Abstract

Long-baseline laser interferometers used for gravitational-wave detection have proven to be very complicated to control. In order to have sufficient sensitivity to astrophysical gravitational waves, a set of multiple coupled optical cavities comprising the interferometer must be brought into resonance with the laser field. A set of multi-input, multi-output servos then lock these cavities into place via feedback control. This procedure, known as lock acquisition, has proven to be a vexing problem and has reduced greatly the reliability and duty factor of the past generation of laser interferometers. In this article, we describe a technique for bringing the interferometer from an uncontrolled state into resonance by using harmonically related external fields to provide a deterministic hierarchical control. This technique reduces the effect of the external seismic disturbances by 4 orders of magnitude and promises to greatly enhance the stability and reliability of the current generation of gravitational-wave detectors. The possibility for using multicolor techniques to overcome current quantum and thermal noise limits is also discussed.

© 2012 Optical Society of America

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2012 (2)

2011 (3)

F. Khalili, S. Danilishin, H. Müller-Ebhardt, H. Miao, Y. Chen, and C. Zhao, “Negative optical inertia for enhancing the sensitivity of future gravitational-wave detectors,” Phys. Rev. D 83, 062003 (2011).
[CrossRef]

The Virgo Collaboration, “Status of the Virgo project,” Class. Quantum Grav. 28, 114002 (2011).
[CrossRef]

S. Schilt, N. Bucalovic, L. Tombez, V. Dolgovskiy, C. Schori, G. D. Domenico, M. Zaffalon, and P. Thomann, “Frequency discriminators for the characterization of narrow-spectrum heterodyne beat signals: Application to the measurement of a sub-hertz carrier-envelope-offset beat in an optical frequency comb,” Rev. Sci. Instrum. 82, 123116 (2011).
[CrossRef]

2010 (2)

The LCGT Collaboration, “Status of LCGT,” Class. Quantum Grav. 27, 084004 (2010).
[CrossRef]

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

2009 (1)

The LIGO Scientific Collaboration, “LIGO: the laser interferometer gravitational-wave observatory,” Rep. Prog. Phys. 72, 076901 (2009).
[CrossRef]

2008 (5)

The LIGO Scientific Collaboration, “The status of GEO 600,” Class. Quantum Grav. 25, 114043 (2008).
[CrossRef]

M. Evans, S. Ballmer, M. Fejer, P. Fritschel, G. Harry, and G. Ogin, “Thermo-optic noise in coated mirrors for high-precision optical measurements,” Phys. Rev. D 78, 102003 (2008).
[CrossRef]

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]

The Virgo Collaboration, “Lock acquisition of the Virgo gravitational wave detector,” Astropart. Phys. 30, 29–38 (2008).
[CrossRef]

K. Numata and J. Camp, “Interferometric testbed for nanometer level stabilization of environmental motion over long time scales,” Appl. Opt. 47, 6832–6841 (2008).
[CrossRef]

2007 (4)

G. M. Harry, M. R. Abernathy, A. E. Becerra-Toledo, H. Armandula, E. Black, K. Dooley, M. Eichenfield, C. Nwabugwu, A. Villar, D. R. M. Crooks, G. Cagnoli, J. Hough, C. R. How, I. MacLaren, P. Murray, S. Reid, S. Rowan, P. H. Sneddon, M. M. Fejer, R. Route, S. D. Penn, P. Ganau, J.-M. Mackowski, C. Michel, L. Pinard, and A. Remillieux, “Titania-doped tantala/silica coatings for gravitational-wave detection,” Class. Quantum Grav. 24, 405–415 (2007).
[CrossRef]

H. Rehbein, H. Müller-Ebhardt, K. Somiya, C. Li, R. Schnabel, K. Danzmann, and Y. Chen, “Local readout enhancement for detuned signal-recycling interferometers,” Phys. Rev. D 76, 062002 (2007).
[CrossRef]

O. P. Lay, S. Dubovitsky, D. A. Shaddock, and B. Ware, “Coherent range-gated laser displacement metrology with compact optical head,” Opt. Lett. 32, 2933–2935 (2007).
[CrossRef]

D. A. Shaddock, “Digitally enhanced heterodyne interferometry,” Opt. Lett. 32, 3355–3357 (2007).
[CrossRef]

2006 (2)

O. Miyakawa, R. Ward, R. Adhikari, B. Abbott, R. Bork, D. Busby, M. Evans, H. Grote, J. Heefner, A. Ivanov, S. Kawamura, F. Kawazoe, S. Sakata, M. Smith, R. Taylor, M. Varvella, S. Vass, and A. Weinstein, “Lock acquisition scheme for the advanced ligo optical configuration,” J. Phys. Conf. Ser. 32, 265 (2006).
[CrossRef]

O. Miyakawa, R. Ward, R. Adhikari, M. Evans, B. Abbott, R. Bork, D. Busby, J. Heefner, A. Ivanov, M. Smith, R. Taylor, S. Vass, A. Weinstein, M. Varvella, S. Kawamura, F. Kawazoe, S. Sakata, and C. Mow-Lowry, “Measurement of optical response of a detuned resonant sideband extraction gravitational wave detector,” Phys. Rev. D 74, 022001 (2006).
[CrossRef]

2004 (2)

S. Greenstein and M. Rosenbluh, “Dynamics of cw intra-cavity second harmonic generation by PPKTP,” Opt. Commun. 238, 319–327 (2004).
[CrossRef]

Y. Aso, M. Ando, K. Kawabe, S. Otsuka, and K. Tsubono, “Stabilization of a Fabry–Perot interferometer using a suspension-point interferometer,” Phys. Lett. A 327, 1–8 (2004).
[CrossRef]

2002 (2)

2000 (1)

G. González, “Suspensions thermal noise in the LIGO gravitational wave detector,” Class. Quantum Grav. 17, 4409–4435 (2000).
[CrossRef]

1995 (1)

1993 (1)

J. Mizuno, K. Strain, P. Nelson, J. Chen, R. Schilling, A. Rüdiger, W. Winkler, and K. Danzmann, “Resonant sideband extraction: a new configuration for interferometric gravitational wave detectors,” Phys. Lett. A 175, 273–276 (1993).
[CrossRef]

1992 (1)

A. Abramovici, W. E. Althouse, R. W. P. 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, and M. E. Zucker, “LIGO: the laser interferometer gravitational-wave observatory,” Science 256, 325–333 (1992).
[CrossRef]

1988 (1)

B. J. Meers, “Recycling in laser-interferometric gravitational-wave detectors,” Phys. Rev. D 38, 2317–2326 (1988).
[CrossRef]

1983 (1)

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

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]

O. Miyakawa, R. Ward, R. Adhikari, B. Abbott, R. Bork, D. Busby, M. Evans, H. Grote, J. Heefner, A. Ivanov, S. Kawamura, F. Kawazoe, S. Sakata, M. Smith, R. Taylor, M. Varvella, S. Vass, and A. Weinstein, “Lock acquisition scheme for the advanced ligo optical configuration,” J. Phys. Conf. Ser. 32, 265 (2006).
[CrossRef]

O. Miyakawa, R. Ward, R. Adhikari, M. Evans, B. Abbott, R. Bork, D. Busby, J. Heefner, A. Ivanov, M. Smith, R. Taylor, S. Vass, A. Weinstein, M. Varvella, S. Kawamura, F. Kawazoe, S. Sakata, and C. Mow-Lowry, “Measurement of optical response of a detuned resonant sideband extraction gravitational wave detector,” Phys. Rev. D 74, 022001 (2006).
[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]

Abernathy, M. R.

