Abstract

We describe the angular sensing and control (ASC) of 4 km detectors of the Laser Interferometer Gravitational-Wave Observatory (LIGO). Enhanced LIGO, the culmination of the first generation LIGO detectors, operated between 2009 and 2010 with about 40 kW of laser power in the arm cavities. In this regime, radiation-pressure effects are significant and induce instabilities in the angular opto-mechanical transfer functions. Here we present and motivate the ASC design in this extreme case and present the results of its implementation in Enhanced LIGO. Highlights of the ASC performance are successful control of opto-mechanical torsional modes, relative mirror motions of 1×107rad rms, and limited impact on in-band strain sensitivity.

© 2013 Optical Society of America

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2012

T. Fricke, N. Smith-Lefebvre, R. Abbott, R. Adhikari, K. Dooley, M. Evans, P. Fritschel, V. Frolov, K. Kawabe, J. Kissel, B. Slagmolen, and S. Waldman, “DC readout experiment in Enhanced LIGO,” Class. Quantum Grav. 29, 065005 (2012).
[CrossRef]

K. L. Dooley, M. A. Arain, D. Feldbaum, V. V. Frolov, M. Heintze, D. Hoak, E. A. Khazanov, A. Lucianetti, R. M. Martin, G. Mueller, O. Palashov, V. Quetschke, D. H. Reitze, R. L. Savage, D. B. Tanner, L. F. Williams, and W. Wu, “Thermal effects in the input optics of the Enhanced Laser Interferometer Gravitational-Wave Observatory interferometers,” Rev. Sci. Instrum. 83, 033109 (2012).
[CrossRef]

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]

L. Barsotti, M. Evans, and P. Fritschel, “Alignment sensing and control in advanced LIGO,” Class. Quantum Grav. 27, 084026 (2010).
[CrossRef]

E. Hirose, K. Kawabe, D. Sigg, R. Adhikari, and P. R. Saulson, “Angular instability due to radiation pressure in the LIGO gravitational-wave detector,” Appl. Opt. 49, 3474–3484 (2010).
[CrossRef]

2009

Y. Fan, L. Merrill, C. Zhao, L. Ju, D. Blair, B. Slagmolen, D. Hosken, A. Brooks, P. Veitch, D. Mudge, and J. Munch, “Observation of optical torsional stiffness in a high optical power cavity,” Appl. Phys. Lett. 94, 081105 (2009).
[CrossRef]

B. P. Abbott, et al. “LIGO: the Laser Interferometer Gravitational-Wave Observatory,” Rep. Prog. Phys. 72, 076901 (2009).
[CrossRef]

2007

2006

J. Sidles and D. Sigg, “Optical torques in suspended Fabry–Perot interferometers,” Phys. Lett. A 354, 167–172 (2006).
[CrossRef]

1998

1997

1994

1991

S. Solimeno, F. Barone, C. de Lisio, L. Di Fiore, L. Milano, and G. Russo, “Fabry–Pérot resonators with oscillating mirrors,” Phys. Rev. A 43, 6227–6240 (1991).
[CrossRef]

1990

1984

Abbott, B. P.

B. P. Abbott, et al. “LIGO: the Laser Interferometer Gravitational-Wave Observatory,” Rep. Prog. Phys. 72, 076901 (2009).
[CrossRef]

Abbott, R.

T. Fricke, N. Smith-Lefebvre, R. Abbott, R. Adhikari, K. Dooley, M. Evans, P. Fritschel, V. Frolov, K. Kawabe, J. Kissel, B. Slagmolen, and S. Waldman, “DC readout experiment in Enhanced LIGO,” Class. Quantum Grav. 29, 065005 (2012).
[CrossRef]

Adhikari, R.

