Abstract

Fast Fourier transform (FFT) simulation was used to calculate the power and spatial distribution of resonant fields in optical cavities. This is an important tool when characterizing the effect of imperfect geometry and mirror aberrations. This method is, however, intrinsically slow when the cavities are of relatively high finesse. When this is the case, an accelerated convergence scheme may be used to calculate the steady-state cavity field with a speed that is orders of magnitude faster. The rate of convergence of this method, however, is unpredictable, as many different factors may detrimentally affect its performance. In addition, its use in multiple cavity configurations is not well understood. An in-depth study of the limitations and optimization of this method is presented, together with a formulation of its use in multiple cavity configurations. This work has not only resulted in consistent improvement in performance and stability of the accelerated convergence method but also allows the simulation of optical configurations, which would not previously have been possible.

© 2014 Optical Society of America

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2013 (1)

G. Vajente, “Fast modal simulation of paraxial optical systems: the MIST open source toolbox,” Class. Quantum Grav. 30, 075014 (2013).
[CrossRef]

2009 (1)

2008 (1)

A. M. Jayich, J. C. Sankey, B. M. Zwickl, C. Yang, J. D. Thompson, S. M. Girvin, A. A. Clerk, F. Marquardt, and J. G. E. Harris, “Dispersive optomechanics: a membrane inside a cavity,” New J. Phys. 10, 095008 (2008).
[CrossRef]

2004 (1)

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–S1074 (2004).
[CrossRef]

2003 (1)

B. Bochner and Y. Hefetz, “Grid-based simulation program for gravitational wave interferometers with realistically imperfect optics,” Phys. Rev. D 68, 082001 (2003).
[CrossRef]

1997 (1)

1994 (1)

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]

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, and G. Natale, “The VIRGO Project: a wide band antenna for gravitational wave detection,” Nucl. Instrum. Methods Phys. Res. A Accel. Spectrom. Detect. Assoc. Equip. 289, 518–525 (1990).
[CrossRef]

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]

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, and G. Natale, “The VIRGO Project: a wide band antenna for gravitational wave detection,” Nucl. Instrum. Methods Phys. Res. A Accel. Spectrom. Detect. Assoc. Equip. 289, 518–525 (1990).
[CrossRef]

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, and G. Natale, “The VIRGO Project: a wide band antenna for gravitational wave detection,” Nucl. Instrum. Methods Phys. Res. A Accel. Spectrom. Detect. Assoc. Equip. 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, and G. Natale, “The VIRGO Project: a wide band antenna for gravitational wave detection,” Nucl. Instrum. Methods Phys. Res. A Accel. Spectrom. Detect. Assoc. Equip. 289, 518–525 (1990).
[CrossRef]

Bochner, B.

B. Bochner and Y. Hefetz, “Grid-based simulation program for gravitational wave interferometers with realistically imperfect optics,” Phys. Rev. D 68, 082001 (2003).
[CrossRef]

B. Bochner, “Modelling the performance of interferometric gravitational-wave detectors with realistically imperfect optics,” Ph.D. dissertation (Massachussets Institute of Technology, 1998).

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, and G. Natale, “The VIRGO Project: a wide band antenna for gravitational wave detection,” Nucl. Instrum. Methods Phys. Res. A Accel. Spectrom. Detect. Assoc. Equip. 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, Y. Gourghoulon, L. E. Holloway, F. Fuligni, V. Iafolla, and G. Natale, “The VIRGO Project: a wide band antenna for gravitational wave detection,” Nucl. Instrum. Methods Phys. Res. A Accel. Spectrom. Detect. Assoc. Equip. 289, 518–525 (1990).
[CrossRef]

Brillet, A.

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]

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, and G. Natale, “The VIRGO Project: a wide band antenna for gravitational wave detection,” Nucl. Instrum. Methods Phys. Res. A Accel. Spectrom. Detect. Assoc. Equip. 289, 518–525 (1990).
[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, Y. Gourghoulon, L. E. Holloway, F. Fuligni, V. Iafolla, and G. Natale, “The VIRGO Project: a wide band antenna for gravitational wave detection,” Nucl. Instrum. Methods Phys. Res. A Accel. Spectrom. Detect. Assoc. Equip. 289, 518–525 (1990).
[CrossRef]

Clerk, A. A.

