Abstract

We present an experimental demonstration of a locking and control scheme for an interferometer using a power-recycled resonant sideband extraction configuration and show that the measured response to mirror vibrations matches an optical model. We discuss some aspects of resonant sideband extraction that are relevant to gravitational-wave detection.

© 2003 Optical Society of America

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  1. J. Mizuno, K. A. Strain, P. G. Nelson, J. M. Chen, R. Schilling, A. Rüdiger, W. Winkler, K. Danzmann, “Resonant sideband extraction: a new configuration for interferometric gravitational-wave detectors,” Phys. Lett. A 175, 273–276 (1993).
    [CrossRef]
  2. R. W. P. Drever, “Interferometric detectors for gravitational radiation,” in Gravitational Radiation, N. Deruelle, T. Piran, eds. (North-Holland, Amsterdam, 1983), pp. 321–337.
  3. A. Abramovici, W. Althouse, W. Drever, Y. Gursel, S. Kawamura, F. Raab, D. Shoemaker, L. Sievers, R. Spero, K. Thorne, R. Vogt, R. Weiss, S. Whitcomb, M. Zucker, “LIGO: the Laser Interferometer Gravitational-Wave Observatory,” Science 256, 325–333 (1992).
    [CrossRef] [PubMed]
  4. M. Ando, K. Tsubono, “TAMA project: design and current status,” in Gravitational Waves, S. Meshkov, ed. (American Institute of Physics, Melville, New York, 1999), pp. 128–139.
  5. R. Passaquieti, “Virgo—an interferometer for gravitational wave detection,” Nucl. Phys. B Proc. Suppl. 85, 241–247 (2000).
    [CrossRef]
  6. B. J. Meers, “Recycling in laser-interferometric gravitational-wave detectors,” Phys. Rev. D 38, 2317–2326 (1988).
    [CrossRef]
  7. K. A. Strain, G. Müller, T. Delker, D. H. Reitze, D. B. Tanner, J. E. Mason, P. A. Willems, D. A. Shaddock, M. B. Gray, C. Mow-Lowry, D. E. McClelland, “Sensing and control in dual-recycling laser interferometer gravitational-wave detectors,” Appl. Opt. 42, 1244–1256 (2003).
    [CrossRef] [PubMed]
  8. L. Schnupp, “Internal modulation schemes,” presented at the European Collaboration Meeting on Interferometric Detection of Gravitational Waves, Sorrento, Italy, 2 Oct. 1988.
  9. M. Regehr, “Signal extraction and control for an interferometric gravitational wave detector,” Ph.D. dissertation (California Institute of Technology, Pasadena, Calif., 1995).
  10. J. Mizuno, “Comparison of optical configurations for laser-interferometric gravitational-wave detectors,” Ph.D. dissertation (Max-Planck-Institute fur Quantenoptik, Garching, Germany, 1995).
  11. There is no useful heterodyne signal in or beyond the arm cavities because there is no sufficient rf sideband amplitude present in the arm cavities to heterodyne against. The light amplitudes at the dark port are just those inside the signal extraction cavity, reduced by the SEM transmission; thus there is no useful additional information about the interferometer degrees of freedom inside the signal extraction cavity.
  12. P. Fritschel, R. Bork, G. González, N. Mavalvala, D. Ouimette, H. Rong, D. Sigg, M. Zucker, “Readout and control of a power-recycled interferometric gravitational-wave antenna,” Appl. Opt. 40, 4988–4998 (2001).
    [CrossRef]
  13. The alert reader may have asked about demodulation at 2f1. This approach is tricky because the approximation of only first-order PM sidebands is not strictly accurate in practice.
  14. A. Freise, G. Heinzel, K. A. Strain, J. Mizuno, K. D. Skeldon, H. Lück, B. Willke, R. Schilling, A. Rüdinger, W. Winkler, K. Danzmann, “Demonstration of detuned dual recycling at the Garching 30m laser interferometer,” Phys. Lett. A 277, 135–142 (2000).
    [CrossRef]
  15. Once again, this is important only in a broadband interferometer. In a detuned interferometer, it does not matter because the relative phases are not preserved when the frequencies are off resonant.
  16. J. Mason, “Signal extraction and optical design for an advanced gravitational wave detector,” Ph.D. dissertation (California Institute of Technology, Pasadena, Calif., 2001).
  17. Twiddle is a Mathematica-based program that solves the self-consistent optical field equations for an interferometer given a set of mirror parameters and spacings and then evaluates transfer functions from mirror motion to output optical sideband fields. See M. Regehr, J. Mason, H. Yamamoto, O. Miyakawa, http://www.phys.ufl.edu/LIGO/LIGO/STAIC.html#9 .
  18. D. Sigg, N. Mavalvala, J. Giaime, P. Fritschel, D. Shoemaker, “Signal extraction in a power-recycled Michelson interferometer with Fabry-Perot arm cavities by use of a multiple-carrier frontal modulation scheme,” Appl. Opt. 37, 5687–5693 (1998).
    [CrossRef]
  19. G. Heinzel, J. Mizuno, R. Schilling, A. Rüdiger, K. Danzmann, “An experimental demonstration of resonant sideband extraction for laser-interferometric gravitational wave detectors,” Phys. Lett. A 217, 305–314 (1996).
    [CrossRef]

