Abstract

We introduce length-sensing and control schemes for the dual-recycled cavity-enhanced Michelson interferometer configuration proposed for the Advanced Laser Interferometer Gravitational Wave Observatory (LIGO). We discuss the principles of this scheme and show methods that allow sensing and control signals to be derived. Experimental verification was carried out in three benchtop experiments that are introduced. We present the implications of the results from these experiments for Advanced LIGO and other future interferometric gravitational-wave detectors.

© 2003 Optical Society of America

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    [CrossRef] [PubMed]
  2. C. Bradaschia, R. Del Fabbro, A. Di Virgilio, A. Giazotto, H. Kautzky, V. Montelatici, D. Passuello, A. Brillet, O. Cregut, P. Hello, C. N. Man, P. T. Manh, A. Marraud, D. Shoemaker, J. Y. Vinet, F. Barone, L. Di Fiore, L. Milano, G. Russo, J. M. Aguirregabiria, H. Bel, J. P. Duruisseau, G. Le Denmat, Ph. Tourrenc, M. Capozzi, M. Longo, M. Lops, I. Pinto, G. Rotoli, T. Damour, S. Bonazzola, J. A. Marck, Y. Gourghoulon, L. E. Holloway, F. Fuligni, V. Iafolla, G. Natale, “The Virgo project: a wide band antenna for gravitational wave detection,” Nucl. Instrum. Methods Phys. Res. A 289, 518–525 (1990).
    [CrossRef]
  3. K. Danzmann, H. Lück, A. Rüdiger, R. Schilling, M. Schrempel, W. Winkler, J. Hough, G. P. Newton, N. A. Robertson, H. Ward, A. M. Campbell, J. E. Logan, D. I. Robertson, K. A. Strain, J. R. J. Bennett, V. Kose, M. Kühne, B. F. Schutz, D. Nicholson, J. Shuttleworth, H. Welling, P. Aufmuth, R. Rinkleff, A. Tünnermann, B. Willke, “GEO 600—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.
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  13. C. Cutler, K. S. Thorne, “An overview of gravitational-wave sources,” in Proceedings of the GR16 Conference on General Relativity and Gravitation, N. Bishop, ed. (World Scientific, Singapore, 2002).
    [CrossRef]
  14. 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]
  15. A. Buonanno, Y. Chen, “Quantum noise in second generation, signal-recycled laser interferometric gravitational-wave detectors,” Phys. Rev. D 64, 77–98 (2001).
    [CrossRef]
  16. K. A. Strain, K. Danzmann, P. G. Nelson, A. Rüdiger, R. Schilling, W. Winkler, “Thermal lensing in recycling interferometric gravitational wave detectors,” Phys. Lett. A 194, 124–132 (1994).
    [CrossRef]
  17. 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]
  18. M. Regehr, “Signal extraction and control for a interferometric gravitational wave detector,” Ph.D. dissertation (California Institute of Technology, Pasadena, Calif., 1995).
  19. P. Fritschel, R. Bork, G. González, N. Mavalvala, D. Ouimette, H. Rong, D. Sigg, M. Zucker, “Readout and control of a power-recycle interferometric gravitational-wave antenna,” Appl. Opt. 40, 4988–4998 (2001).
    [CrossRef]
  20. B. J. Meers, A. Krolak, J. A. Lobo, “Dynamically tuned interferometers for the observation of gravitational waves from coalescing compact binaries,” Phys. Rev. D 47, 2184–2197 (1993).
    [CrossRef]
  21. A. Weinstein, “Advanced LIGO optical configuration, prototyping, and modeling,” Class. Quantum Grav. 19, 1575–1584 (2002).
    [CrossRef]
  22. A. Rüdiger, R. Schilling, L. Schnupp, W. Winkler, H. Billing, K. Maischberger, “A mode selector to suppress fluctuations in laser beam geometry,” Opt. Acta 28, 641–658 (1981).
    [CrossRef]
  23. L. Schnupp, “Internal modulation schemes,” presented at the European Collaboration Meeting on Interferometric Detection of Gravitational Waves, Sorrento, Italy, 2 Oct. 1988.

2003 (3)

2002 (1)

A. Weinstein, “Advanced LIGO optical configuration, prototyping, and modeling,” Class. Quantum Grav. 19, 1575–1584 (2002).
[CrossRef]

2001 (2)

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

A. Buonanno, Y. Chen, “Quantum noise in second generation, signal-recycled laser interferometric gravitational-wave detectors,” Phys. Rev. D 64, 77–98 (2001).
[CrossRef]

1994 (1)

K. A. Strain, K. Danzmann, P. G. Nelson, A. Rüdiger, R. Schilling, W. Winkler, “Thermal lensing in recycling interferometric gravitational wave detectors,” Phys. Lett. A 194, 124–132 (1994).
[CrossRef]

1993 (2)

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]

B. J. Meers, A. Krolak, J. A. Lobo, “Dynamically tuned interferometers for the observation of gravitational waves from coalescing compact binaries,” Phys. Rev. D 47, 2184–2197 (1993).
[CrossRef]

1992 (1)

A. Abramovici, W. Althouse, R. 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]

1991 (1)

E. S. Phinney, “The rate of neutron star binary mergers in the universe: minimal predictions for gravity wave detectors,” Astrophys. J. Lett. 380, L17–L21 (1991).
[CrossRef]

1990 (1)

C. Bradaschia, R. Del Fabbro, A. Di Virgilio, A. Giazotto, H. Kautzky, V. Montelatici, D. Passuello, A. Brillet, O. Cregut, P. Hello, C. N. Man, P. T. Manh, A. Marraud, D. Shoemaker, J. Y. Vinet, F. Barone, L. Di Fiore, L. Milano, G. Russo, J. M. Aguirregabiria, H. Bel, J. P. Duruisseau, G. Le Denmat, Ph. Tourrenc, M. Capozzi, M. Longo, M. Lops, I. Pinto, G. Rotoli, T. Damour, S. Bonazzola, J. A. Marck, Y. Gourghoulon, L. E. Holloway, F. Fuligni, V. Iafolla, G. Natale, “The Virgo project: a wide band antenna for gravitational wave detection,” Nucl. Instrum. Methods Phys. Res. A 289, 518–525 (1990).
[CrossRef]

1988 (1)

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

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]

1981 (1)

A. Rüdiger, R. Schilling, L. Schnupp, W. Winkler, H. Billing, K. Maischberger, “A mode selector to suppress fluctuations in laser beam geometry,” Opt. Acta 28, 641–658 (1981).
[CrossRef]

1887 (1)

A. A. Michelson, E. W. Morley, “On the relative motion of the earth and the luminiferous ether,” Am. J. Sci. 35, 333–345 (1887).
[CrossRef]

Abramovici, A.

A. Abramovici, W. Althouse, R. 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]

Aguirregabiria, J. M.

C. Bradaschia, R. Del Fabbro, A. Di Virgilio, A. Giazotto, H. Kautzky, V. Montelatici, D. Passuello, A. Brillet, O. Cregut, P. Hello, C. N. Man, P. T. Manh, A. Marraud, D. Shoemaker, J. Y. Vinet, F. Barone, L. Di Fiore, L. Milano, G. Russo, J. M. Aguirregabiria, H. Bel, J. P. Duruisseau, G. Le Denmat, Ph. Tourrenc, M. Capozzi, M. Longo, M. Lops, I. Pinto, G. Rotoli, T. Damour, S. Bonazzola, J. A. Marck, Y. Gourghoulon, L. E. Holloway, F. Fuligni, V. Iafolla, G. Natale, “The Virgo project: a wide band antenna for gravitational wave detection,” Nucl. Instrum. Methods Phys. Res. A 289, 518–525 (1990).
[CrossRef]

Althouse, W.

A. Abramovici, W. Althouse, R. 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]

Aufmuth, P.

