Abstract

We use doubly phase modulated light to measure both the length and the linewidth of an optical resonator with high precision. The first modulation is at RF frequencies and is set near a multiple of the free spectral range, whereas the second modulation is at audio frequencies to eliminate offset errors at DC. The light in transmission or in reflection of the optical resonator is demodulated while sweeping the RF frequency over the optical resonance. We derive expressions for the demodulated power in transmission, and show that the zero crossings of the demodulated signal in transmission serve as a precise measure of the cavity linewidth at half maximum intensity. We demonstrate the technique on two resonant cavities, with lengths 16 m and a 4 km, and achieve an absolute length accuracy as low as 70 ppb. The cavity width for the 16 m cavity was determined with an accuracy of approximately 6000 ppm. Through an analysis of the systematic errors we show that this result could be substantially improved with the reduction of technical sources of uncertainty.

© 2015 Optical Society of America

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References

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2015 (1)

The LIGO Scientific Collaboration, “Advanced LIGO,” Class. Quantum Grav. 32, 074001 (2015).
[Crossref]

2014 (2)

W. Zhang, M. J. Martin, C. Benko, J. L. Hall, J. Ye, C. Hagemann, T. Legero, U. Sterr, F. Riehle, G. D. Cole, and M. Aspelmeyer, “Reduction of residual amplitude modulation to 1 × 10−6 for frequency modulation and laser stabilization,” Opt. Lett. 39, 1980 (2014).
[Crossref] [PubMed]

A. Staley, D. Martynov, R. Abbott, R. X. Adhikari, K. Arai, S. Ballmer, L. Barsotti, A. F. Brooks, R. T. DeRosa, S. Dwyer, A. Effler, M. Evans, P. Fritschel, V. V. Frolov, C. Gray, C. J. Guido, R. Gustafson, M. Heintze, D. Hoak, K. Izumi, K. Kawabe, E. J. King, J. S. Kissel, K. Kokeyama, M. Landry, D. E. McClelland, J. Miller, A. Mullavey, B. O’Reilly, J. G. Rollins, J. R. Sanders, R. M. S. Schofield, D. Sigg, B. J. J. Slagmolen, N. D. Smith-Lefebvre, G. Vajente, R. L. Ward, and C. Wipf, “Achieving resonance in the Advanced LIGO gravitational-wave interferometer,” Class. Quantum Grav. 31, 245010 (2014).
[Crossref]

2011 (1)

M. Aketagawa, S. Kimura, T. Yashiki, H. Iwata, T. Q. Banh, and K. Hirata, “Measurement of a free spectral range of a Fabry–Perot cavity using frequency modulation and null method under off-resonance conditions,” Meas. Sci. and Tech. 22, 025302 (2011).
[Crossref]

2010 (1)

M. Aketagawa, T. Yashiki, S. Kimura, and T. Banh, “Free spectral range measurement of Fabry–Perot cavity using frequency modulation,” Int. Jour. of Precision Engineering and Manufacturing 11, 851 (2010).
[Crossref]

2004 (1)

M. Rakhmanov, F. Bondu, O. Debieu, and R. L. Savage, “Characterization of the LIGO 4 km Fabry–Perot cavities via their high-frequency dynamic responses to length and frequency variations,” Class. Quantum Grav. 21, S487 (2004).
[Crossref]

2000 (1)

1999 (2)

1998 (1)

1997 (1)

1992 (2)

T. Andreae, W. Konig, R. Wynands, D. Leibfried, F. Schmidt-Kaler, C. Zimmermann, D. Meschede, and T. W. Hansch, “Absolute frequency measurement of the hydrogen 1S–2S transition and a new value of the Rydberg constant,” Phys. Rev. Lett. 69, 1923–1926 (1992).
[Crossref] [PubMed]

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. Whitecomb, and M. E. Zucker, “LIGO: the Laser Interferometer Gravitational-wave Observatory,” Science 256, 325 (1992).
[Crossref] [PubMed]

1985 (2)

1983 (1)

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

Abbott, R.

A. Staley, D. Martynov, R. Abbott, R. X. Adhikari, K. Arai, S. Ballmer, L. Barsotti, A. F. Brooks, R. T. DeRosa, S. Dwyer, A. Effler, M. Evans, P. Fritschel, V. V. Frolov, C. Gray, C. J. Guido, R. Gustafson, M. Heintze, D. Hoak, K. Izumi, K. Kawabe, E. J. King, J. S. Kissel, K. Kokeyama, M. Landry, D. E. McClelland, J. Miller, A. Mullavey, B. O’Reilly, J. G. Rollins, J. R. Sanders, R. M. S. Schofield, D. Sigg, B. J. J. Slagmolen, N. D. Smith-Lefebvre, G. Vajente, R. L. Ward, and C. Wipf, “Achieving resonance in the Advanced LIGO gravitational-wave interferometer,” Class. Quantum Grav. 31, 245010 (2014).
[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. Whitecomb, and M. E. Zucker, “LIGO: the Laser Interferometer Gravitational-wave Observatory,” Science 256, 325 (1992).
[Crossref] [PubMed]

Adhikari, R. X.

A. Staley, D. Martynov, R. Abbott, R. X. Adhikari, K. Arai, S. Ballmer, L. Barsotti, A. F. Brooks, R. T. DeRosa, S. Dwyer, A. Effler, M. Evans, P. Fritschel, V. V. Frolov, C. Gray, C. J. Guido, R. Gustafson, M. Heintze, D. Hoak, K. Izumi, K. Kawabe, E. J. King, J. S. Kissel, K. Kokeyama, M. Landry, D. E. McClelland, J. Miller, A. Mullavey, B. O’Reilly, J. G. Rollins, J. R. Sanders, R. M. S. Schofield, D. Sigg, B. J. J. Slagmolen, N. D. Smith-Lefebvre, G. Vajente, R. L. Ward, and C. Wipf, “Achieving resonance in the Advanced LIGO gravitational-wave interferometer,” Class. Quantum Grav. 31, 245010 (2014).
[Crossref]

Aketagawa, M.

M. Aketagawa, S. Kimura, T. Yashiki, H. Iwata, T. Q. Banh, and K. Hirata, “Measurement of a free spectral range of a Fabry–Perot cavity using frequency modulation and null method under off-resonance conditions,” Meas. Sci. and Tech. 22, 025302 (2011).
[Crossref]

M. Aketagawa, T. Yashiki, S. Kimura, and T. Banh, “Free spectral range measurement of Fabry–Perot cavity using frequency modulation,” Int. Jour. of Precision Engineering and Manufacturing 11, 851 (2010).
[Crossref]

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. Whitecomb, and M. E. Zucker, “LIGO: the Laser Interferometer Gravitational-wave Observatory,” Science 256, 325 (1992).
[Crossref] [PubMed]

Andreae, T.

T. Andreae, W. Konig, R. Wynands, D. Leibfried, F. Schmidt-Kaler, C. Zimmermann, D. Meschede, and T. W. Hansch, “Absolute frequency measurement of the hydrogen 1S–2S transition and a new value of the Rydberg constant,” Phys. Rev. Lett. 69, 1923–1926 (1992).
[Crossref] [PubMed]

Arai, K.

A. Staley, D. Martynov, R. Abbott, R. X. Adhikari, K. Arai, S. Ballmer, L. Barsotti, A. F. Brooks, R. T. DeRosa, S. Dwyer, A. Effler, M. Evans, P. Fritschel, V. V. Frolov, C. Gray, C. J. Guido, R. Gustafson, M. Heintze, D. Hoak, K. Izumi, K. Kawabe, E. J. King, J. S. Kissel, K. Kokeyama, M. Landry, D. E. McClelland, J. Miller, A. Mullavey, B. O’Reilly, J. G. Rollins, J. R. Sanders, R. M. S. Schofield, D. Sigg, B. J. J. Slagmolen, N. D. Smith-Lefebvre, G. Vajente, R. L. Ward, and C. Wipf, “Achieving resonance in the Advanced LIGO gravitational-wave interferometer,” Class. Quantum Grav. 31, 245010 (2014).
[Crossref]

Araya, A.

Aspelmeyer, M.

Baigent, K. G.

