Abstract

The Virgo interferometer, aimed at detecting gravitational waves, is now in a commissioning phase. Measurements of its optical properties are needed for the understanding of the instrument. We present the techniques developed for the measurement of the optical parameters of Virgo. These parameters are compared with the Virgo specifications.

© 2007 Optical Society of America

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References

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  10. R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, “Laser phase and frequency stabilization using an optical resonator,” Appl. Phys. B 31, 97-105 (1983).
    [Crossref]
  11. T. M. Niebauer, R. Schilling, K. Danzmann, A. Rüdiger, and W. Winkler, “Nonstationary shot noise and its effect on the sensitivity of interferometers,” Phys. Rev. A 43, 5022-5029 (1991).
    [Crossref] [PubMed]
  12. The Virgo Collaboration, “The VIRGO large mirrors: a challenge for low loss coatings,” Class. Quantum Grav. 21, S935-S945 (2004).
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    [Crossref]
  14. D. Babusci, H. Fang, G. Giordano, G. Matone, L. Matone, and V. Sannibale, “Alignment procedure for the VIRGO interferometer: experimental results from the Frascati prototype,” Phys. Lett. A 226, 31-40 (1997).
    [Crossref]
  15. D. Z. Anderson, “Alignment of resonant optical cavities,” Appl. Opt. 23, 2944-2949 (1984).
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  16. B. Caron, L. Derome, R. Flaminio, X. Grave, F. Marion, B. Mours, D. Verkindt, F. Cavalier, and A. Viceré, “A time domain, general purpose simulation program for the VIRGO experiment,” Astropart. Phys. 10, 369-386 (1999).
    [Crossref]
  17. A. Freise, G. Heinzel, H. Luck, R. Schilling, B. Willke, and K. Danzmann, “Frequency domain interferometer simulation with higher-order spatial modes,” Class. Quantum Grav. 21, S1067-1074 (2003).
    [Crossref]
  18. J.-Y. Vinet, P. Hello, C. N. Man, and A. Brillet, “A high accuracy method for the simulation of non-ideal optical cavities,” J. Phys. I 2, 1287-1303 (1992).
    [Crossref]
  19. A. Brillet, J.-Y. Vinet, V. Loriette, J.-M. Mackowski, L. Pinard, and A. Remillieux, “Virtual gravitational wave interferometers with actual mirrors,” Phys. Rev. D 67, 102006 (2003).
    [Crossref]
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  21. B. J. J. Slagmolen, M. B. Gray, K.G. Baigent, and D. E. McClelland, “Phase-sensitive reflection technique for characterization of a Fabry-Perot interferometer,” Appl Opt. 39, 3638-3643 (2000).
    [Crossref]
  22. D. Z. Anderson, J. C. Frisch, and C. S. Masser, “Mirror reflectometer based on optical cavity decay time,” Appl. Opt. 23, 1238-1245 (1984).
    [Crossref] [PubMed]
  23. The Virgo Collaboration, “The commissioning of the central interferometer of the Virgo gravitational wave detector,” Astropart. Phys. 21, 1-22 (2004).
  24. The Virgo Collaboration, “Interferometer signal detection system for the VIRGO experiment,” Class. Quantum Grav. 19, 1857-1863 (2002).

2007 (1)

2006 (4)

D. Sigg, “Status of the LIGO detectors,” Class. Quantum. Grav. 23, S51-S56 (2006).
[Crossref]

The GEO Collaboration, “Status of the GEO600 detector,” Class. Quantum Grav. 23, S71-S78 (2006).

K. Hayama and M. Fujimoto, “Monitoring non-stationary burst-like signals in an interferometric gravitational wave detector,” Class. Quantum Grav. 23, S9-S15 (2006).
[Crossref]

F. Beauville, D. Buskulic, L. Derome, A. Dominjon, R. Flaminio, R. Hermel, F. Marion, A. Masserot, L. Massonnet, B. Mours, F. Moreau, P. Mugnier, J. Ramonet, E. Tournefier, D. Verkindt, O. Veziant, and M. Yvert, “Improvement in the shot noise of a laser interferometer gravitational wave detector by means of an output mode-cleaner,” Class. Quantum Grav. 23, 3235-3250 (2006).
[Crossref]

2004 (2)

The Virgo Collaboration, “The commissioning of the central interferometer of the Virgo gravitational wave detector,” Astropart. Phys. 21, 1-22 (2004).

The Virgo Collaboration, “The VIRGO large mirrors: a challenge for low loss coatings,” Class. Quantum Grav. 21, S935-S945 (2004).

2003 (2)

A. Freise, G. Heinzel, H. Luck, R. Schilling, B. Willke, and K. Danzmann, “Frequency domain interferometer simulation with higher-order spatial modes,” Class. Quantum Grav. 21, S1067-1074 (2003).
[Crossref]

A. Brillet, J.-Y. Vinet, V. Loriette, J.-M. Mackowski, L. Pinard, and A. Remillieux, “Virtual gravitational wave interferometers with actual mirrors,” Phys. Rev. D 67, 102006 (2003).
[Crossref]

2002 (1)

The Virgo Collaboration, “Interferometer signal detection system for the VIRGO experiment,” Class. Quantum Grav. 19, 1857-1863 (2002).

