Abstract

Demodulation of intensity noise in the optical heterodyne detector is analyzed for application in interferometric gravitational-wave detectors. The correlation function and the power spectral density of the demodulated intensity noise are derived, taking into account the effect of bandpass filtering at the photodiode and an arbitrary demodulation waveform. The analysis includes demodulation of the rf-modulated shot noise as a special case of the intensity noise. For shot-noise-limited detection, the signal-to-noise ratio is found as a function of the modulation parameters, and the optimization of the signal-to-noise ratio with respect to the demodulation phase is described.

© 2001 Optical Society of America

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    [CrossRef]

2000

1997

1993

1992

N. Mio, K. Tsubono, “Observation of an effect due to non-stationary shot noise,” Phys. Lett. A 164, 255–258 (1992).
[CrossRef]

A. Abramovici, W. E. Althouse, R. W. Drever, Y. Gürsel, 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, “LIGO: the Laser Interferometer Gravitational-Wave Observatory,” Science 256, 325–333 (1992).
[CrossRef] [PubMed]

1991

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

B. Meers, K. Strain, “Modulation, signal, and quantum noise in interferometers,” Phys. Rev. A 44, 4693–4703 (1991).
[CrossRef] [PubMed]

1990

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

1983

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

Abramovici, A.

A. Abramovici, W. E. Althouse, R. W. Drever, Y. Gürsel, 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, “LIGO: the Laser Interferometer Gravitational-Wave Observatory,” Science 256, 325–333 (1992).
[CrossRef] [PubMed]

Aguirregabiria, J. M.

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

Althouse, W. E.

A. Abramovici, W. E. Althouse, R. W. Drever, Y. Gürsel, 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, “LIGO: the Laser Interferometer Gravitational-Wave Observatory,” Science 256, 325–333 (1992).
[CrossRef] [PubMed]

Bachor, H.-A.

Barone, F.

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

Bel, H.

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

Bendat, J. S.

J. S. Bendat, A. G. Piersol, Random Data. Analysis and Measurement Procedures, 2nd ed. (Wiley, Singapore, 1991).

Bonazzola, S.

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

Bradaschia, C.

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

Brillet, A.

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

Capozzi, M.

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

Cregut, O.

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

Damour, T.

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

Danzmann, K.

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

Davenport, W.

W. Davenport, W. Root, Introduction to the Theory of Random Signals and Noise (McGraw-Hill, New York, 1958).

Delfabbro, R.

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

Difiore, L.

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

Divirgilio, A.

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

Drever, R.

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

Drever, R. W.

A. Abramovici, W. E. Althouse, R. W. Drever, Y. Gürsel, 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, “LIGO: the Laser Interferometer Gravitational-Wave Observatory,” Science 256, 325–333 (1992).
[CrossRef] [PubMed]

Duruisseau, J. P.

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

Ford, G.

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

Fuligni, F.

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

Giazotto, A.

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

Gourghoulon, Y.

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

Gray, M. B.

Gürsel, Y.

A. Abramovici, W. E. Althouse, R. W. Drever, Y. Gürsel, 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, “LIGO: the Laser Interferometer Gravitational-Wave Observatory,” Science 256, 325–333 (1992).
[CrossRef] [PubMed]

Hall, J.

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

Hello, P.

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

Holloway, L. E.

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

Hough, J.

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

Iafolla, V.

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

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

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A. Abramovici, W. E. Althouse, R. W. Drever, Y. Gürsel, 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, “LIGO: the Laser Interferometer Gravitational-Wave Observatory,” Science 256, 325–333 (1992).
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[CrossRef]

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

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

Lops, M.

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

Mann, C. N.

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

Marck, J. A.

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

Marraud, A.