K. Danzmann, H. Lück, A. Rüdiger, R. Schilling, M. Schrempel, W. Winkler, J. Hough, G. P. Newton, N. A. Robertson, H. Ward, A. M. Campbell, J. E. Logan, D. I. Robertson, K. A. Strain, J. R. J. Bennett, V. Kose, M. Kühne, B. F. Schutz, D. Nicholson, J. Shuttleworth, H. Welling, P. Aufmuth, R. Rinkleff, A. Tünnermann, B. Willke, “GEO 600—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.

Barone, F.

C. Bradaschia, R. Del Fabbro, A. Di Virgilio, A. Giazotto, H. Kautzky, V. Montelatici, D. Passuello, A. Brillet, O. Cregut, P. Hello, C. N. Man, P. T. Manh, A. Marraud, D. Shoemaker, J. Y. Vinet, F. Barone, L. Di Fiore, L. Milano, G. Russo, J. M. Aguirregabiria, H. Bel, J. P. Duruisseau, G. Le Denmat, Ph. Tourrenc, M. Capozzi, M. Longo, M. Lops, I. Pinto, G. Rotoli, T. Damour, S. Bonazzola, J. A. Marck, Y. Gourghoulon, L. E. Holloway, F. Fuligni, V. Iafolla, G. Natale, “The Virgo project: a wide band antenna for gravitational wave detection,” Nucl. Instrum. Methods Phys. Res. A 289, 518–525 (1990).
[CrossRef]

Bel, H.

C. Bradaschia, R. Del Fabbro, A. Di Virgilio, A. Giazotto, H. Kautzky, V. Montelatici, D. Passuello, A. Brillet, O. Cregut, P. Hello, C. N. Man, P. T. Manh, A. Marraud, D. Shoemaker, J. Y. Vinet, F. Barone, L. Di Fiore, L. Milano, G. Russo, J. M. Aguirregabiria, H. Bel, J. P. Duruisseau, G. Le Denmat, Ph. Tourrenc, M. Capozzi, M. Longo, M. Lops, I. Pinto, G. Rotoli, T. Damour, S. Bonazzola, J. A. Marck, Y. Gourghoulon, L. E. Holloway, F. Fuligni, V. Iafolla, G. Natale, “The Virgo project: a wide band antenna for gravitational wave detection,” Nucl. Instrum. Methods Phys. Res. A 289, 518–525 (1990).
[CrossRef]

Bennett, J. R. J.

K. Danzmann, H. Lück, A. Rüdiger, R. Schilling, M. Schrempel, W. Winkler, J. Hough, G. P. Newton, N. A. Robertson, H. Ward, A. M. Campbell, J. E. Logan, D. I. Robertson, K. A. Strain, J. R. J. Bennett, V. Kose, M. Kühne, B. F. Schutz, D. Nicholson, J. Shuttleworth, H. Welling, P. Aufmuth, R. Rinkleff, A. Tünnermann, B. Willke, “GEO 600—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.

Billing, H.

A. Rüdiger, R. Schilling, L. Schnupp, W. Winkler, H. Billing, K. Maischberger, “A mode selector to suppress fluctuations in laser beam geometry,” Opt. Acta 28, 641–658 (1981).
[CrossRef]

Bonazzola, S.

C. Bradaschia, R. Del Fabbro, A. Di Virgilio, A. Giazotto, H. Kautzky, V. Montelatici, D. Passuello, A. Brillet, O. Cregut, P. Hello, C. N. Man, P. T. Manh, A. Marraud, D. Shoemaker, J. Y. Vinet, F. Barone, L. Di Fiore, L. Milano, G. Russo, J. M. Aguirregabiria, H. Bel, J. P. Duruisseau, G. Le Denmat, Ph. Tourrenc, M. Capozzi, M. Longo, M. Lops, I. Pinto, G. Rotoli, T. Damour, S. Bonazzola, J. A. Marck, Y. Gourghoulon, L. E. Holloway, F. Fuligni, V. Iafolla, G. Natale, “The Virgo project: a wide band antenna for gravitational wave detection,” Nucl. Instrum. Methods Phys. Res. A 289, 518–525 (1990).
[CrossRef]

Bork, R.

Bradaschia, C.

C. Bradaschia, R. Del Fabbro, A. Di Virgilio, A. Giazotto, H. Kautzky, V. Montelatici, D. Passuello, A. Brillet, O. Cregut, P. Hello, C. N. Man, P. T. Manh, A. Marraud, D. Shoemaker, J. Y. Vinet, F. Barone, L. Di Fiore, L. Milano, G. Russo, J. M. Aguirregabiria, H. Bel, J. P. Duruisseau, G. Le Denmat, Ph. Tourrenc, M. Capozzi, M. Longo, M. Lops, I. Pinto, G. Rotoli, T. Damour, S. Bonazzola, J. A. Marck, Y. Gourghoulon, L. E. Holloway, F. Fuligni, V. Iafolla, G. Natale, “The Virgo project: a wide band antenna for gravitational wave detection,” Nucl. Instrum. Methods Phys. Res. A 289, 518–525 (1990).
[CrossRef]

Brillet, A.

C. Bradaschia, R. Del Fabbro, A. Di Virgilio, A. Giazotto, H. Kautzky, V. Montelatici, D. Passuello, A. Brillet, O. Cregut, P. Hello, C. N. Man, P. T. Manh, A. Marraud, D. Shoemaker, J. Y. Vinet, F. Barone, L. Di Fiore, L. Milano, G. Russo, J. M. Aguirregabiria, H. Bel, J. P. Duruisseau, G. Le Denmat, Ph. Tourrenc, M. Capozzi, M. Longo, M. Lops, I. Pinto, G. Rotoli, T. Damour, S. Bonazzola, J. A. Marck, Y. Gourghoulon, L. E. Holloway, F. Fuligni, V. Iafolla, G. Natale, “The Virgo project: a wide band antenna for gravitational wave detection,” Nucl. Instrum. Methods Phys. Res. A 289, 518–525 (1990).
[CrossRef]

Buonanno, A.

A. Buonanno, Y. Chen, “Quantum noise in second generation, signal-recycled laser interferometric gravitational-wave detectors,” Phys. Rev. D 64, 77–98 (2001).
[CrossRef]

Campbell, A. M.

K. Danzmann, H. Lück, A. Rüdiger, R. Schilling, M. Schrempel, W. Winkler, J. Hough, G. P. Newton, N. A. Robertson, H. Ward, A. M. Campbell, J. E. Logan, D. I. Robertson, K. A. Strain, J. R. J. Bennett, V. Kose, M. Kühne, B. F. Schutz, D. Nicholson, J. Shuttleworth, H. Welling, P. Aufmuth, R. Rinkleff, A. Tünnermann, B. Willke, “GEO 600—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.

Capozzi, M.

C. Bradaschia, R. Del Fabbro, A. Di Virgilio, A. Giazotto, H. Kautzky, V. Montelatici, D. Passuello, A. Brillet, O. Cregut, P. Hello, C. N. Man, P. T. Manh, A. Marraud, D. Shoemaker, J. Y. Vinet, F. Barone, L. Di Fiore, L. Milano, G. Russo, J. M. Aguirregabiria, H. Bel, J. P. Duruisseau, G. Le Denmat, Ph. Tourrenc, M. Capozzi, M. Longo, M. Lops, I. Pinto, G. Rotoli, T. Damour, S. Bonazzola, J. A. Marck, Y. Gourghoulon, L. E. Holloway, F. Fuligni, V. Iafolla, G. Natale, “The Virgo project: a wide band antenna for gravitational wave detection,” Nucl. Instrum. Methods Phys. Res. A 289, 518–525 (1990).
[CrossRef]

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]

Chen, Y.

A. Buonanno, Y. Chen, “Quantum noise in second generation, signal-recycled laser interferometric gravitational-wave detectors,” Phys. Rev. D 64, 77–98 (2001).
[CrossRef]

Cregut, O.