2000 (1)

B. J. J. Slagmolen, M. B. Gray, K.G. Baigent, and D. E. McClelland, “Phase-sensitive reflection technique for characterization of a Fabry-Perot interferometer,” Appl Opt. 39, 3638-3643 (2000).
[Crossref]

1999 (1)

B. Caron, L. Derome, R. Flaminio, X. Grave, F. Marion, B. Mours, D. Verkindt, F. Cavalier, and A. Viceré, “A time domain, general purpose simulation program for the VIRGO experiment,” Astropart. Phys. 10, 369-386 (1999).
[Crossref]

1997 (1)

D. Babusci, H. Fang, G. Giordano, G. Matone, L. Matone, and V. Sannibale, “Alignment procedure for the VIRGO interferometer: experimental results from the Frascati prototype,” Phys. Lett. A 226, 31-40 (1997).
[Crossref]

1992 (1)

J.-Y. Vinet, P. Hello, C. N. Man, and A. Brillet, “A high accuracy method for the simulation of non-ideal optical cavities,” J. Phys. I 2, 1287-1303 (1992).
[Crossref]

1991 (1)

T. M. Niebauer, R. Schilling, K. Danzmann, A. Rüdiger, and W. Winkler, “Nonstationary shot noise and its effect on the sensitivity of interferometers,” Phys. Rev. A 43, 5022-5029 (1991).
[Crossref] [PubMed]

1984 (2)

1983 (1)

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

1963 (1)

M. E. Gersenshtem and V. I. Pustovoit, Sov. Phys. JETP 16, 433 (1963).

1946 (1)

R. V. Pound, “Electronic frequency stabilization of microwave oscillators,” Rev. Sci. Instrum. 17, 490-505 (1946).
[Crossref] [PubMed]

Anderson, D. Z.

Babusci, D.

D. Babusci, H. Fang, G. Giordano, G. Matone, L. Matone, and V. Sannibale, “Alignment procedure for the VIRGO interferometer: experimental results from the Frascati prototype,” Phys. Lett. A 226, 31-40 (1997).
[Crossref]

Baigent, K.G.

B. J. J. Slagmolen, M. B. Gray, K.G. Baigent, and D. E. McClelland, “Phase-sensitive reflection technique for characterization of a Fabry-Perot interferometer,” Appl Opt. 39, 3638-3643 (2000).
[Crossref]

Beauville, F.

F. Beauville, D. Buskulic, L. Derome, A. Dominjon, R. Flaminio, R. Hermel, F. Marion, A. Masserot, L. Massonnet, B. Mours, F. Moreau, P. Mugnier, J. Ramonet, E. Tournefier, D. Verkindt, O. Veziant, and M. Yvert, “Improvement in the shot noise of a laser interferometer gravitational wave detector by means of an output mode-cleaner,” Class. Quantum Grav. 23, 3235-3250 (2006).
[Crossref]

Bondu, F.

Brillet, A.

A. Brillet, J.-Y. Vinet, V. Loriette, J.-M. Mackowski, L. Pinard, and A. Remillieux, “Virtual gravitational wave interferometers with actual mirrors,” Phys. Rev. D 67, 102006 (2003).
[Crossref]

J.-Y. Vinet, P. Hello, C. N. Man, and A. Brillet, “A high accuracy method for the simulation of non-ideal optical cavities,” J. Phys. I 2, 1287-1303 (1992).
[Crossref]

Buskulic, D.

F. Beauville, D. Buskulic, L. Derome, A. Dominjon, R. Flaminio, R. Hermel, F. Marion, A. Masserot, L. Massonnet, B. Mours, F. Moreau, P. Mugnier, J. Ramonet, E. Tournefier, D. Verkindt, O. Veziant, and M. Yvert, “Improvement in the shot noise of a laser interferometer gravitational wave detector by means of an output mode-cleaner,” Class. Quantum Grav. 23, 3235-3250 (2006).
[Crossref]

Caron, B.

B. Caron, L. Derome, R. Flaminio, X. Grave, F. Marion, B. Mours, D. Verkindt, F. Cavalier, and A. Viceré, “A time domain, general purpose simulation program for the VIRGO experiment,” Astropart. Phys. 10, 369-386 (1999).
[Crossref]

Cavalier, F.

B. Caron, L. Derome, R. Flaminio, X. Grave, F. Marion, B. Mours, D. Verkindt, F. Cavalier, and A. Viceré, “A time domain, general purpose simulation program for the VIRGO experiment,” Astropart. Phys. 10, 369-386 (1999).
[Crossref]

Danzmann, K.