C. Bradaschia, R. Delfabbro, A. Divirgilio, A. Giazotto, H. Kautzky, V. Montelatici, D. Passuello, A. Brillet, O. Cregut, P. Hello, C. N. Mann, P. T. Manh, A. Marraud, D. Shoemaker, J. Y. Vinet, F. Barone, L. Difiore, L. Milano, G. Russo, J. M. Aguirregabiria, H. Bel, J. P. Duruisseau, G. Lederman, P. Tourrenc, M. Capozzi, M. Longo, M. Lops, I. Pinto, G. Rotoli, T. Damour, S. Bonazzola, J. A. Marck, Y. Gourghoulon, L. E. Holloway, F. Fuligni, V. Iafolla, G. Natale, “The VIRGO project: a wide band antenna for gravitational-wave detection,” Nucl. Instrum. Methods Phys. Res. A 289, 518–525 (1990).
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C. Bradaschia, R. Delfabbro, A. Divirgilio, A. Giazotto, H. Kautzky, V. Montelatici, D. Passuello, A. Brillet, O. Cregut, P. Hello, C. N. Mann, P. T. Manh, A. Marraud, D. Shoemaker, J. Y. Vinet, F. Barone, L. Difiore, L. Milano, G. Russo, J. M. Aguirregabiria, H. Bel, J. P. Duruisseau, G. Lederman, P. Tourrenc, M. Capozzi, M. Longo, M. Lops, I. Pinto, G. Rotoli, T. Damour, S. Bonazzola, J. A. Marck, Y. Gourghoulon, L. E. Holloway, F. Fuligni, V. Iafolla, G. Natale, “The VIRGO project: a wide band antenna for gravitational-wave detection,” Nucl. Instrum. Methods Phys. Res. A 289, 518–525 (1990).
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N. Mio, K. Tsubono, “Observation of an effect due to non-stationary shot noise,” Phys. Lett. A 164, 255–258 (1992).
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C. Bradaschia, R. Delfabbro, A. Divirgilio, A. Giazotto, H. Kautzky, V. Montelatici, D. Passuello, A. Brillet, O. Cregut, P. Hello, C. N. Mann, P. T. Manh, A. Marraud, D. Shoemaker, J. Y. Vinet, F. Barone, L. Difiore, L. Milano, G. Russo, J. M. Aguirregabiria, H. Bel, J. P. Duruisseau, G. Lederman, P. Tourrenc, M. Capozzi, M. Longo, M. Lops, I. Pinto, G. Rotoli, T. Damour, S. Bonazzola, J. A. Marck, Y. Gourghoulon, L. E. Holloway, F. Fuligni, V. Iafolla, G. Natale, “The VIRGO project: a wide band antenna for gravitational-wave detection,” Nucl. Instrum. Methods Phys. Res. A 289, 518–525 (1990).
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R. Drever, J. Hall, F. Kowalski, J. Hough, G. Ford, A. Munley, H. Ward, “Laser phase and frequency stabilization using an optical resonator,” Appl. Phys. B 31, 97–105 (1983).
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C. Bradaschia, R. Delfabbro, A. Divirgilio, A. Giazotto, H. Kautzky, V. Montelatici, D. Passuello, A. Brillet, O. Cregut, P. Hello, C. N. Mann, P. T. Manh, A. Marraud, D. Shoemaker, J. Y. Vinet, F. Barone, L. Difiore, L. Milano, G. Russo, J. M. Aguirregabiria, H. Bel, J. P. Duruisseau, G. Lederman, P. Tourrenc, M. Capozzi, M. Longo, M. Lops, I. Pinto, G. Rotoli, T. Damour, S. Bonazzola, J. A. Marck, Y. Gourghoulon, L. E. Holloway, F. Fuligni, V. Iafolla, G. Natale, “The VIRGO project: a wide band antenna for gravitational-wave detection,” Nucl. Instrum. Methods Phys. Res. A 289, 518–525 (1990).
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T. Niebauer, R. Schilling, K. Danzmann, A. Rüdiger, W. Winkler, “Nonstationary shot noise and its effect on the sensitivity of interferometers,” Phys. Rev. A 43, 5022–5029 (1991).
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C. Bradaschia, R. Delfabbro, A. Divirgilio, A. Giazotto, H. Kautzky, V. Montelatici, D. Passuello, A. Brillet, O. Cregut, P. Hello, C. N. Mann, P. T. Manh, A. Marraud, D. Shoemaker, J. Y. Vinet, F. Barone, L. Difiore, L. Milano, G. Russo, J. M. Aguirregabiria, H. Bel, J. P. Duruisseau, G. Lederman, P. Tourrenc, M. Capozzi, M. Longo, M. Lops, I. Pinto, G. Rotoli, T. Damour, S. Bonazzola, J. A. Marck, Y. Gourghoulon, L. E. Holloway, F. Fuligni, V. Iafolla, G. Natale, “The VIRGO project: a wide band antenna for gravitational-wave detection,” Nucl. Instrum. Methods Phys. Res. A 289, 518–525 (1990).
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A. Abramovici, W. E. Althouse, R. W. Drever, Y. Gürsel, 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, “LIGO: the Laser Interferometer Gravitational-Wave Observatory,” Science 256, 325–333 (1992).
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C. Bradaschia, R. Delfabbro, A. Divirgilio, A. Giazotto, H. Kautzky, V. Montelatici, D. Passuello, A. Brillet, O. Cregut, P. Hello, C. N. Mann, P. T. Manh, A. Marraud, D. Shoemaker, J. Y. Vinet, F. Barone, L. Difiore, L. Milano, G. Russo, J. M. Aguirregabiria, H. Bel, J. P. Duruisseau, G. Lederman, P. Tourrenc, M. Capozzi, M. Longo, M. Lops, I. Pinto, G. Rotoli, T. Damour, S. Bonazzola, J. A. Marck, Y. Gourghoulon, L. E. Holloway, F. Fuligni, V. Iafolla, G. Natale, “The VIRGO project: a wide band antenna for gravitational-wave detection,” Nucl. Instrum. Methods Phys. Res. A 289, 518–525 (1990).
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T. Niebauer, R. Schilling, K. Danzmann, A. Rüdiger, W. Winkler, “Nonstationary shot noise and its effect on the sensitivity of interferometers,” Phys. Rev. A 43, 5022–5029 (1991).
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Russo, G.