G. M. Harry, M. R. Abernathy, A. E. Becerra-Toledo, H. Armandula, E. Black, K. Dooley, M. Eichenfield, C. Nwabugwu, A. Villar, D. R. M. Crooks, G. Cagnoli, J. Hough, C. R. How, I. MacLaren, P. Murray, S. Reid, S. Rowan, P. H. Sneddon, M. M. Fejer, R. Route, S. D. Penn, P. Ganau, J.-M. Mackowski, C. Michel, L. Pinard, and A. Remillieux, “Titania-doped tantala/silica coatings for gravitational-wave detection,” Class. Quantum Grav. 24, 405–415 (2007).
[CrossRef]

Abramovici, A.

A. Abramovici, W. E. Althouse, R. W. P. 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, and M. E. Zucker, “LIGO: the laser interferometer gravitational-wave observatory,” Science 256, 325–333 (1992).
[CrossRef]

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]

O. Miyakawa, R. Ward, R. Adhikari, M. Evans, B. Abbott, R. Bork, D. Busby, J. Heefner, A. Ivanov, M. Smith, R. Taylor, S. Vass, A. Weinstein, M. Varvella, S. Kawamura, F. Kawazoe, S. Sakata, and C. Mow-Lowry, “Measurement of optical response of a detuned resonant sideband extraction gravitational wave detector,” Phys. Rev. D 74, 022001 (2006).
[CrossRef]

O. Miyakawa, R. Ward, R. Adhikari, B. Abbott, R. Bork, D. Busby, M. Evans, H. Grote, J. Heefner, A. Ivanov, S. Kawamura, F. Kawazoe, S. Sakata, M. Smith, R. Taylor, M. Varvella, S. Vass, and A. Weinstein, “Lock acquisition scheme for the advanced ligo optical configuration,” J. Phys. Conf. Ser. 32, 265 (2006).
[CrossRef]

D. Yeaton-Massey and R. Adhikari, “A new bound on excess frequency noise in second harmonic generation in PPKTP at the 10−19 level,” Opt. Express20, 21019–21024 (2012).

Althouse, W. E.

A. Abramovici, W. E. Althouse, R. W. P. 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, and M. E. Zucker, “LIGO: the laser interferometer gravitational-wave observatory,” Science 256, 325–333 (1992).
[CrossRef]

Ando, M.

Y. Aso, M. Ando, K. Kawabe, S. Otsuka, and K. Tsubono, “Stabilization of a Fabry–Perot interferometer using a suspension-point interferometer,” Phys. Lett. A 327, 1–8 (2004).
[CrossRef]

Armandula, H.

G. M. Harry, M. R. Abernathy, A. E. Becerra-Toledo, H. Armandula, E. Black, K. Dooley, M. Eichenfield, C. Nwabugwu, A. Villar, D. R. M. Crooks, G. Cagnoli, J. Hough, C. R. How, I. MacLaren, P. Murray, S. Reid, S. Rowan, P. H. Sneddon, M. M. Fejer, R. Route, S. D. Penn, P. Ganau, J.-M. Mackowski, C. Michel, L. Pinard, and A. Remillieux, “Titania-doped tantala/silica coatings for gravitational-wave detection,” Class. Quantum Grav. 24, 405–415 (2007).
[CrossRef]

Aso, Y.

Y. Aso, M. Ando, K. Kawabe, S. Otsuka, and K. Tsubono, “Stabilization of a Fabry–Perot interferometer using a suspension-point interferometer,” Phys. Lett. A 327, 1–8 (2004).
[CrossRef]

Ballmer, S.

M. Evans, S. Ballmer, M. Fejer, P. Fritschel, G. Harry, and G. Ogin, “Thermo-optic noise in coated mirrors for high-precision optical measurements,” Phys. Rev. D 78, 102003 (2008).
[CrossRef]

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]

Becerra-Toledo, A. E.

G. M. Harry, M. R. Abernathy, A. E. Becerra-Toledo, H. Armandula, E. Black, K. Dooley, M. Eichenfield, C. Nwabugwu, A. Villar, D. R. M. Crooks, G. Cagnoli, J. Hough, C. R. How, I. MacLaren, P. Murray, S. Reid, S. Rowan, P. H. Sneddon, M. M. Fejer, R. Route, S. D. Penn, P. Ganau, J.-M. Mackowski, C. Michel, L. Pinard, and A. Remillieux, “Titania-doped tantala/silica coatings for gravitational-wave detection,” Class. Quantum Grav. 24, 405–415 (2007).
[CrossRef]

Bhawal, B.

Black, E.

G. M. Harry, M. R. Abernathy, A. E. Becerra-Toledo, H. Armandula, E. Black, K. Dooley, M. Eichenfield, C. Nwabugwu, A. Villar, D. R. M. Crooks, G. Cagnoli, J. Hough, C. R. How, I. MacLaren, P. Murray, S. Reid, S. Rowan, P. H. Sneddon, M. M. Fejer, R. Route, S. D. Penn, P. Ganau, J.-M. Mackowski, C. Michel, L. Pinard, and A. Remillieux, “Titania-doped tantala/silica coatings for gravitational-wave detection,” Class. Quantum Grav. 24, 405–415 (2007).
[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]

O. Miyakawa, R. Ward, R. Adhikari, M. Evans, B. Abbott, R. Bork, D. Busby, J. Heefner, A. Ivanov, M. Smith, R. Taylor, S. Vass, A. Weinstein, M. Varvella, S. Kawamura, F. Kawazoe, S. Sakata, and C. Mow-Lowry, “Measurement of optical response of a detuned resonant sideband extraction gravitational wave detector,” Phys. Rev. D 74, 022001 (2006).
[CrossRef]

O. Miyakawa, R. Ward, R. Adhikari, B. Abbott, R. Bork, D. Busby, M. Evans, H. Grote, J. Heefner, A. Ivanov, S. Kawamura, F. Kawazoe, S. Sakata, M. Smith, R. Taylor, M. Varvella, S. Vass, and A. Weinstein, “Lock acquisition scheme for the advanced ligo optical configuration,” J. Phys. Conf. Ser. 32, 265 (2006).
[CrossRef]

M. Evans, N. Mavalvala, P. Fritschel, R. Bork, B. Bhawal, R. Gustafson, W. Kells, M. Landry, D. Sigg, R. Weiss, S. Whitcomb, and H. Yamamoto, “Lock acquisition of a gravitational-wave interferometer,” Opt. Lett. 27, 598–600 (2002).
[CrossRef]

J. Camp, L. Sievers, R. Bork, and J. Heefner, “Guided lock acquisition in a suspended Fabry–Perot cavity,” Opt. Lett. 20, 2463–2465 (1995).
[CrossRef]

Bucalovic, N.

S. Schilt, N. Bucalovic, L. Tombez, V. Dolgovskiy, C. Schori, G. D. Domenico, M. Zaffalon, and P. Thomann, “Frequency discriminators for the characterization of narrow-spectrum heterodyne beat signals: Application to the measurement of a sub-hertz carrier-envelope-offset beat in an optical frequency comb,” Rev. Sci. Instrum. 82, 123116 (2011).
[CrossRef]

Buonanno, A.

A. Buonanno and Y. Chen, “Signal recycled laser-interferometer gravitational-wave detectors as optical springs,” Phys. Rev. D 65, 042001 (2002).
[CrossRef]

Busby, D.

O. Miyakawa, R. Ward, R. Adhikari, B. Abbott, R. Bork, D. Busby, M. Evans, H. Grote, J. Heefner, A. Ivanov, S. Kawamura, F. Kawazoe, S. Sakata, M. Smith, R. Taylor, M. Varvella, S. Vass, and A. Weinstein, “Lock acquisition scheme for the advanced ligo optical configuration,” J. Phys. Conf. Ser. 32, 265 (2006).
[CrossRef]

O. Miyakawa, R. Ward, R. Adhikari, M. Evans, B. Abbott, R. Bork, D. Busby, J. Heefner, A. Ivanov, M. Smith, R. Taylor, S. Vass, A. Weinstein, M. Varvella, S. Kawamura, F. Kawazoe, S. Sakata, and C. Mow-Lowry, “Measurement of optical response of a detuned resonant sideband extraction gravitational wave detector,” Phys. Rev. D 74, 022001 (2006).
[CrossRef]

Cagnoli, G.