T. Fricke, N. Smith-Lefebvre, R. Abbott, R. Adhikari, K. Dooley, M. Evans, P. Fritschel, V. Frolov, K. Kawabe, J. Kissel, B. Slagmolen, and S. Waldman, “DC readout experiment in Enhanced LIGO,” Class. Quantum Grav. 29, 065005 (2012).
[CrossRef]

E. Hirose, K. Kawabe, D. Sigg, R. Adhikari, and P. R. Saulson, “Angular instability due to radiation pressure in the LIGO gravitational-wave detector,” Appl. Opt. 49, 3474–3484 (2010).
[CrossRef]

R. Adhikari, P. Fritschel, and S. Waldman, “Enhanced LIGO,” (LIGO Laboratory, 2006).

Anderson, D. Z.

Arain, M. A.

K. L. Dooley, M. A. Arain, D. Feldbaum, V. V. Frolov, M. Heintze, D. Hoak, E. A. Khazanov, A. Lucianetti, R. M. Martin, G. Mueller, O. Palashov, V. Quetschke, D. H. Reitze, R. L. Savage, D. B. Tanner, L. F. Williams, and W. Wu, “Thermal effects in the input optics of the Enhanced Laser Interferometer Gravitational-Wave Observatory interferometers,” Rev. Sci. Instrum. 83, 033109 (2012).
[CrossRef]

Barone, F.

S. Solimeno, F. Barone, C. de Lisio, L. Di Fiore, L. Milano, and G. Russo, “Fabry–Pérot resonators with oscillating mirrors,” Phys. Rev. A 43, 6227–6240 (1991).
[CrossRef]

Barsotti, L.

L. Barsotti, M. Evans, and P. Fritschel, “Alignment sensing and control in advanced LIGO,” Class. Quantum Grav. 27, 084026 (2010).
[CrossRef]

L. Barsotti and M. Evans, “Modeling of alignment sensing and control for Enhanced LIGO,” (LIGO Laboratory, 2009).

Blair, D.

Y. Fan, L. Merrill, C. Zhao, L. Ju, D. Blair, B. Slagmolen, D. Hosken, A. Brooks, P. Veitch, D. Mudge, and J. Munch, “Observation of optical torsional stiffness in a high optical power cavity,” Appl. Phys. Lett. 94, 081105 (2009).
[CrossRef]

Brooks, A.

Y. Fan, L. Merrill, C. Zhao, L. Ju, D. Blair, B. Slagmolen, D. Hosken, A. Brooks, P. Veitch, D. Mudge, and J. Munch, “Observation of optical torsional stiffness in a high optical power cavity,” Appl. Phys. Lett. 94, 081105 (2009).
[CrossRef]

de Lisio, C.

S. Solimeno, F. Barone, C. de Lisio, L. Di Fiore, L. Milano, and G. Russo, “Fabry–Pérot resonators with oscillating mirrors,” Phys. Rev. A 43, 6227–6240 (1991).
[CrossRef]

Di Fiore, L.

S. Solimeno, F. Barone, C. de Lisio, L. Di Fiore, L. Milano, and G. Russo, “Fabry–Pérot resonators with oscillating mirrors,” Phys. Rev. A 43, 6227–6240 (1991).
[CrossRef]

Dooley, K.

T. Fricke, N. Smith-Lefebvre, R. Abbott, R. Adhikari, K. Dooley, M. Evans, P. Fritschel, V. Frolov, K. Kawabe, J. Kissel, B. Slagmolen, and S. Waldman, “DC readout experiment in Enhanced LIGO,” Class. Quantum Grav. 29, 065005 (2012).
[CrossRef]

Dooley, K. L.

K. L. Dooley, M. A. Arain, D. Feldbaum, V. V. Frolov, M. Heintze, D. Hoak, E. A. Khazanov, A. Lucianetti, R. M. Martin, G. Mueller, O. Palashov, V. Quetschke, D. H. Reitze, R. L. Savage, D. B. Tanner, L. F. Williams, and W. Wu, “Thermal effects in the input optics of the Enhanced Laser Interferometer Gravitational-Wave Observatory interferometers,” Rev. Sci. Instrum. 83, 033109 (2012).
[CrossRef]

Driggers, J.