C. Bradaschia, R. Delfabbro, A. Divirgilio, A. Giazotto, H. Kautzky, V. Montelatici, D. Passuello, A. Brillet, O. Cregut, P. Hello, C. N. Mann, P. T. Manh, A. Marraud, D. Shoemaker, J. Y. Vinet, F. Barone, L. Difiore, L. Milano, G. Russo, J. M. Aguirregabiria, H. Bel, J. P. Duruisseau, G. Lederman, P. Tourrenc, M. Capozzi, M. Longo, M. Lops, I. Pinto, G. Rotoli, T. Damour, S. Bonazzola, J. A. Marck, Y. Gourghoulon, L. E. Holloway, F. Fuligni, V. Iafolla, G. Natale, “The VIRGO project: a wide band antenna for gravitational-wave detection,” Nucl. Instrum. Methods Phys. Res. A 289, 518–525 (1990).
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Schilling, R.

T. Niebauer, R. Schilling, K. Danzmann, A. Rüdiger, W. Winkler, “Nonstationary shot noise and its effect on the sensitivity of interferometers,” Phys. Rev. A 43, 5022–5029 (1991).
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A. Abramovici, W. E. Althouse, R. W. Drever, Y. Gürsel, 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, “LIGO: the Laser Interferometer Gravitational-Wave Observatory,” Science 256, 325–333 (1992).
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Sievers, L.

A. Abramovici, W. E. Althouse, R. W. Drever, Y. Gürsel, 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, “LIGO: the Laser Interferometer Gravitational-Wave Observatory,” Science 256, 325–333 (1992).
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A. Abramovici, W. E. Althouse, R. W. Drever, Y. Gürsel, 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, “LIGO: the Laser Interferometer Gravitational-Wave Observatory,” Science 256, 325–333 (1992).
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Thorne, K. S.