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H. Rehbein, H. Müller-Ebhardt, K. Somiya, C. Li, R. Schnabel, K. Danzmann, and Y. Chen, “Local readout enhancement for detuned signal-recycling interferometers,” Phys. Rev. D 76, 062002 (2007).
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J. Mizuno, K. Strain, P. Nelson, J. Chen, R. Schilling, A. Rüdiger, W. Winkler, and K. Danzmann, “Resonant sideband extraction: a new configuration for interferometric gravitational wave detectors,” Phys. Lett. A 175, 273–276 (1993).
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G. M. Harry, M. R. Abernathy, A. E. Becerra-Toledo, H. Armandula, E. Black, K. Dooley, M. Eichenfield, C. Nwabugwu, A. Villar, D. R. M. Crooks, G. Cagnoli, J. Hough, C. R. How, I. MacLaren, P. Murray, S. Reid, S. Rowan, P. H. Sneddon, M. M. Fejer, R. Route, S. D. Penn, P. Ganau, J.-M. Mackowski, C. Michel, L. Pinard, and A. Remillieux, “Titania-doped tantala/silica coatings for gravitational-wave detection,” Class. Quantum Grav. 24, 405–415 (2007).
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A. Abramovici, W. E. Althouse, R. W. P. 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, and M. E. Zucker, “LIGO: the laser interferometer gravitational-wave observatory,” Science 256, 325–333 (1992).
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R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, “Laser phase and frequency stabilization using an optical resonator,” Appl. Phys. B 31, 97–105 (1983).
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Eichenfield, M.

G. M. Harry, M. R. Abernathy, A. E. Becerra-Toledo, H. Armandula, E. Black, K. Dooley, M. Eichenfield, C. Nwabugwu, A. Villar, D. R. M. Crooks, G. Cagnoli, J. Hough, C. R. How, I. MacLaren, P. Murray, S. Reid, S. Rowan, P. H. Sneddon, M. M. Fejer, R. Route, S. D. Penn, P. Ganau, J.-M. Mackowski, C. Michel, L. Pinard, and A. Remillieux, “Titania-doped tantala/silica coatings for gravitational-wave detection,” Class. Quantum Grav. 24, 405–415 (2007).
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A. J. Mullavey, B. J. J. Slagmolen, J. Miller, M. Evans, P. Fritschel, D. Sigg, S. J. Waldman, D. A. Shaddock, and D. E. McClelland, “Arm-length stabilisation for interferometric gravitational-wave detectors using frequency-doubled auxiliary lasers,” Opt. Express 20, 81–89 (2012).
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M. Evans, S. Ballmer, M. Fejer, P. Fritschel, G. Harry, and G. Ogin, “Thermo-optic noise in coated mirrors for high-precision optical measurements,” Phys. Rev. D 78, 102003 (2008).
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O. Miyakawa, R. Ward, R. Adhikari, B. Abbott, R. Bork, D. Busby, M. Evans, H. Grote, J. Heefner, A. Ivanov, S. Kawamura, F. Kawazoe, S. Sakata, M. Smith, R. Taylor, M. Varvella, S. Vass, and A. Weinstein, “Lock acquisition scheme for the advanced ligo optical configuration,” J. Phys. Conf. Ser. 32, 265 (2006).
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O. Miyakawa, R. Ward, R. Adhikari, M. Evans, B. Abbott, R. Bork, D. Busby, J. Heefner, A. Ivanov, M. Smith, R. Taylor, S. Vass, A. Weinstein, M. Varvella, S. Kawamura, F. Kawazoe, S. Sakata, and C. Mow-Lowry, “Measurement of optical response of a detuned resonant sideband extraction gravitational wave detector,” Phys. Rev. D 74, 022001 (2006).
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M. Evans, S. Ballmer, M. Fejer, P. Fritschel, G. Harry, and G. Ogin, “Thermo-optic noise in coated mirrors for high-precision optical measurements,” Phys. Rev. D 78, 102003 (2008).
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Fejer, M. M.

G. M. Harry, M. R. Abernathy, A. E. Becerra-Toledo, H. Armandula, E. Black, K. Dooley, M. Eichenfield, C. Nwabugwu, A. Villar, D. R. M. Crooks, G. Cagnoli, J. Hough, C. R. How, I. MacLaren, P. Murray, S. Reid, S. Rowan, P. H. Sneddon, M. M. Fejer, R. Route, S. D. Penn, P. Ganau, J.-M. Mackowski, C. Michel, L. Pinard, and A. Remillieux, “Titania-doped tantala/silica coatings for gravitational-wave detection,” Class. Quantum Grav. 24, 405–415 (2007).
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R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, “Laser phase and frequency stabilization using an optical resonator,” Appl. Phys. B 31, 97–105 (1983).
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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).
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A. J. Mullavey, B. J. J. Slagmolen, J. Miller, M. Evans, P. Fritschel, D. Sigg, S. J. Waldman, D. A. Shaddock, and D. E. McClelland, “Arm-length stabilisation for interferometric gravitational-wave detectors using frequency-doubled auxiliary lasers,” Opt. Express 20, 81–89 (2012).
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M. Evans, S. Ballmer, M. Fejer, P. Fritschel, G. Harry, and G. Ogin, “Thermo-optic noise in coated mirrors for high-precision optical measurements,” Phys. Rev. D 78, 102003 (2008).
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M. Evans, N. Mavalvala, P. Fritschel, R. Bork, B. Bhawal, R. Gustafson, W. Kells, M. Landry, D. Sigg, R. Weiss, S. Whitcomb, and H. Yamamoto, “Lock acquisition of a gravitational-wave interferometer,” Opt. Lett. 27, 598–600 (2002).
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P. Fritschel, D. McClelland, A. Mullavey, D. Shaddock, B. Slagmolen, and S. Waldman, “Advanced LIGO arm length stabilisation requirements,” LIGO DCC T0900095-v2 (LIGO Document Control Center, 2009).

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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).
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A. Abramovici, W. E. Althouse, R. W. P. 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, and M. E. Zucker, “LIGO: the laser interferometer gravitational-wave observatory,” Science 256, 325–333 (1992).
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Gustafson, R.

Hall, J. L.

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, “Laser phase and frequency stabilization using an optical resonator,” Appl. Phys. B 31, 97–105 (1983).
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M. Evans, S. Ballmer, M. Fejer, P. Fritschel, G. Harry, and G. Ogin, “Thermo-optic noise in coated mirrors for high-precision optical measurements,” Phys. Rev. D 78, 102003 (2008).
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Harry, G. M.