A. Freise, G. Heinzel, H. Luck, R. Schilling, B. Willke, and K. Danzmann, “Frequency domain interferometer simulation with higher-order spatial modes,” Class. Quantum Grav. 21, S1067-1074 (2003).
[Crossref]

T. M. Niebauer, R. Schilling, K. Danzmann, A. Rüdiger, and W. Winkler, “Nonstationary shot noise and its effect on the sensitivity of interferometers,” Phys. Rev. A 43, 5022-5029 (1991).
[Crossref] [PubMed]

Debieu, O.

Derome, L.

F. Beauville, D. Buskulic, L. Derome, A. Dominjon, R. Flaminio, R. Hermel, F. Marion, A. Masserot, L. Massonnet, B. Mours, F. Moreau, P. Mugnier, J. Ramonet, E. Tournefier, D. Verkindt, O. Veziant, and M. Yvert, “Improvement in the shot noise of a laser interferometer gravitational wave detector by means of an output mode-cleaner,” Class. Quantum Grav. 23, 3235-3250 (2006).
[Crossref]

B. Caron, L. Derome, R. Flaminio, X. Grave, F. Marion, B. Mours, D. Verkindt, F. Cavalier, and A. Viceré, “A time domain, general purpose simulation program for the VIRGO experiment,” Astropart. Phys. 10, 369-386 (1999).
[Crossref]

Dominjon, A.

F. Beauville, D. Buskulic, L. Derome, A. Dominjon, R. Flaminio, R. Hermel, F. Marion, A. Masserot, L. Massonnet, B. Mours, F. Moreau, P. Mugnier, J. Ramonet, E. Tournefier, D. Verkindt, O. Veziant, and M. Yvert, “Improvement in the shot noise of a laser interferometer gravitational wave detector by means of an output mode-cleaner,” Class. Quantum Grav. 23, 3235-3250 (2006).
[Crossref]

Drever, R. W. P.

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

R. W. P. Drever, in Gravitational Radiation Proceedings, Les Houches Summer Institute, T.Piran and N.Deruelle, eds. (North-Holland, 1982), p. 321.

Fang, H.

D. Babusci, H. Fang, G. Giordano, G. Matone, L. Matone, and V. Sannibale, “Alignment procedure for the VIRGO interferometer: experimental results from the Frascati prototype,” Phys. Lett. A 226, 31-40 (1997).
[Crossref]

Flaminio, R.

F. Beauville, D. Buskulic, L. Derome, A. Dominjon, R. Flaminio, R. Hermel, F. Marion, A. Masserot, L. Massonnet, B. Mours, F. Moreau, P. Mugnier, J. Ramonet, E. Tournefier, D. Verkindt, O. Veziant, and M. Yvert, “Improvement in the shot noise of a laser interferometer gravitational wave detector by means of an output mode-cleaner,” Class. Quantum Grav. 23, 3235-3250 (2006).
[Crossref]

B. Caron, L. Derome, R. Flaminio, X. Grave, F. Marion, B. Mours, D. Verkindt, F. Cavalier, and A. Viceré, “A time domain, general purpose simulation program for the VIRGO experiment,” Astropart. Phys. 10, 369-386 (1999).
[Crossref]

Ford, G. M.

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

Freise, A.

A. Freise, G. Heinzel, H. Luck, R. Schilling, B. Willke, and K. Danzmann, “Frequency domain interferometer simulation with higher-order spatial modes,” Class. Quantum Grav. 21, S1067-1074 (2003).
[Crossref]

Frisch, J. C.

Fujimoto, M.

K. Hayama and M. Fujimoto, “Monitoring non-stationary burst-like signals in an interferometric gravitational wave detector,” Class. Quantum Grav. 23, S9-S15 (2006).
[Crossref]

Gersenshtem, M. E.

M. E. Gersenshtem and V. I. Pustovoit, Sov. Phys. JETP 16, 433 (1963).

Giordano, G.

D. Babusci, H. Fang, G. Giordano, G. Matone, L. Matone, and V. Sannibale, “Alignment procedure for the VIRGO interferometer: experimental results from the Frascati prototype,” Phys. Lett. A 226, 31-40 (1997).
[Crossref]

Grave, X.

B. Caron, L. Derome, R. Flaminio, X. Grave, F. Marion, B. Mours, D. Verkindt, F. Cavalier, and A. Viceré, “A time domain, general purpose simulation program for the VIRGO experiment,” Astropart. Phys. 10, 369-386 (1999).
[Crossref]

Gray, M. B.

B. J. J. Slagmolen, M. B. Gray, K.G. Baigent, and D. E. McClelland, “Phase-sensitive reflection technique for characterization of a Fabry-Perot interferometer,” Appl Opt. 39, 3638-3643 (2000).
[Crossref]

Hall, J. L.

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

Hayama, K.

