Abstract

The effect of radiation pressure on the stability of Fabry–Perot cavities with hanging mirrors is investigated. Such cavities will form an integral part of the laser interferometric gravitational-wave detectors that are being constructed around the globe. The mirrors are hung by means of a pendulum suspension and are locked by servo controls. We assume a realistic servo-control transfer function that satisfies the standard stability criteria. We find that for positive offsets from the resonance of the cavity the system is stable. However, we show that for negative offsets instabilities can occur, although the servo system has the effect of increasing the instability threshold, compared with the nonservoed case. Conditions for stability are finally given, involving the finesse of the cavity, the input power, the mass of the mirrors, the servo gain, and the phase detuning from perfect resonance. Gravitational-wave detectors with arm cavities having a finesse as low as approximately 200 could exhibit instabilities. Some implications for the locking of these detectors are finally given.

© 1998 Optical Society of America

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  1. K. S. Thorne, “Gravitational radiation,” in In 300 Years of Gravitation, S. W. Hawking, W. Israel, eds. (Cambridge U. Press, Cambridge, UK, 1987).
  2. D. Blair, ed., The Detection of Gravitational Waves (Cambridge U. Press, Cambridge, UK, 1991).
    [CrossRef]
  3. A. Giazotto, “Interferometric detection of gravitational waves,” Phys. Rep. 182, 365–425 (1989).
    [CrossRef]
  4. R. W. P. Drever, “Interferometric detectors for gravitational wave detection,” in Gravitational Radiation, N. Deruelle, T. Piran, eds. (North-Holland, Amsterdam, The Netherlands, 1983).
  5. J.-Y. Vinet, B. J. Meers, C. N. Man, A. Brillet, “Optimization of long-baseline interferometers for gravitational-wave detection,” Phys. Rev. D 38, 433–447 (1988).
    [CrossRef]
  6. A. Dorsel, J. D. McCullen, P. Meystre, E. Vignes, H. Walther, “Optical bistability and mirror confinement induced by radiation pressure,” Phys. Rev. Lett. 51, 1550–1553 (1983).
    [CrossRef]
  7. P. Meystre, E. M. Wright, J. D. McCullen, E. Vignes, “Theory of radiation pressure-driven interferometers,” J. Opt. Soc. Am. B 2, 1830–1840 (1985).
    [CrossRef]
  8. N. Deruelle, P. Tourrenc, “The problem of the optical stability of a pendular Fabry–Perot,” in Gravitation, Geometry and Relativistic Physics (Springer, Berlin, 1984), pp. 232–237.
    [CrossRef]
  9. P. Tourrenc, N. Deruelle, “Effects of the time delays in a non-linear pendular Fabry–Perot,” Ann. Phys. Fr. 10, 241–252 (1985).
    [CrossRef]
  10. J. M. Aguirregabiria, L. L. Bel, “Delay-induced instability in a pendular Fabry–Perot cavity,” Phys. Rev. A 36, 3768–3770 (1987).
    [CrossRef] [PubMed]
  11. B. J. Meers, N. MacDonald, “Potential radiation pressure induced instabilities in cavity interferometers,” Phys. Rev. A 40, 3754–3763 (1989).
    [CrossRef] [PubMed]
  12. V. V. Kulagin, V. N. Rudenko, “Dynamics of a free mass interferometric gravitational antenna with small loss suspensions,” Phys. Lett. A 214, 123–126 (1996).
    [CrossRef]
  13. P. Hello, J.-Y. Vinet, “Analytical models of transient thermoelastic deformations of mirrors heated by high power cw laser beams,” J. Phys. (France) 51, 2243–2261 (1990).
    [CrossRef]
  14. S. V. Dhurandhar, P. Hello, B. S. Satyaprakash, J.-Y. Vinet, “Stability of giant Fabry–Perot cavities of interferometric gravitational-wave detectors,” Appl. Opt. 36, 5325–5334 (1997).
    [CrossRef] [PubMed]
  15. B. Caron, A. Dominjon, C. Drezen, R. Flaminio, X. Grave, R. Hermel, F. Marion, L. Massonet, C. Mehmel, R. Morand, B. Mours, V. Sanibale, M. Yvert, “A preliminary study of the locking of an interferometric for gravitational wave detection,” Astropart. Phys. 6, 245–256 (1997).
    [CrossRef]
  16. R. Flaminio, H. Heitmann, “Longitudinal control of an interferometer for the detection of gravitational waves,” Phys. Lett. A 214, 112–122 (1996).
    [CrossRef]
  17. 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, E. Gourgoulhon, L. E. Holloway, F. Fuligni, V. Iafolla, G. Natale, “The VIRGO project: a wide band antenna for gravitational wave detection,” Nucl. Instrum. Methods A 289, 518–525 (1990).
    [CrossRef]
  18. A. Abramovici, W. E. Althouse, R. W. P. Drever, Y. Gursel, S. Kawamura, F. J. Raab, D. Shoemaker, L. Sievers, R. E. Spero, K. S. Thorne, R. E. Vogt, R. Weiss, S. E. Whitcomb, M. E. Zucker, “The Laser Interferometer Gravitational-Wave Observatory,” Science 256, 325–333 (1992).
    [CrossRef] [PubMed]
  19. D. Shoemaker, LIGO team, MIT, Boston, Mass. 02139 (personal communication, 1997).