G. M. Harry, M. R. Abernathy, A. E. Becerra-Toledo, H. Armandula, E. Black, K. Dooley, M. Eichenfield, C. Nwabugwu, A. Villar, D. R. M. Crooks, G. Cagnoli, J. Hough, C. R. How, I. MacLaren, P. Murray, S. Reid, S. Rowan, P. H. Sneddon, M. M. Fejer, R. Route, S. D. Penn, P. Ganau, J.-M. Mackowski, C. Michel, L. Pinard, and A. Remillieux, “Titania-doped tantala/silica coatings for gravitational-wave detection,” Class. Quantum Grav. 24, 405–415 (2007).
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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).
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O. Miyakawa, R. Ward, R. Adhikari, B. Abbott, R. Bork, D. Busby, M. Evans, H. Grote, J. Heefner, A. Ivanov, S. Kawamura, F. Kawazoe, S. Sakata, M. Smith, R. Taylor, M. Varvella, S. Vass, and A. Weinstein, “Lock acquisition scheme for the advanced ligo optical configuration,” J. Phys. Conf. Ser. 32, 265 (2006).
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O. Miyakawa, R. Ward, R. Adhikari, M. Evans, B. Abbott, R. Bork, D. Busby, J. Heefner, A. Ivanov, M. Smith, R. Taylor, S. Vass, A. Weinstein, M. Varvella, S. Kawamura, F. Kawazoe, S. Sakata, and C. Mow-Lowry, “Measurement of optical response of a detuned resonant sideband extraction gravitational wave detector,” Phys. Rev. D 74, 022001 (2006).
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G. M. Harry, M. R. Abernathy, A. E. Becerra-Toledo, H. Armandula, E. Black, K. Dooley, M. Eichenfield, C. Nwabugwu, A. Villar, D. R. M. Crooks, G. Cagnoli, J. Hough, C. R. How, I. MacLaren, P. Murray, S. Reid, S. Rowan, P. H. Sneddon, M. M. Fejer, R. Route, S. D. Penn, P. Ganau, J.-M. Mackowski, C. Michel, L. Pinard, and A. Remillieux, “Titania-doped tantala/silica coatings for gravitational-wave detection,” Class. Quantum Grav. 24, 405–415 (2007).
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R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, “Laser phase and frequency stabilization using an optical resonator,” Appl. Phys. B 31, 97–105 (1983).
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G. M. Harry, M. R. Abernathy, A. E. Becerra-Toledo, H. Armandula, E. Black, K. Dooley, M. Eichenfield, C. Nwabugwu, A. Villar, D. R. M. Crooks, G. Cagnoli, J. Hough, C. R. How, I. MacLaren, P. Murray, S. Reid, S. Rowan, P. H. Sneddon, M. M. Fejer, R. Route, S. D. Penn, P. Ganau, J.-M. Mackowski, C. Michel, L. Pinard, and A. Remillieux, “Titania-doped tantala/silica coatings for gravitational-wave detection,” Class. Quantum Grav. 24, 405–415 (2007).
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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).
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O. Miyakawa, R. Ward, R. Adhikari, M. Evans, B. Abbott, R. Bork, D. Busby, J. Heefner, A. Ivanov, M. Smith, R. Taylor, S. Vass, A. Weinstein, M. Varvella, S. Kawamura, F. Kawazoe, S. Sakata, and C. Mow-Lowry, “Measurement of optical response of a detuned resonant sideband extraction gravitational wave detector,” Phys. Rev. D 74, 022001 (2006).
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O. Miyakawa, R. Ward, R. Adhikari, B. Abbott, R. Bork, D. Busby, M. Evans, H. Grote, J. Heefner, A. Ivanov, S. Kawamura, F. Kawazoe, S. Sakata, M. Smith, R. Taylor, M. Varvella, S. Vass, and A. Weinstein, “Lock acquisition scheme for the advanced ligo optical configuration,” J. Phys. Conf. Ser. 32, 265 (2006).
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O. Miyakawa, R. Ward, R. Adhikari, B. Abbott, R. Bork, D. Busby, M. Evans, H. Grote, J. Heefner, A. Ivanov, S. Kawamura, F. Kawazoe, S. Sakata, M. Smith, R. Taylor, M. Varvella, S. Vass, and A. Weinstein, “Lock acquisition scheme for the advanced ligo optical configuration,” J. Phys. Conf. Ser. 32, 265 (2006).
[CrossRef]

O. Miyakawa, R. Ward, R. Adhikari, M. Evans, B. Abbott, R. Bork, D. Busby, J. Heefner, A. Ivanov, M. Smith, R. Taylor, S. Vass, A. Weinstein, M. Varvella, S. Kawamura, F. Kawazoe, S. Sakata, and C. Mow-Lowry, “Measurement of optical response of a detuned resonant sideband extraction gravitational wave detector,” Phys. Rev. D 74, 022001 (2006).
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A. Abramovici, W. E. Althouse, R. W. P. 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, and M. E. Zucker, “LIGO: the laser interferometer gravitational-wave observatory,” Science 256, 325–333 (1992).
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O. Miyakawa, R. Ward, R. Adhikari, M. Evans, B. Abbott, R. Bork, D. Busby, J. Heefner, A. Ivanov, M. Smith, R. Taylor, S. Vass, A. Weinstein, M. Varvella, S. Kawamura, F. Kawazoe, S. Sakata, and C. Mow-Lowry, “Measurement of optical response of a detuned resonant sideband extraction gravitational wave detector,” Phys. Rev. D 74, 022001 (2006).
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O. Miyakawa, R. Ward, R. Adhikari, B. Abbott, R. Bork, D. Busby, M. Evans, H. Grote, J. Heefner, A. Ivanov, S. Kawamura, F. Kawazoe, S. Sakata, M. Smith, R. Taylor, M. Varvella, S. Vass, and A. Weinstein, “Lock acquisition scheme for the advanced ligo optical configuration,” J. Phys. Conf. Ser. 32, 265 (2006).
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Kells, W.

Khalili, F.

F. Khalili, S. Danilishin, H. Müller-Ebhardt, H. Miao, Y. Chen, and C. Zhao, “Negative optical inertia for enhancing the sensitivity of future gravitational-wave detectors,” Phys. Rev. D 83, 062003 (2011).
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R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, “Laser phase and frequency stabilization using an optical resonator,” Appl. Phys. B 31, 97–105 (1983).
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Landry, M.

Lay, O. P.

Li, C.

H. Rehbein, H. Müller-Ebhardt, K. Somiya, C. Li, R. Schnabel, K. Danzmann, and Y. Chen, “Local readout enhancement for detuned signal-recycling interferometers,” Phys. Rev. D 76, 062002 (2007).
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G. M. Harry, M. R. Abernathy, A. E. Becerra-Toledo, H. Armandula, E. Black, K. Dooley, M. Eichenfield, C. Nwabugwu, A. Villar, D. R. M. Crooks, G. Cagnoli, J. Hough, C. R. How, I. MacLaren, P. Murray, S. Reid, S. Rowan, P. H. Sneddon, M. M. Fejer, R. Route, S. D. Penn, P. Ganau, J.-M. Mackowski, C. Michel, L. Pinard, and A. Remillieux, “Titania-doped tantala/silica coatings for gravitational-wave detection,” Class. Quantum Grav. 24, 405–415 (2007).
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G. M. Harry, M. R. Abernathy, A. E. Becerra-Toledo, H. Armandula, E. Black, K. Dooley, M. Eichenfield, C. Nwabugwu, A. Villar, D. R. M. Crooks, G. Cagnoli, J. Hough, C. R. How, I. MacLaren, P. Murray, S. Reid, S. Rowan, P. H. Sneddon, M. M. Fejer, R. Route, S. D. Penn, P. Ganau, J.-M. Mackowski, C. Michel, L. Pinard, and A. Remillieux, “Titania-doped tantala/silica coatings for gravitational-wave detection,” Class. Quantum Grav. 24, 405–415 (2007).
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McClelland, D.

P. Fritschel, D. McClelland, A. Mullavey, D. Shaddock, B. Slagmolen, and S. Waldman, “Advanced LIGO arm length stabilisation requirements,” LIGO DCC T0900095-v2 (LIGO Document Control Center, 2009).

McClelland, D. E.

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).
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G. M. Harry, M. R. Abernathy, A. E. Becerra-Toledo, H. Armandula, E. Black, K. Dooley, M. Eichenfield, C. Nwabugwu, A. Villar, D. R. M. Crooks, G. Cagnoli, J. Hough, C. R. How, I. MacLaren, P. Murray, S. Reid, S. Rowan, P. H. Sneddon, M. M. Fejer, R. Route, S. D. Penn, P. Ganau, J.-M. Mackowski, C. Michel, L. Pinard, and A. Remillieux, “Titania-doped tantala/silica coatings for gravitational-wave detection,” Class. Quantum Grav. 24, 405–415 (2007).
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Miller, J.