Ballmer, S.

A. Staley, D. Martynov, R. Abbott, R. X. Adhikari, K. Arai, S. Ballmer, L. Barsotti, A. F. Brooks, R. T. DeRosa, S. Dwyer, A. Effler, M. Evans, P. Fritschel, V. V. Frolov, C. Gray, C. J. Guido, R. Gustafson, M. Heintze, D. Hoak, K. Izumi, K. Kawabe, E. J. King, J. S. Kissel, K. Kokeyama, M. Landry, D. E. McClelland, J. Miller, A. Mullavey, B. O’Reilly, J. G. Rollins, J. R. Sanders, R. M. S. Schofield, D. Sigg, B. J. J. Slagmolen, N. D. Smith-Lefebvre, G. Vajente, R. L. Ward, and C. Wipf, “Achieving resonance in the Advanced LIGO gravitational-wave interferometer,” Class. Quantum Grav. 31, 245010 (2014).
[Crossref]

Banh, T.

M. Aketagawa, T. Yashiki, S. Kimura, and T. Banh, “Free spectral range measurement of Fabry–Perot cavity using frequency modulation,” Int. Jour. of Precision Engineering and Manufacturing 11, 851 (2010).
[Crossref]

Banh, T. Q.

M. Aketagawa, S. Kimura, T. Yashiki, H. Iwata, T. Q. Banh, and K. Hirata, “Measurement of a free spectral range of a Fabry–Perot cavity using frequency modulation and null method under off-resonance conditions,” Meas. Sci. and Tech. 22, 025302 (2011).
[Crossref]

Barsotti, L.

A. Staley, D. Martynov, R. Abbott, R. X. Adhikari, K. Arai, S. Ballmer, L. Barsotti, A. F. Brooks, R. T. DeRosa, S. Dwyer, A. Effler, M. Evans, P. Fritschel, V. V. Frolov, C. Gray, C. J. Guido, R. Gustafson, M. Heintze, D. Hoak, K. Izumi, K. Kawabe, E. J. King, J. S. Kissel, K. Kokeyama, M. Landry, D. E. McClelland, J. Miller, A. Mullavey, B. O’Reilly, J. G. Rollins, J. R. Sanders, R. M. S. Schofield, D. Sigg, B. J. J. Slagmolen, N. D. Smith-Lefebvre, G. Vajente, R. L. Ward, and C. Wipf, “Achieving resonance in the Advanced LIGO gravitational-wave interferometer,” Class. Quantum Grav. 31, 245010 (2014).
[Crossref]

Benko, C.

Bjorklund, G. C.

Bondu, F.

M. Rakhmanov, F. Bondu, O. Debieu, and R. L. Savage, “Characterization of the LIGO 4 km Fabry–Perot cavities via their high-frequency dynamic responses to length and frequency variations,” Class. Quantum Grav. 21, S487 (2004).
[Crossref]

Brooks, A. F.

A. Staley, D. Martynov, R. Abbott, R. X. Adhikari, K. Arai, S. Ballmer, L. Barsotti, A. F. Brooks, R. T. DeRosa, S. Dwyer, A. Effler, M. Evans, P. Fritschel, V. V. Frolov, C. Gray, C. J. Guido, R. Gustafson, M. Heintze, D. Hoak, K. Izumi, K. Kawabe, E. J. King, J. S. Kissel, K. Kokeyama, M. Landry, D. E. McClelland, J. Miller, A. Mullavey, B. O’Reilly, J. G. Rollins, J. R. Sanders, R. M. S. Schofield, D. Sigg, B. J. J. Slagmolen, N. D. Smith-Lefebvre, G. Vajente, R. L. Ward, and C. Wipf, “Achieving resonance in the Advanced LIGO gravitational-wave interferometer,” Class. Quantum Grav. 31, 245010 (2014).
[Crossref]

Cole, G. D.

Debieu, O.

M. Rakhmanov, F. Bondu, O. Debieu, and R. L. Savage, “Characterization of the LIGO 4 km Fabry–Perot cavities via their high-frequency dynamic responses to length and frequency variations,” Class. Quantum Grav. 21, S487 (2004).
[Crossref]

DeRosa, R. T.

A. Staley, D. Martynov, R. Abbott, R. X. Adhikari, K. Arai, S. Ballmer, L. Barsotti, A. F. Brooks, R. T. DeRosa, S. Dwyer, A. Effler, M. Evans, P. Fritschel, V. V. Frolov, C. Gray, C. J. Guido, R. Gustafson, M. Heintze, D. Hoak, K. Izumi, K. Kawabe, E. J. King, J. S. Kissel, K. Kokeyama, M. Landry, D. E. McClelland, J. Miller, A. Mullavey, B. O’Reilly, J. G. Rollins, J. R. Sanders, R. M. S. Schofield, D. Sigg, B. J. J. Slagmolen, N. D. Smith-Lefebvre, G. Vajente, R. L. Ward, and C. Wipf, “Achieving resonance in the Advanced LIGO gravitational-wave interferometer,” Class. Quantum Grav. 31, 245010 (2014).
[Crossref]

Drever, R.

R. Drever, J. Hall, F. Kowalski, J. Hough, G. Ford, A. Munley, and H. Ward, “Laser phase and frequency stabilization using an optical resonator,” Appl. Phys. B 31, 97 (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. Whitecomb, and M. E. Zucker, “LIGO: the Laser Interferometer Gravitational-wave Observatory,” Science 256, 325 (1992).
[Crossref] [PubMed]

R. W. P. Drever, The Detection of Gravitational Waves, D. G. Blair, ed. (Cambridge University, 1991).

Dwyer, S.

A. Staley, D. Martynov, R. Abbott, R. X. Adhikari, K. Arai, S. Ballmer, L. Barsotti, A. F. Brooks, R. T. DeRosa, S. Dwyer, A. Effler, M. Evans, P. Fritschel, V. V. Frolov, C. Gray, C. J. Guido, R. Gustafson, M. Heintze, D. Hoak, K. Izumi, K. Kawabe, E. J. King, J. S. Kissel, K. Kokeyama, M. Landry, D. E. McClelland, J. Miller, A. Mullavey, B. O’Reilly, J. G. Rollins, J. R. Sanders, R. M. S. Schofield, D. Sigg, B. J. J. Slagmolen, N. D. Smith-Lefebvre, G. Vajente, R. L. Ward, and C. Wipf, “Achieving resonance in the Advanced LIGO gravitational-wave interferometer,” Class. Quantum Grav. 31, 245010 (2014).
[Crossref]

Effler, A.

A. Staley, D. Martynov, R. Abbott, R. X. Adhikari, K. Arai, S. Ballmer, L. Barsotti, A. F. Brooks, R. T. DeRosa, S. Dwyer, A. Effler, M. Evans, P. Fritschel, V. V. Frolov, C. Gray, C. J. Guido, R. Gustafson, M. Heintze, D. Hoak, K. Izumi, K. Kawabe, E. J. King, J. S. Kissel, K. Kokeyama, M. Landry, D. E. McClelland, J. Miller, A. Mullavey, B. O’Reilly, J. G. Rollins, J. R. Sanders, R. M. S. Schofield, D. Sigg, B. J. J. Slagmolen, N. D. Smith-Lefebvre, G. Vajente, R. L. Ward, and C. Wipf, “Achieving resonance in the Advanced LIGO gravitational-wave interferometer,” Class. Quantum Grav. 31, 245010 (2014).
[Crossref]

Evans, M.

A. Staley, D. Martynov, R. Abbott, R. X. Adhikari, K. Arai, S. Ballmer, L. Barsotti, A. F. Brooks, R. T. DeRosa, S. Dwyer, A. Effler, M. Evans, P. Fritschel, V. V. Frolov, C. Gray, C. J. Guido, R. Gustafson, M. Heintze, D. Hoak, K. Izumi, K. Kawabe, E. J. King, J. S. Kissel, K. Kokeyama, M. Landry, D. E. McClelland, J. Miller, A. Mullavey, B. O’Reilly, J. G. Rollins, J. R. Sanders, R. M. S. Schofield, D. Sigg, B. J. J. Slagmolen, N. D. Smith-Lefebvre, G. Vajente, R. L. Ward, and C. Wipf, “Achieving resonance in the Advanced LIGO gravitational-wave interferometer,” Class. Quantum Grav. 31, 245010 (2014).
[Crossref]

Ford, G.

