Abstract

The birefringence of a low-loss, high-reflectance coating applied to an 8-cm-diameter sapphire crystal grown in the m-axis direction has been mapped. By monitoring the transmission of a high-finesse Fabry–Perot cavity as a function of the polarization of the input light, we find an upper limit for the magnitude of the birefringence of 2.5 × 10-4 rad and an upper limit in the variation in direction of the birefringence of 10 deg. These values are sufficiently small to allow consideration of m-axis sapphire as a substrate material for the optics of the advanced detector at the Laser Interferometer Gravitational Wave Observatory.

© 2001 Optical Society of America

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  1. A. Abramovici, W. Althouse, R. W. P. Drever, Y. Gursel, S. Kawamura, F. J. Raab, D. Shoemaker, L. Sievers, R. E. Spero, R. E. Vogt, R. Weiss, S. E. Whitcomb, M. E. Zucker, “LIGO: the Laser Interferometer Gravitational Wave Observatory,” Science 256, 325–333 (1992).
    [CrossRef] [PubMed]
  2. A. Giazotto, “The Virgo experiment: status of the art,” in First Edoardo Amaldi Conference on Gravitational Wave Experiments, E. Coccia, G. Pizella, F. Ronga, eds. (World Scientific, Singapore, 1995), pp. 86–99.
  3. K. Tsubono, “300-m laser interferometer gravitational wave detector (TAMA300) in Japan,” in First Edoardo Amaldi Conference on Gravitational Wave Experiment, E. Coccia, G. Pizella, F. Ronga, eds. (World Scientific, Singapore, 1995), pp. 112–114.
  4. K. Danzmann, “GEO600—a 600 m laser interferometric gravitational wave antenna,” in First Edoardo Amaldi Conference on Gravitational Wave Experiment, E. Coccia, G. Pizella, F. Ronga, eds. (World Scientific, Singapore, 1995), pp. 100–111.
  5. R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, H. Ward, “Laser phase and frequency stabilization using an optical resonator,” Appl. Phys. B 31, 97–105 (1983).
    [CrossRef]
  6. R. W. P. Drever, J. Hough, A. J. Munley, S.-A. Lee, R. Spero, S. E. Whitcomb, H. Ward, G. M. Ford, M. Hereld, N. A. Robertson, I. Kerr, J. R. Pugh, G. P. Newton, B. Meers, E. D. Brook, Y. Gürsel, “Gravitational wave detectors using laser interferometers and optical cavities,” in Quantum Optics, Experimental Gravity and Measurement Theory, P. Meystre, M. O. Scully, eds. (Plenum, New York, 1983).
    [CrossRef]
  7. A. Gillespie, F. Raab, “Thermally excited vibrations of the mirrors of laser interferometer gravitational-wave detectors,” Phys. Rev. D 52, 577–585 (1995).
    [CrossRef]
  8. V. Braginsky, M. Gorodetsky, S. Vyatchanin, “Thermodynamical fluctuations and photo-thermal shot noise in gravitational antennae,” Phys. Lett. A 264, 1–10 (1999).
    [CrossRef]
  9. W. Winkler, A. Rudiger, R. Schilling, K. Strain, K. Danzmann, “Birefringence-induced losses in interferometers,” Opt. Commun. 112, 245–252 (1994).
    [CrossRef]
  10. K. Strain, University of Glasgow (personal communication, 2000).
  11. D. Jacob, M. Vallet, F. Bretenaker, A. Floch, “Supermirror phase anisotropy measurement,” Opt. Lett. 20, 671–673 (1995).
    [CrossRef] [PubMed]
  12. D. G. Blari, M. Notcutt, C. T. Taylor, E. K. Wong, C. Walsh, A. Leistner, J. Seckold, J.-M. Mackowski, P. Ganau, C. Michel, L. Pinard, “Development of low-loss sapphire mirrors,” Appl. Opt. 36, 337–341 (1997).
    [CrossRef]
  13. P. Micossi, F. Valle, E. Milotti, E. Zavattini, C. Rizzo, G. Ruoso, “Measurement of the birefringence properties of the reflecting surface of an interferential mirror,” Appl. Phys. B 57, 95–98 (1993).
    [CrossRef]
  14. The coating was provided by Research Electro-Optics, Inc., Boulder, Colo.
  15. W. Driscoll, ed., Handbook of Optics (McGraw-Hill, New York, 1978), pp. 10–107.
  16. A. Alexandrovski, Ginzton Laboratory, Stanford University, Stanford, California 94305 (personal communication, 2000).