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).
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O. Miyakawa, R. Ward, R. Adhikari, B. Abbott, R. Bork, D. Busby, M. Evans, H. Grote, J. Heefner, A. Ivanov, S. Kawamura, F. Kawazoe, S. Sakata, M. Smith, R. Taylor, M. Varvella, S. Vass, and A. Weinstein, “Lock acquisition scheme for the advanced ligo optical configuration,” J. Phys. Conf. Ser. 32, 265 (2006).
[CrossRef]

O. Miyakawa, R. Ward, R. Adhikari, M. Evans, B. Abbott, R. Bork, D. Busby, J. Heefner, A. Ivanov, M. Smith, R. Taylor, S. Vass, A. Weinstein, M. Varvella, S. Kawamura, F. Kawazoe, S. Sakata, and C. Mow-Lowry, “Measurement of optical response of a detuned resonant sideband extraction gravitational wave detector,” Phys. Rev. D 74, 022001 (2006).
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Mizuno, J.

J. Mizuno, K. Strain, P. Nelson, J. Chen, R. Schilling, A. Rüdiger, W. Winkler, and K. Danzmann, “Resonant sideband extraction: a new configuration for interferometric gravitational wave detectors,” Phys. Lett. A 175, 273–276 (1993).
[CrossRef]

Mow-Lowry, C.

O. Miyakawa, R. Ward, R. Adhikari, M. Evans, B. Abbott, R. Bork, D. Busby, J. Heefner, A. Ivanov, M. Smith, R. Taylor, S. Vass, A. Weinstein, M. Varvella, S. Kawamura, F. Kawazoe, S. Sakata, and C. Mow-Lowry, “Measurement of optical response of a detuned resonant sideband extraction gravitational wave detector,” Phys. Rev. D 74, 022001 (2006).
[CrossRef]

Mullavey, A.

P. Fritschel, D. McClelland, A. Mullavey, D. Shaddock, B. Slagmolen, and S. Waldman, “Advanced LIGO arm length stabilisation requirements,” LIGO DCC T0900095-v2 (LIGO Document Control Center, 2009).

Mullavey, A. J.

Müller-Ebhardt, H.

F. Khalili, S. Danilishin, H. Müller-Ebhardt, H. Miao, Y. Chen, and C. Zhao, “Negative optical inertia for enhancing the sensitivity of future gravitational-wave detectors,” Phys. Rev. D 83, 062003 (2011).
[CrossRef]

H. Rehbein, H. Müller-Ebhardt, K. Somiya, C. Li, R. Schnabel, K. Danzmann, and Y. Chen, “Local readout enhancement for detuned signal-recycling interferometers,” Phys. Rev. D 76, 062002 (2007).
[CrossRef]

Munley, A. J.

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

Murray, P.

G. M. Harry, M. R. Abernathy, A. E. Becerra-Toledo, H. Armandula, E. Black, K. Dooley, M. Eichenfield, C. Nwabugwu, A. Villar, D. R. M. Crooks, G. Cagnoli, J. Hough, C. R. How, I. MacLaren, P. Murray, S. Reid, S. Rowan, P. H. Sneddon, M. M. Fejer, R. Route, S. D. Penn, P. Ganau, J.-M. Mackowski, C. Michel, L. Pinard, and A. Remillieux, “Titania-doped tantala/silica coatings for gravitational-wave detection,” Class. Quantum Grav. 24, 405–415 (2007).
[CrossRef]

Nelson, P.

J. Mizuno, K. Strain, P. Nelson, J. Chen, R. Schilling, A. Rüdiger, W. Winkler, and K. Danzmann, “Resonant sideband extraction: a new configuration for interferometric gravitational wave detectors,” Phys. Lett. A 175, 273–276 (1993).
[CrossRef]

Numata, K.

Nwabugwu, C.

G. M. Harry, M. R. Abernathy, A. E. Becerra-Toledo, H. Armandula, E. Black, K. Dooley, M. Eichenfield, C. Nwabugwu, A. Villar, D. R. M. Crooks, G. Cagnoli, J. Hough, C. R. How, I. MacLaren, P. Murray, S. Reid, S. Rowan, P. H. Sneddon, M. M. Fejer, R. Route, S. D. Penn, P. Ganau, J.-M. Mackowski, C. Michel, L. Pinard, and A. Remillieux, “Titania-doped tantala/silica coatings for gravitational-wave detection,” Class. Quantum Grav. 24, 405–415 (2007).
[CrossRef]

Ogin, G.

M. Evans, S. Ballmer, M. Fejer, P. Fritschel, G. Harry, and G. Ogin, “Thermo-optic noise in coated mirrors for high-precision optical measurements,” Phys. Rev. D 78, 102003 (2008).
[CrossRef]

Otsuka, S.

Y. Aso, M. Ando, K. Kawabe, S. Otsuka, and K. Tsubono, “Stabilization of a Fabry–Perot interferometer using a suspension-point interferometer,” Phys. Lett. A 327, 1–8 (2004).
[CrossRef]

Penn, S. D.

G. M. Harry, M. R. Abernathy, A. E. Becerra-Toledo, H. Armandula, E. Black, K. Dooley, M. Eichenfield, C. Nwabugwu, A. Villar, D. R. M. Crooks, G. Cagnoli, J. Hough, C. R. How, I. MacLaren, P. Murray, S. Reid, S. Rowan, P. H. Sneddon, M. M. Fejer, R. Route, S. D. Penn, P. Ganau, J.-M. Mackowski, C. Michel, L. Pinard, and A. Remillieux, “Titania-doped tantala/silica coatings for gravitational-wave detection,” Class. Quantum Grav. 24, 405–415 (2007).
[CrossRef]

Pierro, V.

M. Principe, I. M. Pinto, V. Pierro, and R. DeSalvo, “Minimum Brownian noise dichroic dielectric mirror coatings for AdLIGO,” LIGO DCC T080337-v1 (LIGO Document Control Center, 2008).

Pinard, L.

G. M. Harry, M. R. Abernathy, A. E. Becerra-Toledo, H. Armandula, E. Black, K. Dooley, M. Eichenfield, C. Nwabugwu, A. Villar, D. R. M. Crooks, G. Cagnoli, J. Hough, C. R. How, I. MacLaren, P. Murray, S. Reid, S. Rowan, P. H. Sneddon, M. M. Fejer, R. Route, S. D. Penn, P. Ganau, J.-M. Mackowski, C. Michel, L. Pinard, and A. Remillieux, “Titania-doped tantala/silica coatings for gravitational-wave detection,” Class. Quantum Grav. 24, 405–415 (2007).
[CrossRef]

Pinto, I. M.

M. Principe, I. M. Pinto, V. Pierro, and R. DeSalvo, “Minimum Brownian noise dichroic dielectric mirror coatings for AdLIGO,” LIGO DCC T080337-v1 (LIGO Document Control Center, 2008).

Principe, M.

M. Principe, I. M. Pinto, V. Pierro, and R. DeSalvo, “Minimum Brownian noise dichroic dielectric mirror coatings for AdLIGO,” LIGO DCC T080337-v1 (LIGO Document Control Center, 2008).

Raab, F. J.

A. Abramovici, W. E. Althouse, R. W. P. 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, and M. E. Zucker, “LIGO: the laser interferometer gravitational-wave observatory,” Science 256, 325–333 (1992).
[CrossRef]

Rehbein, H.

H. Rehbein, H. Müller-Ebhardt, K. Somiya, C. Li, R. Schnabel, K. Danzmann, and Y. Chen, “Local readout enhancement for detuned signal-recycling interferometers,” Phys. Rev. D 76, 062002 (2007).
[CrossRef]

Reid, S.