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

Fritschel, P.

A. Staley, D. Martynov, R. Abbott, R. X. Adhikari, K. Arai, S. Ballmer, L. Barsotti, A. F. Brooks, R. T. DeRosa, S. Dwyer, A. Effler, M. Evans, P. Fritschel, V. V. Frolov, C. Gray, C. J. Guido, R. Gustafson, M. Heintze, D. Hoak, K. Izumi, K. Kawabe, E. J. King, J. S. Kissel, K. Kokeyama, M. Landry, D. E. McClelland, J. Miller, A. Mullavey, B. O’Reilly, J. G. Rollins, J. R. Sanders, R. M. S. Schofield, D. Sigg, B. J. J. Slagmolen, N. D. Smith-Lefebvre, G. Vajente, R. L. Ward, and C. Wipf, “Achieving resonance in the Advanced LIGO gravitational-wave interferometer,” Class. Quantum Grav. 31, 245010 (2014).
[Crossref]

Frolov, V. V.

A. Staley, D. Martynov, R. Abbott, R. X. Adhikari, K. Arai, S. Ballmer, L. Barsotti, A. F. Brooks, R. T. DeRosa, S. Dwyer, A. Effler, M. Evans, P. Fritschel, V. V. Frolov, C. Gray, C. J. Guido, R. Gustafson, M. Heintze, D. Hoak, K. Izumi, K. Kawabe, E. J. King, J. S. Kissel, K. Kokeyama, M. Landry, D. E. McClelland, J. Miller, A. Mullavey, B. O’Reilly, J. G. Rollins, J. R. Sanders, R. M. S. Schofield, D. Sigg, B. J. J. Slagmolen, N. D. Smith-Lefebvre, G. Vajente, R. L. Ward, and C. Wipf, “Achieving resonance in the Advanced LIGO gravitational-wave interferometer,” Class. Quantum Grav. 31, 245010 (2014).
[Crossref]

Fujimoto, M. K.

Gehrtz, M.

Gray, C.

A. Staley, D. Martynov, R. Abbott, R. X. Adhikari, K. Arai, S. Ballmer, L. Barsotti, A. F. Brooks, R. T. DeRosa, S. Dwyer, A. Effler, M. Evans, P. Fritschel, V. V. Frolov, C. Gray, C. J. Guido, R. Gustafson, M. Heintze, D. Hoak, K. Izumi, K. Kawabe, E. J. King, J. S. Kissel, K. Kokeyama, M. Landry, D. E. McClelland, J. Miller, A. Mullavey, B. O’Reilly, J. G. Rollins, J. R. Sanders, R. M. S. Schofield, D. Sigg, B. J. J. Slagmolen, N. D. Smith-Lefebvre, G. Vajente, R. L. Ward, and C. Wipf, “Achieving resonance in the Advanced LIGO gravitational-wave interferometer,” Class. Quantum Grav. 31, 245010 (2014).
[Crossref]

Gray, M. B.

Guido, C. J.

A. Staley, D. Martynov, R. Abbott, R. X. Adhikari, K. Arai, S. Ballmer, L. Barsotti, A. F. Brooks, R. T. DeRosa, S. Dwyer, A. Effler, M. Evans, P. Fritschel, V. V. Frolov, C. Gray, C. J. Guido, R. Gustafson, M. Heintze, D. Hoak, K. Izumi, K. Kawabe, E. J. King, J. S. Kissel, K. Kokeyama, M. Landry, D. E. McClelland, J. Miller, A. Mullavey, B. O’Reilly, J. G. Rollins, J. R. Sanders, R. M. S. Schofield, D. Sigg, B. J. J. Slagmolen, N. D. Smith-Lefebvre, G. Vajente, R. L. Ward, and C. Wipf, “Achieving resonance in the Advanced LIGO gravitational-wave interferometer,” Class. Quantum Grav. 31, 245010 (2014).
[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. Whitecomb, and M. E. Zucker, “LIGO: the Laser Interferometer Gravitational-wave Observatory,” Science 256, 325 (1992).
[Crossref] [PubMed]

Gustafson, R.

A. Staley, D. Martynov, R. Abbott, R. X. Adhikari, K. Arai, S. Ballmer, L. Barsotti, A. F. Brooks, R. T. DeRosa, S. Dwyer, A. Effler, M. Evans, P. Fritschel, V. V. Frolov, C. Gray, C. J. Guido, R. Gustafson, M. Heintze, D. Hoak, K. Izumi, K. Kawabe, E. J. King, J. S. Kissel, K. Kokeyama, M. Landry, D. E. McClelland, J. Miller, A. Mullavey, B. O’Reilly, J. G. Rollins, J. R. Sanders, R. M. S. Schofield, D. Sigg, B. J. J. Slagmolen, N. D. Smith-Lefebvre, G. Vajente, R. L. Ward, and C. Wipf, “Achieving resonance in the Advanced LIGO gravitational-wave interferometer,” Class. Quantum Grav. 31, 245010 (2014).
[Crossref]

Hagemann, C.

Hall, J.

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

Hall, J. L.

Hansch, T. W.

T. Andreae, W. Konig, R. Wynands, D. Leibfried, F. Schmidt-Kaler, C. Zimmermann, D. Meschede, and T. W. Hansch, “Absolute frequency measurement of the hydrogen 1S–2S transition and a new value of the Rydberg constant,” Phys. Rev. Lett. 69, 1923–1926 (1992).
[Crossref] [PubMed]

Heintze, M.

A. Staley, D. Martynov, R. Abbott, R. X. Adhikari, K. Arai, S. Ballmer, L. Barsotti, A. F. Brooks, R. T. DeRosa, S. Dwyer, A. Effler, M. Evans, P. Fritschel, V. V. Frolov, C. Gray, C. J. Guido, R. Gustafson, M. Heintze, D. Hoak, K. Izumi, K. Kawabe, E. J. King, J. S. Kissel, K. Kokeyama, M. Landry, D. E. McClelland, J. Miller, A. Mullavey, B. O’Reilly, J. G. Rollins, J. R. Sanders, R. M. S. Schofield, D. Sigg, B. J. J. Slagmolen, N. D. Smith-Lefebvre, G. Vajente, R. L. Ward, and C. Wipf, “Achieving resonance in the Advanced LIGO gravitational-wave interferometer,” Class. Quantum Grav. 31, 245010 (2014).
[Crossref]

Hirata, K.

M. Aketagawa, S. Kimura, T. Yashiki, H. Iwata, T. Q. Banh, and K. Hirata, “Measurement of a free spectral range of a Fabry–Perot cavity using frequency modulation and null method under off-resonance conditions,” Meas. Sci. and Tech. 22, 025302 (2011).
[Crossref]

Hoak, D.

A. Staley, D. Martynov, R. Abbott, R. X. Adhikari, K. Arai, S. Ballmer, L. Barsotti, A. F. Brooks, R. T. DeRosa, S. Dwyer, A. Effler, M. Evans, P. Fritschel, V. V. Frolov, C. Gray, C. J. Guido, R. Gustafson, M. Heintze, D. Hoak, K. Izumi, K. Kawabe, E. J. King, J. S. Kissel, K. Kokeyama, M. Landry, D. E. McClelland, J. Miller, A. Mullavey, B. O’Reilly, J. G. Rollins, J. R. Sanders, R. M. S. Schofield, D. Sigg, B. J. J. Slagmolen, N. D. Smith-Lefebvre, G. Vajente, R. L. Ward, and C. Wipf, “Achieving resonance in the Advanced LIGO gravitational-wave interferometer,” Class. Quantum Grav. 31, 245010 (2014).
[Crossref]

Horikoshi, K.

Hough, J.

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

Iwata, H.

M. Aketagawa, S. Kimura, T. Yashiki, H. Iwata, T. Q. Banh, and K. Hirata, “Measurement of a free spectral range of a Fabry–Perot cavity using frequency modulation and null method under off-resonance conditions,” Meas. Sci. and Tech. 22, 025302 (2011).
[Crossref]

Izumi, K.