1999

V. Braginsky, M. Gorodetsky, S. Vyatchanin, “Thermodynamical fluctuations and photo-thermal shot noise in gravitational antennae,” Phys. Lett. A 264, 1–10 (1999).
[CrossRef]

1997

1995

A. Gillespie, F. Raab, “Thermally excited vibrations of the mirrors of laser interferometer gravitational-wave detectors,” Phys. Rev. D 52, 577–585 (1995).
[CrossRef]

D. Jacob, M. Vallet, F. Bretenaker, A. Floch, “Supermirror phase anisotropy measurement,” Opt. Lett. 20, 671–673 (1995).
[CrossRef] [PubMed]

1994

W. Winkler, A. Rudiger, R. Schilling, K. Strain, K. Danzmann, “Birefringence-induced losses in interferometers,” Opt. Commun. 112, 245–252 (1994).
[CrossRef]

1993

P. Micossi, F. Valle, E. Milotti, E. Zavattini, C. Rizzo, G. Ruoso, “Measurement of the birefringence properties of the reflecting surface of an interferential mirror,” Appl. Phys. B 57, 95–98 (1993).
[CrossRef]

1992

A. Abramovici, W. Althouse, R. W. P. Drever, Y. Gursel, S. Kawamura, F. J. Raab, D. Shoemaker, L. Sievers, R. E. Spero, R. E. Vogt, R. Weiss, S. E. Whitcomb, M. E. Zucker, “LIGO: the Laser Interferometer Gravitational Wave Observatory,” Science 256, 325–333 (1992).
[CrossRef] [PubMed]

1983

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

Abramovici, A.

A. Abramovici, W. Althouse, R. W. P. Drever, Y. Gursel, S. Kawamura, F. J. Raab, D. Shoemaker, L. Sievers, R. E. Spero, R. E. Vogt, R. Weiss, S. E. Whitcomb, M. E. Zucker, “LIGO: the Laser Interferometer Gravitational Wave Observatory,” Science 256, 325–333 (1992).
[CrossRef] [PubMed]

Alexandrovski, A.

A. Alexandrovski, Ginzton Laboratory, Stanford University, Stanford, California 94305 (personal communication, 2000).

Althouse, W.

A. Abramovici, W. Althouse, R. W. P. Drever, Y. Gursel, S. Kawamura, F. J. Raab, D. Shoemaker, L. Sievers, R. E. Spero, R. E. Vogt, R. Weiss, S. E. Whitcomb, M. E. Zucker, “LIGO: the Laser Interferometer Gravitational Wave Observatory,” Science 256, 325–333 (1992).
[CrossRef] [PubMed]

Blari, D. G.

Braginsky, V.

V. Braginsky, M. Gorodetsky, S. Vyatchanin, “Thermodynamical fluctuations and photo-thermal shot noise in gravitational antennae,” Phys. Lett. A 264, 1–10 (1999).
[CrossRef]

Bretenaker, F.

Brook, E. D.

R. W. P. Drever, J. Hough, A. J. Munley, S.-A. Lee, R. Spero, S. E. Whitcomb, H. Ward, G. M. Ford, M. Hereld, N. A. Robertson, I. Kerr, J. R. Pugh, G. P. Newton, B. Meers, E. D. Brook, Y. Gürsel, “Gravitational wave detectors using laser interferometers and optical cavities,” in Quantum Optics, Experimental Gravity and Measurement Theory, P. Meystre, M. O. Scully, eds. (Plenum, New York, 1983).
[CrossRef]

Danzmann, K.

W. Winkler, A. Rudiger, R. Schilling, K. Strain, K. Danzmann, “Birefringence-induced losses in interferometers,” Opt. Commun. 112, 245–252 (1994).
[CrossRef]

K. Danzmann, “GEO600—a 600 m laser interferometric gravitational wave antenna,” in First Edoardo Amaldi Conference on Gravitational Wave Experiment, E. Coccia, G. Pizella, F. Ronga, eds. (World Scientific, Singapore, 1995), pp. 100–111.

Drever, R. W. P.