J. Driggers, “Optomechanical alignment instability in LIGO mode cleaners,” (LIGO Laboratory, 2006).

Evans, M.

T. Fricke, N. Smith-Lefebvre, R. Abbott, R. Adhikari, K. Dooley, M. Evans, P. Fritschel, V. Frolov, K. Kawabe, J. Kissel, B. Slagmolen, and S. Waldman, “DC readout experiment in Enhanced LIGO,” Class. Quantum Grav. 29, 065005 (2012).
[CrossRef]

L. Barsotti, M. Evans, and P. Fritschel, “Alignment sensing and control in advanced LIGO,” Class. Quantum Grav. 27, 084026 (2010).
[CrossRef]

L. Barsotti and M. Evans, “Modeling of alignment sensing and control for Enhanced LIGO,” (LIGO Laboratory, 2009).

Fan, Y.

Y. Fan, L. Merrill, C. Zhao, L. Ju, D. Blair, B. Slagmolen, D. Hosken, A. Brooks, P. Veitch, D. Mudge, and J. Munch, “Observation of optical torsional stiffness in a high optical power cavity,” Appl. Phys. Lett. 94, 081105 (2009).
[CrossRef]

Feldbaum, D.

K. L. Dooley, M. A. Arain, D. Feldbaum, V. V. Frolov, M. Heintze, D. Hoak, E. A. Khazanov, A. Lucianetti, R. M. Martin, G. Mueller, O. Palashov, V. Quetschke, D. H. Reitze, R. L. Savage, D. B. Tanner, L. F. Williams, and W. Wu, “Thermal effects in the input optics of the Enhanced Laser Interferometer Gravitational-Wave Observatory interferometers,” Rev. Sci. Instrum. 83, 033109 (2012).
[CrossRef]

Frede, M.

Fricke, T.

T. Fricke, N. Smith-Lefebvre, R. Abbott, R. Adhikari, K. Dooley, M. Evans, P. Fritschel, V. Frolov, K. Kawabe, J. Kissel, B. Slagmolen, and S. Waldman, “DC readout experiment in Enhanced LIGO,” Class. Quantum Grav. 29, 065005 (2012).
[CrossRef]

Fritschel, P.

T. Fricke, N. Smith-Lefebvre, R. Abbott, R. Adhikari, K. Dooley, M. Evans, P. Fritschel, V. Frolov, K. Kawabe, J. Kissel, B. Slagmolen, and S. Waldman, “DC readout experiment in Enhanced LIGO,” Class. Quantum Grav. 29, 065005 (2012).
[CrossRef]

L. Barsotti, M. Evans, and P. Fritschel, “Alignment sensing and control in advanced LIGO,” Class. Quantum Grav. 27, 084026 (2010).
[CrossRef]

P. Fritschel, N. Mavalvala, D. Shoemaker, D. Sigg, M. Zucker, and G. González, “Alignment of an interferometric gravitational wave detector,” Appl. Opt. 37, 6734–6747 (1998).
[CrossRef]

R. Adhikari, P. Fritschel, and S. Waldman, “Enhanced LIGO,” (LIGO Laboratory, 2006).

P. Fritschel and D. Shoemaker, “Alignment sensing/control design requirements document,” (LIGO Laboratory, 1997).

Frolov, V.

T. Fricke, N. Smith-Lefebvre, R. Abbott, R. Adhikari, K. Dooley, M. Evans, P. Fritschel, V. Frolov, K. Kawabe, J. Kissel, B. Slagmolen, and S. Waldman, “DC readout experiment in Enhanced LIGO,” Class. Quantum Grav. 29, 065005 (2012).
[CrossRef]

Frolov, V. V.

K. L. Dooley, M. A. Arain, D. Feldbaum, V. V. Frolov, M. Heintze, D. Hoak, E. A. Khazanov, A. Lucianetti, R. M. Martin, G. Mueller, O. Palashov, V. Quetschke, D. H. Reitze, R. L. Savage, D. B. Tanner, L. F. Williams, and W. Wu, “Thermal effects in the input optics of the Enhanced Laser Interferometer Gravitational-Wave Observatory interferometers,” Rev. Sci. Instrum. 83, 033109 (2012).
[CrossRef]

González, G.