2003 (1)

2001 (1)

2000 (2)

A. Freise, G. Heinzel, K. A. Strain, J. Mizuno, K. D. Skeldon, H. Lück, B. Willke, R. Schilling, A. Rüdinger, W. Winkler, K. Danzmann, “Demonstration of detuned dual recycling at the Garching 30m laser interferometer,” Phys. Lett. A 277, 135–142 (2000).
[CrossRef]

R. Passaquieti, “Virgo—an interferometer for gravitational wave detection,” Nucl. Phys. B Proc. Suppl. 85, 241–247 (2000).
[CrossRef]

1998 (1)

1996 (1)

G. Heinzel, J. Mizuno, R. Schilling, A. Rüdiger, K. Danzmann, “An experimental demonstration of resonant sideband extraction for laser-interferometric gravitational wave detectors,” Phys. Lett. A 217, 305–314 (1996).
[CrossRef]

1993 (1)

J. Mizuno, K. A. Strain, P. G. Nelson, J. M. Chen, R. Schilling, A. Rüdiger, W. Winkler, K. Danzmann, “Resonant sideband extraction: a new configuration for interferometric gravitational-wave detectors,” Phys. Lett. A 175, 273–276 (1993).
[CrossRef]

1992 (1)

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

1988 (1)

B. J. Meers, “Recycling in laser-interferometric gravitational-wave detectors,” Phys. Rev. D 38, 2317–2326 (1988).
[CrossRef]

Abramovici, A.

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

Althouse, W.

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

Ando, M.

M. Ando, K. Tsubono, “TAMA project: design and current status,” in Gravitational Waves, S. Meshkov, ed. (American Institute of Physics, Melville, New York, 1999), pp. 128–139.

Bork, R.

Chen, J. M.

J. Mizuno, K. A. Strain, P. G. Nelson, J. M. Chen, R. Schilling, A. Rüdiger, W. Winkler, K. Danzmann, “Resonant sideband extraction: a new configuration for interferometric gravitational-wave detectors,” Phys. Lett. A 175, 273–276 (1993).
[CrossRef]

Danzmann, K.

A. Freise, G. Heinzel, K. A. Strain, J. Mizuno, K. D. Skeldon, H. Lück, B. Willke, R. Schilling, A. Rüdinger, W. Winkler, K. Danzmann, “Demonstration of detuned dual recycling at the Garching 30m laser interferometer,” Phys. Lett. A 277, 135–142 (2000).
[CrossRef]

G. Heinzel, J. Mizuno, R. Schilling, A. Rüdiger, K. Danzmann, “An experimental demonstration of resonant sideband extraction for laser-interferometric gravitational wave detectors,” Phys. Lett. A 217, 305–314 (1996).
[CrossRef]

J. Mizuno, K. A. Strain, P. G. Nelson, J. M. Chen, R. Schilling, A. Rüdiger, W. Winkler, K. Danzmann, “Resonant sideband extraction: a new configuration for interferometric gravitational-wave detectors,” Phys. Lett. A 175, 273–276 (1993).
[CrossRef]

Delker, T.

Drever, R. W. P.

R. W. P. Drever, “Interferometric detectors for gravitational radiation,” in Gravitational Radiation, N. Deruelle, T. Piran, eds. (North-Holland, Amsterdam, 1983), pp. 321–337.