C. Bradaschia, R. Del Fabbro, A. Di Virgilio, A. Giazotto, H. Kautzky, V. Montelatici, D. Passuello, A. Brillet, O. Cregut, P. Hello, C. N. Man, P. T. Manh, A. Marraud, D. Shoemaker, J. Y. Vinet, F. Barone, L. Di Fiore, L. Milano, G. Russo, J. M. Aguirregabiria, H. Bel, J. P. Duruisseau, G. Le Denmat, Ph. Tourrenc, M. Capozzi, M. Longo, M. Lops, I. Pinto, G. Rotoli, T. Damour, S. Bonazzola, J. A. Marck, Y. Gourghoulon, L. E. Holloway, F. Fuligni, V. Iafolla, G. Natale, “The Virgo project: a wide band antenna for gravitational wave detection,” Nucl. Instrum. Methods Phys. Res. A 289, 518–525 (1990).
[CrossRef]

Cutler, C.

C. Cutler, K. S. Thorne, “An overview of gravitational-wave sources,” in Proceedings of the GR16 Conference on General Relativity and Gravitation, N. Bishop, ed. (World Scientific, Singapore, 2002).
[CrossRef]

Damour, T.

C. Bradaschia, R. Del Fabbro, A. Di Virgilio, A. Giazotto, H. Kautzky, V. Montelatici, D. Passuello, A. Brillet, O. Cregut, P. Hello, C. N. Man, P. T. Manh, A. Marraud, D. Shoemaker, J. Y. Vinet, F. Barone, L. Di Fiore, L. Milano, G. Russo, J. M. Aguirregabiria, H. Bel, J. P. Duruisseau, G. Le Denmat, Ph. Tourrenc, M. Capozzi, M. Longo, M. Lops, I. Pinto, G. Rotoli, T. Damour, S. Bonazzola, J. A. Marck, Y. Gourghoulon, L. E. Holloway, F. Fuligni, V. Iafolla, G. Natale, “The Virgo project: a wide band antenna for gravitational wave detection,” Nucl. Instrum. Methods Phys. Res. A 289, 518–525 (1990).
[CrossRef]

Danzmann, K.

K. A. Strain, K. Danzmann, P. G. Nelson, A. Rüdiger, R. Schilling, W. Winkler, “Thermal lensing in recycling interferometric gravitational wave detectors,” Phys. Lett. A 194, 124–132 (1994).
[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]

K. Danzmann, H. Lück, A. Rüdiger, R. Schilling, M. Schrempel, W. Winkler, J. Hough, G. P. Newton, N. A. Robertson, H. Ward, A. M. Campbell, J. E. Logan, D. I. Robertson, K. A. Strain, J. R. J. Bennett, V. Kose, M. Kühne, B. F. Schutz, D. Nicholson, J. Shuttleworth, H. Welling, P. Aufmuth, R. Rinkleff, A. Tünnermann, B. Willke, “GEO 600—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.

Del Fabbro, R.

C. Bradaschia, R. Del Fabbro, A. Di Virgilio, A. Giazotto, H. Kautzky, V. Montelatici, D. Passuello, A. Brillet, O. Cregut, P. Hello, C. N. Man, P. T. Manh, A. Marraud, D. Shoemaker, J. Y. Vinet, F. Barone, L. Di Fiore, L. Milano, G. Russo, J. M. Aguirregabiria, H. Bel, J. P. Duruisseau, G. Le Denmat, Ph. Tourrenc, M. Capozzi, M. Longo, M. Lops, I. Pinto, G. Rotoli, T. Damour, S. Bonazzola, J. A. Marck, Y. Gourghoulon, L. E. Holloway, F. Fuligni, V. Iafolla, G. Natale, “The Virgo project: a wide band antenna for gravitational wave detection,” Nucl. Instrum. Methods Phys. Res. A 289, 518–525 (1990).
[CrossRef]

Delker, T.

Di Fiore, L.

C. Bradaschia, R. Del Fabbro, A. Di Virgilio, A. Giazotto, H. Kautzky, V. Montelatici, D. Passuello, A. Brillet, O. Cregut, P. Hello, C. N. Man, P. T. Manh, A. Marraud, D. Shoemaker, J. Y. Vinet, F. Barone, L. Di Fiore, L. Milano, G. Russo, J. M. Aguirregabiria, H. Bel, J. P. Duruisseau, G. Le Denmat, Ph. Tourrenc, M. Capozzi, M. Longo, M. Lops, I. Pinto, G. Rotoli, T. Damour, S. Bonazzola, J. A. Marck, Y. Gourghoulon, L. E. Holloway, F. Fuligni, V. Iafolla, G. Natale, “The Virgo project: a wide band antenna for gravitational wave detection,” Nucl. Instrum. Methods Phys. Res. A 289, 518–525 (1990).
[CrossRef]

Di Virgilio, A.

C. Bradaschia, R. Del Fabbro, A. Di Virgilio, A. Giazotto, H. Kautzky, V. Montelatici, D. Passuello, A. Brillet, O. Cregut, P. Hello, C. N. Man, P. T. Manh, A. Marraud, D. Shoemaker, J. Y. Vinet, F. Barone, L. Di Fiore, L. Milano, G. Russo, J. M. Aguirregabiria, H. Bel, J. P. Duruisseau, G. Le Denmat, Ph. Tourrenc, M. Capozzi, M. Longo, M. Lops, I. Pinto, G. Rotoli, T. Damour, S. Bonazzola, J. A. Marck, Y. Gourghoulon, L. E. Holloway, F. Fuligni, V. Iafolla, G. Natale, “The Virgo project: a wide band antenna for gravitational wave detection,” Nucl. Instrum. Methods Phys. Res. A 289, 518–525 (1990).
[CrossRef]

Drever, R.

A. Abramovici, W. Althouse, R. 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]

Drever, R. W. P.

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]

R. W. P. Drever, “Interferometric detectors for gravitational radiation,” in Gravitational Radiation, N. Daruelle, T. Piran, eds. (North-Holland, Amsterdam, 1983), pp. 321–328.

Duruisseau, J. P.

C. Bradaschia, R. Del Fabbro, A. Di Virgilio, A. Giazotto, H. Kautzky, V. Montelatici, D. Passuello, A. Brillet, O. Cregut, P. Hello, C. N. Man, P. T. Manh, A. Marraud, D. Shoemaker, J. Y. Vinet, F. Barone, L. Di Fiore, L. Milano, G. Russo, J. M. Aguirregabiria, H. Bel, J. P. Duruisseau, G. Le Denmat, Ph. Tourrenc, M. Capozzi, M. Longo, M. Lops, I. Pinto, G. Rotoli, T. Damour, S. Bonazzola, J. A. Marck, Y. Gourghoulon, L. E. Holloway, F. Fuligni, V. Iafolla, G. Natale, “The Virgo project: a wide band antenna for gravitational wave detection,” Nucl. Instrum. Methods Phys. Res. A 289, 518–525 (1990).
[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]

Fritschel, P.

Fuligni, F.

C. Bradaschia, R. Del Fabbro, A. Di Virgilio, A. Giazotto, H. Kautzky, V. Montelatici, D. Passuello, A. Brillet, O. Cregut, P. Hello, C. N. Man, P. T. Manh, A. Marraud, D. Shoemaker, J. Y. Vinet, F. Barone, L. Di Fiore, L. Milano, G. Russo, J. M. Aguirregabiria, H. Bel, J. P. Duruisseau, G. Le Denmat, Ph. Tourrenc, M. Capozzi, M. Longo, M. Lops, I. Pinto, G. Rotoli, T. Damour, S. Bonazzola, J. A. Marck, Y. Gourghoulon, L. E. Holloway, F. Fuligni, V. Iafolla, G. Natale, “The Virgo project: a wide band antenna for gravitational wave detection,” Nucl. Instrum. Methods Phys. Res. A 289, 518–525 (1990).
[CrossRef]

Giazotto, A.