A. Abramovici, W. E. Althouse, R. W. Drever, Y. Gürsel, 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, “LIGO: the Laser Interferometer Gravitational-Wave Observatory,” Science 256, 325–333 (1992).
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C. Bradaschia, R. Delfabbro, A. Divirgilio, A. Giazotto, H. Kautzky, V. Montelatici, D. Passuello, A. Brillet, O. Cregut, P. Hello, C. N. Mann, P. T. Manh, A. Marraud, D. Shoemaker, J. Y. Vinet, F. Barone, L. Difiore, L. Milano, G. Russo, J. M. Aguirregabiria, H. Bel, J. P. Duruisseau, G. Lederman, P. Tourrenc, M. Capozzi, M. Longo, M. Lops, I. Pinto, G. Rotoli, T. Damour, S. Bonazzola, J. A. Marck, Y. Gourghoulon, L. E. Holloway, F. Fuligni, V. Iafolla, G. Natale, “The VIRGO project: a wide band antenna for gravitational-wave detection,” Nucl. Instrum. Methods Phys. Res. A 289, 518–525 (1990).
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Vinet, J. Y.

C. Bradaschia, R. Delfabbro, A. Divirgilio, A. Giazotto, H. Kautzky, V. Montelatici, D. Passuello, A. Brillet, O. Cregut, P. Hello, C. N. Mann, P. T. Manh, A. Marraud, D. Shoemaker, J. Y. Vinet, F. Barone, L. Difiore, L. Milano, G. Russo, J. M. Aguirregabiria, H. Bel, J. P. Duruisseau, G. Lederman, P. Tourrenc, M. Capozzi, M. Longo, M. Lops, I. Pinto, G. Rotoli, T. Damour, S. Bonazzola, J. A. Marck, Y. Gourghoulon, L. E. Holloway, F. Fuligni, V. Iafolla, G. Natale, “The VIRGO project: a wide band antenna for gravitational-wave detection,” Nucl. Instrum. Methods Phys. Res. A 289, 518–525 (1990).
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Vogt, R. E.

A. Abramovici, W. E. Althouse, R. W. Drever, Y. Gürsel, 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, “LIGO: the Laser Interferometer Gravitational-Wave Observatory,” Science 256, 325–333 (1992).
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Ward, H.

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Weiss, R.

A. Abramovici, W. E. Althouse, R. W. Drever, Y. Gürsel, 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, “LIGO: the Laser Interferometer Gravitational-Wave Observatory,” Science 256, 325–333 (1992).
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A. Abramovici, W. E. Althouse, R. W. Drever, Y. Gürsel, 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, “LIGO: the Laser Interferometer Gravitational-Wave Observatory,” Science 256, 325–333 (1992).
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T. Niebauer, R. Schilling, K. Danzmann, A. Rüdiger, W. Winkler, “Nonstationary shot noise and its effect on the sensitivity of interferometers,” Phys. Rev. A 43, 5022–5029 (1991).
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A. Abramovici, W. E. Althouse, R. W. Drever, Y. Gürsel, 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, “LIGO: the Laser Interferometer Gravitational-Wave Observatory,” Science 256, 325–333 (1992).
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Appl. Phys. B

R. Drever, J. Hall, F. Kowalski, J. Hough, G. Ford, A. Munley, H. Ward, “Laser phase and frequency stabilization using an optical resonator,” Appl. Phys. B 31, 97–105 (1983).
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C. Bradaschia, R. Delfabbro, A. Divirgilio, A. Giazotto, H. Kautzky, V. Montelatici, D. Passuello, A. Brillet, O. Cregut, P. Hello, C. N. Mann, P. T. Manh, A. Marraud, D. Shoemaker, J. Y. Vinet, F. Barone, L. Difiore, L. Milano, G. Russo, J. M. Aguirregabiria, H. Bel, J. P. Duruisseau, G. Lederman, P. Tourrenc, M. Capozzi, M. Longo, M. Lops, I. Pinto, G. Rotoli, T. Damour, S. Bonazzola, J. A. Marck, Y. Gourghoulon, L. E. Holloway, F. Fuligni, V. Iafolla, G. Natale, “The VIRGO project: a wide band antenna for gravitational-wave detection,” Nucl. Instrum. Methods Phys. Res. A 289, 518–525 (1990).
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Opt. Lett.