1997 (2)

B. Caron, A. Dominjon, C. Drezen, R. Flaminio, X. Grave, R. Hermel, F. Marion, L. Massonet, C. Mehmel, R. Morand, B. Mours, V. Sanibale, M. Yvert, “A preliminary study of the locking of an interferometric for gravitational wave detection,” Astropart. Phys. 6, 245–256 (1997).
[CrossRef]

S. V. Dhurandhar, P. Hello, B. S. Satyaprakash, J.-Y. Vinet, “Stability of giant Fabry–Perot cavities of interferometric gravitational-wave detectors,” Appl. Opt. 36, 5325–5334 (1997).
[CrossRef] [PubMed]

1996 (2)

R. Flaminio, H. Heitmann, “Longitudinal control of an interferometer for the detection of gravitational waves,” Phys. Lett. A 214, 112–122 (1996).
[CrossRef]

V. V. Kulagin, V. N. Rudenko, “Dynamics of a free mass interferometric gravitational antenna with small loss suspensions,” Phys. Lett. A 214, 123–126 (1996).
[CrossRef]

1992 (1)

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

1990 (2)

P. Hello, J.-Y. Vinet, “Analytical models of transient thermoelastic deformations of mirrors heated by high power cw laser beams,” J. Phys. (France) 51, 2243–2261 (1990).
[CrossRef]

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, E. Gourgoulhon, L. E. Holloway, F. Fuligni, V. Iafolla, G. Natale, “The VIRGO project: a wide band antenna for gravitational wave detection,” Nucl. Instrum. Methods A 289, 518–525 (1990).
[CrossRef]

1989 (2)

A. Giazotto, “Interferometric detection of gravitational waves,” Phys. Rep. 182, 365–425 (1989).
[CrossRef]

B. J. Meers, N. MacDonald, “Potential radiation pressure induced instabilities in cavity interferometers,” Phys. Rev. A 40, 3754–3763 (1989).
[CrossRef] [PubMed]

1988 (1)

J.-Y. Vinet, B. J. Meers, C. N. Man, A. Brillet, “Optimization of long-baseline interferometers for gravitational-wave detection,” Phys. Rev. D 38, 433–447 (1988).
[CrossRef]

1987 (1)

J. M. Aguirregabiria, L. L. Bel, “Delay-induced instability in a pendular Fabry–Perot cavity,” Phys. Rev. A 36, 3768–3770 (1987).
[CrossRef] [PubMed]

1985 (2)

P. Tourrenc, N. Deruelle, “Effects of the time delays in a non-linear pendular Fabry–Perot,” Ann. Phys. Fr. 10, 241–252 (1985).
[CrossRef]

P. Meystre, E. M. Wright, J. D. McCullen, E. Vignes, “Theory of radiation pressure-driven interferometers,” J. Opt. Soc. Am. B 2, 1830–1840 (1985).
[CrossRef]

1983 (1)

A. Dorsel, J. D. McCullen, P. Meystre, E. Vignes, H. Walther, “Optical bistability and mirror confinement induced by radiation pressure,” Phys. Rev. Lett. 51, 1550–1553 (1983).
[CrossRef]

Abramovici, A.

A. Abramovici, W. E. Althouse, R. W. P. Drever, Y. Gursel, S. Kawamura, F. J. Raab, D. Shoemaker, L. Sievers, R. E. Spero, K. S. Thorne, R. E. Vogt, R. Weiss, S. E. Whitcomb, M. E. Zucker, “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, E. Gourgoulhon, L. E. Holloway, F. Fuligni, V. Iafolla, G. Natale, “The VIRGO project: a wide band antenna for gravitational wave detection,” Nucl. Instrum. Methods A 289, 518–525 (1990).
[CrossRef]

J. M. Aguirregabiria, L. L. Bel, “Delay-induced instability in a pendular Fabry–Perot cavity,” Phys. Rev. A 36, 3768–3770 (1987).
[CrossRef] [PubMed]

Althouse, W. E.

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

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, E. Gourgoulhon, L. E. Holloway, F. Fuligni, V. Iafolla, G. Natale, “The VIRGO project: a wide band antenna for gravitational wave detection,” Nucl. Instrum. Methods 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, E. Gourgoulhon, L. E. Holloway, F. Fuligni, V. Iafolla, G. Natale, “The VIRGO project: a wide band antenna for gravitational wave detection,” Nucl. Instrum. Methods A 289, 518–525 (1990).
[CrossRef]

Bel, L. L.

J. M. Aguirregabiria, L. L. Bel, “Delay-induced instability in a pendular Fabry–Perot cavity,” Phys. Rev. A 36, 3768–3770 (1987).
[CrossRef] [PubMed]

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, E. Gourgoulhon, L. E. Holloway, F. Fuligni, V. Iafolla, G. Natale, “The VIRGO project: a wide band antenna for gravitational wave detection,” Nucl. Instrum. Methods A 289, 518–525 (1990).
[CrossRef]

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, E. Gourgoulhon, L. E. Holloway, F. Fuligni, V. Iafolla, G. Natale, “The VIRGO project: a wide band antenna for gravitational wave detection,” Nucl. Instrum. Methods 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, E. Gourgoulhon, L. E. Holloway, F. Fuligni, V. Iafolla, G. Natale, “The VIRGO project: a wide band antenna for gravitational wave detection,” Nucl. Instrum. Methods A 289, 518–525 (1990).
[CrossRef]

J.-Y. Vinet, B. J. Meers, C. N. Man, A. Brillet, “Optimization of long-baseline interferometers for gravitational-wave detection,” Phys. Rev. D 38, 433–447 (1988).
[CrossRef]

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, E. Gourgoulhon, L. E. Holloway, F. Fuligni, V. Iafolla, G. Natale, “The VIRGO project: a wide band antenna for gravitational wave detection,” Nucl. Instrum. Methods A 289, 518–525 (1990).
[CrossRef]

Caron, B.