C. Bradaschia, R. Del Fabbro, A. Di Virgilio, A. Giazotto, H. Kautzky, V. Montelatici, D. Passuello, A. Brillet, O. Cregut, P. Hello, C. N. Man, P. T. Manh, A. Marraud, D. Shoemaker, J. Y. Vinet, F. Barone, L. Di Fiore, L. Milano, G. Russo, J. M. Aguirregabiria, H. Bel, J. P. Duruisseau, G. Le Denmat, Ph. Tourrenc, M. Capozzi, M. Longo, M. Lops, I. Pinto, G. Rotoli, T. Damour, S. Bonazzola, J. A. Marck, Y. Gourghoulon, L. E. Holloway, F. Fuligni, V. Iafolla, G. Natale, “The Virgo project: a wide band antenna for gravitational wave detection,” Nucl. Instrum. Methods Phys. Res. A 289, 518–525 (1990).
[CrossRef]

González, G.

Gourghoulon, Y.

C. Bradaschia, R. Del Fabbro, A. Di Virgilio, A. Giazotto, H. Kautzky, V. Montelatici, D. Passuello, A. Brillet, O. Cregut, P. Hello, C. N. Man, P. T. Manh, A. Marraud, D. Shoemaker, J. Y. Vinet, F. Barone, L. Di Fiore, L. Milano, G. Russo, J. M. Aguirregabiria, H. Bel, J. P. Duruisseau, G. Le Denmat, Ph. Tourrenc, M. Capozzi, M. Longo, M. Lops, I. Pinto, G. Rotoli, T. Damour, S. Bonazzola, J. A. Marck, Y. Gourghoulon, L. E. Holloway, F. Fuligni, V. Iafolla, G. Natale, “The Virgo project: a wide band antenna for gravitational wave detection,” Nucl. Instrum. Methods Phys. Res. A 289, 518–525 (1990).
[CrossRef]

Gray, M. B.

Gursel, Y.

A. Abramovici, W. Althouse, R. 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]

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]

Hello, P.

C. Bradaschia, R. Del Fabbro, A. Di Virgilio, A. Giazotto, H. Kautzky, V. Montelatici, D. Passuello, A. Brillet, O. Cregut, P. Hello, C. N. Man, P. T. Manh, A. Marraud, D. Shoemaker, J. Y. Vinet, F. Barone, L. Di Fiore, L. Milano, G. Russo, J. M. Aguirregabiria, H. Bel, J. P. Duruisseau, G. Le Denmat, Ph. Tourrenc, M. Capozzi, M. Longo, M. Lops, I. Pinto, G. Rotoli, T. Damour, S. Bonazzola, J. A. Marck, Y. Gourghoulon, L. E. Holloway, F. Fuligni, V. Iafolla, G. Natale, “The Virgo project: a wide band antenna for gravitational wave detection,” Nucl. Instrum. Methods Phys. Res. A 289, 518–525 (1990).
[CrossRef]

Holloway, L. E.

C. Bradaschia, R. Del Fabbro, A. Di Virgilio, A. Giazotto, H. Kautzky, V. Montelatici, D. Passuello, A. Brillet, O. Cregut, P. Hello, C. N. Man, P. T. Manh, A. Marraud, D. Shoemaker, J. Y. Vinet, F. Barone, L. Di Fiore, L. Milano, G. Russo, J. M. Aguirregabiria, H. Bel, J. P. Duruisseau, G. Le Denmat, Ph. Tourrenc, M. Capozzi, M. Longo, M. Lops, I. Pinto, G. Rotoli, T. Damour, S. Bonazzola, J. A. Marck, Y. Gourghoulon, L. E. Holloway, F. Fuligni, V. Iafolla, G. Natale, “The Virgo project: a wide band antenna for gravitational wave detection,” Nucl. Instrum. Methods Phys. Res. A 289, 518–525 (1990).
[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]

K. Danzmann, H. Lück, A. Rüdiger, R. Schilling, M. Schrempel, W. Winkler, J. Hough, G. P. Newton, N. A. Robertson, H. Ward, A. M. Campbell, J. E. Logan, D. I. Robertson, K. A. Strain, J. R. J. Bennett, V. Kose, M. Kühne, B. F. Schutz, D. Nicholson, J. Shuttleworth, H. Welling, P. Aufmuth, R. Rinkleff, A. Tünnermann, B. Willke, “GEO 600—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.

Iafolla, V.

C. Bradaschia, R. Del Fabbro, A. Di Virgilio, A. Giazotto, H. Kautzky, V. Montelatici, D. Passuello, A. Brillet, O. Cregut, P. Hello, C. N. Man, P. T. Manh, A. Marraud, D. Shoemaker, J. Y. Vinet, F. Barone, L. Di Fiore, L. Milano, G. Russo, J. M. Aguirregabiria, H. Bel, J. P. Duruisseau, G. Le Denmat, Ph. Tourrenc, M. Capozzi, M. Longo, M. Lops, I. Pinto, G. Rotoli, T. Damour, S. Bonazzola, J. A. Marck, Y. Gourghoulon, L. E. Holloway, F. Fuligni, V. Iafolla, G. Natale, “The Virgo project: a wide band antenna for gravitational wave detection,” Nucl. Instrum. Methods Phys. Res. A 289, 518–525 (1990).
[CrossRef]

Kautzky, H.

C. Bradaschia, R. Del Fabbro, A. Di Virgilio, A. Giazotto, H. Kautzky, V. Montelatici, D. Passuello, A. Brillet, O. Cregut, P. Hello, C. N. Man, P. T. Manh, A. Marraud, D. Shoemaker, J. Y. Vinet, F. Barone, L. Di Fiore, L. Milano, G. Russo, J. M. Aguirregabiria, H. Bel, J. P. Duruisseau, G. Le Denmat, Ph. Tourrenc, M. Capozzi, M. Longo, M. Lops, I. Pinto, G. Rotoli, T. Damour, S. Bonazzola, J. A. Marck, Y. Gourghoulon, L. E. Holloway, F. Fuligni, V. Iafolla, G. Natale, “The Virgo project: a wide band antenna for gravitational wave detection,” Nucl. Instrum. Methods Phys. Res. A 289, 518–525 (1990).
[CrossRef]

Kawamura, S.

A. Abramovici, W. Althouse, R. 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]

Kose, V.

K. Danzmann, H. Lück, A. Rüdiger, R. Schilling, M. Schrempel, W. Winkler, J. Hough, G. P. Newton, N. A. Robertson, H. Ward, A. M. Campbell, J. E. Logan, D. I. Robertson, K. A. Strain, J. R. J. Bennett, V. Kose, M. Kühne, B. F. Schutz, D. Nicholson, J. Shuttleworth, H. Welling, P. Aufmuth, R. Rinkleff, A. Tünnermann, B. Willke, “GEO 600—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.

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]

Krolak, A.

B. J. Meers, A. Krolak, J. A. Lobo, “Dynamically tuned interferometers for the observation of gravitational waves from coalescing compact binaries,” Phys. Rev. D 47, 2184–2197 (1993).
[CrossRef]

Kühne, M.

K. Danzmann, H. Lück, A. Rüdiger, R. Schilling, M. Schrempel, W. Winkler, J. Hough, G. P. Newton, N. A. Robertson, H. Ward, A. M. Campbell, J. E. Logan, D. I. Robertson, K. A. Strain, J. R. J. Bennett, V. Kose, M. Kühne, B. F. Schutz, D. Nicholson, J. Shuttleworth, H. Welling, P. Aufmuth, R. Rinkleff, A. Tünnermann, B. Willke, “GEO 600—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.

Le Denmat, G.