A. Staley, D. Martynov, R. Abbott, R. X. Adhikari, K. Arai, S. Ballmer, L. Barsotti, A. F. Brooks, R. T. DeRosa, S. Dwyer, A. Effler, M. Evans, P. Fritschel, V. V. Frolov, C. Gray, C. J. Guido, R. Gustafson, M. Heintze, D. Hoak, K. Izumi, K. Kawabe, E. J. King, J. S. Kissel, K. Kokeyama, M. Landry, D. E. McClelland, J. Miller, A. Mullavey, B. O’Reilly, J. G. Rollins, J. R. Sanders, R. M. S. Schofield, D. Sigg, B. J. J. Slagmolen, N. D. Smith-Lefebvre, G. Vajente, R. L. Ward, and C. Wipf, “Achieving resonance in the Advanced LIGO gravitational-wave interferometer,” Class. Quantum Grav. 31, 245010 (2014).
[Crossref]

Kawabe, K.

A. Staley, D. Martynov, R. Abbott, R. X. Adhikari, K. Arai, S. Ballmer, L. Barsotti, A. F. Brooks, R. T. DeRosa, S. Dwyer, A. Effler, M. Evans, P. Fritschel, V. V. Frolov, C. Gray, C. J. Guido, R. Gustafson, M. Heintze, D. Hoak, K. Izumi, K. Kawabe, E. J. King, J. S. Kissel, K. Kokeyama, M. Landry, D. E. McClelland, J. Miller, A. Mullavey, B. O’Reilly, J. G. Rollins, J. R. Sanders, R. M. S. Schofield, D. Sigg, B. J. J. Slagmolen, N. D. Smith-Lefebvre, G. Vajente, R. L. Ward, and C. Wipf, “Achieving resonance in the Advanced LIGO gravitational-wave interferometer,” Class. Quantum Grav. 31, 245010 (2014).
[Crossref]

A. Araya, S. Telada, K. Tochikubo, S. Taniguchi, R. Takahashi, K. Kawabe, D. Tatsumi, T. Yamazaki, S. Kawamura, S. Miyoki, S. Moriwaki, M. Musha, S. Nagano, M. K. Fujimoto, K. Horikoshi, N. Mio, Y. Naito, A. Takamori, and K. Yamamoto, “Absolute-length determination of a long-baseline Fabry–Perot cavity by means of resonating modulation sidebands,” Appl. Opt. 38, 2848 (1999).
[Crossref]

Kawamura, S.

A. Araya, S. Telada, K. Tochikubo, S. Taniguchi, R. Takahashi, K. Kawabe, D. Tatsumi, T. Yamazaki, S. Kawamura, S. Miyoki, S. Moriwaki, M. Musha, S. Nagano, M. K. Fujimoto, K. Horikoshi, N. Mio, Y. Naito, A. Takamori, and K. Yamamoto, “Absolute-length determination of a long-baseline Fabry–Perot cavity by means of resonating modulation sidebands,” Appl. Opt. 38, 2848 (1999).
[Crossref]

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. Whitecomb, and M. E. Zucker, “LIGO: the Laser Interferometer Gravitational-wave Observatory,” Science 256, 325 (1992).
[Crossref] [PubMed]

Kimura, S.

M. Aketagawa, S. Kimura, T. Yashiki, H. Iwata, T. Q. Banh, and K. Hirata, “Measurement of a free spectral range of a Fabry–Perot cavity using frequency modulation and null method under off-resonance conditions,” Meas. Sci. and Tech. 22, 025302 (2011).
[Crossref]

M. Aketagawa, T. Yashiki, S. Kimura, and T. Banh, “Free spectral range measurement of Fabry–Perot cavity using frequency modulation,” Int. Jour. of Precision Engineering and Manufacturing 11, 851 (2010).
[Crossref]

King, E. J.

A. Staley, D. Martynov, R. Abbott, R. X. Adhikari, K. Arai, S. Ballmer, L. Barsotti, A. F. Brooks, R. T. DeRosa, S. Dwyer, A. Effler, M. Evans, P. Fritschel, V. V. Frolov, C. Gray, C. J. Guido, R. Gustafson, M. Heintze, D. Hoak, K. Izumi, K. Kawabe, E. J. King, J. S. Kissel, K. Kokeyama, M. Landry, D. E. McClelland, J. Miller, A. Mullavey, B. O’Reilly, J. G. Rollins, J. R. Sanders, R. M. S. Schofield, D. Sigg, B. J. J. Slagmolen, N. D. Smith-Lefebvre, G. Vajente, R. L. Ward, and C. Wipf, “Achieving resonance in the Advanced LIGO gravitational-wave interferometer,” Class. Quantum Grav. 31, 245010 (2014).
[Crossref]

Kissel, J. S.

A. Staley, D. Martynov, R. Abbott, R. X. Adhikari, K. Arai, S. Ballmer, L. Barsotti, A. F. Brooks, R. T. DeRosa, S. Dwyer, A. Effler, M. Evans, P. Fritschel, V. V. Frolov, C. Gray, C. J. Guido, R. Gustafson, M. Heintze, D. Hoak, K. Izumi, K. Kawabe, E. J. King, J. S. Kissel, K. Kokeyama, M. Landry, D. E. McClelland, J. Miller, A. Mullavey, B. O’Reilly, J. G. Rollins, J. R. Sanders, R. M. S. Schofield, D. Sigg, B. J. J. Slagmolen, N. D. Smith-Lefebvre, G. Vajente, R. L. Ward, and C. Wipf, “Achieving resonance in the Advanced LIGO gravitational-wave interferometer,” Class. Quantum Grav. 31, 245010 (2014).
[Crossref]

Kokeyama, K.

A. Staley, D. Martynov, R. Abbott, R. X. Adhikari, K. Arai, S. Ballmer, L. Barsotti, A. F. Brooks, R. T. DeRosa, S. Dwyer, A. Effler, M. Evans, P. Fritschel, V. V. Frolov, C. Gray, C. J. Guido, R. Gustafson, M. Heintze, D. Hoak, K. Izumi, K. Kawabe, E. J. King, J. S. Kissel, K. Kokeyama, M. Landry, D. E. McClelland, J. Miller, A. Mullavey, B. O’Reilly, J. G. Rollins, J. R. Sanders, R. M. S. Schofield, D. Sigg, B. J. J. Slagmolen, N. D. Smith-Lefebvre, G. Vajente, R. L. Ward, and C. Wipf, “Achieving resonance in the Advanced LIGO gravitational-wave interferometer,” Class. Quantum Grav. 31, 245010 (2014).
[Crossref]

Konig, W.

T. Andreae, W. Konig, R. Wynands, D. Leibfried, F. Schmidt-Kaler, C. Zimmermann, D. Meschede, and T. W. Hansch, “Absolute frequency measurement of the hydrogen 1S–2S transition and a new value of the Rydberg constant,” Phys. Rev. Lett. 69, 1923–1926 (1992).
[Crossref] [PubMed]

Kowalski, F.

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

Landry, M.

A. Staley, D. Martynov, R. Abbott, R. X. Adhikari, K. Arai, S. Ballmer, L. Barsotti, A. F. Brooks, R. T. DeRosa, S. Dwyer, A. Effler, M. Evans, P. Fritschel, V. V. Frolov, C. Gray, C. J. Guido, R. Gustafson, M. Heintze, D. Hoak, K. Izumi, K. Kawabe, E. J. King, J. S. Kissel, K. Kokeyama, M. Landry, D. E. McClelland, J. Miller, A. Mullavey, B. O’Reilly, J. G. Rollins, J. R. Sanders, R. M. S. Schofield, D. Sigg, B. J. J. Slagmolen, N. D. Smith-Lefebvre, G. Vajente, R. L. Ward, and C. Wipf, “Achieving resonance in the Advanced LIGO gravitational-wave interferometer,” Class. Quantum Grav. 31, 245010 (2014).
[Crossref]

Legero, T.

Leibfried, D.