A. M. Jayich, J. C. Sankey, B. M. Zwickl, C. Yang, J. D. Thompson, S. M. Girvin, A. A. Clerk, F. Marquardt, and J. G. E. Harris, “Dispersive optomechanics: a membrane inside a cavity,” New J. Phys. 10, 095008 (2008).
[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, and G. Natale, “The VIRGO Project: a wide band antenna for gravitational wave detection,” Nucl. Instrum. Methods Phys. Res. A Accel. Spectrom. Detect. Assoc. Equip. 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, Y. Gourghoulon, L. E. Holloway, F. Fuligni, V. Iafolla, and G. Natale, “The VIRGO Project: a wide band antenna for gravitational wave detection,” Nucl. Instrum. Methods Phys. Res. A Accel. Spectrom. Detect. Assoc. Equip. 289, 518–525 (1990).
[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–S1074 (2004).
[CrossRef]

W. Winkler, R. Schilling, K. Danzmann, J. Mizuno, A. Rüdiger, and K. A. Strain, “Light scattering described in the mode picture,” Appl. Opt. 33, 7547–7550 (1994).
[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, Y. Gourghoulon, L. E. Holloway, F. Fuligni, V. Iafolla, and G. Natale, “The VIRGO Project: a wide band antenna for gravitational wave detection,” Nucl. Instrum. Methods Phys. Res. A Accel. Spectrom. Detect. Assoc. Equip. 289, 518–525 (1990).
[CrossRef]

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, and G. Natale, “The VIRGO Project: a wide band antenna for gravitational wave detection,” Nucl. Instrum. Methods Phys. Res. A Accel. Spectrom. Detect. Assoc. Equip. 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, and G. Natale, “The VIRGO Project: a wide band antenna for gravitational wave detection,” Nucl. Instrum. Methods Phys. Res. A Accel. Spectrom. Detect. Assoc. Equip. 289, 518–525 (1990).
[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]

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, and G. Natale, “The VIRGO Project: a wide band antenna for gravitational wave detection,” Nucl. Instrum. Methods Phys. Res. A Accel. Spectrom. Detect. Assoc. Equip. 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, 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–S1074 (2004).
[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, Y. Gourghoulon, L. E. Holloway, F. Fuligni, V. Iafolla, and G. Natale, “The VIRGO Project: a wide band antenna for gravitational wave detection,” Nucl. Instrum. Methods Phys. Res. A Accel. Spectrom. Detect. Assoc. Equip. 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, and G. Natale, “The VIRGO Project: a wide band antenna for gravitational wave detection,” Nucl. Instrum. Methods Phys. Res. A Accel. Spectrom. Detect. Assoc. Equip. 289, 518–525 (1990).
[CrossRef]

Girvin, S. M.

A. M. Jayich, J. C. Sankey, B. M. Zwickl, C. Yang, J. D. Thompson, S. M. Girvin, A. A. Clerk, F. Marquardt, and J. G. E. Harris, “Dispersive optomechanics: a membrane inside a cavity,” New J. Phys. 10, 095008 (2008).
[CrossRef]

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, and G. Natale, “The VIRGO Project: a wide band antenna for gravitational wave detection,” Nucl. Instrum. Methods Phys. Res. A Accel. Spectrom. Detect. Assoc. Equip. 289, 518–525 (1990).
[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]

Harris, J. G. E.

A. M. Jayich, J. C. Sankey, B. M. Zwickl, C. Yang, J. D. Thompson, S. M. Girvin, A. A. Clerk, F. Marquardt, and J. G. E. Harris, “Dispersive optomechanics: a membrane inside a cavity,” New J. Phys. 10, 095008 (2008).
[CrossRef]

Hefetz, Y.