K. Hayama and M. Fujimoto, “Monitoring non-stationary burst-like signals in an interferometric gravitational wave detector,” Class. Quantum Grav. 23, S9-S15 (2006).
[Crossref]

Heinzel, G.

A. Freise, G. Heinzel, H. Luck, R. Schilling, B. Willke, and K. Danzmann, “Frequency domain interferometer simulation with higher-order spatial modes,” Class. Quantum Grav. 21, S1067-1074 (2003).
[Crossref]

Hello, P.

J.-Y. Vinet, P. Hello, C. N. Man, and A. Brillet, “A high accuracy method for the simulation of non-ideal optical cavities,” J. Phys. I 2, 1287-1303 (1992).
[Crossref]

Hermel, R.

F. Beauville, D. Buskulic, L. Derome, A. Dominjon, R. Flaminio, R. Hermel, F. Marion, A. Masserot, L. Massonnet, B. Mours, F. Moreau, P. Mugnier, J. Ramonet, E. Tournefier, D. Verkindt, O. Veziant, and M. Yvert, “Improvement in the shot noise of a laser interferometer gravitational wave detector by means of an output mode-cleaner,” Class. Quantum Grav. 23, 3235-3250 (2006).
[Crossref]

Hough, J.

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

Kowalski, F. V.

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

Loriette, V.

A. Brillet, J.-Y. Vinet, V. Loriette, J.-M. Mackowski, L. Pinard, and A. Remillieux, “Virtual gravitational wave interferometers with actual mirrors,” Phys. Rev. D 67, 102006 (2003).
[Crossref]

Luck, H.

A. Freise, G. Heinzel, H. Luck, R. Schilling, B. Willke, and K. Danzmann, “Frequency domain interferometer simulation with higher-order spatial modes,” Class. Quantum Grav. 21, S1067-1074 (2003).
[Crossref]

Mackowski, J.-M.

A. Brillet, J.-Y. Vinet, V. Loriette, J.-M. Mackowski, L. Pinard, and A. Remillieux, “Virtual gravitational wave interferometers with actual mirrors,” Phys. Rev. D 67, 102006 (2003).
[Crossref]

Man, C. N.

J.-Y. Vinet, P. Hello, C. N. Man, and A. Brillet, “A high accuracy method for the simulation of non-ideal optical cavities,” J. Phys. I 2, 1287-1303 (1992).
[Crossref]

Marion, F.

F. Beauville, D. Buskulic, L. Derome, A. Dominjon, R. Flaminio, R. Hermel, F. Marion, A. Masserot, L. Massonnet, B. Mours, F. Moreau, P. Mugnier, J. Ramonet, E. Tournefier, D. Verkindt, O. Veziant, and M. Yvert, “Improvement in the shot noise of a laser interferometer gravitational wave detector by means of an output mode-cleaner,” Class. Quantum Grav. 23, 3235-3250 (2006).
[Crossref]

B. Caron, L. Derome, R. Flaminio, X. Grave, F. Marion, B. Mours, D. Verkindt, F. Cavalier, and A. Viceré, “A time domain, general purpose simulation program for the VIRGO experiment,” Astropart. Phys. 10, 369-386 (1999).
[Crossref]

Masser, C. S.

Masserot, A.

F. Beauville, D. Buskulic, L. Derome, A. Dominjon, R. Flaminio, R. Hermel, F. Marion, A. Masserot, L. Massonnet, B. Mours, F. Moreau, P. Mugnier, J. Ramonet, E. Tournefier, D. Verkindt, O. Veziant, and M. Yvert, “Improvement in the shot noise of a laser interferometer gravitational wave detector by means of an output mode-cleaner,” Class. Quantum Grav. 23, 3235-3250 (2006).
[Crossref]

Massonnet, L.

F. Beauville, D. Buskulic, L. Derome, A. Dominjon, R. Flaminio, R. Hermel, F. Marion, A. Masserot, L. Massonnet, B. Mours, F. Moreau, P. Mugnier, J. Ramonet, E. Tournefier, D. Verkindt, O. Veziant, and M. Yvert, “Improvement in the shot noise of a laser interferometer gravitational wave detector by means of an output mode-cleaner,” Class. Quantum Grav. 23, 3235-3250 (2006).
[Crossref]

Matone, G.

D. Babusci, H. Fang, G. Giordano, G. Matone, L. Matone, and V. Sannibale, “Alignment procedure for the VIRGO interferometer: experimental results from the Frascati prototype,” Phys. Lett. A 226, 31-40 (1997).
[Crossref]

Matone, L.

D. Babusci, H. Fang, G. Giordano, G. Matone, L. Matone, and V. Sannibale, “Alignment procedure for the VIRGO interferometer: experimental results from the Frascati prototype,” Phys. Lett. A 226, 31-40 (1997).
[Crossref]

McClelland, D. E.

B. J. J. Slagmolen, M. B. Gray, K.G. Baigent, and D. E. McClelland, “Phase-sensitive reflection technique for characterization of a Fabry-Perot interferometer,” Appl Opt. 39, 3638-3643 (2000).
[Crossref]

Moreau, F.