Drever, W.

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

Freise, A.

A. Freise, G. Heinzel, K. A. Strain, J. Mizuno, K. D. Skeldon, H. Lück, B. Willke, R. Schilling, A. Rüdinger, W. Winkler, K. Danzmann, “Demonstration of detuned dual recycling at the Garching 30m laser interferometer,” Phys. Lett. A 277, 135–142 (2000).
[CrossRef]

Fritschel, P.

Giaime, J.

González, G.

Gray, M. B.

Gursel, Y.

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

Heinzel, G.

A. Freise, G. Heinzel, K. A. Strain, J. Mizuno, K. D. Skeldon, H. Lück, B. Willke, R. Schilling, A. Rüdinger, W. Winkler, K. Danzmann, “Demonstration of detuned dual recycling at the Garching 30m laser interferometer,” Phys. Lett. A 277, 135–142 (2000).
[CrossRef]

G. Heinzel, J. Mizuno, R. Schilling, A. Rüdiger, K. Danzmann, “An experimental demonstration of resonant sideband extraction for laser-interferometric gravitational wave detectors,” Phys. Lett. A 217, 305–314 (1996).
[CrossRef]

Kawamura, S.

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

Lück, H.

A. Freise, G. Heinzel, K. A. Strain, J. Mizuno, K. D. Skeldon, H. Lück, B. Willke, R. Schilling, A. Rüdinger, W. Winkler, K. Danzmann, “Demonstration of detuned dual recycling at the Garching 30m laser interferometer,” Phys. Lett. A 277, 135–142 (2000).
[CrossRef]

Mason, J.

J. Mason, “Signal extraction and optical design for an advanced gravitational wave detector,” Ph.D. dissertation (California Institute of Technology, Pasadena, Calif., 2001).

Mason, J. E.

Mavalvala, N.

McClelland, D. E.

Meers, B. J.

B. J. Meers, “Recycling in laser-interferometric gravitational-wave detectors,” Phys. Rev. D 38, 2317–2326 (1988).
[CrossRef]

Mizuno, J.

A. Freise, G. Heinzel, K. A. Strain, J. Mizuno, K. D. Skeldon, H. Lück, B. Willke, R. Schilling, A. Rüdinger, W. Winkler, K. Danzmann, “Demonstration of detuned dual recycling at the Garching 30m laser interferometer,” Phys. Lett. A 277, 135–142 (2000).
[CrossRef]

G. Heinzel, J. Mizuno, R. Schilling, A. Rüdiger, K. Danzmann, “An experimental demonstration of resonant sideband extraction for laser-interferometric gravitational wave detectors,” Phys. Lett. A 217, 305–314 (1996).
[CrossRef]

J. Mizuno, K. A. Strain, P. G. Nelson, J. M. Chen, R. Schilling, A. Rüdiger, W. Winkler, K. Danzmann, “Resonant sideband extraction: a new configuration for interferometric gravitational-wave detectors,” Phys. Lett. A 175, 273–276 (1993).
[CrossRef]

J. Mizuno, “Comparison of optical configurations for laser-interferometric gravitational-wave detectors,” Ph.D. dissertation (Max-Planck-Institute fur Quantenoptik, Garching, Germany, 1995).

Mow-Lowry, C.

Müller, G.

Nelson, P. G.

J. Mizuno, K. A. Strain, P. G. Nelson, J. M. Chen, R. Schilling, A. Rüdiger, W. Winkler, K. Danzmann, “Resonant sideband extraction: a new configuration for interferometric gravitational-wave detectors,” Phys. Lett. A 175, 273–276 (1993).
[CrossRef]

Ouimette, D.

Passaquieti, R.

R. Passaquieti, “Virgo—an interferometer for gravitational wave detection,” Nucl. Phys. B Proc. Suppl. 85, 241–247 (2000).
[CrossRef]

Raab, F.

A. Abramovici, W. Althouse, W. Drever, Y. Gursel, S. Kawamura, F. Raab, D. Shoemaker, L. Sievers, R. Spero, K. Thorne, R. Vogt, R. Weiss, S. Whitcomb, M. 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).

Reitze, D. H.

Rong, H.

Rüdiger, A.