T. Andreae, W. Konig, R. Wynands, D. Leibfried, F. Schmidt-Kaler, C. Zimmermann, D. Meschede, and T. W. Hansch, “Absolute frequency measurement of the hydrogen 1S–2S transition and a new value of the Rydberg constant,” Phys. Rev. Lett. 69, 1923–1926 (1992).
[Crossref] [PubMed]

Manson, P. J.

P. J. Manson, “High precision free spectral range measurement using a phase modulated laser beam,” Rev. of Sci. Inst. 70, 3834 (1999).
[Crossref]

Martin, M. J.

Martynov, D.

A. Staley, D. Martynov, R. Abbott, R. X. Adhikari, K. Arai, S. Ballmer, L. Barsotti, A. F. Brooks, R. T. DeRosa, S. Dwyer, A. Effler, M. Evans, P. Fritschel, V. V. Frolov, C. Gray, C. J. Guido, R. Gustafson, M. Heintze, D. Hoak, K. Izumi, K. Kawabe, E. J. King, J. S. Kissel, K. Kokeyama, M. Landry, D. E. McClelland, J. Miller, A. Mullavey, B. O’Reilly, J. G. Rollins, J. R. Sanders, R. M. S. Schofield, D. Sigg, B. J. J. Slagmolen, N. D. Smith-Lefebvre, G. Vajente, R. L. Ward, and C. Wipf, “Achieving resonance in the Advanced LIGO gravitational-wave interferometer,” Class. Quantum Grav. 31, 245010 (2014).
[Crossref]

McClelland, D. E.

A. Staley, D. Martynov, R. Abbott, R. X. Adhikari, K. Arai, S. Ballmer, L. Barsotti, A. F. Brooks, R. T. DeRosa, S. Dwyer, A. Effler, M. Evans, P. Fritschel, V. V. Frolov, C. Gray, C. J. Guido, R. Gustafson, M. Heintze, D. Hoak, K. Izumi, K. Kawabe, E. J. King, J. S. Kissel, K. Kokeyama, M. Landry, D. E. McClelland, J. Miller, A. Mullavey, B. O’Reilly, J. G. Rollins, J. R. Sanders, R. M. S. Schofield, D. Sigg, B. J. J. Slagmolen, N. D. Smith-Lefebvre, G. Vajente, R. L. Ward, and C. Wipf, “Achieving resonance in the Advanced LIGO gravitational-wave interferometer,” Class. Quantum Grav. 31, 245010 (2014).
[Crossref]

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

Meschede, D.

T. Andreae, W. Konig, R. Wynands, D. Leibfried, F. Schmidt-Kaler, C. Zimmermann, D. Meschede, and T. W. Hansch, “Absolute frequency measurement of the hydrogen 1S–2S transition and a new value of the Rydberg constant,” Phys. Rev. Lett. 69, 1923–1926 (1992).
[Crossref] [PubMed]

Miller, J.

A. Staley, D. Martynov, R. Abbott, R. X. Adhikari, K. Arai, S. Ballmer, L. Barsotti, A. F. Brooks, R. T. DeRosa, S. Dwyer, A. Effler, M. Evans, P. Fritschel, V. V. Frolov, C. Gray, C. J. Guido, R. Gustafson, M. Heintze, D. Hoak, K. Izumi, K. Kawabe, E. J. King, J. S. Kissel, K. Kokeyama, M. Landry, D. E. McClelland, J. Miller, A. Mullavey, B. O’Reilly, J. G. Rollins, J. R. Sanders, R. M. S. Schofield, D. Sigg, B. J. J. Slagmolen, N. D. Smith-Lefebvre, G. Vajente, R. L. Ward, and C. Wipf, “Achieving resonance in the Advanced LIGO gravitational-wave interferometer,” Class. Quantum Grav. 31, 245010 (2014).
[Crossref]

Mio, N.

Miyoki, S.

Moriwaki, S.

Mullavey, A.

A. Staley, D. Martynov, R. Abbott, R. X. Adhikari, K. Arai, S. Ballmer, L. Barsotti, A. F. Brooks, R. T. DeRosa, S. Dwyer, A. Effler, M. Evans, P. Fritschel, V. V. Frolov, C. Gray, C. J. Guido, R. Gustafson, M. Heintze, D. Hoak, K. Izumi, K. Kawabe, E. J. King, J. S. Kissel, K. Kokeyama, M. Landry, D. E. McClelland, J. Miller, A. Mullavey, B. O’Reilly, J. G. Rollins, J. R. Sanders, R. M. S. Schofield, D. Sigg, B. J. J. Slagmolen, N. D. Smith-Lefebvre, G. Vajente, R. L. Ward, and C. Wipf, “Achieving resonance in the Advanced LIGO gravitational-wave interferometer,” Class. Quantum Grav. 31, 245010 (2014).
[Crossref]

Munley, A.

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

Musha, M.

Nagano, S.

Naito, Y.

O’Reilly, B.

A. Staley, D. Martynov, R. Abbott, R. X. Adhikari, K. Arai, S. Ballmer, L. Barsotti, A. F. Brooks, R. T. DeRosa, S. Dwyer, A. Effler, M. Evans, P. Fritschel, V. V. Frolov, C. Gray, C. J. Guido, R. Gustafson, M. Heintze, D. Hoak, K. Izumi, K. Kawabe, E. J. King, J. S. Kissel, K. Kokeyama, M. Landry, D. E. McClelland, J. Miller, A. Mullavey, B. O’Reilly, J. G. Rollins, J. R. Sanders, R. M. S. Schofield, D. Sigg, B. J. J. Slagmolen, N. D. Smith-Lefebvre, G. Vajente, R. L. Ward, and C. Wipf, “Achieving resonance in the Advanced LIGO gravitational-wave interferometer,” Class. Quantum Grav. 31, 245010 (2014).
[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. Whitecomb, and M. E. Zucker, “LIGO: the Laser Interferometer Gravitational-wave Observatory,” Science 256, 325 (1992).
[Crossref] [PubMed]

Rakhmanov, M.

M. Rakhmanov, F. Bondu, O. Debieu, and R. L. Savage, “Characterization of the LIGO 4 km Fabry–Perot cavities via their high-frequency dynamic responses to length and frequency variations,” Class. Quantum Grav. 21, S487 (2004).
[Crossref]

Riehle, F.

Rollins, J. G.

A. Staley, D. Martynov, R. Abbott, R. X. Adhikari, K. Arai, S. Ballmer, L. Barsotti, A. F. Brooks, R. T. DeRosa, S. Dwyer, A. Effler, M. Evans, P. Fritschel, V. V. Frolov, C. Gray, C. J. Guido, R. Gustafson, M. Heintze, D. Hoak, K. Izumi, K. Kawabe, E. J. King, J. S. Kissel, K. Kokeyama, M. Landry, D. E. McClelland, J. Miller, A. Mullavey, B. O’Reilly, J. G. Rollins, J. R. Sanders, R. M. S. Schofield, D. Sigg, B. J. J. Slagmolen, N. D. Smith-Lefebvre, G. Vajente, R. L. Ward, and C. Wipf, “Achieving resonance in the Advanced LIGO gravitational-wave interferometer,” Class. Quantum Grav. 31, 245010 (2014).
[Crossref]

Sanders, J. R.

A. Staley, D. Martynov, R. Abbott, R. X. Adhikari, K. Arai, S. Ballmer, L. Barsotti, A. F. Brooks, R. T. DeRosa, S. Dwyer, A. Effler, M. Evans, P. Fritschel, V. V. Frolov, C. Gray, C. J. Guido, R. Gustafson, M. Heintze, D. Hoak, K. Izumi, K. Kawabe, E. J. King, J. S. Kissel, K. Kokeyama, M. Landry, D. E. McClelland, J. Miller, A. Mullavey, B. O’Reilly, J. G. Rollins, J. R. Sanders, R. M. S. Schofield, D. Sigg, B. J. J. Slagmolen, N. D. Smith-Lefebvre, G. Vajente, R. L. Ward, and C. Wipf, “Achieving resonance in the Advanced LIGO gravitational-wave interferometer,” Class. Quantum Grav. 31, 245010 (2014).
[Crossref]

Savage, R. L.