A. Abramovici, W. Althouse, R. W. P. Drever, Y. Gursel, S. Kawamura, F. J. Raab, D. Shoemaker, L. Sievers, R. E. Spero, R. E. Vogt, R. Weiss, S. E. Whitcomb, M. E. Zucker, “LIGO: the Laser Interferometer Gravitational Wave Observatory,” Science 256, 325–333 (1992).
[CrossRef] [PubMed]

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

R. W. P. Drever, J. Hough, A. J. Munley, S.-A. Lee, R. Spero, S. E. Whitcomb, H. Ward, G. M. Ford, M. Hereld, N. A. Robertson, I. Kerr, J. R. Pugh, G. P. Newton, B. Meers, E. D. Brook, Y. Gürsel, “Gravitational wave detectors using laser interferometers and optical cavities,” in Quantum Optics, Experimental Gravity and Measurement Theory, P. Meystre, M. O. Scully, eds. (Plenum, New York, 1983).
[CrossRef]

Floch, A.

Ford, G. M.

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

R. W. P. Drever, J. Hough, A. J. Munley, S.-A. Lee, R. Spero, S. E. Whitcomb, H. Ward, G. M. Ford, M. Hereld, N. A. Robertson, I. Kerr, J. R. Pugh, G. P. Newton, B. Meers, E. D. Brook, Y. Gürsel, “Gravitational wave detectors using laser interferometers and optical cavities,” in Quantum Optics, Experimental Gravity and Measurement Theory, P. Meystre, M. O. Scully, eds. (Plenum, New York, 1983).
[CrossRef]

Ganau, P.

Giazotto, A.

A. Giazotto, “The Virgo experiment: status of the art,” in First Edoardo Amaldi Conference on Gravitational Wave Experiments, E. Coccia, G. Pizella, F. Ronga, eds. (World Scientific, Singapore, 1995), pp. 86–99.

Gillespie, A.

A. Gillespie, F. Raab, “Thermally excited vibrations of the mirrors of laser interferometer gravitational-wave detectors,” Phys. Rev. D 52, 577–585 (1995).
[CrossRef]

Gorodetsky, M.

V. Braginsky, M. Gorodetsky, S. Vyatchanin, “Thermodynamical fluctuations and photo-thermal shot noise in gravitational antennae,” Phys. Lett. A 264, 1–10 (1999).
[CrossRef]

Gursel, Y.

A. Abramovici, W. Althouse, R. W. P. Drever, Y. Gursel, S. Kawamura, F. J. Raab, D. Shoemaker, L. Sievers, R. E. Spero, R. E. Vogt, R. Weiss, S. E. Whitcomb, M. E. Zucker, “LIGO: the Laser Interferometer Gravitational Wave Observatory,” Science 256, 325–333 (1992).
[CrossRef] [PubMed]

Gürsel, Y.

R. W. P. Drever, J. Hough, A. J. Munley, S.-A. Lee, R. Spero, S. E. Whitcomb, H. Ward, G. M. Ford, M. Hereld, N. A. Robertson, I. Kerr, J. R. Pugh, G. P. Newton, B. Meers, E. D. Brook, Y. Gürsel, “Gravitational wave detectors using laser interferometers and optical cavities,” in Quantum Optics, Experimental Gravity and Measurement Theory, P. Meystre, M. O. Scully, eds. (Plenum, New York, 1983).
[CrossRef]

Hall, J. L.

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

Hereld, M.

R. W. P. Drever, J. Hough, A. J. Munley, S.-A. Lee, R. Spero, S. E. Whitcomb, H. Ward, G. M. Ford, M. Hereld, N. A. Robertson, I. Kerr, J. R. Pugh, G. P. Newton, B. Meers, E. D. Brook, Y. Gürsel, “Gravitational wave detectors using laser interferometers and optical cavities,” in Quantum Optics, Experimental Gravity and Measurement Theory, P. Meystre, M. O. Scully, eds. (Plenum, New York, 1983).
[CrossRef]

Hough, J.

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

R. W. P. Drever, J. Hough, A. J. Munley, S.-A. Lee, R. Spero, S. E. Whitcomb, H. Ward, G. M. Ford, M. Hereld, N. A. Robertson, I. Kerr, J. R. Pugh, G. P. Newton, B. Meers, E. D. Brook, Y. Gürsel, “Gravitational wave detectors using laser interferometers and optical cavities,” in Quantum Optics, Experimental Gravity and Measurement Theory, P. Meystre, M. O. Scully, eds. (Plenum, New York, 1983).
[CrossRef]

Jacob, D.