B. Caron, A. Dominjon, C. Drezen, R. Flaminio, X. Grave, R. Hermel, F. Marion, L. Massonet, C. Mehmel, R. Morand, B. Mours, V. Sanibale, M. Yvert, “A preliminary study of the locking of an interferometric for gravitational wave detection,” Astropart. Phys. 6, 245–256 (1997).
[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, E. Gourgoulhon, L. E. Holloway, F. Fuligni, V. Iafolla, G. Natale, “The VIRGO project: a wide band antenna for gravitational wave detection,” Nucl. Instrum. Methods A 289, 518–525 (1990).
[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, E. Gourgoulhon, L. E. Holloway, F. Fuligni, V. Iafolla, G. Natale, “The VIRGO project: a wide band antenna for gravitational wave detection,” Nucl. Instrum. Methods A 289, 518–525 (1990).
[CrossRef]

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, E. Gourgoulhon, L. E. Holloway, F. Fuligni, V. Iafolla, G. Natale, “The VIRGO project: a wide band antenna for gravitational wave detection,” Nucl. Instrum. Methods A 289, 518–525 (1990).
[CrossRef]

Deruelle, N.

P. Tourrenc, N. Deruelle, “Effects of the time delays in a non-linear pendular Fabry–Perot,” Ann. Phys. Fr. 10, 241–252 (1985).
[CrossRef]

N. Deruelle, P. Tourrenc, “The problem of the optical stability of a pendular Fabry–Perot,” in Gravitation, Geometry and Relativistic Physics (Springer, Berlin, 1984), pp. 232–237.
[CrossRef]

Dhurandhar, S. V.

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, E. Gourgoulhon, L. E. Holloway, F. Fuligni, V. Iafolla, G. Natale, “The VIRGO project: a wide band antenna for gravitational wave detection,” Nucl. Instrum. Methods 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, E. Gourgoulhon, L. E. Holloway, F. Fuligni, V. Iafolla, G. Natale, “The VIRGO project: a wide band antenna for gravitational wave detection,” Nucl. Instrum. Methods A 289, 518–525 (1990).
[CrossRef]

Dominjon, A.

B. Caron, A. Dominjon, C. Drezen, R. Flaminio, X. Grave, R. Hermel, F. Marion, L. Massonet, C. Mehmel, R. Morand, B. Mours, V. Sanibale, M. Yvert, “A preliminary study of the locking of an interferometric for gravitational wave detection,” Astropart. Phys. 6, 245–256 (1997).
[CrossRef]

Dorsel, A.

A. Dorsel, J. D. McCullen, P. Meystre, E. Vignes, H. Walther, “Optical bistability and mirror confinement induced by radiation pressure,” Phys. Rev. Lett. 51, 1550–1553 (1983).
[CrossRef]

Drever, R. W. P.

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

R. W. P. Drever, “Interferometric detectors for gravitational wave detection,” in Gravitational Radiation, N. Deruelle, T. Piran, eds. (North-Holland, Amsterdam, The Netherlands, 1983).

Drezen, C.

B. Caron, A. Dominjon, C. Drezen, R. Flaminio, X. Grave, R. Hermel, F. Marion, L. Massonet, C. Mehmel, R. Morand, B. Mours, V. Sanibale, M. Yvert, “A preliminary study of the locking of an interferometric for gravitational wave detection,” Astropart. Phys. 6, 245–256 (1997).
[CrossRef]

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, E. Gourgoulhon, L. E. Holloway, F. Fuligni, V. Iafolla, G. Natale, “The VIRGO project: a wide band antenna for gravitational wave detection,” Nucl. Instrum. Methods A 289, 518–525 (1990).
[CrossRef]

Flaminio, R.

B. Caron, A. Dominjon, C. Drezen, R. Flaminio, X. Grave, R. Hermel, F. Marion, L. Massonet, C. Mehmel, R. Morand, B. Mours, V. Sanibale, M. Yvert, “A preliminary study of the locking of an interferometric for gravitational wave detection,” Astropart. Phys. 6, 245–256 (1997).
[CrossRef]

R. Flaminio, H. Heitmann, “Longitudinal control of an interferometer for the detection of gravitational waves,” Phys. Lett. A 214, 112–122 (1996).
[CrossRef]

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, E. Gourgoulhon, L. E. Holloway, F. Fuligni, V. Iafolla, G. Natale, “The VIRGO project: a wide band antenna for gravitational wave detection,” Nucl. Instrum. Methods 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, E. Gourgoulhon, L. E. Holloway, F. Fuligni, V. Iafolla, G. Natale, “The VIRGO project: a wide band antenna for gravitational wave detection,” Nucl. Instrum. Methods A 289, 518–525 (1990).
[CrossRef]

A. Giazotto, “Interferometric detection of gravitational waves,” Phys. Rep. 182, 365–425 (1989).
[CrossRef]

Gourgoulhon, 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, E. Gourgoulhon, L. E. Holloway, F. Fuligni, V. Iafolla, G. Natale, “The VIRGO project: a wide band antenna for gravitational wave detection,” Nucl. Instrum. Methods A 289, 518–525 (1990).
[CrossRef]

Grave, X.