F. Beauville, D. Buskulic, L. Derome, A. Dominjon, R. Flaminio, R. Hermel, F. Marion, A. Masserot, L. Massonnet, B. Mours, F. Moreau, P. Mugnier, J. Ramonet, E. Tournefier, D. Verkindt, O. Veziant, and M. Yvert, “Improvement in the shot noise of a laser interferometer gravitational wave detector by means of an output mode-cleaner,” Class. Quantum Grav. 23, 3235-3250 (2006).
[Crossref]

Mours, B.

F. Beauville, D. Buskulic, L. Derome, A. Dominjon, R. Flaminio, R. Hermel, F. Marion, A. Masserot, L. Massonnet, B. Mours, F. Moreau, P. Mugnier, J. Ramonet, E. Tournefier, D. Verkindt, O. Veziant, and M. Yvert, “Improvement in the shot noise of a laser interferometer gravitational wave detector by means of an output mode-cleaner,” Class. Quantum Grav. 23, 3235-3250 (2006).
[Crossref]

B. Caron, L. Derome, R. Flaminio, X. Grave, F. Marion, B. Mours, D. Verkindt, F. Cavalier, and A. Viceré, “A time domain, general purpose simulation program for the VIRGO experiment,” Astropart. Phys. 10, 369-386 (1999).
[Crossref]

Mugnier, P.

F. Beauville, D. Buskulic, L. Derome, A. Dominjon, R. Flaminio, R. Hermel, F. Marion, A. Masserot, L. Massonnet, B. Mours, F. Moreau, P. Mugnier, J. Ramonet, E. Tournefier, D. Verkindt, O. Veziant, and M. Yvert, “Improvement in the shot noise of a laser interferometer gravitational wave detector by means of an output mode-cleaner,” Class. Quantum Grav. 23, 3235-3250 (2006).
[Crossref]

Munley, A. J.

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

Niebauer, T. M.

T. M. Niebauer, R. Schilling, K. Danzmann, A. Rüdiger, and W. Winkler, “Nonstationary shot noise and its effect on the sensitivity of interferometers,” Phys. Rev. A 43, 5022-5029 (1991).
[Crossref] [PubMed]

Pinard, L.

A. Brillet, J.-Y. Vinet, V. Loriette, J.-M. Mackowski, L. Pinard, and A. Remillieux, “Virtual gravitational wave interferometers with actual mirrors,” Phys. Rev. D 67, 102006 (2003).
[Crossref]

Pound, R. V.

R. V. Pound, “Electronic frequency stabilization of microwave oscillators,” Rev. Sci. Instrum. 17, 490-505 (1946).
[Crossref] [PubMed]

Pustovoit, V. I.

M. E. Gersenshtem and V. I. Pustovoit, Sov. Phys. JETP 16, 433 (1963).

Ramonet, J.

F. Beauville, D. Buskulic, L. Derome, A. Dominjon, R. Flaminio, R. Hermel, F. Marion, A. Masserot, L. Massonnet, B. Mours, F. Moreau, P. Mugnier, J. Ramonet, E. Tournefier, D. Verkindt, O. Veziant, and M. Yvert, “Improvement in the shot noise of a laser interferometer gravitational wave detector by means of an output mode-cleaner,” Class. Quantum Grav. 23, 3235-3250 (2006).
[Crossref]

Remillieux, A.

A. Brillet, J.-Y. Vinet, V. Loriette, J.-M. Mackowski, L. Pinard, and A. Remillieux, “Virtual gravitational wave interferometers with actual mirrors,” Phys. Rev. D 67, 102006 (2003).
[Crossref]

Rüdiger, A.

T. M. Niebauer, R. Schilling, K. Danzmann, A. Rüdiger, and W. Winkler, “Nonstationary shot noise and its effect on the sensitivity of interferometers,” Phys. Rev. A 43, 5022-5029 (1991).
[Crossref] [PubMed]

Sannibale, V.

D. Babusci, H. Fang, G. Giordano, G. Matone, L. Matone, and V. Sannibale, “Alignment procedure for the VIRGO interferometer: experimental results from the Frascati prototype,” Phys. Lett. A 226, 31-40 (1997).
[Crossref]

Schilling, R.

A. Freise, G. Heinzel, H. Luck, R. Schilling, B. Willke, and K. Danzmann, “Frequency domain interferometer simulation with higher-order spatial modes,” Class. Quantum Grav. 21, S1067-1074 (2003).
[Crossref]

T. M. Niebauer, R. Schilling, K. Danzmann, A. Rüdiger, and W. Winkler, “Nonstationary shot noise and its effect on the sensitivity of interferometers,” Phys. Rev. A 43, 5022-5029 (1991).
[Crossref] [PubMed]

Sigg, D.

