Abstract

Length and g-factor are fundamental parameters that characterize optical cavities. We developed a technique to measure these parameters in situ by determining the frequency spacing between the resonances of fundamental and spatial modes of an optical cavity. Two laser beams are injected into the cavity, and their relative frequency is scanned by a phase-lock loop, while the cavity is locked to either laser. The measurement of the amplitude of their beat note in transmission reveals the resonances of the longitudinal and the transverse modes of the cavity and their spacing. This method proves particularly useful to characterize complex optical systems, including very long and/or coupled optical cavities, as in gravitational-wave interferometers. This technique and the results of its application to the coupled cavities of a 40 m-long gravitational-wave interferometer prototype are presented here.

© 2012 Optical Society of America

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2010 (4)

T. Accadia and The Virgo Collaboration, “Status and perspectives of the Virgo gravitational wave detector,” J. Phys.: Conf. Ser. 23, 012074 (2010).

K. Kuroda, “Status of LCGT,” Classical Quantum Gravity 27, 084004 (2010).
[CrossRef]

H. Grote and The GEO Collaboration, “The GEO 600 status,” Class. Quantum Grav. 27, 084003 (2010).

G. M. Harry and The LIGO Scientific Collaboration, “Advanced LIGO: the next generation of gravitational wave detectors,” Class. Quantum Grav. 27, 084006 (2010).
[CrossRef]

2009 (1)

B. P. Abbott and The LIGO Scientific Collaboration, “LIGO: The Laser Interferometer Gravitational-wave Observatory,” Rept. Prog. Phys. 72, 076901 (2009).
[CrossRef]

2008 (2)

R. L. Ward, R. Adhikari, B. Abbott, R. Abbott, D. Barron, R. Bork, T. Fricke, V. Frolov, J. Heefner, A. Ivanov, O. Miyakawa, K. McKenzie, B. Slagmolen, M. Smith, R. Taylor, S. Vass, S. Waldman, and A. Weinstein, “DC readout experiment at the Caltech 40 m prototype interferometer,” Class. Quantum Grav. 25, 114030 (2008).
[CrossRef]

B. Willke, K. Danzmann, M. Frede, P. King, D. Kracht, P. Kwee, O. Puncken, R. L. Savage, B. Schulz, F. Seifert, C. Veltkamp, S. Wagner, P. Weels, and L. Winkelmann, “Stabilized lasers for advanced gravitational wave detectors,” Class. Quantum Grav. 25, 114040 (2008).
[CrossRef]

2007 (1)

S. Habraken and G. Nienhuis, “Modes of a twisted optical cavity,” Phys. Rev. A 75, 033819 (2007).
[CrossRef]

2004 (2)

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 laser frequency variations,” Class. Quantum Grav. 21, S487–S492 (2004).
[CrossRef]

J. Ye, “Absolute measurement of a long, arbitrary distance to less than an optical fringe,” Opt. Lett. 29, 1153–1155 (2004).
[CrossRef]

2002 (2)

D. Redding, M. Regehr, and L. Sievers, “Dynamic models of Fabry–Perot interferometers,” Appl. Opt. 41, 2894–2906 (2002).
[CrossRef]

A. Weinstein, “Advanced LIGO optical configuration and prototyping effort,” Class. Quantum Grav. 19, 1575–1584 (2002).
[CrossRef]

1999 (2)

1998 (1)

1995 (1)

1994 (1)

1989 (1)

1984 (2)

R. DeVoe and R. Brewer, “Laser-frequency division and stabilization,” Phys. Rev. A 30, 2827–2829 (1984).
[CrossRef]

D. Z. Anderson, “Alignment of resonant optical cavities,” Appl. Opt. 23, 2944–2949 (1984).
[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: Lasers Opt. 31, 97–105 (1983).
[CrossRef]

1979 (1)

Abbott, B.

R. L. Ward, R. Adhikari, B. Abbott, R. Abbott, D. Barron, R. Bork, T. Fricke, V. Frolov, J. Heefner, A. Ivanov, O. Miyakawa, K. McKenzie, B. Slagmolen, M. Smith, R. Taylor, S. Vass, S. Waldman, and A. Weinstein, “DC readout experiment at the Caltech 40 m prototype interferometer,” Class. Quantum Grav. 25, 114030 (2008).
[CrossRef]

Abbott, B. P.

B. P. Abbott and The LIGO Scientific Collaboration, “LIGO: The Laser Interferometer Gravitational-wave Observatory,” Rept. Prog. Phys. 72, 076901 (2009).
[CrossRef]

Abbott, R.