B. Caron, A. Dominjon, C. Drezen, R. Flaminio, X. Grave, R. Hermel, F. Marion, L. Massonet, C. Mehmel, R. Morand, B. Mours, V. Sanibale, M. Yvert, “A preliminary study of the locking of an interferometric for gravitational wave detection,” Astropart. Phys. 6, 245–256 (1997).
[CrossRef]

Gursel, Y.

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

Heitmann, H.

R. Flaminio, H. Heitmann, “Longitudinal control of an interferometer for the detection of gravitational waves,” Phys. Lett. A 214, 112–122 (1996).
[CrossRef]

Hello, P.

S. V. Dhurandhar, P. Hello, B. S. Satyaprakash, J.-Y. Vinet, “Stability of giant Fabry–Perot cavities of interferometric gravitational-wave detectors,” Appl. Opt. 36, 5325–5334 (1997).
[CrossRef] [PubMed]

P. Hello, J.-Y. Vinet, “Analytical models of transient thermoelastic deformations of mirrors heated by high power cw laser beams,” J. Phys. (France) 51, 2243–2261 (1990).
[CrossRef]

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, E. Gourgoulhon, L. E. Holloway, F. Fuligni, V. Iafolla, G. Natale, “The VIRGO project: a wide band antenna for gravitational wave detection,” Nucl. Instrum. Methods A 289, 518–525 (1990).
[CrossRef]

Hermel, R.

B. Caron, A. Dominjon, C. Drezen, R. Flaminio, X. Grave, R. Hermel, F. Marion, L. Massonet, C. Mehmel, R. Morand, B. Mours, V. Sanibale, M. Yvert, “A preliminary study of the locking of an interferometric for gravitational wave detection,” Astropart. Phys. 6, 245–256 (1997).
[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, E. Gourgoulhon, L. E. Holloway, F. Fuligni, V. Iafolla, G. Natale, “The VIRGO project: a wide band antenna for gravitational wave detection,” Nucl. Instrum. Methods A 289, 518–525 (1990).
[CrossRef]

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, E. Gourgoulhon, L. E. Holloway, F. Fuligni, V. Iafolla, G. Natale, “The VIRGO project: a wide band antenna for gravitational wave detection,” Nucl. Instrum. Methods 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, E. Gourgoulhon, L. E. Holloway, F. Fuligni, V. Iafolla, G. Natale, “The VIRGO project: a wide band antenna for gravitational wave detection,” Nucl. Instrum. Methods A 289, 518–525 (1990).
[CrossRef]

Kawamura, S.

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

Kulagin, V. V.

V. V. Kulagin, V. N. Rudenko, “Dynamics of a free mass interferometric gravitational antenna with small loss suspensions,” Phys. Lett. A 214, 123–126 (1996).
[CrossRef]

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, E. Gourgoulhon, L. E. Holloway, F. Fuligni, V. Iafolla, G. Natale, “The VIRGO project: a wide band antenna for gravitational wave detection,” Nucl. Instrum. Methods A 289, 518–525 (1990).
[CrossRef]

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, E. Gourgoulhon, L. E. Holloway, F. Fuligni, V. Iafolla, G. Natale, “The VIRGO project: a wide band antenna for gravitational wave detection,” Nucl. Instrum. Methods 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, E. Gourgoulhon, L. E. Holloway, F. Fuligni, V. Iafolla, G. Natale, “The VIRGO project: a wide band antenna for gravitational wave detection,” Nucl. Instrum. Methods A 289, 518–525 (1990).
[CrossRef]

MacDonald, N.

B. J. Meers, N. MacDonald, “Potential radiation pressure induced instabilities in cavity interferometers,” Phys. Rev. A 40, 3754–3763 (1989).
[CrossRef] [PubMed]

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, E. Gourgoulhon, L. E. Holloway, F. Fuligni, V. Iafolla, G. Natale, “The VIRGO project: a wide band antenna for gravitational wave detection,” Nucl. Instrum. Methods A 289, 518–525 (1990).
[CrossRef]

J.-Y. Vinet, B. J. Meers, C. N. Man, A. Brillet, “Optimization of long-baseline interferometers for gravitational-wave detection,” Phys. Rev. D 38, 433–447 (1988).
[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, E. Gourgoulhon, L. E. Holloway, F. Fuligni, V. Iafolla, G. Natale, “The VIRGO project: a wide band antenna for gravitational wave detection,” Nucl. Instrum. Methods 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, E. Gourgoulhon, L. E. Holloway, F. Fuligni, V. Iafolla, G. Natale, “The VIRGO project: a wide band antenna for gravitational wave detection,” Nucl. Instrum. Methods A 289, 518–525 (1990).
[CrossRef]

Marion, F.

B. Caron, A. Dominjon, C. Drezen, R. Flaminio, X. Grave, R. Hermel, F. Marion, L. Massonet, C. Mehmel, R. Morand, B. Mours, V. Sanibale, M. Yvert, “A preliminary study of the locking of an interferometric for gravitational wave detection,” Astropart. Phys. 6, 245–256 (1997).
[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, E. Gourgoulhon, L. E. Holloway, F. Fuligni, V. Iafolla, G. Natale, “The VIRGO project: a wide band antenna for gravitational wave detection,” Nucl. Instrum. Methods A 289, 518–525 (1990).
[CrossRef]

Massonet, L.