G. Heinzel, J. Mizuno, R. Schilling, A. Rüdiger, K. Danzmann, “An experimental demonstration of resonant sideband extraction for laser-interferometric gravitational wave detectors,” Phys. Lett. A 217, 305–314 (1996).
[CrossRef]

J. Mizuno, K. A. Strain, P. G. Nelson, J. M. Chen, R. Schilling, A. Rüdiger, W. Winkler, K. Danzmann, “Resonant sideband extraction: a new configuration for interferometric gravitational-wave detectors,” Phys. Lett. A 175, 273–276 (1993).
[CrossRef]

Rüdinger, A.

A. Freise, G. Heinzel, K. A. Strain, J. Mizuno, K. D. Skeldon, H. Lück, B. Willke, R. Schilling, A. Rüdinger, W. Winkler, K. Danzmann, “Demonstration of detuned dual recycling at the Garching 30m laser interferometer,” Phys. Lett. A 277, 135–142 (2000).
[CrossRef]

Schilling, R.

A. Freise, G. Heinzel, K. A. Strain, J. Mizuno, K. D. Skeldon, H. Lück, B. Willke, R. Schilling, A. Rüdinger, W. Winkler, K. Danzmann, “Demonstration of detuned dual recycling at the Garching 30m laser interferometer,” Phys. Lett. A 277, 135–142 (2000).
[CrossRef]

G. Heinzel, J. Mizuno, R. Schilling, A. Rüdiger, K. Danzmann, “An experimental demonstration of resonant sideband extraction for laser-interferometric gravitational wave detectors,” Phys. Lett. A 217, 305–314 (1996).
[CrossRef]

J. Mizuno, K. A. Strain, P. G. Nelson, J. M. Chen, R. Schilling, A. Rüdiger, W. Winkler, K. Danzmann, “Resonant sideband extraction: a new configuration for interferometric gravitational-wave detectors,” Phys. Lett. A 175, 273–276 (1993).
[CrossRef]

Schnupp, L.

L. Schnupp, “Internal modulation schemes,” presented at the European Collaboration Meeting on Interferometric Detection of Gravitational Waves, Sorrento, Italy, 2 Oct. 1988.

Shaddock, D. A.

Shoemaker, D.

D. Sigg, N. Mavalvala, J. Giaime, P. Fritschel, D. Shoemaker, “Signal extraction in a power-recycled Michelson interferometer with Fabry-Perot arm cavities by use of a multiple-carrier frontal modulation scheme,” Appl. Opt. 37, 5687–5693 (1998).
[CrossRef]

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

Sievers, L.

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

Sigg, D.

Skeldon, K. D.

A. Freise, G. Heinzel, K. A. Strain, J. Mizuno, K. D. Skeldon, H. Lück, B. Willke, R. Schilling, A. Rüdinger, W. Winkler, K. Danzmann, “Demonstration of detuned dual recycling at the Garching 30m laser interferometer,” Phys. Lett. A 277, 135–142 (2000).
[CrossRef]

Spero, R.

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

Strain, K. A.

K. A. Strain, G. Müller, T. Delker, D. H. Reitze, D. B. Tanner, J. E. Mason, P. A. Willems, D. A. Shaddock, M. B. Gray, C. Mow-Lowry, D. E. McClelland, “Sensing and control in dual-recycling laser interferometer gravitational-wave detectors,” Appl. Opt. 42, 1244–1256 (2003).
[CrossRef] [PubMed]

A. Freise, G. Heinzel, K. A. Strain, J. Mizuno, K. D. Skeldon, H. Lück, B. Willke, R. Schilling, A. Rüdinger, W. Winkler, K. Danzmann, “Demonstration of detuned dual recycling at the Garching 30m laser interferometer,” Phys. Lett. A 277, 135–142 (2000).
[CrossRef]

J. Mizuno, K. A. Strain, P. G. Nelson, J. M. Chen, R. Schilling, A. Rüdiger, W. Winkler, K. Danzmann, “Resonant sideband extraction: a new configuration for interferometric gravitational-wave detectors,” Phys. Lett. A 175, 273–276 (1993).
[CrossRef]

Tanner, D. B.

Thorne, K.

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

Tsubono, K.