G. M. Harry, M. R. Abernathy, A. E. Becerra-Toledo, H. Armandula, E. Black, K. Dooley, M. Eichenfield, C. Nwabugwu, A. Villar, D. R. M. Crooks, G. Cagnoli, J. Hough, C. R. How, I. MacLaren, P. Murray, S. Reid, S. Rowan, P. H. Sneddon, M. M. Fejer, R. Route, S. D. Penn, P. Ganau, J.-M. Mackowski, C. Michel, L. Pinard, and A. Remillieux, “Titania-doped tantala/silica coatings for gravitational-wave detection,” Class. Quantum Grav. 24, 405–415 (2007).
[CrossRef]

Remillieux, A.

G. M. Harry, M. R. Abernathy, A. E. Becerra-Toledo, H. Armandula, E. Black, K. Dooley, M. Eichenfield, C. Nwabugwu, A. Villar, D. R. M. Crooks, G. Cagnoli, J. Hough, C. R. How, I. MacLaren, P. Murray, S. Reid, S. Rowan, P. H. Sneddon, M. M. Fejer, R. Route, S. D. Penn, P. Ganau, J.-M. Mackowski, C. Michel, L. Pinard, and A. Remillieux, “Titania-doped tantala/silica coatings for gravitational-wave detection,” Class. Quantum Grav. 24, 405–415 (2007).
[CrossRef]

Rosenbluh, M.

S. Greenstein and M. Rosenbluh, “Dynamics of cw intra-cavity second harmonic generation by PPKTP,” Opt. Commun. 238, 319–327 (2004).
[CrossRef]

Route, R.

G. M. Harry, M. R. Abernathy, A. E. Becerra-Toledo, H. Armandula, E. Black, K. Dooley, M. Eichenfield, C. Nwabugwu, A. Villar, D. R. M. Crooks, G. Cagnoli, J. Hough, C. R. How, I. MacLaren, P. Murray, S. Reid, S. Rowan, P. H. Sneddon, M. M. Fejer, R. Route, S. D. Penn, P. Ganau, J.-M. Mackowski, C. Michel, L. Pinard, and A. Remillieux, “Titania-doped tantala/silica coatings for gravitational-wave detection,” Class. Quantum Grav. 24, 405–415 (2007).
[CrossRef]

Rowan, S.

G. M. Harry, M. R. Abernathy, A. E. Becerra-Toledo, H. Armandula, E. Black, K. Dooley, M. Eichenfield, C. Nwabugwu, A. Villar, D. R. M. Crooks, G. Cagnoli, J. Hough, C. R. How, I. MacLaren, P. Murray, S. Reid, S. Rowan, P. H. Sneddon, M. M. Fejer, R. Route, S. D. Penn, P. Ganau, J.-M. Mackowski, C. Michel, L. Pinard, and A. Remillieux, “Titania-doped tantala/silica coatings for gravitational-wave detection,” Class. Quantum Grav. 24, 405–415 (2007).
[CrossRef]

Rüdiger, A.

J. Mizuno, K. Strain, P. Nelson, J. Chen, R. Schilling, A. Rüdiger, W. Winkler, and K. Danzmann, “Resonant sideband extraction: a new configuration for interferometric gravitational wave detectors,” Phys. Lett. A 175, 273–276 (1993).
[CrossRef]

Sakata, S.

O. Miyakawa, R. Ward, R. Adhikari, M. Evans, B. Abbott, R. Bork, D. Busby, J. Heefner, A. Ivanov, M. Smith, R. Taylor, S. Vass, A. Weinstein, M. Varvella, S. Kawamura, F. Kawazoe, S. Sakata, and C. Mow-Lowry, “Measurement of optical response of a detuned resonant sideband extraction gravitational wave detector,” Phys. Rev. D 74, 022001 (2006).
[CrossRef]

O. Miyakawa, R. Ward, R. Adhikari, B. Abbott, R. Bork, D. Busby, M. Evans, H. Grote, J. Heefner, A. Ivanov, S. Kawamura, F. Kawazoe, S. Sakata, M. Smith, R. Taylor, M. Varvella, S. Vass, and A. Weinstein, “Lock acquisition scheme for the advanced ligo optical configuration,” J. Phys. Conf. Ser. 32, 265 (2006).
[CrossRef]

Schilling, R.

J. Mizuno, K. Strain, P. Nelson, J. Chen, R. Schilling, A. Rüdiger, W. Winkler, and K. Danzmann, “Resonant sideband extraction: a new configuration for interferometric gravitational wave detectors,” Phys. Lett. A 175, 273–276 (1993).
[CrossRef]

Schilt, S.

S. Schilt, N. Bucalovic, L. Tombez, V. Dolgovskiy, C. Schori, G. D. Domenico, M. Zaffalon, and P. Thomann, “Frequency discriminators for the characterization of narrow-spectrum heterodyne beat signals: Application to the measurement of a sub-hertz carrier-envelope-offset beat in an optical frequency comb,” Rev. Sci. Instrum. 82, 123116 (2011).
[CrossRef]

Schnabel, R.

H. Rehbein, H. Müller-Ebhardt, K. Somiya, C. Li, R. Schnabel, K. Danzmann, and Y. Chen, “Local readout enhancement for detuned signal-recycling interferometers,” Phys. Rev. D 76, 062002 (2007).
[CrossRef]

Schori, C.

S. Schilt, N. Bucalovic, L. Tombez, V. Dolgovskiy, C. Schori, G. D. Domenico, M. Zaffalon, and P. Thomann, “Frequency discriminators for the characterization of narrow-spectrum heterodyne beat signals: Application to the measurement of a sub-hertz carrier-envelope-offset beat in an optical frequency comb,” Rev. Sci. Instrum. 82, 123116 (2011).
[CrossRef]

Shaddock, D.

P. Fritschel, D. McClelland, A. Mullavey, D. Shaddock, B. Slagmolen, and S. Waldman, “Advanced LIGO arm length stabilisation requirements,” LIGO DCC T0900095-v2 (LIGO Document Control Center, 2009).

Shaddock, D. A.

Shapiro, B. N.

K. A. Strain and B. N. Shapiro, “Damping and local control of mirror suspensions for laser interferometric gravitational wave detectors,” Rev. Sci. Instrum. 83, 044501 (2012).
[CrossRef]

Shoemaker, D.

A. Abramovici, W. E. Althouse, R. W. P. 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, and M. E. Zucker, “LIGO: the laser interferometer gravitational-wave observatory,” Science 256, 325–333 (1992).
[CrossRef]

Sievers, L.

J. Camp, L. Sievers, R. Bork, and J. Heefner, “Guided lock acquisition in a suspended Fabry–Perot cavity,” Opt. Lett. 20, 2463–2465 (1995).
[CrossRef]

A. Abramovici, W. E. Althouse, R. W. P. 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, and M. E. Zucker, “LIGO: the laser interferometer gravitational-wave observatory,” Science 256, 325–333 (1992).
[CrossRef]

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]

P. Fritschel, D. McClelland, A. Mullavey, D. Shaddock, B. Slagmolen, and S. Waldman, “Advanced LIGO arm length stabilisation requirements,” LIGO DCC T0900095-v2 (LIGO Document Control Center, 2009).

Slagmolen, B. J. J.