B. Caron, A. Dominjon, C. Drezen, R. Flaminio, X. Grave, R. Hermel, F. Marion, L. Massonet, C. Mehmel, R. Morand, B. Mours, V. Sanibale, M. Yvert, “A preliminary study of the locking of an interferometric for gravitational wave detection,” Astropart. Phys. 6, 245–256 (1997).
[CrossRef]

McCullen, J. D.

P. Meystre, E. M. Wright, J. D. McCullen, E. Vignes, “Theory of radiation pressure-driven interferometers,” J. Opt. Soc. Am. B 2, 1830–1840 (1985).
[CrossRef]

A. Dorsel, J. D. McCullen, P. Meystre, E. Vignes, H. Walther, “Optical bistability and mirror confinement induced by radiation pressure,” Phys. Rev. Lett. 51, 1550–1553 (1983).
[CrossRef]

Meers, B. J.

B. J. Meers, N. MacDonald, “Potential radiation pressure induced instabilities in cavity interferometers,” Phys. Rev. A 40, 3754–3763 (1989).
[CrossRef] [PubMed]

J.-Y. Vinet, B. J. Meers, C. N. Man, A. Brillet, “Optimization of long-baseline interferometers for gravitational-wave detection,” Phys. Rev. D 38, 433–447 (1988).
[CrossRef]

Mehmel, C.

B. Caron, A. Dominjon, C. Drezen, R. Flaminio, X. Grave, R. Hermel, F. Marion, L. Massonet, C. Mehmel, R. Morand, B. Mours, V. Sanibale, M. Yvert, “A preliminary study of the locking of an interferometric for gravitational wave detection,” Astropart. Phys. 6, 245–256 (1997).
[CrossRef]

Meystre, P.

P. Meystre, E. M. Wright, J. D. McCullen, E. Vignes, “Theory of radiation pressure-driven interferometers,” J. Opt. Soc. Am. B 2, 1830–1840 (1985).
[CrossRef]

A. Dorsel, J. D. McCullen, P. Meystre, E. Vignes, H. Walther, “Optical bistability and mirror confinement induced by radiation pressure,” Phys. Rev. Lett. 51, 1550–1553 (1983).
[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, E. Gourgoulhon, L. E. Holloway, F. Fuligni, V. Iafolla, G. Natale, “The VIRGO project: a wide band antenna for gravitational wave detection,” Nucl. Instrum. Methods A 289, 518–525 (1990).
[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, E. Gourgoulhon, L. E. Holloway, F. Fuligni, V. Iafolla, G. Natale, “The VIRGO project: a wide band antenna for gravitational wave detection,” Nucl. Instrum. Methods A 289, 518–525 (1990).
[CrossRef]

Morand, R.

B. Caron, A. Dominjon, C. Drezen, R. Flaminio, X. Grave, R. Hermel, F. Marion, L. Massonet, C. Mehmel, R. Morand, B. Mours, V. Sanibale, M. Yvert, “A preliminary study of the locking of an interferometric for gravitational wave detection,” Astropart. Phys. 6, 245–256 (1997).
[CrossRef]

Mours, B.

B. Caron, A. Dominjon, C. Drezen, R. Flaminio, X. Grave, R. Hermel, F. Marion, L. Massonet, C. Mehmel, R. Morand, B. Mours, V. Sanibale, M. Yvert, “A preliminary study of the locking of an interferometric for gravitational wave detection,” Astropart. Phys. 6, 245–256 (1997).
[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, E. Gourgoulhon, L. E. Holloway, F. Fuligni, V. Iafolla, G. Natale, “The VIRGO project: a wide band antenna for gravitational wave detection,” Nucl. Instrum. Methods A 289, 518–525 (1990).
[CrossRef]

Passuello, D.

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, E. Gourgoulhon, L. E. Holloway, F. Fuligni, V. Iafolla, G. Natale, “The VIRGO project: a wide band antenna for gravitational wave detection,” Nucl. Instrum. Methods A 289, 518–525 (1990).
[CrossRef]

Pinto, I.

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, E. Gourgoulhon, L. E. Holloway, F. Fuligni, V. Iafolla, G. Natale, “The VIRGO project: a wide band antenna for gravitational wave detection,” Nucl. Instrum. Methods A 289, 518–525 (1990).
[CrossRef]

Raab, F. J.

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

Rotoli, 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, E. Gourgoulhon, L. E. Holloway, F. Fuligni, V. Iafolla, G. Natale, “The VIRGO project: a wide band antenna for gravitational wave detection,” Nucl. Instrum. Methods A 289, 518–525 (1990).
[CrossRef]

Rudenko, V. N.

V. V. Kulagin, V. N. Rudenko, “Dynamics of a free mass interferometric gravitational antenna with small loss suspensions,” Phys. Lett. A 214, 123–126 (1996).
[CrossRef]

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, E. Gourgoulhon, L. E. Holloway, F. Fuligni, V. Iafolla, G. Natale, “The VIRGO project: a wide band antenna for gravitational wave detection,” Nucl. Instrum. Methods A 289, 518–525 (1990).
[CrossRef]

Sanibale, V.

B. Caron, A. Dominjon, C. Drezen, R. Flaminio, X. Grave, R. Hermel, F. Marion, L. Massonet, C. Mehmel, R. Morand, B. Mours, V. Sanibale, M. Yvert, “A preliminary study of the locking of an interferometric for gravitational wave detection,” Astropart. Phys. 6, 245–256 (1997).
[CrossRef]

Satyaprakash, B. S.

Shoemaker, D.