D. Sigg, “Status of the LIGO detectors,” Class. Quantum. Grav. 23, S51-S56 (2006).
[Crossref]

Slagmolen, B. J. J.

B. J. J. Slagmolen, M. B. Gray, K.G. Baigent, and D. E. McClelland, “Phase-sensitive reflection technique for characterization of a Fabry-Perot interferometer,” Appl Opt. 39, 3638-3643 (2000).
[Crossref]

Tournefier, E.

F. Beauville, D. Buskulic, L. Derome, A. Dominjon, R. Flaminio, R. Hermel, F. Marion, A. Masserot, L. Massonnet, B. Mours, F. Moreau, P. Mugnier, J. Ramonet, E. Tournefier, D. Verkindt, O. Veziant, and M. Yvert, “Improvement in the shot noise of a laser interferometer gravitational wave detector by means of an output mode-cleaner,” Class. Quantum Grav. 23, 3235-3250 (2006).
[Crossref]

Verkindt, D.

F. Beauville, D. Buskulic, L. Derome, A. Dominjon, R. Flaminio, R. Hermel, F. Marion, A. Masserot, L. Massonnet, B. Mours, F. Moreau, P. Mugnier, J. Ramonet, E. Tournefier, D. Verkindt, O. Veziant, and M. Yvert, “Improvement in the shot noise of a laser interferometer gravitational wave detector by means of an output mode-cleaner,” Class. Quantum Grav. 23, 3235-3250 (2006).
[Crossref]

B. Caron, L. Derome, R. Flaminio, X. Grave, F. Marion, B. Mours, D. Verkindt, F. Cavalier, and A. Viceré, “A time domain, general purpose simulation program for the VIRGO experiment,” Astropart. Phys. 10, 369-386 (1999).
[Crossref]

Veziant, O.

F. Beauville, D. Buskulic, L. Derome, A. Dominjon, R. Flaminio, R. Hermel, F. Marion, A. Masserot, L. Massonnet, B. Mours, F. Moreau, P. Mugnier, J. Ramonet, E. Tournefier, D. Verkindt, O. Veziant, and M. Yvert, “Improvement in the shot noise of a laser interferometer gravitational wave detector by means of an output mode-cleaner,” Class. Quantum Grav. 23, 3235-3250 (2006).
[Crossref]

Viceré, A.

B. Caron, L. Derome, R. Flaminio, X. Grave, F. Marion, B. Mours, D. Verkindt, F. Cavalier, and A. Viceré, “A time domain, general purpose simulation program for the VIRGO experiment,” Astropart. Phys. 10, 369-386 (1999).
[Crossref]

Vinet, J.-Y.

A. Brillet, J.-Y. Vinet, V. Loriette, J.-M. Mackowski, L. Pinard, and A. Remillieux, “Virtual gravitational wave interferometers with actual mirrors,” Phys. Rev. D 67, 102006 (2003).
[Crossref]

J.-Y. Vinet, P. Hello, C. N. Man, and A. Brillet, “A high accuracy method for the simulation of non-ideal optical cavities,” J. Phys. I 2, 1287-1303 (1992).
[Crossref]

Ward, H.

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

Weiss, R.

R. Weiss, Quarterly Progress Report of the Research Laboratory of Electronics 105, (MIT, 1972), p. 379.
[PubMed]

Willke, B.

A. Freise, G. Heinzel, H. Luck, R. Schilling, B. Willke, and K. Danzmann, “Frequency domain interferometer simulation with higher-order spatial modes,” Class. Quantum Grav. 21, S1067-1074 (2003).
[Crossref]

Winkler, W.

T. M. Niebauer, R. Schilling, K. Danzmann, A. Rüdiger, and W. Winkler, “Nonstationary shot noise and its effect on the sensitivity of interferometers,” Phys. Rev. A 43, 5022-5029 (1991).
[Crossref] [PubMed]

Yvert, M.

F. Beauville, D. Buskulic, L. Derome, A. Dominjon, R. Flaminio, R. Hermel, F. Marion, A. Masserot, L. Massonnet, B. Mours, F. Moreau, P. Mugnier, J. Ramonet, E. Tournefier, D. Verkindt, O. Veziant, and M. Yvert, “Improvement in the shot noise of a laser interferometer gravitational wave detector by means of an output mode-cleaner,” Class. Quantum Grav. 23, 3235-3250 (2006).
[Crossref]

Appl Opt. (1)

B. J. J. Slagmolen, M. B. Gray, K.G. Baigent, and D. E. McClelland, “Phase-sensitive reflection technique for characterization of a Fabry-Perot interferometer,” Appl Opt. 39, 3638-3643 (2000).
[Crossref]

Appl. Opt. (3)

Appl. Phys. B (1)

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

Astropart. Phys. (2)

B. Caron, L. Derome, R. Flaminio, X. Grave, F. Marion, B. Mours, D. Verkindt, F. Cavalier, and A. Viceré, “A time domain, general purpose simulation program for the VIRGO experiment,” Astropart. Phys. 10, 369-386 (1999).
[Crossref]

The Virgo Collaboration, “The commissioning of the central interferometer of the Virgo gravitational wave detector,” Astropart. Phys. 21, 1-22 (2004).