R. L. Ward, R. Adhikari, B. Abbott, R. Abbott, D. Barron, R. Bork, T. Fricke, V. Frolov, J. Heefner, A. Ivanov, O. Miyakawa, K. McKenzie, B. Slagmolen, M. Smith, R. Taylor, S. Vass, S. Waldman, and A. Weinstein, “DC readout experiment at the Caltech 40 m prototype interferometer,” Class. Quantum Grav. 25, 114030 (2008).
[CrossRef]

Accadia, T.

T. Accadia and The Virgo Collaboration, “Status and perspectives of the Virgo gravitational wave detector,” J. Phys.: Conf. Ser. 23, 012074 (2010).

Adhikari, R.

R. L. Ward, R. Adhikari, B. Abbott, R. Abbott, D. Barron, R. Bork, T. Fricke, V. Frolov, J. Heefner, A. Ivanov, O. Miyakawa, K. McKenzie, B. Slagmolen, M. Smith, R. Taylor, S. Vass, S. Waldman, and A. Weinstein, “DC readout experiment at the Caltech 40 m prototype interferometer,” Class. Quantum Grav. 25, 114030 (2008).
[CrossRef]

Anderson, D. Z.

Araya, A.

Armor, J. B.

Barron, D.

R. L. Ward, R. Adhikari, B. Abbott, R. Abbott, D. Barron, R. Bork, T. Fricke, V. Frolov, J. Heefner, A. Ivanov, O. Miyakawa, K. McKenzie, B. Slagmolen, M. Smith, R. Taylor, S. Vass, S. Waldman, and A. Weinstein, “DC readout experiment at the Caltech 40 m prototype interferometer,” Class. Quantum Grav. 25, 114030 (2008).
[CrossRef]

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 laser frequency variations,” Class. Quantum Grav. 21, S487–S492 (2004).
[CrossRef]

Bork, R.

R. L. Ward, R. Adhikari, B. Abbott, R. Abbott, D. Barron, R. Bork, T. Fricke, V. Frolov, J. Heefner, A. Ivanov, O. Miyakawa, K. McKenzie, B. Slagmolen, M. Smith, R. Taylor, S. Vass, S. Waldman, and A. Weinstein, “DC readout experiment at the Caltech 40 m prototype interferometer,” Class. Quantum Grav. 25, 114030 (2008).
[CrossRef]

Brewer, R.

R. DeVoe and R. Brewer, “Laser-frequency division and stabilization,” Phys. Rev. A 30, 2827–2829 (1984).
[CrossRef]

Burow, R.

Danzmann, K.

B. Willke, K. Danzmann, M. Frede, P. King, D. Kracht, P. Kwee, O. Puncken, R. L. Savage, B. Schulz, F. Seifert, C. Veltkamp, S. Wagner, P. Weels, and L. Winkelmann, “Stabilized lasers for advanced gravitational wave detectors,” Class. Quantum Grav. 25, 114040 (2008).
[CrossRef]

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 laser frequency variations,” Class. Quantum Grav. 21, S487–S492 (2004).
[CrossRef]

DeVoe, R.

R. DeVoe and R. Brewer, “Laser-frequency division and stabilization,” Phys. Rev. A 30, 2827–2829 (1984).
[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: Lasers Opt. 31, 97–105 (1983).
[CrossRef]

Elssner, K.-E.

Evans, M.

M. Rakhmanov, M. Evans, and H. Yamamoto, “An optical vernier technique for in situ measurement of the length of long Fabry–Perot cavities,” Meas. Sci. Technol. 10, 190–194 (1999).
[CrossRef]

Ford, G. M.

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

Frede, M.

B. Willke, K. Danzmann, M. Frede, P. King, D. Kracht, P. Kwee, O. Puncken, R. L. Savage, B. Schulz, F. Seifert, C. Veltkamp, S. Wagner, P. Weels, and L. Winkelmann, “Stabilized lasers for advanced gravitational wave detectors,” Class. Quantum Grav. 25, 114040 (2008).
[CrossRef]

Fricke, T.

R. L. Ward, R. Adhikari, B. Abbott, R. Abbott, D. Barron, R. Bork, T. Fricke, V. Frolov, J. Heefner, A. Ivanov, O. Miyakawa, K. McKenzie, B. Slagmolen, M. Smith, R. Taylor, S. Vass, S. Waldman, and A. Weinstein, “DC readout experiment at the Caltech 40 m prototype interferometer,” Class. Quantum Grav. 25, 114030 (2008).
[CrossRef]

Fritschel, P.