B. Bochner and Y. Hefetz, “Grid-based simulation program for gravitational wave interferometers with realistically imperfect optics,” Phys. Rev. D 68, 082001 (2003).
[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–S1074 (2004).
[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]

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, and G. Natale, “The VIRGO Project: a wide band antenna for gravitational wave detection,” Nucl. Instrum. Methods Phys. Res. A Accel. Spectrom. Detect. Assoc. Equip. 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, and G. Natale, “The VIRGO Project: a wide band antenna for gravitational wave detection,” Nucl. Instrum. Methods Phys. Res. A Accel. Spectrom. Detect. Assoc. Equip. 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, and H. Ward, “Laser phase and frequency stabilization using an optical resonator,” Appl. Phys. B 31, 97–105 (1983).
[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, Y. Gourghoulon, L. E. Holloway, F. Fuligni, V. Iafolla, and G. Natale, “The VIRGO Project: a wide band antenna for gravitational wave detection,” Nucl. Instrum. Methods Phys. Res. A Accel. Spectrom. Detect. Assoc. Equip. 289, 518–525 (1990).
[CrossRef]

Jayich, A. M.

A. M. Jayich, J. C. Sankey, B. M. Zwickl, C. Yang, J. D. Thompson, S. M. Girvin, A. A. Clerk, F. Marquardt, and J. G. E. Harris, “Dispersive optomechanics: a membrane inside a cavity,” New J. Phys. 10, 095008 (2008).
[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, and G. Natale, “The VIRGO Project: a wide band antenna for gravitational wave detection,” Nucl. Instrum. Methods Phys. Res. A Accel. Spectrom. Detect. Assoc. Equip. 289, 518–525 (1990).
[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]

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, and G. Natale, “The VIRGO Project: a wide band antenna for gravitational wave detection,” Nucl. Instrum. Methods Phys. Res. A Accel. Spectrom. Detect. Assoc. Equip. 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, Y. Gourghoulon, L. E. Holloway, F. Fuligni, V. Iafolla, and G. Natale, “The VIRGO Project: a wide band antenna for gravitational wave detection,” Nucl. Instrum. Methods Phys. Res. A Accel. Spectrom. Detect. Assoc. Equip. 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, and G. Natale, “The VIRGO Project: a wide band antenna for gravitational wave detection,” Nucl. Instrum. Methods Phys. Res. A Accel. Spectrom. Detect. Assoc. Equip. 289, 518–525 (1990).
[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–S1074 (2004).
[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]

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, and G. Natale, “The VIRGO Project: a wide band antenna for gravitational wave detection,” Nucl. Instrum. Methods Phys. Res. A Accel. Spectrom. Detect. Assoc. Equip. 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, and G. Natale, “The VIRGO Project: a wide band antenna for gravitational wave detection,” Nucl. Instrum. Methods Phys. Res. A Accel. Spectrom. Detect. Assoc. Equip. 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, and G. Natale, “The VIRGO Project: a wide band antenna for gravitational wave detection,” Nucl. Instrum. Methods Phys. Res. A Accel. Spectrom. Detect. Assoc. Equip. 289, 518–525 (1990).
[CrossRef]

Marquardt, F.

A. M. Jayich, J. C. Sankey, B. M. Zwickl, C. Yang, J. D. Thompson, S. M. Girvin, A. A. Clerk, F. Marquardt, and J. G. E. Harris, “Dispersive optomechanics: a membrane inside a cavity,” New J. Phys. 10, 095008 (2008).
[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, and G. Natale, “The VIRGO Project: a wide band antenna for gravitational wave detection,” Nucl. Instrum. Methods Phys. Res. A Accel. Spectrom. Detect. Assoc. Equip. 289, 518–525 (1990).
[CrossRef]

Matsushima, K.

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, and G. Natale, “The VIRGO Project: a wide band antenna for gravitational wave detection,” Nucl. Instrum. Methods Phys. Res. A Accel. Spectrom. Detect. Assoc. Equip. 289, 518–525 (1990).
[CrossRef]

Mizuno, J.