Class. Quantum Grav. (6)

The Virgo Collaboration, “Interferometer signal detection system for the VIRGO experiment,” Class. Quantum Grav. 19, 1857-1863 (2002).

A. Freise, G. Heinzel, H. Luck, R. Schilling, B. Willke, and K. Danzmann, “Frequency domain interferometer simulation with higher-order spatial modes,” Class. Quantum Grav. 21, S1067-1074 (2003).
[Crossref]

The Virgo Collaboration, “The VIRGO large mirrors: a challenge for low loss coatings,” Class. Quantum Grav. 21, S935-S945 (2004).

F. Beauville, D. Buskulic, L. Derome, A. Dominjon, R. Flaminio, R. Hermel, F. Marion, A. Masserot, L. Massonnet, B. Mours, F. Moreau, P. Mugnier, J. Ramonet, E. Tournefier, D. Verkindt, O. Veziant, and M. Yvert, “Improvement in the shot noise of a laser interferometer gravitational wave detector by means of an output mode-cleaner,” Class. Quantum Grav. 23, 3235-3250 (2006).
[Crossref]

The GEO Collaboration, “Status of the GEO600 detector,” Class. Quantum Grav. 23, S71-S78 (2006).

K. Hayama and M. Fujimoto, “Monitoring non-stationary burst-like signals in an interferometric gravitational wave detector,” Class. Quantum Grav. 23, S9-S15 (2006).
[Crossref]

Class. Quantum. Grav. (1)

D. Sigg, “Status of the LIGO detectors,” Class. Quantum. Grav. 23, S51-S56 (2006).
[Crossref]

J. Phys. I (1)

J.-Y. Vinet, P. Hello, C. N. Man, and A. Brillet, “A high accuracy method for the simulation of non-ideal optical cavities,” J. Phys. I 2, 1287-1303 (1992).
[Crossref]

Phys. Lett. A (1)

D. Babusci, H. Fang, G. Giordano, G. Matone, L. Matone, and V. Sannibale, “Alignment procedure for the VIRGO interferometer: experimental results from the Frascati prototype,” Phys. Lett. A 226, 31-40 (1997).
[Crossref]

Phys. Rev. A (1)

T. M. Niebauer, R. Schilling, K. Danzmann, A. Rüdiger, and W. Winkler, “Nonstationary shot noise and its effect on the sensitivity of interferometers,” Phys. Rev. A 43, 5022-5029 (1991).
[Crossref] [PubMed]

Phys. Rev. D (1)

A. Brillet, J.-Y. Vinet, V. Loriette, J.-M. Mackowski, L. Pinard, and A. Remillieux, “Virtual gravitational wave interferometers with actual mirrors,” Phys. Rev. D 67, 102006 (2003).
[Crossref]

Rev. Sci. Instrum. (1)

R. V. Pound, “Electronic frequency stabilization of microwave oscillators,” Rev. Sci. Instrum. 17, 490-505 (1946).
[Crossref] [PubMed]

Sov. Phys. JETP (1)

M. E. Gersenshtem and V. I. Pustovoit, Sov. Phys. JETP 16, 433 (1963).

Other (4)

R. Weiss, Quarterly Progress Report of the Research Laboratory of Electronics 105, (MIT, 1972), p. 379.
[PubMed]

R. W. P. Drever, in Gravitational Radiation Proceedings, Les Houches Summer Institute, T.Piran and N.Deruelle, eds. (North-Holland, 1982), p. 321.

The Virgo Collaboration, Final Design Report, VIR-TRE-DIR-1000-13 (1997).

The Virgo Collaboration, “The status of Virgo,” in HEP2005 International Europhysics Conference on High Energy Physics, PoS(HEP2005)029 (2005).

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Figures (11)

Fig. 1
Fig. 1

(Color online) Optical scheme of Virgo.

Fig. 2
Fig. 2

Shot-noise-limited sensitivity as a function of the modulation depth for several values of sideband transmission (T) and contrast defect ( 1 C ) : T = 0.4 , 1 C = 10 5 (solid curve), T = 0.2 , 1 C = 3 × 10 5 (dashed curve), T = 0.1 , 1 C = 3 × 10 5 (dotted curve), and T = 0.1 , 1 C = 3 × 10 4 (dashed–dotted curve).

Fig. 3
Fig. 3

Intensity reflection operator of the full interferometer with real maps. The modes are ordered { 00 , 01 , 10 , 02 , 11 , 20 , 03 , } . Off-diagonal elements show coupling between modes inside the interferometer induced by surface defects. Diagonal elements slightly differ from unity mainly due to the finite size of the coatings.

Fig. 4
Fig. 4

(Color online) Power transmitted by a free FP cavity.