Phys. Lett. A

N. Mio, K. Tsubono, “Observation of an effect due to non-stationary shot noise,” Phys. Lett. A 164, 255–258 (1992).
[CrossRef]

Phys. Rev. A

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

B. Meers, K. Strain, “Modulation, signal, and quantum noise in interferometers,” Phys. Rev. A 44, 4693–4703 (1991).
[CrossRef] [PubMed]

Science

A. Abramovici, W. E. Althouse, R. W. Drever, Y. Gürsel, 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, “LIGO: the Laser Interferometer Gravitational-Wave Observatory,” Science 256, 325–333 (1992).
[CrossRef] [PubMed]

Other

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This observation was made by F. Raab during a discussion of the nonstationary shot noise in the 40-m prototype of LIGO interferometers at Caltech, Pasadena, Calif., (1996).

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[CrossRef]

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Figures (4)

Fig. 1
Fig. 1

Example of the optical heterodyne detection scheme.

Fig. 2
Fig. 2

Typical spectrum of the rf-modulated photocurrent at the output of the LIGO rf photodetector. The modulation frequency Ω is approximately 24.7 MHz.

Fig. 3
Fig. 3

Transfer function of a typical LIGO rf photodiode. The upper plot shows the magnitude of the transfer function; the lower plot shows its phase. The peak of the transfer function is 24.7 MHz, and the width of the peak is 3.8 MHz. The notch at 49.4 MHz was introduced to suppress the second harmonic of the rf photocurrent.

Fig. 4
Fig. 4

Function of the demodulation phase represented by the y factor. The dashed curve corresponds to ideal (100% modulation) detection; the solid curve corresponds to detection with the parameters of the LIGO interferometers. The optimal demodulation points are marked by x.

Equations (95)