Frolov, V.

R. L. Ward, R. Adhikari, B. Abbott, R. Abbott, D. Barron, R. Bork, T. Fricke, V. Frolov, J. Heefner, A. Ivanov, O. Miyakawa, K. McKenzie, B. Slagmolen, M. Smith, R. Taylor, S. Vass, S. Waldman, and A. Weinstein, “DC readout experiment at the Caltech 40 m prototype interferometer,” Class. Quantum Grav. 25, 114030 (2008).
[CrossRef]

Fujimoto, M.-K.

Giaime, J.

Grote, H.

H. Grote and The GEO Collaboration, “The GEO 600 status,” Class. Quantum Grav. 27, 084003 (2010).

Grzanna, J.

Habraken, S.

S. Habraken and G. Nienhuis, “Modes of a twisted optical cavity,” Phys. Rev. A 75, 033819 (2007).
[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: Lasers Opt. 31, 97–105 (1983).
[CrossRef]

Harry, G. M.

G. M. Harry and The LIGO Scientific Collaboration, “Advanced LIGO: the next generation of gravitational wave detectors,” Class. Quantum Grav. 27, 084006 (2010).
[CrossRef]

Heefner, J.

R. L. Ward, R. Adhikari, B. Abbott, R. Abbott, D. Barron, R. Bork, T. Fricke, V. Frolov, J. Heefner, A. Ivanov, O. Miyakawa, K. McKenzie, B. Slagmolen, M. Smith, R. Taylor, S. Vass, S. Waldman, and A. Weinstein, “DC readout experiment at the Caltech 40 m prototype interferometer,” Class. Quantum Grav. 25, 114030 (2008).
[CrossRef]

Horikoshi, K.

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: Lasers Opt. 31, 97–105 (1983).
[CrossRef]

Ivanov, A.

R. L. Ward, R. Adhikari, B. Abbott, R. Abbott, D. Barron, R. Bork, T. Fricke, V. Frolov, J. Heefner, A. Ivanov, O. Miyakawa, K. McKenzie, B. Slagmolen, M. Smith, R. Taylor, S. Vass, S. Waldman, and A. Weinstein, “DC readout experiment at the Caltech 40 m prototype interferometer,” Class. Quantum Grav. 25, 114030 (2008).
[CrossRef]

Kawabe, K.

Kawamura, S.

King, P.

B. Willke, K. Danzmann, M. Frede, P. King, D. Kracht, P. Kwee, O. Puncken, R. L. Savage, B. Schulz, F. Seifert, C. Veltkamp, S. Wagner, P. Weels, and L. Winkelmann, “Stabilized lasers for advanced gravitational wave detectors,” Class. Quantum Grav. 25, 114040 (2008).
[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: Lasers Opt. 31, 97–105 (1983).
[CrossRef]

Kracht, D.

B. Willke, K. Danzmann, M. Frede, P. King, D. Kracht, P. Kwee, O. Puncken, R. L. Savage, B. Schulz, F. Seifert, C. Veltkamp, S. Wagner, P. Weels, and L. Winkelmann, “Stabilized lasers for advanced gravitational wave detectors,” Class. Quantum Grav. 25, 114040 (2008).
[CrossRef]

Kuroda, K.

K. Kuroda, “Status of LCGT,” Classical Quantum Gravity 27, 084004 (2010).
[CrossRef]

Kwee, P.

B. Willke, K. Danzmann, M. Frede, P. King, D. Kracht, P. Kwee, O. Puncken, R. L. Savage, B. Schulz, F. Seifert, C. Veltkamp, S. Wagner, P. Weels, and L. Winkelmann, “Stabilized lasers for advanced gravitational wave detectors,” Class. Quantum Grav. 25, 114040 (2008).
[CrossRef]

Mavalvala, N.

McKenzie, K.

R. L. Ward, R. Adhikari, B. Abbott, R. Abbott, D. Barron, R. Bork, T. Fricke, V. Frolov, J. Heefner, A. Ivanov, O. Miyakawa, K. McKenzie, B. Slagmolen, M. Smith, R. Taylor, S. Vass, S. Waldman, and A. Weinstein, “DC readout experiment at the Caltech 40 m prototype interferometer,” Class. Quantum Grav. 25, 114030 (2008).
[CrossRef]

Mio, N.

Miyakawa, O.