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]

Hefetz, Y.

Heintze, M.

K. L. Dooley, M. A. Arain, D. Feldbaum, V. V. Frolov, M. Heintze, D. Hoak, E. A. Khazanov, A. Lucianetti, R. M. Martin, G. Mueller, O. Palashov, V. Quetschke, D. H. Reitze, R. L. Savage, D. B. Tanner, L. F. Williams, and W. Wu, “Thermal effects in the input optics of the Enhanced Laser Interferometer Gravitational-Wave Observatory interferometers,” Rev. Sci. Instrum. 83, 033109 (2012).
[CrossRef]

Hirose, E.

Hoak, D.

K. L. Dooley, M. A. Arain, D. Feldbaum, V. V. Frolov, M. Heintze, D. Hoak, E. A. Khazanov, A. Lucianetti, R. M. Martin, G. Mueller, O. Palashov, V. Quetschke, D. H. Reitze, R. L. Savage, D. B. Tanner, L. F. Williams, and W. Wu, “Thermal effects in the input optics of the Enhanced Laser Interferometer Gravitational-Wave Observatory interferometers,” Rev. Sci. Instrum. 83, 033109 (2012).
[CrossRef]

Hosken, D.

Y. Fan, L. Merrill, C. Zhao, L. Ju, D. Blair, B. Slagmolen, D. Hosken, A. Brooks, P. Veitch, D. Mudge, and J. Munch, “Observation of optical torsional stiffness in a high optical power cavity,” Appl. Phys. Lett. 94, 081105 (2009).
[CrossRef]

Ju, L.

Y. Fan, L. Merrill, C. Zhao, L. Ju, D. Blair, B. Slagmolen, D. Hosken, A. Brooks, P. Veitch, D. Mudge, and J. Munch, “Observation of optical torsional stiffness in a high optical power cavity,” Appl. Phys. Lett. 94, 081105 (2009).
[CrossRef]

Kawabe, K.

T. Fricke, N. Smith-Lefebvre, R. Abbott, R. Adhikari, K. Dooley, M. Evans, P. Fritschel, V. Frolov, K. Kawabe, J. Kissel, B. Slagmolen, and S. Waldman, “DC readout experiment in Enhanced LIGO,” Class. Quantum Grav. 29, 065005 (2012).
[CrossRef]

E. Hirose, K. Kawabe, D. Sigg, R. Adhikari, and P. R. Saulson, “Angular instability due to radiation pressure in the LIGO gravitational-wave detector,” Appl. Opt. 49, 3474–3484 (2010).
[CrossRef]

Khazanov, E. A.

K. L. Dooley, M. A. Arain, D. Feldbaum, V. V. Frolov, M. Heintze, D. Hoak, E. A. Khazanov, A. Lucianetti, R. M. Martin, G. Mueller, O. Palashov, V. Quetschke, D. H. Reitze, R. L. Savage, D. B. Tanner, L. F. Williams, and W. Wu, “Thermal effects in the input optics of the Enhanced Laser Interferometer Gravitational-Wave Observatory interferometers,” Rev. Sci. Instrum. 83, 033109 (2012).
[CrossRef]

Kissel, J.

T. Fricke, N. Smith-Lefebvre, R. Abbott, R. Adhikari, K. Dooley, M. Evans, P. Fritschel, V. Frolov, K. Kawabe, J. Kissel, B. Slagmolen, and S. Waldman, “DC readout experiment in Enhanced LIGO,” Class. Quantum Grav. 29, 065005 (2012).
[CrossRef]

Kracht, D.

Kwee, P.

Lucianetti, A.