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, and G. Natale, “The VIRGO Project: a wide band antenna for gravitational wave detection,” Nucl. Instrum. Methods Phys. Res. A Accel. Spectrom. Detect. Assoc. Equip. 289, 518–525 (1990).
[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]

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, and G. Natale, “The VIRGO Project: a wide band antenna for gravitational wave detection,” Nucl. Instrum. Methods Phys. Res. A Accel. Spectrom. Detect. Assoc. Equip. 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, Y. Gourghoulon, L. E. Holloway, F. Fuligni, V. Iafolla, and G. Natale, “The VIRGO Project: a wide band antenna for gravitational wave detection,” Nucl. Instrum. Methods Phys. Res. A Accel. Spectrom. Detect. Assoc. Equip. 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, Y. Gourghoulon, L. E. Holloway, F. Fuligni, V. Iafolla, and G. Natale, “The VIRGO Project: a wide band antenna for gravitational wave detection,” Nucl. Instrum. Methods Phys. Res. A Accel. Spectrom. Detect. Assoc. Equip. 289, 518–525 (1990).
[CrossRef]

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, Y. Gourghoulon, L. E. Holloway, F. Fuligni, V. Iafolla, and G. Natale, “The VIRGO Project: a wide band antenna for gravitational wave detection,” Nucl. Instrum. Methods Phys. Res. A Accel. Spectrom. Detect. Assoc. Equip. 289, 518–525 (1990).
[CrossRef]

Rüdiger, A.

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, and G. Natale, “The VIRGO Project: a wide band antenna for gravitational wave detection,” Nucl. Instrum. Methods Phys. Res. A Accel. Spectrom. Detect. Assoc. Equip. 289, 518–525 (1990).
[CrossRef]

Saha, P.

Sankey, J. C.

A. M. Jayich, J. C. Sankey, B. M. Zwickl, C. Yang, J. D. Thompson, S. M. Girvin, A. A. Clerk, F. Marquardt, and J. G. E. Harris, “Dispersive optomechanics: a membrane inside a cavity,” New J. Phys. 10, 095008 (2008).
[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–S1074 (2004).
[CrossRef]

W. Winkler, R. Schilling, K. Danzmann, J. Mizuno, A. Rüdiger, and K. A. Strain, “Light scattering described in the mode picture,” Appl. Opt. 33, 7547–7550 (1994).
[CrossRef]

Shimobaba, T.

Shoemaker, 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, Y. Gourghoulon, L. E. Holloway, F. Fuligni, V. Iafolla, and G. Natale, “The VIRGO Project: a wide band antenna for gravitational wave detection,” Nucl. Instrum. Methods Phys. Res. A Accel. Spectrom. Detect. Assoc. Equip. 289, 518–525 (1990).
[CrossRef]

Siegman, A. E.

A. E. Siegman, Lasers (University Science, 1986).

Strain, K. A.

Thompson, J. D.

A. M. Jayich, J. C. Sankey, B. M. Zwickl, C. Yang, J. D. Thompson, S. M. Girvin, A. A. Clerk, F. Marquardt, and J. G. E. Harris, “Dispersive optomechanics: a membrane inside a cavity,” New J. Phys. 10, 095008 (2008).
[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, Y. Gourghoulon, L. E. Holloway, F. Fuligni, V. Iafolla, and G. Natale, “The VIRGO Project: a wide band antenna for gravitational wave detection,” Nucl. Instrum. Methods Phys. Res. A Accel. Spectrom. Detect. Assoc. Equip. 289, 518–525 (1990).
[CrossRef]

Vajente, G.

G. Vajente, “Fast modal simulation of paraxial optical systems: the MIST open source toolbox,” Class. Quantum Grav. 30, 075014 (2013).
[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, Y. Gourghoulon, L. E. Holloway, F. Fuligni, V. Iafolla, and G. Natale, “The VIRGO Project: a wide band antenna for gravitational wave detection,” Nucl. Instrum. Methods Phys. Res. A Accel. Spectrom. Detect. Assoc. Equip. 289, 518–525 (1990).
[CrossRef]

Vinet, J.-Y.

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]

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–S1074 (2004).
[CrossRef]

Winkler, W.

Yang, C.

