigorously determined. Using the Laser Interferometer Gravitational Wave Observatory (LIGO) optical configuration of a power recycled Michelson interferometer with Fabry–Perot arm cavities as an example, we calculate the excess noise after the input filter cavity (mode cleaner) and the dependence of the detector strain sensitivity on laser frequency and amplitude noise, radio frequency oscillator noise, and scattered-light phase noise. We find that noise on the radio frequency sidebands generally limits the detector’s sensitivity.

© 2000 Optical Society of America

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  1. A. Abramovici, W. Althouse, R. W. P. Drever, Y. Gursel, S. Kawamura, F. J. Raab, D. Shoemaker, L. Sievers, R. E. Spero, R. E. Vogt, R. Weiss, S. E. Whitcomb, M. E. Zucker, “LIGO: The Laser Interferometer Gravitational-Wave Observatory,” Science 256, 325–333 (1992).
    [CrossRef] [PubMed]
  2. A. Giazotto, “The VIRGO experiment: status of the art,” in First Edoardo Amaldi Conference on Gravitational Wave Experiments, E. Coccia, G. Pizella, F. Ronga, eds. (World Scientific, Singapore, 1995), pp. 86–99.
  3. K. Tsubono, “300-m laser interferometer gravitational wave detector (TAMA300) in Japan,” in First Edoardo Amaldi Conference on Gravitational Wave Experiments, E. Coccia, G. Pizella, F. Ronga, eds. (World Scientific, Singapore, 1995), pp. 112–114.
  4. K. Danzmann, “GEO600—a 600 m laser interferometric gravitational wave antenna,” in First Edoardo Amaldi Conference on Gravitational Wave Experiments, E. Coccia, G. Pizella, F. Ronga, eds. (World Scientific, Singapore, 1995), pp. 100–111.
  5. R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, H. Ward, “Laser phase and frequency stabilization using an optical resonator,” Appl. Phys. B 31, 97–105 (1983).
    [CrossRef]
  6. R. Drever, in Quantum Optics, Experimental Gravity and Measurement Theory, P. Meystre, M. Scully, eds. (Plenum, New York, 1983), pp. 503–514.
  7. A. Siegman, Lasers (University Science, Mill Valley, Calif., 1986), Chap. 11.
  8. M. Regehr, “Signal extraction and control for an interferometric gravitational wave detector,” Ph.D. dissertation (California Institute of Technology, Pasadena, Calif., 1995).
  9. K. D. Skeldon, K. A. Strain, “Response of a Fabry–Perot optical cavity to phase-modulation sidebands for use in electro-optic control systems,” Appl. Opt. 36, 6802–6808 (1997).
    [CrossRef]
  10. S. Whitcomb, “Optics Development for LIGO,” in Proceedings of the TAMA International Workshop on Gravitational Wave Detection, K. Tsubono, M.-K. Fujimoto, K. Kuroda, eds. (Universal Academy Press, Tokyo, 1996), pp. 229–239.
  11. Marconi model 2023.
  12. D. E. McClelland, J. B. Camp, J. Mason, W. Kells, S. E. Whitcomb, “Arm cavity resonant sideband control for laser interferometric gravitational wave detectors,” Opt. Lett. 24, 1014–1016 (1999).
    [CrossRef]

1999 (1)

1997 (1)

1992 (1)

A. Abramovici, W. Althouse, R. W. P. Drever, Y. Gursel, S. Kawamura, F. J. Raab, D. Shoemaker, L. Sievers, R. E. Spero, R. E. Vogt, R. Weiss, S. E. Whitcomb, M. E. Zucker, “LIGO: The Laser Interferometer Gravitational-Wave Observatory,” Science 256, 325–333 (1992).
[CrossRef] [PubMed]

1983 (1)

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, H. Ward, “Laser phase and frequency stabilization using an optical resonator,” Appl. Phys. B 31, 97–105 (1983).
[CrossRef]

Abramovici, A.

A. Abramovici, W. Althouse, R. W. P. Drever, Y. Gursel, S. Kawamura, F. J. Raab, D. Shoemaker, L. Sievers, R. E. Spero, R. E. Vogt, R. Weiss, S. E. Whitcomb, M. E. Zucker, “LIGO: The Laser Interferometer Gravitational-Wave Observatory,” Science 256, 325–333 (1992).
[CrossRef] [PubMed]

Althouse, W.