K. L. Dooley, M. A. Arain, D. Feldbaum, V. V. Frolov, M. Heintze, D. Hoak, E. A. Khazanov, A. Lucianetti, R. M. Martin, G. Mueller, O. Palashov, V. Quetschke, D. H. Reitze, R. L. Savage, D. B. Tanner, L. F. Williams, and W. Wu, “Thermal effects in the input optics of the Enhanced Laser Interferometer Gravitational-Wave Observatory interferometers,” Rev. Sci. Instrum. 83, 033109 (2012).
[CrossRef]

Martin, R. M.

K. L. Dooley, M. A. Arain, D. Feldbaum, V. V. Frolov, M. Heintze, D. Hoak, E. A. Khazanov, A. Lucianetti, R. M. Martin, G. Mueller, O. Palashov, V. Quetschke, D. H. Reitze, R. L. Savage, D. B. Tanner, L. F. Williams, and W. Wu, “Thermal effects in the input optics of the Enhanced Laser Interferometer Gravitational-Wave Observatory interferometers,” Rev. Sci. Instrum. 83, 033109 (2012).
[CrossRef]

Mavalvala, N.

Meers, B. J.

Merrill, L.

Y. Fan, L. Merrill, C. Zhao, L. Ju, D. Blair, B. Slagmolen, D. Hosken, A. Brooks, P. Veitch, D. Mudge, and J. Munch, “Observation of optical torsional stiffness in a high optical power cavity,” Appl. Phys. Lett. 94, 081105 (2009).
[CrossRef]

Milano, L.

S. Solimeno, F. Barone, C. de Lisio, L. Di Fiore, L. Milano, and G. Russo, “Fabry–Pérot resonators with oscillating mirrors,” Phys. Rev. A 43, 6227–6240 (1991).
[CrossRef]

Morrison, E.

Mudge, D.

Y. Fan, L. Merrill, C. Zhao, L. Ju, D. Blair, B. Slagmolen, D. Hosken, A. Brooks, P. Veitch, D. Mudge, and J. Munch, “Observation of optical torsional stiffness in a high optical power cavity,” Appl. Phys. Lett. 94, 081105 (2009).
[CrossRef]

Mueller, G.

K. L. Dooley, M. A. Arain, D. Feldbaum, V. V. Frolov, M. Heintze, D. Hoak, E. A. Khazanov, A. Lucianetti, R. M. Martin, G. Mueller, O. Palashov, V. Quetschke, D. H. Reitze, R. L. Savage, D. B. Tanner, L. F. Williams, and W. Wu, “Thermal effects in the input optics of the Enhanced Laser Interferometer Gravitational-Wave Observatory interferometers,” Rev. Sci. Instrum. 83, 033109 (2012).
[CrossRef]

Munch, J.

Y. Fan, L. Merrill, C. Zhao, L. Ju, D. Blair, B. Slagmolen, D. Hosken, A. Brooks, P. Veitch, D. Mudge, and J. Munch, “Observation of optical torsional stiffness in a high optical power cavity,” Appl. Phys. Lett. 94, 081105 (2009).
[CrossRef]

Palashov, O.

K. L. Dooley, M. A. Arain, D. Feldbaum, V. V. Frolov, M. Heintze, D. Hoak, E. A. Khazanov, A. Lucianetti, R. M. Martin, G. Mueller, O. Palashov, V. Quetschke, D. H. Reitze, R. L. Savage, D. B. Tanner, L. F. Williams, and W. Wu, “Thermal effects in the input optics of the Enhanced Laser Interferometer Gravitational-Wave Observatory interferometers,” Rev. Sci. Instrum. 83, 033109 (2012).
[CrossRef]

Quetschke, V.

K. L. Dooley, M. A. Arain, D. Feldbaum, V. V. Frolov, M. Heintze, D. Hoak, E. A. Khazanov, A. Lucianetti, R. M. Martin, G. Mueller, O. Palashov, V. Quetschke, D. H. Reitze, R. L. Savage, D. B. Tanner, L. F. Williams, and W. Wu, “Thermal effects in the input optics of the Enhanced Laser Interferometer Gravitational-Wave Observatory interferometers,” Rev. Sci. Instrum. 83, 033109 (2012).
[CrossRef]

Reitze, D. H.