R. L. Ward, R. Adhikari, B. Abbott, R. Abbott, D. Barron, R. Bork, T. Fricke, V. Frolov, J. Heefner, A. Ivanov, O. Miyakawa, K. McKenzie, B. Slagmolen, M. Smith, R. Taylor, S. Vass, S. Waldman, and A. Weinstein, “DC readout experiment at the Caltech 40 m prototype interferometer,” Class. Quantum Grav. 25, 114030 (2008).
[CrossRef]

Miyoki, S.

Moriwaki, S.

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: Lasers Opt. 31, 97–105 (1983).
[CrossRef]

Musha, M.

Nagano, S.

Naito, Y.

Nienhuis, G.

S. Habraken and G. Nienhuis, “Modes of a twisted optical cavity,” Phys. Rev. A 75, 033819 (2007).
[CrossRef]

Puncken, O.

B. Willke, K. Danzmann, M. Frede, P. King, D. Kracht, P. Kwee, O. Puncken, R. L. Savage, B. Schulz, F. Seifert, C. Veltkamp, S. Wagner, P. Weels, and L. Winkelmann, “Stabilized lasers for advanced gravitational wave detectors,” Class. Quantum Grav. 25, 114040 (2008).
[CrossRef]

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 laser frequency variations,” Class. Quantum Grav. 21, S487–S492 (2004).
[CrossRef]

M. Rakhmanov, M. Evans, and H. Yamamoto, “An optical vernier technique for in situ measurement of the length of long Fabry–Perot cavities,” Meas. Sci. Technol. 10, 190–194 (1999).
[CrossRef]

Redding, D.

Regehr, M.

Robinson, S. R.

Savage, R. L.

B. Willke, K. Danzmann, M. Frede, P. King, D. Kracht, P. Kwee, O. Puncken, R. L. Savage, B. Schulz, F. Seifert, C. Veltkamp, S. Wagner, P. Weels, and L. Winkelmann, “Stabilized lasers for advanced gravitational wave detectors,” Class. Quantum Grav. 25, 114040 (2008).
[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 laser frequency variations,” Class. Quantum Grav. 21, S487–S492 (2004).
[CrossRef]

Schulz, B.

B. Willke, K. Danzmann, M. Frede, P. King, D. Kracht, P. Kwee, O. Puncken, R. L. Savage, B. Schulz, F. Seifert, C. Veltkamp, S. Wagner, P. Weels, and L. Winkelmann, “Stabilized lasers for advanced gravitational wave detectors,” Class. Quantum Grav. 25, 114040 (2008).
[CrossRef]

Schulz, G.

Seifert, F.

B. Willke, K. Danzmann, M. Frede, P. King, D. Kracht, P. Kwee, O. Puncken, R. L. Savage, B. Schulz, F. Seifert, C. Veltkamp, S. Wagner, P. Weels, and L. Winkelmann, “Stabilized lasers for advanced gravitational wave detectors,” Class. Quantum Grav. 25, 114040 (2008).
[CrossRef]

Shoemaker, D.

Siegman, A.

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

Sievers, L.

Sigg, D.

Slagmolen, B.

R. L. Ward, R. Adhikari, B. Abbott, R. Abbott, D. Barron, R. Bork, T. Fricke, V. Frolov, J. Heefner, A. Ivanov, O. Miyakawa, K. McKenzie, B. Slagmolen, M. Smith, R. Taylor, S. Vass, S. Waldman, and A. Weinstein, “DC readout experiment at the Caltech 40 m prototype interferometer,” Class. Quantum Grav. 25, 114030 (2008).
[CrossRef]

Smith, M.

R. L. Ward, R. Adhikari, B. Abbott, R. Abbott, D. Barron, R. Bork, T. Fricke, V. Frolov, J. Heefner, A. Ivanov, O. Miyakawa, K. McKenzie, B. Slagmolen, M. Smith, R. Taylor, S. Vass, S. Waldman, and A. Weinstein, “DC readout experiment at the Caltech 40 m prototype interferometer,” Class. Quantum Grav. 25, 114030 (2008).
[CrossRef]

Spolaczyk, R.

Stochino, A.

A. Stochino, “Design and characterization of optical cavities and length sensing and control system of an advanced gravitational wave interferometer,” Ph.D. thesis (University of Siena, 2010). LIGO Document P1000148, available at https://dcc.ligo.org .

Takahashi, R.

Takamori, A.

Taniguchi, S.

Tatsumi, D.

Taylor, R.