A. Abramovici, W. Althouse, R. W. P. Drever, Y. Gursel, S. Kawamura, F. J. Raab, D. Shoemaker, L. Sievers, R. E. Spero, R. E. Vogt, R. Weiss, S. E. Whitcomb, M. E. Zucker, “LIGO: The Laser Interferometer Gravitational-Wave Observatory,” Science 256, 325–333 (1992).
[CrossRef] [PubMed]

Camp, J. B.

Danzmann, K.

K. Danzmann, “GEO600—a 600 m laser interferometric gravitational wave antenna,” in First Edoardo Amaldi Conference on Gravitational Wave Experiments, E. Coccia, G. Pizella, F. Ronga, eds. (World Scientific, Singapore, 1995), pp. 100–111.

Drever, R.

R. Drever, in Quantum Optics, Experimental Gravity and Measurement Theory, P. Meystre, M. Scully, eds. (Plenum, New York, 1983), pp. 503–514.

Drever, R. W. P.

A. Abramovici, W. Althouse, R. W. P. Drever, Y. Gursel, S. Kawamura, F. J. Raab, D. Shoemaker, L. Sievers, R. E. Spero, R. E. Vogt, R. Weiss, S. E. Whitcomb, M. E. Zucker, “LIGO: The Laser Interferometer Gravitational-Wave Observatory,” Science 256, 325–333 (1992).
[CrossRef] [PubMed]

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, H. Ward, “Laser phase and frequency stabilization using an optical resonator,” Appl. Phys. B 31, 97–105 (1983).
[CrossRef]

Ford, G. M.

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, H. Ward, “Laser phase and frequency stabilization using an optical resonator,” Appl. Phys. B 31, 97–105 (1983).
[CrossRef]

Giazotto, A.

A. Giazotto, “The VIRGO experiment: status of the art,” in First Edoardo Amaldi Conference on Gravitational Wave Experiments, E. Coccia, G. Pizella, F. Ronga, eds. (World Scientific, Singapore, 1995), pp. 86–99.

Gursel, Y.

A. Abramovici, W. Althouse, R. W. P. Drever, Y. Gursel, S. Kawamura, F. J. Raab, D. Shoemaker, L. Sievers, R. E. Spero, R. E. Vogt, R. Weiss, S. E. Whitcomb, M. E. Zucker, “LIGO: The Laser Interferometer Gravitational-Wave Observatory,” Science 256, 325–333 (1992).
[CrossRef] [PubMed]

Hall, J. L.

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, H. Ward, “Laser phase and frequency stabilization using an optical resonator,” Appl. Phys. B 31, 97–105 (1983).
[CrossRef]

Hough, J.

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, H. Ward, “Laser phase and frequency stabilization using an optical resonator,” Appl. Phys. B 31, 97–105 (1983).
[CrossRef]

Kawamura, S.

A. Abramovici, W. Althouse, R. W. P. Drever, Y. Gursel, S. Kawamura, F. J. Raab, D. Shoemaker, L. Sievers, R. E. Spero, R. E. Vogt, R. Weiss, S. E. Whitcomb, M. E. Zucker, “LIGO: The Laser Interferometer Gravitational-Wave Observatory,” Science 256, 325–333 (1992).
[CrossRef] [PubMed]

Kells, W.

Kowalski, F. V.

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, H. Ward, “Laser phase and frequency stabilization using an optical resonator,” Appl. Phys. B 31, 97–105 (1983).
[CrossRef]

Mason, J.

McClelland, D. E.

Munley, A. J.

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, H. Ward, “Laser phase and frequency stabilization using an optical resonator,” Appl. Phys. B 31, 97–105 (1983).
[CrossRef]

Raab, F. J.

A. Abramovici, W. Althouse, R. W. P. Drever, Y. Gursel, S. Kawamura, F. J. Raab, D. Shoemaker, L. Sievers, R. E. Spero, R. E. Vogt, R. Weiss, S. E. Whitcomb, M. E. Zucker, “LIGO: The Laser Interferometer Gravitational-Wave Observatory,” Science 256, 325–333 (1992).
[CrossRef] [PubMed]

Regehr, M.

M. Regehr, “Signal extraction and control for an interferometric gravitational wave detector,” Ph.D. dissertation (California Institute of Technology, Pasadena, Calif., 1995).

Shoemaker, D.

A. Abramovici, W. Althouse, R. W. P. Drever, Y. Gursel, S. Kawamura, F. J. Raab, D. Shoemaker, L. Sievers, R. E. Spero, R. E. Vogt, R. Weiss, S. E. Whitcomb, M. E. Zucker, “LIGO: The Laser Interferometer Gravitational-Wave Observatory,” Science 256, 325–333 (1992).
[CrossRef] [PubMed]

Siegman, A.