M. Rakhmanov, F. Bondu, O. Debieu, and R. L. Savage, “Characterization of the LIGO 4 km Fabry–Perot cavities via their high-frequency dynamic responses to length and frequency variations,” Class. Quantum Grav. 21, S487 (2004).
[Crossref]

Schmidt-Kaler, F.

T. Andreae, W. Konig, R. Wynands, D. Leibfried, F. Schmidt-Kaler, C. Zimmermann, D. Meschede, and T. W. Hansch, “Absolute frequency measurement of the hydrogen 1S–2S transition and a new value of the Rydberg constant,” Phys. Rev. Lett. 69, 1923–1926 (1992).
[Crossref] [PubMed]

Schofield, R. M. S.

A. Staley, D. Martynov, R. Abbott, R. X. Adhikari, K. Arai, S. Ballmer, L. Barsotti, A. F. Brooks, R. T. DeRosa, S. Dwyer, A. Effler, M. Evans, P. Fritschel, V. V. Frolov, C. Gray, C. J. Guido, R. Gustafson, M. Heintze, D. Hoak, K. Izumi, K. Kawabe, E. J. King, J. S. Kissel, K. Kokeyama, M. Landry, D. E. McClelland, J. Miller, A. Mullavey, B. O’Reilly, J. G. Rollins, J. R. Sanders, R. M. S. Schofield, D. Sigg, B. J. J. Slagmolen, N. D. Smith-Lefebvre, G. Vajente, R. L. Ward, and C. Wipf, “Achieving resonance in the Advanced LIGO gravitational-wave interferometer,” Class. Quantum Grav. 31, 245010 (2014).
[Crossref]

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. Whitecomb, and M. E. Zucker, “LIGO: the Laser Interferometer Gravitational-wave Observatory,” Science 256, 325 (1992).
[Crossref] [PubMed]

Siegman, A. E.

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

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. Whitecomb, and M. E. Zucker, “LIGO: the Laser Interferometer Gravitational-wave Observatory,” Science 256, 325 (1992).
[Crossref] [PubMed]

Sigg, D.

A. Staley, D. Martynov, R. Abbott, R. X. Adhikari, K. Arai, S. Ballmer, L. Barsotti, A. F. Brooks, R. T. DeRosa, S. Dwyer, A. Effler, M. Evans, P. Fritschel, V. V. Frolov, C. Gray, C. J. Guido, R. Gustafson, M. Heintze, D. Hoak, K. Izumi, K. Kawabe, E. J. King, J. S. Kissel, K. Kokeyama, M. Landry, D. E. McClelland, J. Miller, A. Mullavey, B. O’Reilly, J. G. Rollins, J. R. Sanders, R. M. S. Schofield, D. Sigg, B. J. J. Slagmolen, N. D. Smith-Lefebvre, G. Vajente, R. L. Ward, and C. Wipf, “Achieving resonance in the Advanced LIGO gravitational-wave interferometer,” Class. Quantum Grav. 31, 245010 (2014).
[Crossref]

Skeldon, K. D.

Slagmolen, B. J. J.

A. Staley, D. Martynov, R. Abbott, R. X. Adhikari, K. Arai, S. Ballmer, L. Barsotti, A. F. Brooks, R. T. DeRosa, S. Dwyer, A. Effler, M. Evans, P. Fritschel, V. V. Frolov, C. Gray, C. J. Guido, R. Gustafson, M. Heintze, D. Hoak, K. Izumi, K. Kawabe, E. J. King, J. S. Kissel, K. Kokeyama, M. Landry, D. E. McClelland, J. Miller, A. Mullavey, B. O’Reilly, J. G. Rollins, J. R. Sanders, R. M. S. Schofield, D. Sigg, B. J. J. Slagmolen, N. D. Smith-Lefebvre, G. Vajente, R. L. Ward, and C. Wipf, “Achieving resonance in the Advanced LIGO gravitational-wave interferometer,” Class. Quantum Grav. 31, 245010 (2014).
[Crossref]

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

Smith-Lefebvre, N. D.

A. Staley, D. Martynov, R. Abbott, R. X. Adhikari, K. Arai, S. Ballmer, L. Barsotti, A. F. Brooks, R. T. DeRosa, S. Dwyer, A. Effler, M. Evans, P. Fritschel, V. V. Frolov, C. Gray, C. J. Guido, R. Gustafson, M. Heintze, D. Hoak, K. Izumi, K. Kawabe, E. J. King, J. S. Kissel, K. Kokeyama, M. Landry, D. E. McClelland, J. Miller, A. Mullavey, B. O’Reilly, J. G. Rollins, J. R. Sanders, R. M. S. Schofield, D. Sigg, B. J. J. Slagmolen, N. D. Smith-Lefebvre, G. Vajente, R. L. Ward, and C. Wipf, “Achieving resonance in the Advanced LIGO gravitational-wave interferometer,” Class. Quantum Grav. 31, 245010 (2014).
[Crossref]

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. Whitecomb, and M. E. Zucker, “LIGO: the Laser Interferometer Gravitational-wave Observatory,” Science 256, 325 (1992).
[Crossref] [PubMed]

Staley, A.

A. Staley, D. Martynov, R. Abbott, R. X. Adhikari, K. Arai, S. Ballmer, L. Barsotti, A. F. Brooks, R. T. DeRosa, S. Dwyer, A. Effler, M. Evans, P. Fritschel, V. V. Frolov, C. Gray, C. J. Guido, R. Gustafson, M. Heintze, D. Hoak, K. Izumi, K. Kawabe, E. J. King, J. S. Kissel, K. Kokeyama, M. Landry, D. E. McClelland, J. Miller, A. Mullavey, B. O’Reilly, J. G. Rollins, J. R. Sanders, R. M. S. Schofield, D. Sigg, B. J. J. Slagmolen, N. D. Smith-Lefebvre, G. Vajente, R. L. Ward, and C. Wipf, “Achieving resonance in the Advanced LIGO gravitational-wave interferometer,” Class. Quantum Grav. 31, 245010 (2014).
[Crossref]

Sterr, U.

Strain, K. A.

Takahashi, R.

Takamori, A.

Taniguchi, S.

Tatsumi, D.

Telada, S.

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. Whitecomb, and M. E. Zucker, “LIGO: the Laser Interferometer Gravitational-wave Observatory,” Science 256, 325 (1992).
[Crossref] [PubMed]

Tochikubo, K.

Vajente, G.

A. Staley, D. Martynov, R. Abbott, R. X. Adhikari, K. Arai, S. Ballmer, L. Barsotti, A. F. Brooks, R. T. DeRosa, S. Dwyer, A. Effler, M. Evans, P. Fritschel, V. V. Frolov, C. Gray, C. J. Guido, R. Gustafson, M. Heintze, D. Hoak, K. Izumi, K. Kawabe, E. J. King, J. S. Kissel, K. Kokeyama, M. Landry, D. E. McClelland, J. Miller, A. Mullavey, B. O’Reilly, J. G. Rollins, J. R. Sanders, R. M. S. Schofield, D. Sigg, B. J. J. Slagmolen, N. D. Smith-Lefebvre, G. Vajente, R. L. Ward, and C. Wipf, “Achieving resonance in the Advanced LIGO gravitational-wave interferometer,” Class. Quantum Grav. 31, 245010 (2014).
[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. Whitecomb, and M. E. Zucker, “LIGO: the Laser Interferometer Gravitational-wave Observatory,” Science 256, 325 (1992).
[Crossref] [PubMed]

Ward, H.

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

Ward, R. L.