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]

O. Miyakawa, R. Ward, R. Adhikari, B. Abbott, R. Bork, D. Busby, M. Evans, H. Grote, J. Heefner, A. Ivanov, S. Kawamura, F. Kawazoe, S. Sakata, M. Smith, R. Taylor, M. Varvella, S. Vass, and A. Weinstein, “Lock acquisition scheme for the advanced ligo optical configuration,” J. Phys. Conf. Ser. 32, 265 (2006).
[CrossRef]

O. Miyakawa, R. Ward, R. Adhikari, M. Evans, B. Abbott, R. Bork, D. Busby, J. Heefner, A. Ivanov, M. Smith, R. Taylor, S. Vass, A. Weinstein, M. Varvella, S. Kawamura, F. Kawazoe, S. Sakata, and C. Mow-Lowry, “Measurement of optical response of a detuned resonant sideband extraction gravitational wave detector,” Phys. Rev. D 74, 022001 (2006).
[CrossRef]

Sneddon, P. H.

G. M. Harry, M. R. Abernathy, A. E. Becerra-Toledo, H. Armandula, E. Black, K. Dooley, M. Eichenfield, C. Nwabugwu, A. Villar, D. R. M. Crooks, G. Cagnoli, J. Hough, C. R. How, I. MacLaren, P. Murray, S. Reid, S. Rowan, P. H. Sneddon, M. M. Fejer, R. Route, S. D. Penn, P. Ganau, J.-M. Mackowski, C. Michel, L. Pinard, and A. Remillieux, “Titania-doped tantala/silica coatings for gravitational-wave detection,” Class. Quantum Grav. 24, 405–415 (2007).
[CrossRef]

Somiya, K.

H. Rehbein, H. Müller-Ebhardt, K. Somiya, C. Li, R. Schnabel, K. Danzmann, and Y. Chen, “Local readout enhancement for detuned signal-recycling interferometers,” Phys. Rev. D 76, 062002 (2007).
[CrossRef]

Spero, R. E.

A. Abramovici, W. E. Althouse, R. W. P. 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, and M. E. Zucker, “LIGO: the laser interferometer gravitational-wave observatory,” Science 256, 325–333 (1992).
[CrossRef]

Strain, K.

J. Mizuno, K. Strain, P. Nelson, J. Chen, R. Schilling, A. Rüdiger, W. Winkler, and K. Danzmann, “Resonant sideband extraction: a new configuration for interferometric gravitational wave detectors,” Phys. Lett. A 175, 273–276 (1993).
[CrossRef]

Strain, K. A.

K. A. Strain and B. N. Shapiro, “Damping and local control of mirror suspensions for laser interferometric gravitational wave detectors,” Rev. Sci. Instrum. 83, 044501 (2012).
[CrossRef]

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]

O. Miyakawa, R. Ward, R. Adhikari, M. Evans, B. Abbott, R. Bork, D. Busby, J. Heefner, A. Ivanov, M. Smith, R. Taylor, S. Vass, A. Weinstein, M. Varvella, S. Kawamura, F. Kawazoe, S. Sakata, and C. Mow-Lowry, “Measurement of optical response of a detuned resonant sideband extraction gravitational wave detector,” Phys. Rev. D 74, 022001 (2006).
[CrossRef]

O. Miyakawa, R. Ward, R. Adhikari, B. Abbott, R. Bork, D. Busby, M. Evans, H. Grote, J. Heefner, A. Ivanov, S. Kawamura, F. Kawazoe, S. Sakata, M. Smith, R. Taylor, M. Varvella, S. Vass, and A. Weinstein, “Lock acquisition scheme for the advanced ligo optical configuration,” J. Phys. Conf. Ser. 32, 265 (2006).
[CrossRef]

Thomann, P.

S. Schilt, N. Bucalovic, L. Tombez, V. Dolgovskiy, C. Schori, G. D. Domenico, M. Zaffalon, and P. Thomann, “Frequency discriminators for the characterization of narrow-spectrum heterodyne beat signals: Application to the measurement of a sub-hertz carrier-envelope-offset beat in an optical frequency comb,” Rev. Sci. Instrum. 82, 123116 (2011).
[CrossRef]

Thorne, K. S.

A. Abramovici, W. E. Althouse, R. W. P. 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, and M. E. Zucker, “LIGO: the laser interferometer gravitational-wave observatory,” Science 256, 325–333 (1992).
[CrossRef]

Tombez, L.

S. Schilt, N. Bucalovic, L. Tombez, V. Dolgovskiy, C. Schori, G. D. Domenico, M. Zaffalon, and P. Thomann, “Frequency discriminators for the characterization of narrow-spectrum heterodyne beat signals: Application to the measurement of a sub-hertz carrier-envelope-offset beat in an optical frequency comb,” Rev. Sci. Instrum. 82, 123116 (2011).
[CrossRef]

Tsubono, K.

Y. Aso, M. Ando, K. Kawabe, S. Otsuka, and K. Tsubono, “Stabilization of a Fabry–Perot interferometer using a suspension-point interferometer,” Phys. Lett. A 327, 1–8 (2004).
[CrossRef]

Varvella, M.

O. Miyakawa, R. Ward, R. Adhikari, B. Abbott, R. Bork, D. Busby, M. Evans, H. Grote, J. Heefner, A. Ivanov, S. Kawamura, F. Kawazoe, S. Sakata, M. Smith, R. Taylor, M. Varvella, S. Vass, and A. Weinstein, “Lock acquisition scheme for the advanced ligo optical configuration,” J. Phys. Conf. Ser. 32, 265 (2006).
[CrossRef]

O. Miyakawa, R. Ward, R. Adhikari, M. Evans, B. Abbott, R. Bork, D. Busby, J. Heefner, A. Ivanov, M. Smith, R. Taylor, S. Vass, A. Weinstein, M. Varvella, S. Kawamura, F. Kawazoe, S. Sakata, and C. Mow-Lowry, “Measurement of optical response of a detuned resonant sideband extraction gravitational wave detector,” Phys. Rev. D 74, 022001 (2006).
[CrossRef]

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]

O. Miyakawa, R. Ward, R. Adhikari, B. Abbott, R. Bork, D. Busby, M. Evans, H. Grote, J. Heefner, A. Ivanov, S. Kawamura, F. Kawazoe, S. Sakata, M. Smith, R. Taylor, M. Varvella, S. Vass, and A. Weinstein, “Lock acquisition scheme for the advanced ligo optical configuration,” J. Phys. Conf. Ser. 32, 265 (2006).
[CrossRef]

O. Miyakawa, R. Ward, R. Adhikari, M. Evans, B. Abbott, R. Bork, D. Busby, J. Heefner, A. Ivanov, M. Smith, R. Taylor, S. Vass, A. Weinstein, M. Varvella, S. Kawamura, F. Kawazoe, S. Sakata, and C. Mow-Lowry, “Measurement of optical response of a detuned resonant sideband extraction gravitational wave detector,” Phys. Rev. D 74, 022001 (2006).
[CrossRef]

Villar, A.

G. M. Harry, M. R. Abernathy, A. E. Becerra-Toledo, H. Armandula, E. Black, K. Dooley, M. Eichenfield, C. Nwabugwu, A. Villar, D. R. M. Crooks, G. Cagnoli, J. Hough, C. R. How, I. MacLaren, P. Murray, S. Reid, S. Rowan, P. H. Sneddon, M. M. Fejer, R. Route, S. D. Penn, P. Ganau, J.-M. Mackowski, C. Michel, L. Pinard, and A. Remillieux, “Titania-doped tantala/silica coatings for gravitational-wave detection,” Class. Quantum Grav. 24, 405–415 (2007).
[CrossRef]

Vogt, R. E.

A. Abramovici, W. E. Althouse, R. W. P. 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, and M. E. Zucker, “LIGO: the laser interferometer gravitational-wave observatory,” Science 256, 325–333 (1992).
[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]

P. Fritschel, D. McClelland, A. Mullavey, D. Shaddock, B. Slagmolen, and S. Waldman, “Advanced LIGO arm length stabilisation requirements,” LIGO DCC T0900095-v2 (LIGO Document Control Center, 2009).

Waldman, S. J.

Ward, H.