A. Siegman, Lasers (University Science, Mill Valley, Calif., 1986), Chap. 11.

Sievers, L.

A. Abramovici, W. Althouse, R. W. P. Drever, Y. Gursel, S. Kawamura, F. J. Raab, D. Shoemaker, L. Sievers, R. E. Spero, R. E. Vogt, R. Weiss, S. E. Whitcomb, M. E. Zucker, “LIGO: The Laser Interferometer Gravitational-Wave Observatory,” Science 256, 325–333 (1992).
[CrossRef] [PubMed]

Skeldon, K. D.

Spero, R. E.

A. Abramovici, W. Althouse, R. W. P. Drever, Y. Gursel, S. Kawamura, F. J. Raab, D. Shoemaker, L. Sievers, R. E. Spero, R. E. Vogt, R. Weiss, S. E. Whitcomb, M. E. Zucker, “LIGO: The Laser Interferometer Gravitational-Wave Observatory,” Science 256, 325–333 (1992).
[CrossRef] [PubMed]

Strain, K. A.

Tsubono, K.

K. Tsubono, “300-m laser interferometer gravitational wave detector (TAMA300) in Japan,” in First Edoardo Amaldi Conference on Gravitational Wave Experiments, E. Coccia, G. Pizella, F. Ronga, eds. (World Scientific, Singapore, 1995), pp. 112–114.

Vogt, R. E.

A. Abramovici, W. Althouse, R. W. P. Drever, Y. Gursel, S. Kawamura, F. J. Raab, D. Shoemaker, L. Sievers, R. E. Spero, R. E. Vogt, R. Weiss, S. E. Whitcomb, M. E. Zucker, “LIGO: The Laser Interferometer Gravitational-Wave Observatory,” Science 256, 325–333 (1992).
[CrossRef] [PubMed]

Ward, H.

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, H. Ward, “Laser phase and frequency stabilization using an optical resonator,” Appl. Phys. B 31, 97–105 (1983).
[CrossRef]

Weiss, R.

A. Abramovici, W. Althouse, R. W. P. Drever, Y. Gursel, S. Kawamura, F. J. Raab, D. Shoemaker, L. Sievers, R. E. Spero, R. E. Vogt, R. Weiss, S. E. Whitcomb, M. E. Zucker, “LIGO: The Laser Interferometer Gravitational-Wave Observatory,” Science 256, 325–333 (1992).
[CrossRef] [PubMed]

Whitcomb, S.

S. Whitcomb, “Optics Development for LIGO,” in Proceedings of the TAMA International Workshop on Gravitational Wave Detection, K. Tsubono, M.-K. Fujimoto, K. Kuroda, eds. (Universal Academy Press, Tokyo, 1996), pp. 229–239.

Whitcomb, S. E.

D. E. McClelland, J. B. Camp, J. Mason, W. Kells, S. E. Whitcomb, “Arm cavity resonant sideband control for laser interferometric gravitational wave detectors,” Opt. Lett. 24, 1014–1016 (1999).
[CrossRef]

A. Abramovici, W. Althouse, R. W. P. Drever, Y. Gursel, S. Kawamura, F. J. Raab, D. Shoemaker, L. Sievers, R. E. Spero, R. E. Vogt, R. Weiss, S. E. Whitcomb, M. E. Zucker, “LIGO: The Laser Interferometer Gravitational-Wave Observatory,” Science 256, 325–333 (1992).
[CrossRef] [PubMed]

Zucker, M. E.

A. Abramovici, W. Althouse, R. W. P. Drever, Y. Gursel, S. Kawamura, F. J. Raab, D. Shoemaker, L. Sievers, R. E. Spero, R. E. Vogt, R. Weiss, S. E. Whitcomb, M. E. Zucker, “LIGO: The Laser Interferometer Gravitational-Wave Observatory,” Science 256, 325–333 (1992).
[CrossRef] [PubMed]

Appl. Opt. (1)

Appl. Phys. B (1)

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, H. Ward, “Laser phase and frequency stabilization using an optical resonator,” Appl. Phys. B 31, 97–105 (1983).
[CrossRef]

Opt. Lett. (1)

Science (1)

A. Abramovici, W. Althouse, R. W. P. Drever, Y. Gursel, S. Kawamura, F. J. Raab, D. Shoemaker, L. Sievers, R. E. Spero, R. E. Vogt, R. Weiss, S. E. Whitcomb, M. E. Zucker, “LIGO: The Laser Interferometer Gravitational-Wave Observatory,” Science 256, 325–333 (1992).
[CrossRef] [PubMed]

Other (8)

A. Giazotto, “The VIRGO experiment: status of the art,” in First Edoardo Amaldi Conference on Gravitational Wave Experiments, E. Coccia, G. Pizella, F. Ronga, eds. (World Scientific, Singapore, 1995), pp. 86–99.