M. Ando, K. Tsubono, “TAMA project: design and current status,” in Gravitational Waves, S. Meshkov, ed. (American Institute of Physics, Melville, New York, 1999), pp. 128–139.

Vogt, R.

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

Weiss, R.

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

Whitcomb, S.

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

Willems, P. A.

Willke, B.

A. Freise, G. Heinzel, K. A. Strain, J. Mizuno, K. D. Skeldon, H. Lück, B. Willke, R. Schilling, A. Rüdinger, W. Winkler, K. Danzmann, “Demonstration of detuned dual recycling at the Garching 30m laser interferometer,” Phys. Lett. A 277, 135–142 (2000).
[CrossRef]

Winkler, W.

A. Freise, G. Heinzel, K. A. Strain, J. Mizuno, K. D. Skeldon, H. Lück, B. Willke, R. Schilling, A. Rüdinger, W. Winkler, K. Danzmann, “Demonstration of detuned dual recycling at the Garching 30m laser interferometer,” Phys. Lett. A 277, 135–142 (2000).
[CrossRef]

J. Mizuno, K. A. Strain, P. G. Nelson, J. M. Chen, R. Schilling, A. Rüdiger, W. Winkler, K. Danzmann, “Resonant sideband extraction: a new configuration for interferometric gravitational-wave detectors,” Phys. Lett. A 175, 273–276 (1993).
[CrossRef]

Zucker, M.

P. Fritschel, R. Bork, G. González, N. Mavalvala, D. Ouimette, H. Rong, D. Sigg, M. Zucker, “Readout and control of a power-recycled interferometric gravitational-wave antenna,” Appl. Opt. 40, 4988–4998 (2001).
[CrossRef]

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

Appl. Opt. (3)

Nucl. Phys. B Proc. Suppl. (1)

R. Passaquieti, “Virgo—an interferometer for gravitational wave detection,” Nucl. Phys. B Proc. Suppl. 85, 241–247 (2000).
[CrossRef]

Phys. Lett. A (3)

A. Freise, G. Heinzel, K. A. Strain, J. Mizuno, K. D. Skeldon, H. Lück, B. Willke, R. Schilling, A. Rüdinger, W. Winkler, K. Danzmann, “Demonstration of detuned dual recycling at the Garching 30m laser interferometer,” Phys. Lett. A 277, 135–142 (2000).
[CrossRef]

J. Mizuno, K. A. Strain, P. G. Nelson, J. M. Chen, R. Schilling, A. Rüdiger, W. Winkler, K. Danzmann, “Resonant sideband extraction: a new configuration for interferometric gravitational-wave detectors,” Phys. Lett. A 175, 273–276 (1993).
[CrossRef]

G. Heinzel, J. Mizuno, R. Schilling, A. Rüdiger, K. Danzmann, “An experimental demonstration of resonant sideband extraction for laser-interferometric gravitational wave detectors,” Phys. Lett. A 217, 305–314 (1996).
[CrossRef]

Phys. Rev. D (1)

B. J. Meers, “Recycling in laser-interferometric gravitational-wave detectors,” Phys. Rev. D 38, 2317–2326 (1988).
[CrossRef]

Science (1)

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

Other (10)

M. Ando, K. Tsubono, “TAMA project: design and current status,” in Gravitational Waves, S. Meshkov, ed. (American Institute of Physics, Melville, New York, 1999), pp. 128–139.

R. W. P. Drever, “Interferometric detectors for gravitational radiation,” in Gravitational Radiation, N. Deruelle, T. Piran, eds. (North-Holland, Amsterdam, 1983), pp. 321–337.

L. Schnupp, “Internal modulation schemes,” presented at the European Collaboration Meeting on Interferometric Detection of Gravitational Waves, Sorrento, Italy, 2 Oct. 1988.

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

J. Mizuno, “Comparison of optical configurations for laser-interferometric gravitational-wave detectors,” Ph.D. dissertation (Max-Planck-Institute fur Quantenoptik, Garching, Germany, 1995).

There is no useful heterodyne signal in or beyond the arm cavities because there is no sufficient rf sideband amplitude present in the arm cavities to heterodyne against. The light amplitudes at the dark port are just those inside the signal extraction cavity, reduced by the SEM transmission; thus there is no useful additional information about the interferometer degrees of freedom inside the signal extraction cavity.