C. Bradaschia, R. Del Fabbro, A. Di Virgilio, A. Giazotto, H. Kautzky, V. Montelatici, D. Passuello, A. Brillet, O. Cregut, P. Hello, C. N. Man, P. T. Manh, A. Marraud, D. Shoemaker, J. Y. Vinet, F. Barone, L. Di Fiore, L. Milano, G. Russo, J. M. Aguirregabiria, H. Bel, J. P. Duruisseau, G. Le Denmat, Ph. Tourrenc, M. Capozzi, M. Longo, M. Lops, I. Pinto, G. Rotoli, T. Damour, S. Bonazzola, J. A. Marck, Y. Gourghoulon, L. E. Holloway, F. Fuligni, V. Iafolla, G. Natale, “The Virgo project: a wide band antenna for gravitational wave detection,” Nucl. Instrum. Methods Phys. Res. A 289, 518–525 (1990).
[CrossRef]

Lobo, J. A.

B. J. Meers, A. Krolak, J. A. Lobo, “Dynamically tuned interferometers for the observation of gravitational waves from coalescing compact binaries,” Phys. Rev. D 47, 2184–2197 (1993).
[CrossRef]

Logan, J. E.

K. Danzmann, H. Lück, A. Rüdiger, R. Schilling, M. Schrempel, W. Winkler, J. Hough, G. P. Newton, N. A. Robertson, H. Ward, A. M. Campbell, J. E. Logan, D. I. Robertson, K. A. Strain, J. R. J. Bennett, V. Kose, M. Kühne, B. F. Schutz, D. Nicholson, J. Shuttleworth, H. Welling, P. Aufmuth, R. Rinkleff, A. Tünnermann, B. Willke, “GEO 600—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.

Longo, M.

C. Bradaschia, R. Del Fabbro, A. Di Virgilio, A. Giazotto, H. Kautzky, V. Montelatici, D. Passuello, A. Brillet, O. Cregut, P. Hello, C. N. Man, P. T. Manh, A. Marraud, D. Shoemaker, J. Y. Vinet, F. Barone, L. Di Fiore, L. Milano, G. Russo, J. M. Aguirregabiria, H. Bel, J. P. Duruisseau, G. Le Denmat, Ph. Tourrenc, M. Capozzi, M. Longo, M. Lops, I. Pinto, G. Rotoli, T. Damour, S. Bonazzola, J. A. Marck, Y. Gourghoulon, L. E. Holloway, F. Fuligni, V. Iafolla, G. Natale, “The Virgo project: a wide band antenna for gravitational wave detection,” Nucl. Instrum. Methods Phys. Res. A 289, 518–525 (1990).
[CrossRef]

Lops, M.

C. Bradaschia, R. Del Fabbro, A. Di Virgilio, A. Giazotto, H. Kautzky, V. Montelatici, D. Passuello, A. Brillet, O. Cregut, P. Hello, C. N. Man, P. T. Manh, A. Marraud, D. Shoemaker, J. Y. Vinet, F. Barone, L. Di Fiore, L. Milano, G. Russo, J. M. Aguirregabiria, H. Bel, J. P. Duruisseau, G. Le Denmat, Ph. Tourrenc, M. Capozzi, M. Longo, M. Lops, I. Pinto, G. Rotoli, T. Damour, S. Bonazzola, J. A. Marck, Y. Gourghoulon, L. E. Holloway, F. Fuligni, V. Iafolla, G. Natale, “The Virgo project: a wide band antenna for gravitational wave detection,” Nucl. Instrum. Methods Phys. Res. A 289, 518–525 (1990).
[CrossRef]

Lück, H.

K. Danzmann, H. Lück, A. Rüdiger, R. Schilling, M. Schrempel, W. Winkler, J. Hough, G. P. Newton, N. A. Robertson, H. Ward, A. M. Campbell, J. E. Logan, D. I. Robertson, K. A. Strain, J. R. J. Bennett, V. Kose, M. Kühne, B. F. Schutz, D. Nicholson, J. Shuttleworth, H. Welling, P. Aufmuth, R. Rinkleff, A. Tünnermann, B. Willke, “GEO 600—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.

Maischberger, K.

A. Rüdiger, R. Schilling, L. Schnupp, W. Winkler, H. Billing, K. Maischberger, “A mode selector to suppress fluctuations in laser beam geometry,” Opt. Acta 28, 641–658 (1981).
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Man, C. N.

C. Bradaschia, R. Del Fabbro, A. Di Virgilio, A. Giazotto, H. Kautzky, V. Montelatici, D. Passuello, A. Brillet, O. Cregut, P. Hello, C. N. Man, P. T. Manh, A. Marraud, D. Shoemaker, J. Y. Vinet, F. Barone, L. Di Fiore, L. Milano, G. Russo, J. M. Aguirregabiria, H. Bel, J. P. Duruisseau, G. Le Denmat, Ph. Tourrenc, M. Capozzi, M. Longo, M. Lops, I. Pinto, G. Rotoli, T. Damour, S. Bonazzola, J. A. Marck, Y. Gourghoulon, L. E. Holloway, F. Fuligni, V. Iafolla, G. Natale, “The Virgo project: a wide band antenna for gravitational wave detection,” Nucl. Instrum. Methods Phys. Res. A 289, 518–525 (1990).
[CrossRef]

Manh, P. T.

C. Bradaschia, R. Del Fabbro, A. Di Virgilio, A. Giazotto, H. Kautzky, V. Montelatici, D. Passuello, A. Brillet, O. Cregut, P. Hello, C. N. Man, P. T. Manh, A. Marraud, D. Shoemaker, J. Y. Vinet, F. Barone, L. Di Fiore, L. Milano, G. Russo, J. M. Aguirregabiria, H. Bel, J. P. Duruisseau, G. Le Denmat, Ph. Tourrenc, M. Capozzi, M. Longo, M. Lops, I. Pinto, G. Rotoli, T. Damour, S. Bonazzola, J. A. Marck, Y. Gourghoulon, L. E. Holloway, F. Fuligni, V. Iafolla, G. Natale, “The Virgo project: a wide band antenna for gravitational wave detection,” Nucl. Instrum. Methods Phys. Res. A 289, 518–525 (1990).
[CrossRef]

Marck, J. A.

C. Bradaschia, R. Del Fabbro, A. Di Virgilio, A. Giazotto, H. Kautzky, V. Montelatici, D. Passuello, A. Brillet, O. Cregut, P. Hello, C. N. Man, P. T. Manh, A. Marraud, D. Shoemaker, J. Y. Vinet, F. Barone, L. Di Fiore, L. Milano, G. Russo, J. M. Aguirregabiria, H. Bel, J. P. Duruisseau, G. Le Denmat, Ph. Tourrenc, M. Capozzi, M. Longo, M. Lops, I. Pinto, G. Rotoli, T. Damour, S. Bonazzola, J. A. Marck, Y. Gourghoulon, L. E. Holloway, F. Fuligni, V. Iafolla, G. Natale, “The Virgo project: a wide band antenna for gravitational wave detection,” Nucl. Instrum. Methods Phys. Res. A 289, 518–525 (1990).
[CrossRef]

Marraud, A.

C. Bradaschia, R. Del Fabbro, A. Di Virgilio, A. Giazotto, H. Kautzky, V. Montelatici, D. Passuello, A. Brillet, O. Cregut, P. Hello, C. N. Man, P. T. Manh, A. Marraud, D. Shoemaker, J. Y. Vinet, F. Barone, L. Di Fiore, L. Milano, G. Russo, J. M. Aguirregabiria, H. Bel, J. P. Duruisseau, G. Le Denmat, Ph. Tourrenc, M. Capozzi, M. Longo, M. Lops, I. Pinto, G. Rotoli, T. Damour, S. Bonazzola, J. A. Marck, Y. Gourghoulon, L. E. Holloway, F. Fuligni, V. Iafolla, G. Natale, “The Virgo project: a wide band antenna for gravitational wave detection,” Nucl. Instrum. Methods Phys. Res. A 289, 518–525 (1990).
[CrossRef]

Mason, J. E.