A. Staley, D. Martynov, R. Abbott, R. X. Adhikari, K. Arai, S. Ballmer, L. Barsotti, A. F. Brooks, R. T. DeRosa, S. Dwyer, A. Effler, M. Evans, P. Fritschel, V. V. Frolov, C. Gray, C. J. Guido, R. Gustafson, M. Heintze, D. Hoak, K. Izumi, K. Kawabe, E. J. King, J. S. Kissel, K. Kokeyama, M. Landry, D. E. McClelland, J. Miller, A. Mullavey, B. O’Reilly, J. G. Rollins, J. R. Sanders, R. M. S. Schofield, D. Sigg, B. J. J. Slagmolen, N. D. Smith-Lefebvre, G. Vajente, R. L. Ward, and C. Wipf, “Achieving resonance in the Advanced LIGO gravitational-wave interferometer,” Class. Quantum Grav. 31, 245010 (2014).
[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. Whitecomb, and M. E. Zucker, “LIGO: the Laser Interferometer Gravitational-wave Observatory,” Science 256, 325 (1992).
[Crossref] [PubMed]

Whitecomb, 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. Whitecomb, and M. E. Zucker, “LIGO: the Laser Interferometer Gravitational-wave Observatory,” Science 256, 325 (1992).
[Crossref] [PubMed]

Whittaker, E. A.

Wipf, C.

A. Staley, D. Martynov, R. Abbott, R. X. Adhikari, K. Arai, S. Ballmer, L. Barsotti, A. F. Brooks, R. T. DeRosa, S. Dwyer, A. Effler, M. Evans, P. Fritschel, V. V. Frolov, C. Gray, C. J. Guido, R. Gustafson, M. Heintze, D. Hoak, K. Izumi, K. Kawabe, E. J. King, J. S. Kissel, K. Kokeyama, M. Landry, D. E. McClelland, J. Miller, A. Mullavey, B. O’Reilly, J. G. Rollins, J. R. Sanders, R. M. S. Schofield, D. Sigg, B. J. J. Slagmolen, N. D. Smith-Lefebvre, G. Vajente, R. L. Ward, and C. Wipf, “Achieving resonance in the Advanced LIGO gravitational-wave interferometer,” Class. Quantum Grav. 31, 245010 (2014).
[Crossref]

Wong, N. C.

Wynands, R.

T. Andreae, W. Konig, R. Wynands, D. Leibfried, F. Schmidt-Kaler, C. Zimmermann, D. Meschede, and T. W. Hansch, “Absolute frequency measurement of the hydrogen 1S–2S transition and a new value of the Rydberg constant,” Phys. Rev. Lett. 69, 1923–1926 (1992).
[Crossref] [PubMed]

Yamamoto, K.

Yamazaki, T.

Yashiki, T.

M. Aketagawa, S. Kimura, T. Yashiki, H. Iwata, T. Q. Banh, and K. Hirata, “Measurement of a free spectral range of a Fabry–Perot cavity using frequency modulation and null method under off-resonance conditions,” Meas. Sci. and Tech. 22, 025302 (2011).
[Crossref]

M. Aketagawa, T. Yashiki, S. Kimura, and T. Banh, “Free spectral range measurement of Fabry–Perot cavity using frequency modulation,” Int. Jour. of Precision Engineering and Manufacturing 11, 851 (2010).
[Crossref]

Ye, J.

Zhang, W.

Zimmermann, C.

T. Andreae, W. Konig, R. Wynands, D. Leibfried, F. Schmidt-Kaler, C. Zimmermann, D. Meschede, and T. W. Hansch, “Absolute frequency measurement of the hydrogen 1S–2S transition and a new value of the Rydberg constant,” Phys. Rev. Lett. 69, 1923–1926 (1992).
[Crossref] [PubMed]

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. Whitecomb, and M. E. Zucker, “LIGO: the Laser Interferometer Gravitational-wave Observatory,” Science 256, 325 (1992).
[Crossref] [PubMed]

Appl. Opt. (4)

Appl. Phys. B (1)

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

Class. Quantum Grav. (3)

A. Staley, D. Martynov, R. Abbott, R. X. Adhikari, K. Arai, S. Ballmer, L. Barsotti, A. F. Brooks, R. T. DeRosa, S. Dwyer, A. Effler, M. Evans, P. Fritschel, V. V. Frolov, C. Gray, C. J. Guido, R. Gustafson, M. Heintze, D. Hoak, K. Izumi, K. Kawabe, E. J. King, J. S. Kissel, K. Kokeyama, M. Landry, D. E. McClelland, J. Miller, A. Mullavey, B. O’Reilly, J. G. Rollins, J. R. Sanders, R. M. S. Schofield, D. Sigg, B. J. J. Slagmolen, N. D. Smith-Lefebvre, G. Vajente, R. L. Ward, and C. Wipf, “Achieving resonance in the Advanced LIGO gravitational-wave interferometer,” Class. Quantum Grav. 31, 245010 (2014).
[Crossref]

The LIGO Scientific Collaboration, “Advanced LIGO,” Class. Quantum Grav. 32, 074001 (2015).
[Crossref]

M. Rakhmanov, F. Bondu, O. Debieu, and R. L. Savage, “Characterization of the LIGO 4 km Fabry–Perot cavities via their high-frequency dynamic responses to length and frequency variations,” Class. Quantum Grav. 21, S487 (2004).
[Crossref]

Int. Jour. of Precision Engineering and Manufacturing (1)

M. Aketagawa, T. Yashiki, S. Kimura, and T. Banh, “Free spectral range measurement of Fabry–Perot cavity using frequency modulation,” Int. Jour. of Precision Engineering and Manufacturing 11, 851 (2010).
[Crossref]

J. Opt. Soc. Am. B (2)

Meas. Sci. and Tech. (1)

M. Aketagawa, S. Kimura, T. Yashiki, H. Iwata, T. Q. Banh, and K. Hirata, “Measurement of a free spectral range of a Fabry–Perot cavity using frequency modulation and null method under off-resonance conditions,” Meas. Sci. and Tech. 22, 025302 (2011).
[Crossref]

Opt. Lett. (1)

Phys. Rev. Lett. (1)

T. Andreae, W. Konig, R. Wynands, D. Leibfried, F. Schmidt-Kaler, C. Zimmermann, D. Meschede, and T. W. Hansch, “Absolute frequency measurement of the hydrogen 1S–2S transition and a new value of the Rydberg constant,” Phys. Rev. Lett. 69, 1923–1926 (1992).
[Crossref] [PubMed]

Rev. of Sci. Inst. (1)

P. J. Manson, “High precision free spectral range measurement using a phase modulated laser beam,” Rev. of Sci. Inst. 70, 3834 (1999).
[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. Whitecomb, and M. E. Zucker, “LIGO: the Laser Interferometer Gravitational-wave Observatory,” Science 256, 325 (1992).
[Crossref] [PubMed]

Other (2)

R. W. P. Drever, The Detection of Gravitational Waves, D. G. Blair, ed. (Cambridge University, 1991).

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

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Figures (5)

Fig. 1
Fig. 1 Measurement setup. A laser beam is doubly phase modulated using an electro-optic modulator (EOM) and then locked to an optical cavity. The first phase modulation is used for deriving a cavity length signal using the Pound-Drever-Hall reflection locking technique. The second phase modulation is used to generate RF sidebands near a multiple of the full spectral range.
Fig. 2
Fig. 2 Double demodulation signal in transmission of a cavity with ϕ a → 0. Shown are the RF in-phase and quadrature-phase signals assuming the audio modulation frequency is small compared to the cavity linewidth. The finesse of the cavity is F = 156. The exact position of the secondary zero crossings also depends on the time delay between the optical path and the RF demodulation path. The signals are shown for zero delay.
Fig. 3
Fig. 3 The black dashed traces represent the fit of Eq. (1) to the double-demodulated data for a 16 m cavity. For this data, the audio modulation frequency was 1 kHz, and the RF modulation frequency was scanned from 9.08 to 9.12 MHz. The deviation from the model around 9.095 MHz is due to an unknown feature in the signal path. Masking out the data in a 5 kHz band around this feature does not change the results of the parameter estimation.
Fig. 4
Fig. 4 The green arrow represents the laser frequency, which has an offset δ f from the locking point. The RF sidebands produced by the first phase modulation are depicted by the blue arrows. An additional modulation at audio frequencies fa produces four audio sidebands as seen by the pink arrows. In this case δ ffa. The plotted amplitudes are arbitrary and depend on the modulation depths.
Fig. 5
Fig. 5 Double demodulation signal in reflection of a cavity. Shown are the RF in-phase and quadrature-phase signals assuming the audio modulation frequency is small compared to the cavity linewidth. The solid curve represent a cavity with equal transmission front and rear mirrors, whereas the dashed lines represent a cavity with a high reflector as the rear mirror. In both cases the finesse is F = 156.