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

Ward, R.

O. Miyakawa, R. Ward, R. Adhikari, M. Evans, B. Abbott, R. Bork, D. Busby, J. Heefner, A. Ivanov, M. Smith, R. Taylor, S. Vass, A. Weinstein, M. Varvella, S. Kawamura, F. Kawazoe, S. Sakata, and C. Mow-Lowry, “Measurement of optical response of a detuned resonant sideband extraction gravitational wave detector,” Phys. Rev. D 74, 022001 (2006).
[CrossRef]

O. Miyakawa, R. Ward, R. Adhikari, B. Abbott, R. Bork, D. Busby, M. Evans, H. Grote, J. Heefner, A. Ivanov, S. Kawamura, F. Kawazoe, S. Sakata, M. Smith, R. Taylor, M. Varvella, S. Vass, and A. Weinstein, “Lock acquisition scheme for the advanced ligo optical configuration,” J. Phys. Conf. Ser. 32, 265 (2006).
[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]

Ware, B.

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]

O. Miyakawa, R. Ward, R. Adhikari, M. Evans, B. Abbott, R. Bork, D. Busby, J. Heefner, A. Ivanov, M. Smith, R. Taylor, S. Vass, A. Weinstein, M. Varvella, S. Kawamura, F. Kawazoe, S. Sakata, and C. Mow-Lowry, “Measurement of optical response of a detuned resonant sideband extraction gravitational wave detector,” Phys. Rev. D 74, 022001 (2006).
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A. Abramovici, W. E. Althouse, R. W. P. 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, and M. E. Zucker, “LIGO: the laser interferometer gravitational-wave observatory,” Science 256, 325–333 (1992).
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D. Yeaton-Massey and R. Adhikari, “A new bound on excess frequency noise in second harmonic generation in PPKTP at the 10−19 level,” Opt. Express20, 21019–21024 (2012).

Zaffalon, M.

S. Schilt, N. Bucalovic, L. Tombez, V. Dolgovskiy, C. Schori, G. D. Domenico, M. Zaffalon, and P. Thomann, “Frequency discriminators for the characterization of narrow-spectrum heterodyne beat signals: Application to the measurement of a sub-hertz carrier-envelope-offset beat in an optical frequency comb,” Rev. Sci. Instrum. 82, 123116 (2011).
[CrossRef]

Zhao, C.

F. Khalili, S. Danilishin, H. Müller-Ebhardt, H. Miao, Y. Chen, and C. Zhao, “Negative optical inertia for enhancing the sensitivity of future gravitational-wave detectors,” Phys. Rev. D 83, 062003 (2011).
[CrossRef]

Zucker, M. E.

A. Abramovici, W. E. Althouse, R. W. P. 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, and M. E. Zucker, “LIGO: the laser interferometer gravitational-wave observatory,” Science 256, 325–333 (1992).
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Science (1)

A. Abramovici, W. E. Althouse, R. W. P. 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, and M. E. Zucker, “LIGO: the laser interferometer gravitational-wave observatory,” Science 256, 325–333 (1992).
[CrossRef]

Other (4)

D. Yeaton-Massey and R. Adhikari, “A new bound on excess frequency noise in second harmonic generation in PPKTP at the 10−19 level,” Opt. Express20, 21019–21024 (2012).

D. H. Wolaver, Phase-Locked Loop Circuit Design (PTR Prentice-Hall, 1991).

M. Principe, I. M. Pinto, V. Pierro, and R. DeSalvo, “Minimum Brownian noise dichroic dielectric mirror coatings for AdLIGO,” LIGO DCC T080337-v1 (LIGO Document Control Center, 2008).

P. Fritschel, D. McClelland, A. Mullavey, D. Shaddock, B. Slagmolen, and S. Waldman, “Advanced LIGO arm length stabilisation requirements,” LIGO DCC T0900095-v2 (LIGO Document Control Center, 2009).

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Figures (8)

Fig. 1.
Fig. 1.

Experimental setup. Red lines indicate the path of the 1064 nm PSL beam, and green lines indicate the path of the 532 nm AUX beam. The colored regions correspond to logical sections of the control and readout, described in more detail in Section 3. Optics in shadow are part of the larger interferometer not used in this experiment.

Fig. 2.
Fig. 2.

Spectral reflectivity of one of the dichroic cavity mirrors.

Fig. 3.
Fig. 3.

Sequence of the arm length control as a function of time. The intracavity power and detuning are for the 1064 nm PSL beam.

Fig. 4.
Fig. 4.

Delay-line frequency discriminator. Components used: comparator, Analog Devices AD9696; RF amplifier, Mini-Circuits ZHL-1A; power-splitter, Mini-Circuits ZBSC-413+; delay-line cables, RG-58 C/U; mixer, Mini-Circuits ZP-3+; low-pass filters, Mini-Circuits BLP-1.9; preamplifier, Stanford Research SR560.

Fig. 5.
Fig. 5.

Block diagram of the control scheme and noise source model for the experiment. The colored blocks correspond to the colored blocks in the setup diagram in Fig. 1. The various individual control elements are described in the text and in Appendix A.

Fig. 6.
Fig. 6.

Sweep of cavity length control offset through the 1064 nm (PSL) resonance of the cavity. A detuning of 100 kHz corresponds to a cavity displacement of 6.7 nm.

Fig. 7.
Fig. 7.

Residual displacement noise at 1064 nm, and noise budget of the locked cavity. The right vertical axis indicates the corresponding frequency noise at 1064 nm. The solid red curve is the overall residual cavity displacement measured by the out-of-loop PSL PDH detector, while the red dashed curve is the residual displacement RMS integrated from high frequency. The colored dashed–dotted curves represent the estimated noise contributions from various fundamental noise sources, while the solid colored curves are the measured or estimated levels of the various technical noise sources.

Fig. 8.
Fig. 8.

Bode plot of control model transfer functions. The green trace is the full open-loop transfer function of the arm length servo control loop. The blue and red traces are the transfer functions from external disturbances to residual displacement, for AUX/PSL common and differential sensing.

Tables (3)

Tables Icon

Table 1. Cavity Properties of the Arm Cavity, at 1064 nm as Seen from the Vertex, and 532 nm as Seen from the Cavity End

Tables Icon

Table 2. Zeros, Poles, and Gain of the Control Model Blocks

Tables Icon

Table 3. Values of Fundamental Constants, and Material Properties and Variables for the 40 m Mirror Coatings a

Equations (17)

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

V D f .
d L L = d ν ν ,
C AUX ( f ) = 1 1 + i ( f / f c ) ,
H AUX ( f ) = i ( f / f c ) 1 + i ( f / f c ) ,
G ALS D DFD F ALS A TM ,
n ( f ) = X ( f ) S ( f ) ,
S sus ( f ) = 4 k B T ( 2 π f ) 2 R [ Y ( f ) ] ,
Y ( f ) = 1 M i f / ( 2 π f p 2 ) 1 + i ϕ p ( f / f p ) 2 ,
S BR ( f ) = 4 k B T 2 π f ϕ eff ( 1 P 2 ) E a ,
S TO Δ T ( f ) = 2 2 k B T 2 a 2 π f κ s ,
S TO ( f ) = S TO Δ T ( f ) Γ tc ( χ fsm Δ α ¯ d β ¯ λ ) 2 ,
S δ T Δ T ( f ) = [ δ T ( f ) C ( f ) j ( f ) ] 2 ,
δ T ( f ) = 3 × 10 3 ( 0.01 Hz f ) K Hz ,
j ( f ) = 4 ϵ σ T 3 2 π f κ ρ c ,
S PD ( f ) = 2 S V ( f ) V RF 2 f 2 ,
X ( f ) = k n ( 1 + i f / z n ) m ( 1 + i f / p m ) .
L ν = ν L ,

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