Mavalvala, N.

McClelland, D. E.

Meers, B. J.

B. J. Meers, A. Krolak, J. A. Lobo, “Dynamically tuned interferometers for the observation of gravitational waves from coalescing compact binaries,” Phys. Rev. D 47, 2184–2197 (1993).
[CrossRef]

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

Michelson, A. A.

A. A. Michelson, E. W. Morley, “On the relative motion of the earth and the luminiferous ether,” Am. J. Sci. 35, 333–345 (1887).
[CrossRef]

Milano, L.

C. Bradaschia, R. Del Fabbro, A. Di Virgilio, A. Giazotto, H. Kautzky, V. Montelatici, D. Passuello, A. Brillet, O. Cregut, P. Hello, C. N. Man, P. T. Manh, A. Marraud, D. Shoemaker, J. Y. Vinet, F. Barone, L. Di Fiore, L. Milano, G. Russo, J. M. Aguirregabiria, H. Bel, J. P. Duruisseau, G. Le Denmat, Ph. Tourrenc, M. Capozzi, M. Longo, M. Lops, I. Pinto, G. Rotoli, T. Damour, S. Bonazzola, J. A. Marck, Y. Gourghoulon, L. E. Holloway, F. Fuligni, V. Iafolla, G. Natale, “The Virgo project: a wide band antenna for gravitational wave detection,” Nucl. Instrum. Methods Phys. Res. A 289, 518–525 (1990).
[CrossRef]

Mizuno, J.

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]

Montelatici, V.

C. Bradaschia, R. Del Fabbro, A. Di Virgilio, A. Giazotto, H. Kautzky, V. Montelatici, D. Passuello, A. Brillet, O. Cregut, P. Hello, C. N. Man, P. T. Manh, A. Marraud, D. Shoemaker, J. Y. Vinet, F. Barone, L. Di Fiore, L. Milano, G. Russo, J. M. Aguirregabiria, H. Bel, J. P. Duruisseau, G. Le Denmat, Ph. Tourrenc, M. Capozzi, M. Longo, M. Lops, I. Pinto, G. Rotoli, T. Damour, S. Bonazzola, J. A. Marck, Y. Gourghoulon, L. E. Holloway, F. Fuligni, V. Iafolla, G. Natale, “The Virgo project: a wide band antenna for gravitational wave detection,” Nucl. Instrum. Methods Phys. Res. A 289, 518–525 (1990).
[CrossRef]

Morley, E. W.

A. A. Michelson, E. W. Morley, “On the relative motion of the earth and the luminiferous ether,” Am. J. Sci. 35, 333–345 (1887).
[CrossRef]

Mow-Lowry, C.

Müller, G.

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]

Natale, G.

C. Bradaschia, R. Del Fabbro, A. Di Virgilio, A. Giazotto, H. Kautzky, V. Montelatici, D. Passuello, A. Brillet, O. Cregut, P. Hello, C. N. Man, P. T. Manh, A. Marraud, D. Shoemaker, J. Y. Vinet, F. Barone, L. Di Fiore, L. Milano, G. Russo, J. M. Aguirregabiria, H. Bel, J. P. Duruisseau, G. Le Denmat, Ph. Tourrenc, M. Capozzi, M. Longo, M. Lops, I. Pinto, G. Rotoli, T. Damour, S. Bonazzola, J. A. Marck, Y. Gourghoulon, L. E. Holloway, F. Fuligni, V. Iafolla, G. Natale, “The Virgo project: a wide band antenna for gravitational wave detection,” Nucl. Instrum. Methods Phys. Res. A 289, 518–525 (1990).
[CrossRef]

Nelson, P. G.

K. A. Strain, K. Danzmann, P. G. Nelson, A. Rüdiger, R. Schilling, W. Winkler, “Thermal lensing in recycling interferometric gravitational wave detectors,” Phys. Lett. A 194, 124–132 (1994).
[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]

Newton, G. P.

K. Danzmann, H. Lück, A. Rüdiger, R. Schilling, M. Schrempel, W. Winkler, J. Hough, G. P. Newton, N. A. Robertson, H. Ward, A. M. Campbell, J. E. Logan, D. I. Robertson, K. A. Strain, J. R. J. Bennett, V. Kose, M. Kühne, B. F. Schutz, D. Nicholson, J. Shuttleworth, H. Welling, P. Aufmuth, R. Rinkleff, A. Tünnermann, B. Willke, “GEO 600—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.

Nicholson, D.

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C. Bradaschia, R. Del Fabbro, A. Di Virgilio, A. Giazotto, H. Kautzky, V. Montelatici, D. Passuello, A. Brillet, O. Cregut, P. Hello, C. N. Man, P. T. Manh, A. Marraud, D. Shoemaker, J. Y. Vinet, F. Barone, L. Di Fiore, L. Milano, G. Russo, J. M. Aguirregabiria, H. Bel, J. P. Duruisseau, G. Le Denmat, Ph. Tourrenc, M. Capozzi, M. Longo, M. Lops, I. Pinto, G. Rotoli, T. Damour, S. Bonazzola, J. A. Marck, Y. Gourghoulon, L. E. Holloway, F. Fuligni, V. Iafolla, G. Natale, “The Virgo project: a wide band antenna for gravitational wave detection,” Nucl. Instrum. Methods Phys. Res. A 289, 518–525 (1990).
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A. Abramovici, W. Althouse, R. 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).
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K. Danzmann, H. Lück, A. Rüdiger, R. Schilling, M. Schrempel, W. Winkler, J. Hough, G. P. Newton, N. A. Robertson, H. Ward, A. M. Campbell, J. E. Logan, D. I. Robertson, K. A. Strain, J. R. J. Bennett, V. Kose, M. Kühne, B. F. Schutz, D. Nicholson, J. Shuttleworth, H. Welling, P. Aufmuth, R. Rinkleff, A. Tünnermann, B. Willke, “GEO 600—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.

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K. Danzmann, H. Lück, A. Rüdiger, R. Schilling, M. Schrempel, W. Winkler, J. Hough, G. P. Newton, N. A. Robertson, H. Ward, A. M. Campbell, J. E. Logan, D. I. Robertson, K. A. Strain, J. R. J. Bennett, V. Kose, M. Kühne, B. F. Schutz, D. Nicholson, J. Shuttleworth, H. Welling, P. Aufmuth, R. Rinkleff, A. Tünnermann, B. Willke, “GEO 600—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.

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K. Danzmann, H. Lück, A. Rüdiger, R. Schilling, M. Schrempel, W. Winkler, J. Hough, G. P. Newton, N. A. Robertson, H. Ward, A. M. Campbell, J. E. Logan, D. I. Robertson, K. A. Strain, J. R. J. Bennett, V. Kose, M. Kühne, B. F. Schutz, D. Nicholson, J. Shuttleworth, H. Welling, P. Aufmuth, R. Rinkleff, A. Tünnermann, B. Willke, “GEO 600—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.

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C. Bradaschia, R. Del Fabbro, A. Di Virgilio, A. Giazotto, H. Kautzky, V. Montelatici, D. Passuello, A. Brillet, O. Cregut, P. Hello, C. N. Man, P. T. Manh, A. Marraud, D. Shoemaker, J. Y. Vinet, F. Barone, L. Di Fiore, L. Milano, G. Russo, J. M. Aguirregabiria, H. Bel, J. P. Duruisseau, G. Le Denmat, Ph. Tourrenc, M. Capozzi, M. Longo, M. Lops, I. Pinto, G. Rotoli, T. Damour, S. Bonazzola, J. A. Marck, Y. Gourghoulon, L. E. Holloway, F. Fuligni, V. Iafolla, G. Natale, “The Virgo project: a wide band antenna for gravitational wave detection,” Nucl. Instrum. Methods Phys. Res. A 289, 518–525 (1990).
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K. A. Strain, K. Danzmann, P. G. Nelson, A. Rüdiger, R. Schilling, W. Winkler, “Thermal lensing in recycling interferometric gravitational wave detectors,” Phys. Lett. A 194, 124–132 (1994).
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Russo, G.