Tables (3)

Tables Icon

Table 1 Results from the fit of Eq. (1) to the data of the 16 m input mode cleaner cavity.

Tables Icon

Table 2 The top rows show the derived length and cavity pole from the fit for the 16 m cavity. The bottom rows show the free spectral range and exact length for the 4 km cavity, here N = 666. The statistical uncertainties from fitting the data are presented. The systematic errors are discussed is Section 5.3.

Tables Icon

Table 3 Estimated systematic errors in Hertz to the measured frequencies of the main zero crossing (length) and difference between the secondary zero crossings divided by two (used for the cavity pole). The frequency errors are split among the length and linewidth measurements for the 16 m cavity; the linewidth was not measured for the 4 km cavity. These systematic uncertainties are estimated with a 67% confidence level.

Equations (29)

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S t r ( ϕ f , ϕ a ) = S t r ( ϕ f ) ( 1 R ) ( e i ϕ f R ) ( e i ϕ f + i ϕ a R ) ( e i ϕ f e i ϕ a R ) ( 1 2 R cos ϕ a + R 2 ) × { e 2 i ϕ a 1 2 i ϕ a ( e i ϕ f ( 1 R ) R ( 1 2 R cos ϕ a + R ) ) audio in-phase ( e i ϕ a 1 ) 2 2 ϕ a ( e i ϕ f ( 1 + R ) + R ( 1 2 R cos ϕ a R ) ) audio quad-phase
S t r ( ϕ f ) = p 0 g t r 2 R e i ϕ f 1 e i ϕ f ( e i ϕ f R ) 2 = p 0 g t r 2 2 R ( 1 2 R cos ϕ f + R 2 ) 2 sin ϕ f 2 × [ sin ϕ f 2 ( 1 + 2 R ( 1 + 2 cos ϕ f ) R 2 ) + i cos ϕ f 2 ( 1 2 R ( 1 2 cos ϕ f ) R 2 ) ] w i t h p 0 = 2 π δ f f FSR Γ P in , g t r 2 = ( 1 r 1 2 ) ( 1 r 2 2 ) ( 1 R ) 2 , R = r 1 r 2 , f FSR = c 2 L , ϕ a = 2 π f a f FSR and ϕ f = 2 π f RF f FSR .
lim ϕ a 0 S t r I ( ϕ f , ϕ a ) = S t r ( ϕ f ) and lim ϕ a 0 S t r Q ( ϕ f , ϕ a ) = 0
f ± = ± f FSR π sin 1 ( π 2 F R ) + n f FSR = ± f pole R + n f FSR with f pole f FSR 2 F and F = π R 1 R .
d S t r d ϕ f | ϕ f = 0 = p 0 g t r 2 R ( 1 R ) 2 2 R d S t r d ϕ f | ϕ f = 0 ±
Δ f RF shot = ( 1 R ) 2 R 2 h c λ g t r 2 P in T ( 1 δ f Γ ) ( f FSR 2 π ) 2
f ± ( ϕ a ) = f ± ( 1 + ϕ a 2 R f ± 2 ) .
Δ f RF phase ( 1 R ) Δ ϕ RF f FSR 2 π Δ ϕ RF f pole .
( 1 + ε Γ cos ( 2 π f RF t ψ ) ) ( 1 + η δ f 2 π f a sin 2 π f a t ) ,
S t r AM ( ϕ f ) = p 0 g t r 2 R e i ϕ f 1 + e i ϕ f 2 R ( e i ϕ f R ) 2 e i ψ ε η .
S t r AM ( 0 ) = p 0 g t r 2 2 R 1 R e i ψ ε η .
L = 16.471701 m ± 3 µ m (stat) ± 1 µ m (sys)
L = 3994 . 4692 m ± 0.2 mm (stat) ± 0.2 mm (sys) .
f pole = 8804 Hz ± 10 Hz ( stat ) ± 52 Hz ( sys ) .
E t = t ( ϕ ) E i n c
t ( ϕ ) = t 1 t 2 1 r 1 r 2 e i ϕ = g t ( 1 R ) 1 R e i ϕ .
E i n c = E 0 e i N ω FSR t e i δ ω t e i Γ cos ω RF t .
E t = E 0 e i ω 0 t { J 0 ( Γ ) t ( ϕ c ) + i J 1 ( Γ ) t ( ϕ u p s b ) e i ω RF t + i J 1 ( Γ ) t ( ϕ l o w s b ) e i ω RF t }
ϕ c = δ ω f FSR ϕ up,low sb = ± ω RF + δ ω f FSR = ± ϕ f + ϕ c .
P t RF = 2 J 0 ( Γ ) J 1 ( Γ ) P in × { Im [ t ( ϕ c ) t * ( ϕ low sb ) t * ( ϕ c ) t ( ϕ up sb ) ] cos ( ω RF t ) + Re [ t ( ϕ c ) t * ( ϕ low sb ) t * ( ϕ c ) t ( ϕ up sb ) ] sin ( ω RF t ) }
J 0 ( Γ ) 1 , J 1 ( Γ ) Γ / 2 , e i ϕ c 1 + i ϕ c
E i n c = E 0 e i N ω FSR t e i δ ω / ω a sin ω a t e i Γ cos ω RF t .
E t = E 0 e i ω 0 t × [ J 0 ( Γ ) F ( ϕ c ) + i J 1 ( Γ ) F ( ϕ low sb ) e i ω RF t + i J 1 ( Γ ) F ( ϕ up sb ) e i ω RF t ] , F ( ϕ ) = J 0 ( δ ω / ω a ) t ( ϕ ) + J 1 ( δ ω / ω a ) t ( ϕ + ϕ a ) e i ω a t J 1 ( δ ω / ω a ) t ( ϕ ϕ a ) e i ω a t
r ( θ ) = r 1 + t 1 2 r 2 e i ϕ 1 r 1 r 2 e i ϕ
S refl ( ϕ f , ϕ a ) = S refl ( ϕ f ) e i ϕ a ( 1 R ) ( e i ϕ f R ) ( e i ϕ f + i ϕ a R ) ( e i ϕ f R e i ϕ a ) ( 1 2 R cos ϕ a + R 2 ) ( e i ϕ f r 2 2 ) × { × sin ϕ a ϕ a [ ( e 2 i ϕ f + R r 2 2 ) ( 1 R ) e i ϕ f ( ( 1 + R ) ( R r 2 2 ) 2 cos ϕ a ( R 2 r 2 2 ) ) ] ( cos ϕ a 1 ) ϕ a [ ( e 2 i ϕ f + R r 2 2 ) ( 1 + R ) e i ϕ f ( ( 1 R ) ( R r 2 2 ) 2 cos ϕ a ( R 2 + r 2 2 ) ) ]
S refl ( ϕ f ) = p 0 g refl 2 R ( 1 e i ϕ f ) ( r 2 2 e i ϕ f ) ( e i ϕ f R ) 2 = p 0 g refl 2 2 R ( 1 2 R cos ϕ f + R 2 ) 2 sin ϕ f 2 × [ sin ϕ f 2 ( 1 + 2 R ( 1 + 2 cos ϕ f ) ( R 2 + r 2 2 ) + R r 2 2 ( 2 + R ) ) + i cos ϕ f 2 ( 1 2 R ( 1 2 cos ϕ f ) ( R 2 r 2 2 ) + R r 2 2 ( 2 R ) ) ]
lim ϕ a 0 S refl I ( ϕ f , ϕ a ) = S refl ( ϕ f ) and lim ϕ a 0 S refl Q ( ϕ f , ϕ a ) = 0.
f ± = ± f FSR π sin 1 ( π 2 F R ( R r 2 2 + 3 r 2 2 3 R 1 ) ( 1 R ) ( R 2 + r 2 2 ) ) ± f FSR π sin 1 ( π 2 F 2 r 1 1 + r 1 2 ) for r 2 1
d S refl d ϕ f | ϕ f = 0 = p 0 g refl 2 R ( 1 r 2 2 ) ( 1 R ) 2 = d S t r d ϕ f | ϕ f = 0

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