A. M. Jayich, J. C. Sankey, B. M. Zwickl, C. Yang, J. D. Thompson, S. M. Girvin, A. A. Clerk, F. Marquardt, and J. G. E. Harris, “Dispersive optomechanics: a membrane inside a cavity,” New J. Phys. 10, 095008 (2008).
[CrossRef]

Zwickl, B. M.

A. M. Jayich, J. C. Sankey, B. M. Zwickl, C. Yang, J. D. Thompson, S. M. Girvin, A. A. Clerk, F. Marquardt, and J. G. E. Harris, “Dispersive optomechanics: a membrane inside a cavity,” New J. Phys. 10, 095008 (2008).
[CrossRef]

Appl. Opt. (1)

Appl. Phys. B (1)

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

Class. Quantum Grav. (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–S1074 (2004).
[CrossRef]

G. Vajente, “Fast modal simulation of paraxial optical systems: the MIST open source toolbox,” Class. Quantum Grav. 30, 075014 (2013).
[CrossRef]

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

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]

New J. Phys. (1)

A. M. Jayich, J. C. Sankey, B. M. Zwickl, C. Yang, J. D. Thompson, S. M. Girvin, A. A. Clerk, F. Marquardt, and J. G. E. Harris, “Dispersive optomechanics: a membrane inside a cavity,” New J. Phys. 10, 095008 (2008).
[CrossRef]

Nucl. Instrum. Methods Phys. Res. A Accel. Spectrom. Detect. Assoc. Equip. (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, and G. Natale, “The VIRGO Project: a wide band antenna for gravitational wave detection,” Nucl. Instrum. Methods Phys. Res. A Accel. Spectrom. Detect. Assoc. Equip. 289, 518–525 (1990).
[CrossRef]

Opt. Express (1)

Phys. Rev. D (1)

B. Bochner and Y. Hefetz, “Grid-based simulation program for gravitational wave interferometers with realistically imperfect optics,” Phys. Rev. D 68, 082001 (2003).
[CrossRef]

Other (4)

B. Bochner, “Modelling the performance of interferometric gravitational-wave detectors with realistically imperfect optics,” Ph.D. dissertation (Massachussets Institute of Technology, 1998).

MATLAB, The MathWorks, Inc., Natick, Massachusetts, USA.

A. E. Siegman, Lasers (University Science, 1986).

Multiprecision Computing Toolbox, Advanpix, Yokohama, Japan.

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Figures (12)

Fig. 1.
Fig. 1.

Definition of field propagated to, reflected off, and transmitted through a thin mirror.

Fig. 2.
Fig. 2.

Definition of field and operators in the simulation of a single Fabry–Perot cavity.

Fig. 3.
Fig. 3.

Comparison of figure-of-merit δ and δ for standard and accelerated convergence. δ and δ for standard convergence are superposed. Concave–concave cavity of length 3000 m was used for this case, with a radius of curvature for the input and end mirror being 1420 and 1683 m, respectively. Transmission values of input and end mirrors were 1.4% and 1 ppm, respectively. Mirror diameters were 350 mm. Input beam was mode-matched to the cavity.

Fig. 4.
Fig. 4.

Comparison of convergence with two different algorithms. Solid lines: when starting with an arbitrary microscopic cavity length and converging the field while modifying the phase of M after each iteration. Dashed lines: when starting with the resonant microscopic length and converging without modifying the phase of M.

Fig. 5.
Fig. 5.

Comparison of three numerical configurations for calculating Eq. (16).

Fig. 6.
Fig. 6.

Comparison of convergence when realistic mirror maps, with varying rms, are added to cavity mirrors. Plots for standard convergence case are superposed.

Fig. 7.
Fig. 7.

Improvement in accelerated convergence by using smoothed and averaged acceleration in the case of perfect mirrors (red) and realistic mirrors with rms 5×101nm. In the case of N=1, M=1 corresponds to the standard accelerated convergence. Cases N=9, M=1 and N=1, M=5 carry out the same number of propagations per iteration.

Fig. 8.
Fig. 8.

Schematic diagram showing limiting condition for onset of FFT aliasing.

Fig. 9.
Fig. 9.