The alert reader may have asked about demodulation at 2f1. This approach is tricky because the approximation of only first-order PM sidebands is not strictly accurate in practice.

Once again, this is important only in a broadband interferometer. In a detuned interferometer, it does not matter because the relative phases are not preserved when the frequencies are off resonant.

J. Mason, “Signal extraction and optical design for an advanced gravitational wave detector,” Ph.D. dissertation (California Institute of Technology, Pasadena, Calif., 2001).

Twiddle is a Mathematica-based program that solves the self-consistent optical field equations for an interferometer given a set of mirror parameters and spacings and then evaluates transfer functions from mirror motion to output optical sideband fields. See M. Regehr, J. Mason, H. Yamamoto, O. Miyakawa, http://www.phys.ufl.edu/LIGO/LIGO/STAIC.html#9 .

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Figures (5)

Fig. 1
Fig. 1

Optical layout of the RSE interferometer. r PRM, r bs, and r SEM are the reflectivities of the power-recycling mirror, the beam splitter, and the signal extraction mirror, respectively. r ac1 and r ac2 are the reflectivities of the in-line and perpendicular arm cavities. Sign conventions for the mirror reflectivities are indicated.

Fig. 2
Fig. 2

Layout of the optical table for the RSE experiment. The dark line of the interferometer mirrors indicates the highly reflective side of the optic. The two beams going to the optical spectrum analyzer do not actually perform any interference. At any one time, one of the beams was blocked so that the other could be analyzed. SM, steering mirror; BS, beam splitter; EOM, electro-optic modulator.

Fig. 3
Fig. 3

Measurement of the RSE gravitational-wave transfer function, relative to the same measurement in the FPM. The modeled predictions are the dashed curves.

Fig. 4
Fig. 4

RSE transfer function of Fig. 3, as well as one with an offset added to the ϕ s signal. Model-predicted transfer functions are shown in dashed lighter colors. For clarity, the additionally detuned magnitude data are shifted downward by 1.5.

Fig. 5
Fig. 5

RSE transfer function sensitivity to the demodulation phase. The measured change in the demodulation phase from the curve in Fig. 3 is 46°, whereas the modeled value that matches the data was 43°. Model-predicted curves are shown in dashed lighter colors.

Tables (5)

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Table 1 Matrix of Discriminants for an Optimized Broadband Interferometera

Tables Icon

Table 2 Demodulation Phase Changes for the DRM Relative to the FPM

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Table 3 Powers in the DRM as Measured by the OSAa

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Table 4 DRM Matrix of Discriminantsa

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Table 5 Matrix of Discriminants for the RSE Interferometera

Equations (19)

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Tccω=tItSEM exp-iωτa+τs+ϕdt/21-rIrE exp-iωτa-rIrSEM exp-iωτs+ϕdt+rErSEM1-AIexp-iωτa+τs+ϕdt.
S=2|T1E1T2E2|cosφ-ψ,
S=2T0T+*-T-*cosα-2T0T+*+T-*sinα,
Ei=TiEldi,
Mt,j=|El|2d1d2T1ϕj T2* expiβt+T1T2*ϕjexpiβt
Mt,j=|El|2J0J1T0ϕjT- expiβt+T+ exp-iβt*+T0T-ϕjexpiβt+T+ϕjexp-iβt*
T=itPRM1-arac sinϕ-tSEM exp-iϕ++ϕs/21+rPRM1-arac cosϕ-exp-iϕ+-rSEM1-arac cosϕ-exp-iϕs-rPRMrSEMrac21-a2 exp-iϕ++ϕs,
ϕ-=Ωmodl1-l2c=Ωmodδc.
δ=cΩmodarccos1-arPRM+rSEM1+rPRMrSEM1-a2,
δ=cΩmodarccos1-arSEM-rPRM1-rPRMrSEM1-a2.
ϕ±SB=ϕcarrier±Ωmod2lc.
±Ωmod2lc=nπ-ϕdt,
δlSEC=ϕdtcΩmod,
δl=ϕdtc2πfmod=27.8 cm.
oiij=APZTPopticsSPD+mixer.
o1i1S1P111-1H2P21A1S1P11A1,
o2i2S2P221-1/2A2,
o2i1S2P211-2H2P21A1S2P21A1,
o1i20.

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