C. Bradaschia, R. Del Fabbro, A. Di Virgilio, A. Giazotto, H. Kautzky, V. Montelatici, D. Passuello, A. Brillet, O. Cregut, P. Hello, C. N. Man, P. T. Manh, A. Marraud, D. Shoemaker, J. Y. Vinet, F. Barone, L. Di Fiore, L. Milano, G. Russo, J. M. Aguirregabiria, H. Bel, J. P. Duruisseau, G. Le Denmat, Ph. Tourrenc, M. Capozzi, M. Longo, M. Lops, I. Pinto, G. Rotoli, T. Damour, S. Bonazzola, J. A. Marck, Y. Gourghoulon, L. E. Holloway, F. Fuligni, V. Iafolla, G. Natale, “The Virgo project: a wide band antenna for gravitational wave detection,” Nucl. Instrum. Methods Phys. Res. A 289, 518–525 (1990).
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K. A. Strain, K. Danzmann, P. G. Nelson, A. Rüdiger, R. Schilling, W. Winkler, “Thermal lensing in recycling interferometric gravitational wave detectors,” Phys. Lett. A 194, 124–132 (1994).
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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).
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A. Rüdiger, R. Schilling, L. Schnupp, W. Winkler, H. Billing, K. Maischberger, “A mode selector to suppress fluctuations in laser beam geometry,” Opt. Acta 28, 641–658 (1981).
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A. Rüdiger, R. Schilling, L. Schnupp, W. Winkler, H. Billing, K. Maischberger, “A mode selector to suppress fluctuations in laser beam geometry,” Opt. Acta 28, 641–658 (1981).
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K. Danzmann, H. Lück, A. Rüdiger, R. Schilling, M. Schrempel, W. Winkler, J. Hough, G. P. Newton, N. A. Robertson, H. Ward, A. M. Campbell, J. E. Logan, D. I. Robertson, K. A. Strain, J. R. J. Bennett, V. Kose, M. Kühne, B. F. Schutz, D. Nicholson, J. Shuttleworth, H. Welling, P. Aufmuth, R. Rinkleff, A. Tünnermann, B. Willke, “GEO 600—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.

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A. Abramovici, W. Althouse, R. 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).
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K. Danzmann, H. Lück, A. Rüdiger, R. Schilling, M. Schrempel, W. Winkler, J. Hough, G. P. Newton, N. A. Robertson, H. Ward, A. M. Campbell, J. E. Logan, D. I. Robertson, K. A. Strain, J. R. J. Bennett, V. Kose, M. Kühne, B. F. Schutz, D. Nicholson, J. Shuttleworth, H. Welling, P. Aufmuth, R. Rinkleff, A. Tünnermann, B. Willke, “GEO 600—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.

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A. Abramovici, W. Althouse, R. 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).
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Spero, R.

A. Abramovici, W. Althouse, R. 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).
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K. A. Strain, K. Danzmann, P. G. Nelson, A. Rüdiger, R. Schilling, W. Winkler, “Thermal lensing in recycling interferometric gravitational wave detectors,” Phys. Lett. A 194, 124–132 (1994).
[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).
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K. Danzmann, H. Lück, A. Rüdiger, R. Schilling, M. Schrempel, W. Winkler, J. Hough, G. P. Newton, N. A. Robertson, H. Ward, A. M. Campbell, J. E. Logan, D. I. Robertson, K. A. Strain, J. R. J. Bennett, V. Kose, M. Kühne, B. F. Schutz, D. Nicholson, J. Shuttleworth, H. Welling, P. Aufmuth, R. Rinkleff, A. Tünnermann, B. Willke, “GEO 600—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.

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A. Abramovici, W. Althouse, R. 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).
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C. Bradaschia, R. Del Fabbro, A. Di Virgilio, A. Giazotto, H. Kautzky, V. Montelatici, D. Passuello, A. Brillet, O. Cregut, P. Hello, C. N. Man, P. T. Manh, A. Marraud, D. Shoemaker, J. Y. Vinet, F. Barone, L. Di Fiore, L. Milano, G. Russo, J. M. Aguirregabiria, H. Bel, J. P. Duruisseau, G. Le Denmat, Ph. Tourrenc, M. Capozzi, M. Longo, M. Lops, I. Pinto, G. Rotoli, T. Damour, S. Bonazzola, J. A. Marck, Y. Gourghoulon, L. E. Holloway, F. Fuligni, V. Iafolla, G. Natale, “The Virgo project: a wide band antenna for gravitational wave detection,” Nucl. Instrum. Methods Phys. Res. A 289, 518–525 (1990).
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Tünnermann, A.

K. Danzmann, H. Lück, A. Rüdiger, R. Schilling, M. Schrempel, W. Winkler, J. Hough, G. P. Newton, N. A. Robertson, H. Ward, A. M. Campbell, J. E. Logan, D. I. Robertson, K. A. Strain, J. R. J. Bennett, V. Kose, M. Kühne, B. F. Schutz, D. Nicholson, J. Shuttleworth, H. Welling, P. Aufmuth, R. Rinkleff, A. Tünnermann, B. Willke, “GEO 600—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.

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C. Bradaschia, R. Del Fabbro, A. Di Virgilio, A. Giazotto, H. Kautzky, V. Montelatici, D. Passuello, A. Brillet, O. Cregut, P. Hello, C. N. Man, P. T. Manh, A. Marraud, D. Shoemaker, J. Y. Vinet, F. Barone, L. Di Fiore, L. Milano, G. Russo, J. M. Aguirregabiria, H. Bel, J. P. Duruisseau, G. Le Denmat, Ph. Tourrenc, M. Capozzi, M. Longo, M. Lops, I. Pinto, G. Rotoli, T. Damour, S. Bonazzola, J. A. Marck, Y. Gourghoulon, L. E. Holloway, F. Fuligni, V. Iafolla, G. Natale, “The Virgo project: a wide band antenna for gravitational wave detection,” Nucl. Instrum. Methods Phys. Res. A 289, 518–525 (1990).
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A. Abramovici, W. Althouse, R. 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).
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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).
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K. Danzmann, H. Lück, A. Rüdiger, R. Schilling, M. Schrempel, W. Winkler, J. Hough, G. P. Newton, N. A. Robertson, H. Ward, A. M. Campbell, J. E. Logan, D. I. Robertson, K. A. Strain, J. R. J. Bennett, V. Kose, M. Kühne, B. F. Schutz, D. Nicholson, J. Shuttleworth, H. Welling, P. Aufmuth, R. Rinkleff, A. Tünnermann, B. Willke, “GEO 600—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.

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Welling, H.

K. Danzmann, H. Lück, A. Rüdiger, R. Schilling, M. Schrempel, W. Winkler, J. Hough, G. P. Newton, N. A. Robertson, H. Ward, A. M. Campbell, J. E. Logan, D. I. Robertson, K. A. Strain, J. R. J. Bennett, V. Kose, M. Kühne, B. F. Schutz, D. Nicholson, J. Shuttleworth, H. Welling, P. Aufmuth, R. Rinkleff, A. Tünnermann, B. Willke, “GEO 600—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.

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A. Abramovici, W. Althouse, R. 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).
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K. Danzmann, H. Lück, A. Rüdiger, R. Schilling, M. Schrempel, W. Winkler, J. Hough, G. P. Newton, N. A. Robertson, H. Ward, A. M. Campbell, J. E. Logan, D. I. Robertson, K. A. Strain, J. R. J. Bennett, V. Kose, M. Kühne, B. F. Schutz, D. Nicholson, J. Shuttleworth, H. Welling, P. Aufmuth, R. Rinkleff, A. Tünnermann, B. Willke, “GEO 600—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.