Comparison of convergence with (dashed lines) and without (solid lines) aliasing filter using perfect cavity mirrors (red curves) and mirror maps having rms of 5×101 (blue curves).

Fig. 10.
Fig. 10.

Definition of field and operators in the simulation of a double Fabry–Perot cavity.

Fig. 11.
Fig. 11.

Comparison of convergence for a double cavity using single cavity acceleration (red lines) and coupled cavity acceleration (blue lines). For clarity, the figure-of-merit has been shown only for the low power cavity. First cavity is concave–convex of length 11.953 m and second cavity is concave–concave of length 3000 m. Radius of curvature values for input, middle, and end mirrors were 1431 m, 1420 m, and 1683 m, respectively. Transmission values of input, middle, and end mirrors were 5%, 1.4%, and 1 ppm, respectively. Mirror diameters were 350 mm. Input beam was mode-matched to the first cavity.

Fig. 12.
Fig. 12.

Comparison of convergence for a double cavity using single cavity acceleration (red line) and coupled cavity acceleration (blue lines). For clarity, the figure-of-merit has been shown only for the low power cavity. First cavity is concave–flat of length 59.5 mm and second cavity is flat–concave of length 59.5 mm. Radius of curvature for the input and end mirrors was 200 mm. Transmission values of input, middle, and end mirrors were 1 ppm, 96%, and 1 ppm, respectively. Mirror diameters were 1.2 mm. Input beam was mode-matched to first cavity.

Equations (41)

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EB(x,y)=P[EA(x,y)].
EB(x,y)=F1[M(kx,ky)·F[EA(x,y)]],
M(kx,ky)=exp[ikL+ikx2+ky22kL],
ER(x,y)=RB[EB(x,y)],
ET(x,y)=TB[EB(x,y)].
ER(x,y)=irD(x,y)exp[2ikH(x,y)]EB(x,y),
ET(x,y)=tD(x,y)exp[ikG(x,y)]EB(x,y),
En+1=Et+A[En],
En+1=anEn+bnEn+1
Δn+1=En+1(Et+A[En+1]).
Δn+1=an(EnA[En])+bn(En+1A[En+1])Et.
D=[EnA[En]En+1A[En+1]]TXA=[anbn],
Δn+1=DXAEt.
e=Δn+1*Δn+1=(XA+D+Et*)(DXAEt),
(D+D)XA=D+Et,
XA=(D+D)1(D+Et).
δ=|En*EnEn+1*En+1|En+1*En+1.
δ=2(En*En+1*)(EnEn+1)En+1*En+1.
ϕ=Arg((A[En])*En),
M(kx,ky)=eϕ/2M(kx,ky).
D+D=USV+.
(D+D)1=VSrecU+.
En+1=anEn+bnEn+1+cnEn+2++dnEn+N.
EnM=1Mj=0M1En+j.
En+1=anEnM+bnEn+MM++cnEn+NMM.
θcW2L.
θλρ.
ρc=W2Lλ.
EA,n+1=EA,t+D[EB,n]+A[EA,n]
EB,n+1=EB,t+B[EB,n]+C[EA,n].
EA,n+1=aEA,n+bEA,n+1
EB,n+1=cEB,n+dEB,n+1.
ΔA,n+1=EA,n+1[EA,t+D[EB,n+1]+A[EA,n+1]]
ΔB,n+1=EB,n+1[EB,t+B[EB,n+1]+C[EA,n+1]].
XA=(ab)XB=(cd)FA=(EA,nA[EA,n]EA,n+1A[EA,n+1])FB=(EB,nB[EB,n]EB,n+1B[EB,n+1])GA=(C[EA,n]C[EA,n+1])GB=(D[EB,n]D[EB,n+1]),
ΔA,n+1=FATXAGBTXBEt,A
ΔB,n+1=FBTXBGATXAEt,B.
eA=ΔA,n+1*ΔA,n+1
eB=ΔB,n+1*ΔB,n+1
(FA+FA)XA(FA+GB)XB=FA+Et,A
(FB+FB)XB(FB+GA)XA=FB+Et,B.

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