Fig. 5
Fig. 5

Open loop transfer function of the lock of laser frequency on the cavity, at ∼1 MHz. Solid curve, measured data; dotted curve, fitted curve.

Fig. 6
Fig. 6

(Color online) Time decay experiment: power transmitted by the IMC, after a fast change of input laser frequency.

Fig. 7
Fig. 7

(Color online) Open loop transfer function of the lock of laser frequency on the cavity, around the frequency of the TEM 02 mode (726 kHz). Solid curve, measured data; dotted curve, result of the fit.

Fig. 8
Fig. 8

Size of the beam after 3   km along two orthogonal axis as a function of the input telescope length tuning. The curves represent the result of the simulation while the dots are the experimental measurements. The wider black curve shows the power transmitted by the cavity as predicted by simulation (Ref. 17).

Fig. 9
Fig. 9

Profile of the Airy peak without dynamical effects (dotted curve) and with dynamical effects (solid curve) for a speed of 10 μm∕s.

Fig. 10
Fig. 10

Example of the measurement of the speed of the FP cavities: the dots represent the TEM 00 peak positions, and the curve shows the length l(t) fitted to these points.

Fig. 11
Fig. 11

Recycling gain of the sidebands as predicted by simulation as a function of the radius of curvature (in meters) of the power recycling mirror. The simulation is done for a 12 m long FP cavity, with flat input mirror and curved end mirror M1. The transmissions of the input and end mirrors are set, respectively, to 7.8% and 1.4% so that the behavior of this cavity is identical to the Virgo recycling cavity for the sidebands.

Tables (2)

Tables Icon

Table 2 Radius of Curvature of the End Mirrors a

Equations (30)

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Δ h sn ( f ) = λ 2 π L h ν 2 P 0 π 2 F J 0 2 ( m ) G ( 1 C ) + 6 T J 1 2 ( m ) 2 J 0 ( m ) J 1 ( m ) G T × 1 + ( f f 0 ) 2 ,
E 2 ( x , y , z ) = FT 1 ( FT ( E 1 ( x , y , z 0 ) ) × exp [ i p 2 + q 2 2 k | z z 0 | ] ) = FT 1 ( FT ( E 1 ( x , y , z 0 ) ) × P ) ,
Ecav n + 1 = t 1 E 0 r 1 r 2 M 1 P L M 2 P L Ecav n ,
r i , j m , n = x , y g i , j ( x , y ) r ( x , y ) exp ( 4 i π z ( x , y ) ) × g m , n * ( x , y ) d x d y ,
u ( x , y ) = i , j u i j g i , j ( x , y ) ,
u m n = i , j r i , j m , n u i j .
f mod = n FSR IMC = n c 2 L IMC ,
f mod = f sep + n FSR FP ,
T = 4 T 1 T 2 ( T 1 + T 2 + L RT ) 2 ,
T 1 + T 2 + L RT = 4 π f P FSR .
y = A exp ( i ϕ ) ( 1 + i ( f FSR ) / f Z 1 + i ( f FSR ) / f P ) ,
y = A exp ( ϕ ) ( 1 M 2 1 1 + i ( f f 02 ) / f P )
F = c 4 f P L IMC .
FSR = c 2 L IMC ,
F = π r 1 r 2 1 r 1 r 2 ,
f sep = ν 01 ν 00 = c 2 π L FP   arccos   1 L FP R 2 .
d n m 00 ( n + m ) d 00 00 = 1 π   arccos   1 L FP R 2 ,
f mod = ν USB ν carrier + 125 FSR = c 2 L FP ( d USB carrier d 00 00 ) + 125 FSR ,
r FP = r i r e ( 1 L ) 1 r i r e ,
ω c 2 l r e c = 0 [ 2 π ]
ω ± Ω c 2 l r e c = π + ϕ FP [ 2 π ]
Ω c 2 l r e c = π + ϕ FP [ 2 π ] .
G = ( t P R 1 + r P R r FP ) 2 ,
G S B = ( t P R 1 cos ( Ω Δ l c ) r P R r FP S B ) 2 ,
G 00 = T P R P d c recycled P d c recombined ,     G S B 00 = 2 T P R P 2 Ω recycled P 2 Ω recombined ,
G 00 = 33 ± 1 ,     G S B 00 = 20 ± 1 .
T = G S B sin 2 ( Ω Δ l c ) = ( t P R r FP S B sin ( Ω Δ l c ) 1 cos ( Ω Δ l c ) r P R r FP S B ) 2 .
P d c = P 0 ( J 0 ( m ) 2 1 C 2 + 2 T recomb J 1 ( m ) 2 ) ,
P d c = P 0 ( G J 0 ( m ) 2 1 C 2 + 2 T J 1 ( m ) 2 ) .
OG = 4 P i n 00 T d f J 0 ( m ) J 1 ( m ) 2 F π 2 π λ G T   W / m ,

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