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

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, E. Gourgoulhon, L. E. Holloway, F. Fuligni, V. Iafolla, G. Natale, “The VIRGO project: a wide band antenna for gravitational wave detection,” Nucl. Instrum. Methods A 289, 518–525 (1990).
[CrossRef]

D. Shoemaker, LIGO team, MIT, Boston, Mass. 02139 (personal communication, 1997).

Sievers, L.

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

Spero, R. E.

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

Thorne, K. S.

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

K. S. Thorne, “Gravitational radiation,” in In 300 Years of Gravitation, S. W. Hawking, W. Israel, eds. (Cambridge U. Press, Cambridge, UK, 1987).

Tourrenc, P.

P. Tourrenc, N. Deruelle, “Effects of the time delays in a non-linear pendular Fabry–Perot,” Ann. Phys. Fr. 10, 241–252 (1985).
[CrossRef]

N. Deruelle, P. Tourrenc, “The problem of the optical stability of a pendular Fabry–Perot,” in Gravitation, Geometry and Relativistic Physics (Springer, Berlin, 1984), pp. 232–237.
[CrossRef]

Tourrenc, Ph.

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, E. Gourgoulhon, L. E. Holloway, F. Fuligni, V. Iafolla, G. Natale, “The VIRGO project: a wide band antenna for gravitational wave detection,” Nucl. Instrum. Methods A 289, 518–525 (1990).
[CrossRef]

Vignes, E.

P. Meystre, E. M. Wright, J. D. McCullen, E. Vignes, “Theory of radiation pressure-driven interferometers,” J. Opt. Soc. Am. B 2, 1830–1840 (1985).
[CrossRef]

A. Dorsel, J. D. McCullen, P. Meystre, E. Vignes, H. Walther, “Optical bistability and mirror confinement induced by radiation pressure,” Phys. Rev. Lett. 51, 1550–1553 (1983).
[CrossRef]

Vinet, J. 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, E. Gourgoulhon, L. E. Holloway, F. Fuligni, V. Iafolla, G. Natale, “The VIRGO project: a wide band antenna for gravitational wave detection,” Nucl. Instrum. Methods A 289, 518–525 (1990).
[CrossRef]

Vinet, J.-Y.

S. V. Dhurandhar, P. Hello, B. S. Satyaprakash, J.-Y. Vinet, “Stability of giant Fabry–Perot cavities of interferometric gravitational-wave detectors,” Appl. Opt. 36, 5325–5334 (1997).
[CrossRef] [PubMed]

P. Hello, J.-Y. Vinet, “Analytical models of transient thermoelastic deformations of mirrors heated by high power cw laser beams,” J. Phys. (France) 51, 2243–2261 (1990).
[CrossRef]

J.-Y. Vinet, B. J. Meers, C. N. Man, A. Brillet, “Optimization of long-baseline interferometers for gravitational-wave detection,” Phys. Rev. D 38, 433–447 (1988).
[CrossRef]

Vogt, R. E.

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

Walther, H.

A. Dorsel, J. D. McCullen, P. Meystre, E. Vignes, H. Walther, “Optical bistability and mirror confinement induced by radiation pressure,” Phys. Rev. Lett. 51, 1550–1553 (1983).
[CrossRef]

Weiss, R.

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

Whitcomb, S. E.

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

Wright, E. M.

Yvert, M.

B. Caron, A. Dominjon, C. Drezen, R. Flaminio, X. Grave, R. Hermel, F. Marion, L. Massonet, C. Mehmel, R. Morand, B. Mours, V. Sanibale, M. Yvert, “A preliminary study of the locking of an interferometric for gravitational wave detection,” Astropart. Phys. 6, 245–256 (1997).
[CrossRef]

Zucker, M. E.

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

Ann. Phys. Fr. (1)

P. Tourrenc, N. Deruelle, “Effects of the time delays in a non-linear pendular Fabry–Perot,” Ann. Phys. Fr. 10, 241–252 (1985).
[CrossRef]

Appl. Opt. (1)

Astropart. Phys. (1)

B. Caron, A. Dominjon, C. Drezen, R. Flaminio, X. Grave, R. Hermel, F. Marion, L. Massonet, C. Mehmel, R. Morand, B. Mours, V. Sanibale, M. Yvert, “A preliminary study of the locking of an interferometric for gravitational wave detection,” Astropart. Phys. 6, 245–256 (1997).
[CrossRef]

J. Opt. Soc. Am. B (1)

J. Phys. (France) (1)

P. Hello, J.-Y. Vinet, “Analytical models of transient thermoelastic deformations of mirrors heated by high power cw laser beams,” J. Phys. (France) 51, 2243–2261 (1990).
[CrossRef]

Nucl. Instrum. Methods A (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, E. Gourgoulhon, L. E. Holloway, F. Fuligni, V. Iafolla, G. Natale, “The VIRGO project: a wide band antenna for gravitational wave detection,” Nucl. Instrum. Methods A 289, 518–525 (1990).
[CrossRef]

Phys. Lett. A (2)

V. V. Kulagin, V. N. Rudenko, “Dynamics of a free mass interferometric gravitational antenna with small loss suspensions,” Phys. Lett. A 214, 123–126 (1996).
[CrossRef]

R. Flaminio, H. Heitmann, “Longitudinal control of an interferometer for the detection of gravitational waves,” Phys. Lett. A 214, 112–122 (1996).
[CrossRef]

Phys. Rep. (1)

A. Giazotto, “Interferometric detection of gravitational waves,” Phys. Rep. 182, 365–425 (1989).
[CrossRef]

Phys. Rev. A (2)