R. L. Ward, R. Adhikari, B. Abbott, R. Abbott, D. Barron, R. Bork, T. Fricke, V. Frolov, J. Heefner, A. Ivanov, O. Miyakawa, K. McKenzie, B. Slagmolen, M. Smith, R. Taylor, S. Vass, S. Waldman, and A. Weinstein, “DC readout experiment at the Caltech 40 m prototype interferometer,” Class. Quantum Grav. 25, 114030 (2008).
[CrossRef]

Telada, S.

Tochikubo, K.

Ueda, K.

Uehara, N.

Vass, S.

R. L. Ward, R. Adhikari, B. Abbott, R. Abbott, D. Barron, R. Bork, T. Fricke, V. Frolov, J. Heefner, A. Ivanov, O. Miyakawa, K. McKenzie, B. Slagmolen, M. Smith, R. Taylor, S. Vass, S. Waldman, and A. Weinstein, “DC readout experiment at the Caltech 40 m prototype interferometer,” Class. Quantum Grav. 25, 114030 (2008).
[CrossRef]

Veltkamp, C.

B. Willke, K. Danzmann, M. Frede, P. King, D. Kracht, P. Kwee, O. Puncken, R. L. Savage, B. Schulz, F. Seifert, C. Veltkamp, S. Wagner, P. Weels, and L. Winkelmann, “Stabilized lasers for advanced gravitational wave detectors,” Class. Quantum Grav. 25, 114040 (2008).
[CrossRef]

Vogel, A.

Wagner, S.

B. Willke, K. Danzmann, M. Frede, P. King, D. Kracht, P. Kwee, O. Puncken, R. L. Savage, B. Schulz, F. Seifert, C. Veltkamp, S. Wagner, P. Weels, and L. Winkelmann, “Stabilized lasers for advanced gravitational wave detectors,” Class. Quantum Grav. 25, 114040 (2008).
[CrossRef]

Waldman, S.

R. L. Ward, R. Adhikari, B. Abbott, R. Abbott, D. Barron, R. Bork, T. Fricke, V. Frolov, J. Heefner, A. Ivanov, O. Miyakawa, K. McKenzie, B. Slagmolen, M. Smith, R. Taylor, S. Vass, S. Waldman, and A. Weinstein, “DC readout experiment at the Caltech 40 m prototype interferometer,” Class. Quantum Grav. 25, 114030 (2008).
[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: Lasers Opt. 31, 97–105 (1983).
[CrossRef]

Ward, R. L.

R. L. Ward, R. Adhikari, B. Abbott, R. Abbott, D. Barron, R. Bork, T. Fricke, V. Frolov, J. Heefner, A. Ivanov, O. Miyakawa, K. McKenzie, B. Slagmolen, M. Smith, R. Taylor, S. Vass, S. Waldman, and A. Weinstein, “DC readout experiment at the Caltech 40 m prototype interferometer,” Class. Quantum Grav. 25, 114030 (2008).
[CrossRef]

R. L. Ward, “Length sensing and control of a prototype advanced interferometric gravitational wave detector,” Ph.D. thesis (California Institute of Technology, 2010).

Weels, P.

B. Willke, K. Danzmann, M. Frede, P. King, D. Kracht, P. Kwee, O. Puncken, R. L. Savage, B. Schulz, F. Seifert, C. Veltkamp, S. Wagner, P. Weels, and L. Winkelmann, “Stabilized lasers for advanced gravitational wave detectors,” Class. Quantum Grav. 25, 114040 (2008).
[CrossRef]

Weinstein, A.

R. L. Ward, R. Adhikari, B. Abbott, R. Abbott, D. Barron, R. Bork, T. Fricke, V. Frolov, J. Heefner, A. Ivanov, O. Miyakawa, K. McKenzie, B. Slagmolen, M. Smith, R. Taylor, S. Vass, S. Waldman, and A. Weinstein, “DC readout experiment at the Caltech 40 m prototype interferometer,” Class. Quantum Grav. 25, 114030 (2008).
[CrossRef]

A. Weinstein, “Advanced LIGO optical configuration and prototyping effort,” Class. Quantum Grav. 19, 1575–1584 (2002).
[CrossRef]

Willke, B.

B. Willke, K. Danzmann, M. Frede, P. King, D. Kracht, P. Kwee, O. Puncken, R. L. Savage, B. Schulz, F. Seifert, C. Veltkamp, S. Wagner, P. Weels, and L. Winkelmann, “Stabilized lasers for advanced gravitational wave detectors,” Class. Quantum Grav. 25, 114040 (2008).
[CrossRef]

Winkelmann, L.