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Ωn=nΩ,
Pt=n=- Pn expiΩnt,
P-n=Pn*,
It=χPt,
It=n=- In expiΩnt,
Ĩω=2π n=- InδTω-Ωn,
Ĩω=n=- Ĩnω-Ωn,
ĨΩn+ωĨnω,
V˜pdω=Z˜ωĨω.
Z˜-ω=Z˜ω*,
Z˜Ω=R exp-iβ,
Z˜Ω±ωZ˜Ω
Vmixt=DtVpdt,
V˜mixω=- D˜ω-ωV˜pdωdω2π.
V˜ω=V˜mixω||ω|ΔΩ.
Dt=sinΩt-γ,
Dt=4πn=1,3,5,1n sin nΩt-γ.
Dt=-i n=- dn expinΩt-γ,
d1=-d-1=1/2.
dn=0,n=even2/πn,n=odd.
D˜ω=-2πi n=- dn exp-inγδTω-Ωn.
V˜mixω=-i n=- dn exp-inγZ˜ω-ΩnĨω-Ωn.
V˜ω-i n=- dn exp-inγZ˜ω-ΩnĨ-nω.
|Z˜ω±Ωn|  R,
V˜ω-id-1 expiγZ˜ω+ΩĨ1ω-id1exp-iγZ˜ω-ΩĨ-1ω,
V˜ω=-id-1 expiγ-βRĨ1ω-id1 exp-iγ-βRĨ-1ω.
Vt=-2d1R Imexpiγ-βI1t,
Vt=-2d1RI1tsinγ-β,
V˜ω=-2d1RĨ1ωsinγ-β.
γ=β+π/2+πN,
δIt=χδPt.
Jt=It+δIt,
It=EJt,
CIt, tEδItδIt,
C˜Iω, ω=EδĨωδĨω*,
C˜Iω, ω=-T/2T/2-T/2T/2 exp-iωt-ωt×CIt, tdtdt.
δV˜ω=-i n=- dn exp-inγZ˜ω-ΩnδĨω-Ωn.
C˜Vω, ω=EδV˜ωδV˜ω*.
C˜Vω, ω=m=-n=- dmdn* exp-im-nγ×Z˜ω-ΩmZ˜ω-Ωn*×C˜Iω-Ωm, ω-Ωn.
SVω=limTC˜Vω, ωT,
δV˜ω=-id-1 expiγZ˜ω+ΩδĨω+Ω-id1 exp-iγZ˜ω-ΩδĨω-Ω.
CIt, t=CIt-t.
C˜Iω, ω=2πSIωδTω-ω,
C˜Vω, ω=2πSVωδTω-ω,
SVω=n=- |dn|2|Z˜ω-Ωn|2SIω-Ωn.
SVω=|d1|2|Z˜ω-Ω|2SIω-Ω+|d1|2|Z˜ω+Ω|2SIω+Ω.
SVω2|d1|2R2SIΩ.
SIΩ  SI0.
SVω=|d1|2|Z˜ω-Ω|2SIω-Ω+|d1|2|Z˜ω+Ω|2SIω+Ω-2|d1|2 Reexp2iγ×Z˜ω-Ω*Z˜ω+ΩQIω.
QIω=limTC˜Iω+Ω, ω-ΩT,
SVω=2|d1|2R2SIΩ-2|d1|2R2 Reexp2iβ-γQI0.
C˜Iω, ω=qĨω-ω,
C˜Iω, ω=2πq n=- InδTω-ω-Ωn.
C˜Vω, ω=2πSVωδTω-ω,
SVω=m=-n=- dmdn* exp-im-nγ×qIn-mZ˜ω-ΩmZ˜ω-Ωn*.
SVω=qd12I0|Z˜ω-Ω|2+|Z˜ω+Ω|2-2qd12 ReI2Z˜ω-Ω*Z˜ω+Ωexp2iγ.
SIω=qI0,
QIω=qI2.
SVω2qd12R2(I0-ReI2 exp2iγ-β).
I2=I0/2,
It=I01+cos 2Ωt.
SVω2qd12R2I01-12 cos 2γ-β.
SNR2=|Vt|2¯SVωgΔω,
SNR2=-|V˜ω|2SVωdω2π,
y=sin2γ-β1-Rez exp2iγ-β.
z=QI0SIΩ
y/γ=0.
γ=β+arctanRez-1Imz+πN,
yopt=1-Rez1-|z|2.
yopt1.
z=I2/I0.
|I2|I0/2,
|z|1/2.
z=±1/2.
2/3yopt2.
F˜ω=-T/2T/2 exp-iωtFtdt.
Ft=- expiωtF˜ωdω2π.
2πδTω=-T/2T/2 exp-iωtdt,
CVω, ω=m=-n=- dmdn* exp-im-nγ×Z˜ω-ΩmZ˜ω-Ωn*×2πq p=- IpδTω-ω+Ωm-n+p.
δTω-ω+Ωm-n+pδn-m,pδTω-ω.
CVω, ω=2πδTω-ω×m=-n=- dmdn* exp-im-nγ×qIn-mZ˜ω-ΩmZ˜ω-Ωn*,
Jt=q k=1K δt-tk.
ntdt=ItqNdt.
δt-tk¯=-T/2T/2 δt-tkntkdtk=nt.
pK=NKK! exp-N,
KK=0 KpK=N.
EJt=q k=1Kδt-tk¯=qKnt=qNnt.
CIt, t=EJtJt-ItIt.
EJtJt=q2k=1Km=1Kδt-tkδt-tm¯.
δt-tkδt-tm¯=-T/2T/2 δt-tkδt-tkntkdtk=ntδt-t.
δt-tkδt-tm¯=δt-tk¯δt-tm¯=ntnt.
K2-KK=0K2-KpK=N2.
EJtJt=q2Nntδt-t+q2N2ntnt=qItδt-t+ItIt.
CIt, t=qItδt-t,
C˜Iω, ω=qĨω-ω,

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