K. Tsubono, “300-m laser interferometer gravitational wave detector (TAMA300) in Japan,” in First Edoardo Amaldi Conference on Gravitational Wave Experiments, E. Coccia, G. Pizella, F. Ronga, eds. (World Scientific, Singapore, 1995), pp. 112–114.

K. Danzmann, “GEO600—a 600 m laser interferometric gravitational wave antenna,” in First Edoardo Amaldi Conference on Gravitational Wave Experiments, E. Coccia, G. Pizella, F. Ronga, eds. (World Scientific, Singapore, 1995), pp. 100–111.

R. Drever, in Quantum Optics, Experimental Gravity and Measurement Theory, P. Meystre, M. Scully, eds. (Plenum, New York, 1983), pp. 503–514.

A. Siegman, Lasers (University Science, Mill Valley, Calif., 1986), Chap. 11.

M. Regehr, “Signal extraction and control for an interferometric gravitational wave detector,” Ph.D. dissertation (California Institute of Technology, Pasadena, Calif., 1995).

S. Whitcomb, “Optics Development for LIGO,” in Proceedings of the TAMA International Workshop on Gravitational Wave Detection, K. Tsubono, M.-K. Fujimoto, K. Kuroda, eds. (Universal Academy Press, Tokyo, 1996), pp. 229–239.

Marconi model 2023.

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Figures (7)

Fig. 1
Fig. 1

Schematic of the detector showing laser, phase modulator, mode-cleaner filter cavity, and interferometer, including the recycling cavity (formed by recycling mirror RM, beam splitter BS, and input test mass ITM) and Fabry–Perot arm cavities (formed by ITM and end test mass ETM). Carrier light (solid lines) and sideband light (dashed lines) are shown offset for clarity. A differential arm length change will combine carrier and sidebands at the gw port, where they are detected and demodulated to yield the output signal. Lengths are not drawn to scale.

Fig. 2
Fig. 2

Frequency spectrum of light, showing audio noise sidebands about both carrier and rf sideband frequencies. Eab, electric field component of rf index a and audio index b.

Fig. 3
Fig. 3

Diagram of mode cleaner, showing input and output mirror reflectivities and equilibrium fields. We take the curved mirror reflectivity to be unity.

Fig. 4
Fig. 4

Interferometer mirrors and input and output fields. l1 and l2 are the recycling cavity lengths, rr is the recycling mirror reflectivity, and Ed is the dark port field. ITM, input test mass; ETM, end test mass.

Fig. 5
Fig. 5

Offset of frequency components from mode-cleaner resonances. The curve plots reflected intensity versus frequency of the incident light.

Fig. 6
Fig. 6

Reflectivity of the arm cavity for the carrier field. The input mirror reflectivity is rf, and the end mirror reflectivity is 1.

Fig. 7
Fig. 7

Arm cavity circulating fields. Es is a source field of audio sidebands from arm cavity motion.

Tables (4)

Tables Icon

Table 1 Frequency Spectrum of Noise Sources

Tables Icon

Table 2 Noise Couplings after Mode Cleaner at 100 Hz

Tables Icon

Table 3 Noise Couplings at GW Output at 100 Hz

Tables Icon

Table 4 Symbols and Their Nominal Values in the Initial LIGO Configuration

Equations (50)