B. Willke, K. Danzmann, M. Frede, P. King, D. Kracht, P. Kwee, O. Puncken, R. L. Savage, B. Schulz, F. Seifert, C. Veltkamp, S. Wagner, P. Weels, and L. Winkelmann, “Stabilized lasers for advanced gravitational wave detectors,” Class. Quantum Grav. 25, 114040 (2008).
[CrossRef]

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M. Rakhmanov, M. Evans, and H. Yamamoto, “An optical vernier technique for in situ measurement of the length of long Fabry–Perot cavities,” Meas. Sci. Technol. 10, 190–194 (1999).
[CrossRef]

Yamamoto, K.

Yamazaki, T.

Ye, J.

Appl. Opt. (8)

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Appl. Phys. B: Lasers Opt. (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: Lasers Opt. 31, 97–105 (1983).
[CrossRef]

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H. Grote and The GEO Collaboration, “The GEO 600 status,” Class. Quantum Grav. 27, 084003 (2010).

R. L. Ward, R. Adhikari, B. Abbott, R. Abbott, D. Barron, R. Bork, T. Fricke, V. Frolov, J. Heefner, A. Ivanov, O. Miyakawa, K. McKenzie, B. Slagmolen, M. Smith, R. Taylor, S. Vass, S. Waldman, and A. Weinstein, “DC readout experiment at the Caltech 40 m prototype interferometer,” Class. Quantum Grav. 25, 114030 (2008).
[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 laser frequency variations,” Class. Quantum Grav. 21, S487–S492 (2004).
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A. Weinstein, “Advanced LIGO optical configuration and prototyping effort,” Class. Quantum Grav. 19, 1575–1584 (2002).
[CrossRef]

G. M. Harry and The LIGO Scientific Collaboration, “Advanced LIGO: the next generation of gravitational wave detectors,” Class. Quantum Grav. 27, 084006 (2010).
[CrossRef]

B. Willke, K. Danzmann, M. Frede, P. King, D. Kracht, P. Kwee, O. Puncken, R. L. Savage, B. Schulz, F. Seifert, C. Veltkamp, S. Wagner, P. Weels, and L. Winkelmann, “Stabilized lasers for advanced gravitational wave detectors,” Class. Quantum Grav. 25, 114040 (2008).
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J. Phys.: Conf. Ser. (1)

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M. Rakhmanov, M. Evans, and H. Yamamoto, “An optical vernier technique for in situ measurement of the length of long Fabry–Perot cavities,” Meas. Sci. Technol. 10, 190–194 (1999).
[CrossRef]

Opt. Lett. (1)

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Figures (4)

Fig. 1.
Fig. 1.

Interferometer setup for the X arm measurement. While the arm to be measured is locked to laser 1 (main) by PDH locking, the rest of the interferometer is held misaligned. Laser 2 is phase-locked to laser 1, and it is then injected through the signal recycling mirror (SRM). A beat note is detected in transmission by a spectrum analyzer. Its amplitude is recorded as the PLL’s LO frequency and swept through several FSRs.

Fig. 2.
Fig. 2.

Laser frequency scan of a cavity resonance (left) and linear fit of 10 resonant frequencies (right).

Fig. 3.
Fig. 3.

Measurement of TMS in the Y arm. The curves are the results of the frequency scans for the horizontal and vertical modes, respectively. In the upper plot, the left peak is the cavity’s fundamental resonance, while the two peaks on the right are the resonances of the spatial modes (zoomed-in in the lower plots). A fit of the data points in these peaks (continuous lines) is used to determine their frequencies.

Fig. 4.
Fig. 4.

Frequency scan of the PRC: measured beat power (bold dots) and fitting curve (continuous line).

Tables (1)

Tables Icon

Table 1. Summary of Measurements on the Arm Cavities and on the PRCa

Equations (7)

Equations on this page are rendered with MathJax. Learn more.

νFSR=c2L,
νTMS=νFSRm+nπcos1g1g2,
g=g1g2.
νTMS=νFSR[mπcos1g1xg2x+nπcos1g1yg2y],
=mνTMS,x+nνTMS,y,
PPD(f)=P01+(ff0)2/fc2+Poff,
Tprc=|tprmritmei2Δωlprc/csin(Δωlasy/c)1+rprmritmei2Δωlprc/ccos(Δωlasy/c)|2,

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