K. L. Dooley, M. A. Arain, D. Feldbaum, V. V. Frolov, M. Heintze, D. Hoak, E. A. Khazanov, A. Lucianetti, R. M. Martin, G. Mueller, O. Palashov, V. Quetschke, D. H. Reitze, R. L. Savage, D. B. Tanner, L. F. Williams, and W. Wu, “Thermal effects in the input optics of the Enhanced Laser Interferometer Gravitational-Wave Observatory interferometers,” Rev. Sci. Instrum. 83, 033109 (2012).
[CrossRef]

Robertson, D. I.

Russo, G.

S. Solimeno, F. Barone, C. de Lisio, L. Di Fiore, L. Milano, and G. Russo, “Fabry–Pérot resonators with oscillating mirrors,” Phys. Rev. A 43, 6227–6240 (1991).
[CrossRef]

Sampas, N. M.

Saulson, P. R.

Savage, R. L.

K. L. Dooley, M. A. Arain, D. Feldbaum, V. V. Frolov, M. Heintze, D. Hoak, E. A. Khazanov, A. Lucianetti, R. M. Martin, G. Mueller, O. Palashov, V. Quetschke, D. H. Reitze, R. L. Savage, D. B. Tanner, L. F. Williams, and W. Wu, “Thermal effects in the input optics of the Enhanced Laser Interferometer Gravitational-Wave Observatory interferometers,” Rev. Sci. Instrum. 83, 033109 (2012).
[CrossRef]

Schulz, B.

Seifert, F.

Shoemaker, D.

Sidles, J.

J. Sidles and D. Sigg, “Optical torques in suspended Fabry–Perot interferometers,” Phys. Lett. A 354, 167–172 (2006).
[CrossRef]

Sidles, J. A.

J. A. Sidles and D. Sigg, “Optical torques in suspended Fabry-Perot interferometers,” (LIGO Laboratory, 2003).

Siegman, A. E.

A. E. Siegman, Lasers, 1st ed. (University Science Books, 1986).

Sigg, D.

Slagmolen, B.

T. Fricke, N. Smith-Lefebvre, R. Abbott, R. Adhikari, K. Dooley, M. Evans, P. Fritschel, V. Frolov, K. Kawabe, J. Kissel, B. Slagmolen, and S. Waldman, “DC readout experiment in Enhanced LIGO,” Class. Quantum Grav. 29, 065005 (2012).
[CrossRef]

Y. Fan, L. Merrill, C. Zhao, L. Ju, D. Blair, B. Slagmolen, D. Hosken, A. Brooks, P. Veitch, D. Mudge, and J. Munch, “Observation of optical torsional stiffness in a high optical power cavity,” Appl. Phys. Lett. 94, 081105 (2009).
[CrossRef]

Smith-Lefebvre, N.

T. Fricke, N. Smith-Lefebvre, R. Abbott, R. Adhikari, K. Dooley, M. Evans, P. Fritschel, V. Frolov, K. Kawabe, J. Kissel, B. Slagmolen, and S. Waldman, “DC readout experiment in Enhanced LIGO,” Class. Quantum Grav. 29, 065005 (2012).
[CrossRef]

Solimeno, S.

S. Solimeno, F. Barone, C. de Lisio, L. Di Fiore, L. Milano, and G. Russo, “Fabry–Pérot resonators with oscillating mirrors,” Phys. Rev. A 43, 6227–6240 (1991).
[CrossRef]

Tanner, D. B.