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E=E0 exp(iω0t),
ϕL(t)=2πυ0t+2πδυωsin ωt.
EL=E0(exp(iω0t)+πδυω{exp[i(ω0+ω)t]-exp[i(ω0-ω)t]}).
Ei=EL exp(iAosc),Aosc=Γ cos Ωt=EL1+iΓ2[exp(iΩt)+exp(-iΩt)],Γ1;
Ei=E0exp(iω0t)+πδυω{exp[i(ω0+ω)t]-exp[i(ω0-ω)t]}+iΓ2{exp[i(ω0+Ω)t]+exp[i(ω0-Ω)t]}+iπδυΓ2ω{exp[i(ω0+ω+Ω)t]-exp[i(ω0-ω+Ω)t]+exp[i(ω0+ω-Ω)t]-exp[i(ω0-ω-Ω)t]}.
Epn=Escat exp(iω0t)×1+iΓ2[exp(iΩt)+exp(-iΩt)]×{exp[i2kxs cos(ωt)]}=Escat exp(iω0t)×1+iΓ2[exp(iΩt)+exp(-iΩt)]×{1+ikxs[exp(iωt)+exp(-iωt)]}
Et=tmEi-rmEr,
Er=Et exp(-iΦ)rm,
Em=Et exp(-iΦ/2)tm,
Em=tm2Ei exp(-iΦ/2)1+rm2 exp(-iΦ).
2kLm=(2m+1)π,
2LmΩc=(2n)π,
ΦC=2kLm=2c(ω0+ω)(Lm+dxm)=π+2c(ωLm+ω0dxm),
ΦS=2k+Ω+dΩcLm=π+2c(ωLm+ω0dxm+dΩLm),
exp(iΦ)1+iΦ.
Emc=iEic1+iωLmc+kdxm1+2iGmωLmc+kdxm,
Ems=iEis1+iωLmc+kdxm+dΩLmc1+2iGmωLmc+kdxm+dΩLmc
Emc=iEic1-2iGmωLmc+kdxm,
Ems=iEis1-2iGmωLmc+kdxm+dΩLmc.
Ed=Em2tr[r2 exp(-iϕ2)-r1 exp(-iϕ1)]1+rr2[r1 exp(-iϕ1)+r2 exp(-iϕ2)],
Edc=Emc2trΔr1+rrrc,
rc=r0+irfωωc+iGakdxa1+iωωc,
Edc=Emc2trGrc×Acm1+irfωωc+iGakdxa-+ikdxr-1+iωωcc,
Eds=-iEmstrGrsΩδc+ωδc+kdxr-,
Edc=Epnc1+irfωωc+iGakdxa-+ikdxr-1+iωωc.
Eds=-EmstrGrsiΩδc+kdxr-,
Edc=Epnc2tfGa1+iωωc.
ip=8ehυ0ΓPGm2πLmc2(δυdΩ),
Is=e2Phυ01/2.
I=ehυ0ΓPtr2GrcGrsΩδcπδυωAcm.
I=12ehυ0ΓPtr2GrcGrsΩδc(Gakxa-).
Is=e4Phυ0trGrsΩδcΓ221/2.
rc=rf+tf2 exp(-iΦ)1+rf exp(-iΦ),
Φ=2k+ωc(L+dxa)=π+2Lωc+2kdxa,
rc=r0+irfωωc+kGadxa1+iωωc,
Ea=Es+Er=Es+Ea exp-i2k+ωcL(-rf)
Ea=Es(1-rf)1+iωωc,
Ed=Estf(1-rf)1+iωωc.
=E02trGrctf1-rf{1+ikxa[exp(iωt)+exp(-iωt)]}.
Ed=E02trGrcGa{1+ikxa[exp(iωt)+exp(-iωt)]}1+iωωc.
E=Re{[E1 exp(iω1t)+E2 exp(iω2t)]exp(iω0t)},
ip=EE*¯={E1E2* exp[i(ω1-ω2)t]+c.c.}=2 Re{E1E2* exp[i(ω1-ω2)t]},
ip=2 Re{E00E-1-1* exp[i(Ω+ω)t]+E00E-11* exp[i(Ω-ω)t]+E11E00* exp[i(Ω+ω)t]+E1-1E00* exp[i(Ω-ω)t]+E0-1E-10* exp[i(Ω-ω)t]+E10E0-1* exp[i(Ω+ω)t]+E01E-10* exp[i(Ω+ω)t]+E10E01* exp[i(Ω-ω)t]},
V=ip sin Ωtdt,
V=-Im[E00(E-1-1*-E1-1*)+E00*(E11-E-11)+E01(E-10*-E10*)+E0-1*(E10-E-10)exp(iωt)],
Mag[V]=|E00(E-1-1*-E1-1*)+E00*(E11-E-11)+E01(E-10*-E10*)+E0-1*(E10-E-10)|.
V=ip cos Ωtdt,
Mag[V]=|E00(E-1-1*+E1-1*)+E00*(E11+E-11)+E01(E-10*+E10*)+E0-1*(E10+E-10)|.
A=Γ{sin Ωt+(a0/2)[cos(Ω+ω)t+cos(Ω-ω)t]}.
V=Re[(E00E-10*+E10E00*)exp(iΩt)]a02[cos(Ω+ω)t+cos(Ω-ω)t]dt=-Re(E00E-10*+E10E00*)a0 cos(ωt).

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