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K. A. Strain, K. Danzmann, P. G. Nelson, A. Rüdiger, R. Schilling, W. Winkler, “Thermal lensing in recycling interferometric gravitational wave detectors,” Phys. Lett. A 194, 124–132 (1994).
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P. Fritschel, R. Bork, G. González, N. Mavalvala, D. Ouimette, H. Rong, D. Sigg, M. Zucker, “Readout and control of a power-recycle interferometric gravitational-wave antenna,” Appl. Opt. 40, 4988–4998 (2001).
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The idea of power recycling was proposed simultaneously by R. Schilling, Max-Planck-Institut fuer Quantenoptik, Garching, Germany.

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Figures (5)

Fig. 1
Fig. 1

Simplified diagram of an initial LIGO interferometer. Each interferometer consists of two arm cavities formed between the mirrors input test mass [ITM1(2)] and end test mass [ETM1(2)] of length L 1 and L 2 of approximately 4000 m, whereas the other distances are of the order of a few meters. The beam splitter (BS) and power-recycling (PR) mirror are shown, the function of the latter is discussed in the text. The input light, from the injection optics, enters at the left, and the signal is detected at the dark port (DP) photodetector. Note that it is important to distinguish the macroscopic mirror spacings from the microscopic values that determine the phase of the light at refection from the optics. Microscopic displacements are described by their effect on the phase of the light fields, modulo one cycle. BP, bright port; DP, dark port; PO, pickoff.

Fig. 2
Fig. 2

Example sensitivity target for future instruments such as Advanced LIGO. The strain-noise amplitude spectral density is plotted over the frequency range of useful sensitivity. The solid curve shows an estimate of the total noise from all contributions, whereas the dashed curve shows just the noise associated with the optical sensing system. Over much of the frequency band shown, the proposed sensitivity is at least an order of magnitude better than that of first-generation instruments.

Fig. 3
Fig. 3

Comparison of the sensitivity of power-recycling and dual-recycling interferometers. The solid curve shows the optical performance limit with power recycling only, whereas the dashed curve shows the result with the variant of dual recycling known as resonant sideband extraction. The parameters used are those proposed for Advanced LIGO (the most important of which are given in the text and are also those used in Fig. 2), except that the effect of signal recycling was suppressed in curve a.

Fig. 4
Fig. 4

Advanced LIGO interferometer consists of two arm cavities formed between the mirrors ITM1(2) and ETM1(2) of length L 1 and L 2. The distances of the arm cavities from the beam splitter (BS) are l1 and l2. The power-recycling (PR) mirror at a distance l p in front of the beam splitter and the signal-recycling (SR) mirror at ls behind the beam splitter complete the interferometer. The lengths L i of the arm cavities are approximately 4000 m whereas the other distances are of the order of a few meters. These distances depend on the final length-sensing scheme and have to match the used modulation frequencies. Note that it is important to distinguish these macroscopic mirror spacings from the microscopic quantities that determine the phase of the light at refection from the optics. Microscopic displacements are described by their effect on the phase of the light fields. BP, bright port; DP, dark port; PO, pickoff.

Fig. 5
Fig. 5

Fields at the different locations in the interferometer. E r is the field that is reflected at the power-recycling mirror outside of the interferometer. It will be detected at the bright port (BP). E t is the field that is transmitted through the whole interferometer. It will be detected at the dark port (DP). The subscript n of all the other fields E n m denotes the mirror at which the field is calculated. The superscript m denotes the direction of the field. The pickoff (PO) field is proportional to E p o .

Tables (1)

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Table 1 Five Relevant Longitudinal Degrees of Freedom in an Advanced LIGO Interferometera

Equations (43)

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Ein=E0 expiω0t+m sin Ωt E0expiω0t+m2expiω0+Ωt-m2expiω0-Ωt,
Eout=E0T0 expiω0t+m2 T+ expiω0+Ωt-m2 T- expiω0-Ωt,
T0=Tω0, T+=Tω0+Ω, T-=Tω0-Ω.
I  |E0|2+2m|E0|2T0T+*-T-*cosΩt+T0T+*+T-*sinΩt,
S=2T0T+*-T-*cosα-2T0T+*+T-*sinα,
Ein=E1+E2 expiΩtexpiω0t.
I=|T1E1|2+|T2E2|2+2|T1E1T2E2|cosΩt+φ,
S=2|T1E1T2E2|cosφ-ψ.
Er=tpEpi+rpEin, Et=tsEsi, Epo=-rpEpi+tpEin, Epi=rbEI2o exp-iklp+l2+tbEI1o×exp-iklp+l1, Eso=rsEsi, Esi=-rbEI1o exp-ikls+l1+tbEI2o×exp-ikls+l2, EI1i=-rbEso exp-ikls+l1+tbEpo×exp-iklp+l1, EI1o=rcav1kEI1i, EI2i=rbEpo exp-iklp+l2+tbEso×exp-ikls+l2, EI2o=rcav2kEI2i.
rcav12=1-a12×+rI12-1-AI121-AE122exp-i2kL121-rI121-AE122exp-i2kL12.
AI=1-rI2-tI2  1, AE=1-rE2  1.
Ecav12=tI12EI12i1-rI12rE12 exp-i2kL12.
Trk=rp1-rsρs exp-i2kls+rp2+tp2exp-i2klpρp+rsXM exp-i2kls1-rsρs exp-i2kls+rpρp exp-i2klp+rsrpXM exp-i2kls+lp,Ttk=tstpτ exp-iklp+ls1-rsρs exp-i2kls+rpρp exp-i2klp+rprsXM exp-i2kls+lp,Tpok=tp1-rsρs exp-i2kls1-rsρs exp-i2kls+rpρp exp-i2klp+rprsXM exp-i2kls+lp.
ρpk=exp-ikl¯rb2rcav2+tb2rcav1coskl-+irb2rcav2-tb2rcav1sinkl-,
ρsk=exp-ikl¯rb2rcav1+tb2rcav2coskl--irb2rcav1-tb2rcav2sinkl-,
τk=exp-ikl¯tbrb×rcav1-rcav2coskl--ircav1+rcav2sinkl-,
XMk=τ2k-ρpkρsk,
rcav12Φ12-1+a12+2A12TI12+iΦ124TI12,
T12=t122TI
A12AI12+1+rI2 AE12
kcl-=N2π+ϕ-,
coskcl-1,
sinkcl-ϕ-.
ρpkc-exp-ikcl¯1-a¯-2A¯TI-i 2Φ+TIρskc,
τkcexp-ikcl¯iϕ-+2Φ-TI+2ΔATI+Δa,
XM=-exp-i2kcl¯1-2a¯-4A¯TI-i 4Φ+TI.
a¯=a1+a22,
Δa=a1-a22,
A¯=A1+A22,
ΔA=A1-A22,
Φ+=Φ1+Φ2,
Φ-=Φ1-Φ2.
Trkc=Tr0kc+iTIϕ++2Φ+tr0kc,
Tr0kc-TpTI+2TIa¯+4A¯TpTI+2TIa¯+4A¯,
tr0kc4TpTITITp+2TIa¯+4A¯2,
Ttkctt0kciTIϕ-+2Φ-+ΔA+TIΔa,
tt0kc4tstpTITITs+2TIa¯+4A¯TITs+2TIa¯+4A¯,
TpkcTp0kc-iTIϕ++2Φ+tp0kc,
Tp0kc2tpTITITp+2TIa¯+4A¯,
tp0kc4tpTITpTI+2TIa¯+4A¯2.
A¯TI, ΔATI  1,
exp-ikc2lp+l¯1+iϕ+, exp-ikc2ls+l¯-1-iϕs.
rsrs exp-iϕs, tsts exp-iϕs/2

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