J. M. Aguirregabiria, L. L. Bel, “Delay-induced instability in a pendular Fabry–Perot cavity,” Phys. Rev. A 36, 3768–3770 (1987).
[CrossRef] [PubMed]

B. J. Meers, N. MacDonald, “Potential radiation pressure induced instabilities in cavity interferometers,” Phys. Rev. A 40, 3754–3763 (1989).
[CrossRef] [PubMed]

Phys. Rev. D (1)

J.-Y. Vinet, B. J. Meers, C. N. Man, A. Brillet, “Optimization of long-baseline interferometers for gravitational-wave detection,” Phys. Rev. D 38, 433–447 (1988).
[CrossRef]

Phys. Rev. Lett. (1)

A. Dorsel, J. D. McCullen, P. Meystre, E. Vignes, H. Walther, “Optical bistability and mirror confinement induced by radiation pressure,” Phys. Rev. Lett. 51, 1550–1553 (1983).
[CrossRef]

Science (1)

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

Other (5)

D. Shoemaker, LIGO team, MIT, Boston, Mass. 02139 (personal communication, 1997).

N. Deruelle, P. Tourrenc, “The problem of the optical stability of a pendular Fabry–Perot,” in Gravitation, Geometry and Relativistic Physics (Springer, Berlin, 1984), pp. 232–237.
[CrossRef]

R. W. P. Drever, “Interferometric detectors for gravitational wave detection,” in Gravitational Radiation, N. Deruelle, T. Piran, eds. (North-Holland, Amsterdam, The Netherlands, 1983).

K. S. Thorne, “Gravitational radiation,” in In 300 Years of Gravitation, S. W. Hawking, W. Israel, eds. (Cambridge U. Press, Cambridge, UK, 1987).

D. Blair, ed., The Detection of Gravitational Waves (Cambridge U. Press, Cambridge, UK, 1991).
[CrossRef]

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Figures (7)

Fig. 1
Fig. 1

Electric fields in a Fabry–Perot cavity with front-mirror reflectivity r 0 and a suspended end mirror with reflectivity r 1.

Fig. 2
Fig. 2

(a) Schematic depicting the force experienced by the end mirror versus the displacement. (b) The corresponding potential. Points (1) and (2) represent unstable and stable equilibrium, respectively.

Fig. 3
Fig. 3

Schematic indicating the servo loop: G, pendulum suspension transfer function; H, servo transfer function; F ext, the force caused by the radiation pressure; x out, the total displacement of the mirror; x free, the displacement of the mirror without the servo.

Fig. 4
Fig. 4

Plot of |GH| (the product of the pendulum suspension and servo transfer functions) versus the frequency in hertz.

Fig. 5
Fig. 5

Migration of the real parts of the relevant roots toward the half-plane Re(σ) > 0 as the input power increases. The other parameters are fixed: H 0 = 2.24 × 109 kg s-3, M = 28 kg, R = 0.94, and δ = -0.01. Here instability arises for an input power of approximately 8 kW.

Fig. 6
Fig. 6

Critical input power P crit (in kilowatts) versus the cavity phase detuning δ in the case of a Virgo-like configuration: H 0 = 2.24 × 109 kg s-3, M = 28 kg, but for different finesses. With a finesse of 50 and a power in the recycling cavity of typically approximately 1 kW, the Virgo arm cavities are always stable whatever δ is. We see also the influence of the finesse: if the finesse would have to be increased, everything else being constant, instability could occur for a finesse above 100.

Fig. 7
Fig. 7

Critical input power P crit (in kilowatts) versus the cavity phase detuning δ in the case of a LIGO-like configuration: M = 10.7 kg, R = 0.985 (finesse of approximately 200). The two curves correspond to two servo-loop gains. Solid curve, same gain as in Fig. 6: H 0 = 2.24 × 109 kg s-3. Dashed curve, H 0 = 0.86 × 109 kg s-3, corresponding to the same ratio H 0/M as in Fig. 6. We see clearly the action of the gain.

Equations (45)