K. L. Dooley, M. A. Arain, D. Feldbaum, V. V. Frolov, M. Heintze, D. Hoak, E. A. Khazanov, A. Lucianetti, R. M. Martin, G. Mueller, O. Palashov, V. Quetschke, D. H. Reitze, R. L. Savage, D. B. Tanner, L. F. Williams, and W. Wu, “Thermal effects in the input optics of the Enhanced Laser Interferometer Gravitational-Wave Observatory interferometers,” Rev. Sci. Instrum. 83, 033109 (2012).
[CrossRef]

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Y. Fan, L. Merrill, C. Zhao, L. Ju, D. Blair, B. Slagmolen, D. Hosken, A. Brooks, P. Veitch, D. Mudge, and J. Munch, “Observation of optical torsional stiffness in a high optical power cavity,” Appl. Phys. Lett. 94, 081105 (2009).
[CrossRef]

Waldman, S.

T. Fricke, N. Smith-Lefebvre, R. Abbott, R. Adhikari, K. Dooley, M. Evans, P. Fritschel, V. Frolov, K. Kawabe, J. Kissel, B. Slagmolen, and S. Waldman, “DC readout experiment in Enhanced LIGO,” Class. Quantum Grav. 29, 065005 (2012).
[CrossRef]

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K. L. Dooley, M. A. Arain, D. Feldbaum, V. V. Frolov, M. Heintze, D. Hoak, E. A. Khazanov, A. Lucianetti, R. M. Martin, G. Mueller, O. Palashov, V. Quetschke, D. H. Reitze, R. L. Savage, D. B. Tanner, L. F. Williams, and W. Wu, “Thermal effects in the input optics of the Enhanced Laser Interferometer Gravitational-Wave Observatory interferometers,” Rev. Sci. Instrum. 83, 033109 (2012).
[CrossRef]

Willke, B.

Wu, W.

K. L. Dooley, M. A. Arain, D. Feldbaum, V. V. Frolov, M. Heintze, D. Hoak, E. A. Khazanov, A. Lucianetti, R. M. Martin, G. Mueller, O. Palashov, V. Quetschke, D. H. Reitze, R. L. Savage, D. B. Tanner, L. F. Williams, and W. Wu, “Thermal effects in the input optics of the Enhanced Laser Interferometer Gravitational-Wave Observatory interferometers,” Rev. Sci. Instrum. 83, 033109 (2012).
[CrossRef]

Zhao, C.

Y. Fan, L. Merrill, C. Zhao, L. Ju, D. Blair, B. Slagmolen, D. Hosken, A. Brooks, P. Veitch, D. Mudge, and J. Munch, “Observation of optical torsional stiffness in a high optical power cavity,” Appl. Phys. Lett. 94, 081105 (2009).
[CrossRef]

Zucker, M.

Appl. Opt.

Appl. Phys. Lett.

Y. Fan, L. Merrill, C. Zhao, L. Ju, D. Blair, B. Slagmolen, D. Hosken, A. Brooks, P. Veitch, D. Mudge, and J. Munch, “Observation of optical torsional stiffness in a high optical power cavity,” Appl. Phys. Lett. 94, 081105 (2009).
[CrossRef]

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[CrossRef]

L. Barsotti, M. Evans, and P. Fritschel, “Alignment sensing and control in advanced LIGO,” Class. Quantum Grav. 27, 084026 (2010).
[CrossRef]

T. Fricke, N. Smith-Lefebvre, R. Abbott, R. Adhikari, K. Dooley, M. Evans, P. Fritschel, V. Frolov, K. Kawabe, J. Kissel, B. Slagmolen, and S. Waldman, “DC readout experiment in Enhanced LIGO,” Class. Quantum Grav. 29, 065005 (2012).
[CrossRef]

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[CrossRef]

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Two signals are derived from WFS2.

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Figures (9)

Fig. 1.
Fig. 1.

Power-recycled Fabry–Perot Michelson interferometer layout, with ASC system superimposed. The eight actively aligned mirrors (ITMs, ETMs, MMTs, BS, and RM) and the ASC sensors (WFS, QPDs, and camera) are shown. All additional optics are omitted for simplicity. The QPD and beam-centering servos provide drift control on minute time scales. The wavefront sensing (WFS) servo maintains the alignment of the interferometer mirrors with respect to each other up to several Hz. Both I and Q phases are used from WFS2, whereas only one quadrature is read out from each of the other WFS. The carrier field is E0, and sideband fields E1 and E2 are, respectively, resonant and nonresonant in the power-recycling cavity. All test masses are suspended as single-stage pendula, as depicted in the upper right corner, and are outfitted with magnet-coil actuators to control angular and longitudinal degrees of freedom.

Fig. 2.
Fig. 2.

Noise budget of an alignment sensor (WFS1) for the pitch degree of freedom. Curves for seismic noise, suspension thermal noise, and sensor noise are shown. Note that direct seismic and suspension thermal noises are small in the GW band, and the largest motions are impressed by our control system. Sensing noise dominates above approximately 20 Hz where the seismic isolation stacks strongly isolate.

Fig. 3.
Fig. 3.

Block diagram of major components of the angular control servo. The input matrix is the inverse of the sensing matrix presented in Table 3. Components within the dashed box are analog.

Fig. 4.
Fig. 4.

Measured opto-mechanical transfer functions at different powers for the (a) soft and (b) hard degrees of freedom. The resonant frequency increases with power for the hard mode and decreases with power for the soft mode, which eventually becomes unstable. Pcirc=9kW was a typical operating power for Initial LIGO, and Pcirc=40kW is the highest of powers reached for Enhanced LIGO. Solid curves indicate fits to the measured data points.

Fig. 5.
Fig. 5.

Open-loop gains (pitch) of the five WFS loops as measured with 10 kW circulating power. All have a phase margin of 40° to 50°. All UGFs are around 1 Hz with the exception of the dSoft degrees of freedom whose UGF is 5 Hz.

Fig. 6.
Fig. 6.

Residual motion of the opto-mechanical degrees of freedom during a 17 kW lock. Dashed lines are the rms integrated from the right; note that the rms is dominated by the approximately 1 Hz pendular motion. Sensor noise represented in the opto-mechanical eigenbasis is also shown.

Fig. 7.
Fig. 7.

Beam spot motion (pitch) on the ITM and ETM mirrors during a 27 kW lock at night. Dashed lines are the integrated spectral density. For pitch and yaw, the rms beam spot motion is 1 mm on the ETMs and 0.8 mm on the ITMs.

Fig. 8.
Fig. 8.

Displacement sensitivity noise budget during a lock with 24 kW circulating power. (a) Break down of the noise budget of the alignment feedback (pitch) degrees of freedom to displacement sensitivity. The two soft modes contribute more than the hard modes. The RM alignment feedback is not shown because its contribution is insignificant. (b) Noise budget of interferometer displacement sensitivity, showing several key noise sources. Angular control limits the sensitivity up to 55 Hz. Pitch and yaw contributions are added in quadrature because they are decoupled.

Fig. 9.
Fig. 9.

Resonant frequency of the opto-mechanical modes for pitch as a function of circulating power, comparing Advanced and Enhanced LIGO. Only at the highest of Advanced LIGO powers (about 800 kW circulating power, or 125 W input power) will the soft mode become unstable. Models are plotted up to the highest of their respective design powers.

Tables (3)

Tables Icon

Table 1. Resonant Frequencies (Pitch) in Hertz for Soft and Hard Opto-Mechanical Modesa

Tables Icon

Table 2. WFS Output Matrix for Pitch (Yaw)a

Tables Icon

Table 3. Sensing Matrix in Units of [V/rad] (Pitch)a

Equations (8)

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

ΔL(f)=dspotRMS×θmirror(f)+θmirrorRMS×dspot(f)
kS,H=k0(g1+g2)±(g1g2)2+42,
vS=[1,k0kSk0g1],
vH=[k0k0g2kH,1],
fS,H=12πkp+kS,HI,
g1=gITM=1L/RITM=0.726,
g2=gETM=1L/RETM=0.460,
Pcirc=PinεgPRCTBSgϕ,

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