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δ ϕ t = 2 k δ x t = 2 kx 0 sin   ω t ,
E 1 t = t 0 E 0 t + r 0 E 2 t ,
E 2 t = r 1 E 1 t - τ exp - i δ ϕ t - τ / 2 .
E 1 t = t 0 E 0 t + r 0 r 1 E 1 t - τ × exp - 2 ikx 0 sin   ω t - τ / 2 .
E ˜ 1 ω l = t 0 E ˜ 0 ω l + R E ˜ 1 ω l exp - i ω l τ - R E ˜ 1 ω l - ω exp - i ω l - ω 2 τ + R E ˜ 1 ω l + ω exp - i ω l + ω / 2 τ , E ˜ 1 ω l - ω = t 0 E ˜ 0 ω l - ω + R E ˜ 1 ω l - ω exp - i ω l - ω τ + R E ˜ 1 ω l exp - i ω l - ω / 2 τ , E ˜ 1 ω l + ω = t 0 E ˜ 0 ω l + ω + R E ˜ 1 ω l + ω exp - i ω l + ω τ - R E ˜ 1 ω l exp - i ω l + ω / 2 τ .
E ˜ k ω l E ˜ k ω l - ω 0 E ˜ k ω l + ω 0 = E ˜ k ,     k = 0 ,   1 ,
E ˜ 1 = χ E ˜ 0 ,
χ = t 0 1 - Re - i ω l τ - t 0 Re - i ω l - ω 2 τ [ 1 - Re - i ω l τ ] 1 - Re [ - i ω l - ω τ t 0 Re - i ω l + ω 2 τ 1 - Re - i ω l τ 1 - Re - i ω l + ω τ t 0 Re - i ω l - ω 2 τ 1 - Re - i ω l τ 1 - Re - i ω l - ω τ t 0 1 - Re - i ω l - ω τ 0 - t 0 Re - i ω l + ω 2 τ 1 - Re - i ω l τ 1 - Re - i ω l + ω τ 0 t 0 1 - Re - i ω l + ω τ .
E 1 t = { χ 11 exp i ω l t + χ 21 exp i ω l - ω t + χ 31 exp i ω l + ω t E ˜ 0 ω l .
E ˜ 1 ω = E ˜ 1 ω exp - i ω τ / 2 ,
I dc δ = | χ 11 E 0 ω l exp - i ω l τ / 2 | 2 = t 0 2 | E 0 ω l | 2 1 - 2 R   cos δ + R 2 ,
F tot = 2 I dc A eff / c - M ω p 2 x .
δ I t = χ 11 * χ 21 | E 0 | 2 exp - i ω t - τ / 2 + χ 11 * χ 31 | E 0 | 2 exp i ω t - τ / 2 + c . c .
δ Ĩ ω = 2 it 0 2 R | E 0 | 2   sin   δ   exp - i δ s | 1 - Re - i δ | 2 1 - Re - i δ + δ s 1 - Re i δ - δ s ,
δ P ˜ ω P 0 = K ˜ ω δ x ˜ ω ,
K ˜ ω = - 4 kRt 0 2 sin   δ   exp - i δ s | 1 - Re - i δ | 2 1 - Re - i δ + δ s 1 - Re i δ - δ s .
K ˜ ω = - g δ f Ω ,
Ω = ω τ stor = ω τ / 1 - R .
g δ = 4 kRt 0 2 sin   δ 1 - R 4 1 + F   sin 2   δ / 2 1 2 R 2 - R   cos   δ ,
f Ω = Ω 0 2 + 2 i λ Ω - Ω 2 ,
Ω 0 2 = 1 + F   sin 2   δ / 2 2 R 2 - R   cos   δ , λ = R cos   δ - R 1 - R 2 R 2 - R   cos   δ , F = 4 R 1 - R 2 .
K Ω = 0 = - 4 kRt 0 2 sin   δ 1 - R 4 1 + F   sin 2   δ / 2 2 1 P 0 d P dc d x ,
M x ¨ + γ x ˙ + ω p 2 x = F rp t + F servo t ,
x out = x free 1 + GH ,
x free = GF ext .
F total = F ext + F servo = x out G = F ext 1 + GH .
G = 1 M s - s 1 s - s 1 * ,
H = H 0 s - s 2 s - s 2 * s - s 3 s - s 3 * s 2 s + 2 π s - s 4 s - s 4 * ,
F ext s = 2   K s c   x out s .
2 c   K s G s = 1 + G s H s .
σ 2 σ + σ 0 σ - σ 4 σ - σ 4 * σ rp + σ 2 σ - σ 1 σ - σ 1 * Ω 0 2 + 2 λ σ + σ 2 σ + σ 0 σ - σ 4 σ - σ 4 * + k Ω 0 2 + 2 λ σ + σ 2 σ - σ 2 σ - σ 2 * σ - σ 3 σ - σ 3 * = 0 .
σ rp = 2 P 0 g δ τ s 2 Mc ,
k = H 0 τ s 3 M ,
σ 0 = 2 π τ s ,
σ i = s i τ s .
κ δ ,   P 0 ,   R = σ rp / Ω 0 2 = 2 P 0 g δ τ s 2 Ω 0 2 Mc .
u 3 - κ + | σ 4 | 2 - 2 σ 0   Re σ 4 u 2 + | σ 4 | 2 - 2 σ 0   Re σ 4 κ - 2 k Re σ 2 + Re σ 3 u + 2 k Re σ 3 | σ 2 | 2 + Re ( σ 2 | σ 3 | 2 = 0 .
α 4 = | σ 4 | 2 - 2 σ 0   Re σ 4 , β 23 = - 2 k Re σ 2 + Re σ 3 , γ 23 = - 2 k Re σ 3 | σ 2 | 2 + Re σ 2 | σ 3 | 2 ,
α 4 2 κ crit 2 + 2 α 4 β 23 - 2 γ 23 κ crit + β 23 2 - 4 α 4 γ 23 = 0 .
= π 1 - Θ / Θ π / Θ ,     if   Θ     1 .
κ α ,   P 0 ,   Θ = α 1 + α 2 - 3 Θ 1 + 1.5 Θ 1 + α 2 3 Θ 2 32 π τ s 2 λ Mc   P 0 .
- α 1 + α 2 - 3 Θ 1 + 1.5 Θ 1 + α 2 3 Θ 2   P 0 < λ Mc 32 π | κ crit | τ s 2 .
P crit = λ Mc 32 π | κ crit | τ s 2 1 + α 2 3 Θ 2 α 1 + α 2 - 3 Θ 1 + 1.5 Θ ,
P crit = P char 1 + α 2 3 Θ 2 α 1 + α 2 - 3 Θ 1 + 1.5 Θ ,
P char = λ Mc 32 π | κ crit | τ s 2 340 M 28   kg λ 1064   nm | κ crit | 6.18 × 10 - 4 kW .

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