Kawamura, S.

A. Abramovici, W. Althouse, R. W. P. Drever, Y. Gursel, S. Kawamura, F. J. Raab, D. Shoemaker, L. Sievers, R. E. Spero, R. E. Vogt, R. Weiss, S. E. Whitcomb, M. E. Zucker, “LIGO: the Laser Interferometer Gravitational Wave Observatory,” Science 256, 325–333 (1992).
[CrossRef] [PubMed]

Kerr, I.

R. W. P. Drever, J. Hough, A. J. Munley, S.-A. Lee, R. Spero, S. E. Whitcomb, H. Ward, G. M. Ford, M. Hereld, N. A. Robertson, I. Kerr, J. R. Pugh, G. P. Newton, B. Meers, E. D. Brook, Y. Gürsel, “Gravitational wave detectors using laser interferometers and optical cavities,” in Quantum Optics, Experimental Gravity and Measurement Theory, P. Meystre, M. O. Scully, eds. (Plenum, New York, 1983).
[CrossRef]

Kowalski, F. V.

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

Lee, S.-A.

R. W. P. Drever, J. Hough, A. J. Munley, S.-A. Lee, R. Spero, S. E. Whitcomb, H. Ward, G. M. Ford, M. Hereld, N. A. Robertson, I. Kerr, J. R. Pugh, G. P. Newton, B. Meers, E. D. Brook, Y. Gürsel, “Gravitational wave detectors using laser interferometers and optical cavities,” in Quantum Optics, Experimental Gravity and Measurement Theory, P. Meystre, M. O. Scully, eds. (Plenum, New York, 1983).
[CrossRef]

Leistner, A.

Mackowski, J.-M.

Meers, B.

R. W. P. Drever, J. Hough, A. J. Munley, S.-A. Lee, R. Spero, S. E. Whitcomb, H. Ward, G. M. Ford, M. Hereld, N. A. Robertson, I. Kerr, J. R. Pugh, G. P. Newton, B. Meers, E. D. Brook, Y. Gürsel, “Gravitational wave detectors using laser interferometers and optical cavities,” in Quantum Optics, Experimental Gravity and Measurement Theory, P. Meystre, M. O. Scully, eds. (Plenum, New York, 1983).
[CrossRef]

Michel, C.

Micossi, P.

P. Micossi, F. Valle, E. Milotti, E. Zavattini, C. Rizzo, G. Ruoso, “Measurement of the birefringence properties of the reflecting surface of an interferential mirror,” Appl. Phys. B 57, 95–98 (1993).
[CrossRef]

Milotti, E.

P. Micossi, F. Valle, E. Milotti, E. Zavattini, C. Rizzo, G. Ruoso, “Measurement of the birefringence properties of the reflecting surface of an interferential mirror,” Appl. Phys. B 57, 95–98 (1993).
[CrossRef]

Munley, A. J.

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

R. W. P. Drever, J. Hough, A. J. Munley, S.-A. Lee, R. Spero, S. E. Whitcomb, H. Ward, G. M. Ford, M. Hereld, N. A. Robertson, I. Kerr, J. R. Pugh, G. P. Newton, B. Meers, E. D. Brook, Y. Gürsel, “Gravitational wave detectors using laser interferometers and optical cavities,” in Quantum Optics, Experimental Gravity and Measurement Theory, P. Meystre, M. O. Scully, eds. (Plenum, New York, 1983).
[CrossRef]

Newton, G. P.

R. W. P. Drever, J. Hough, A. J. Munley, S.-A. Lee, R. Spero, S. E. Whitcomb, H. Ward, G. M. Ford, M. Hereld, N. A. Robertson, I. Kerr, J. R. Pugh, G. P. Newton, B. Meers, E. D. Brook, Y. Gürsel, “Gravitational wave detectors using laser interferometers and optical cavities,” in Quantum Optics, Experimental Gravity and Measurement Theory, P. Meystre, M. O. Scully, eds. (Plenum, New York, 1983).
[CrossRef]

Notcutt, M.

Pinard, L.

Pugh, J. R.

R. W. P. Drever, J. Hough, A. J. Munley, S.-A. Lee, R. Spero, S. E. Whitcomb, H. Ward, G. M. Ford, M. Hereld, N. A. Robertson, I. Kerr, J. R. Pugh, G. P. Newton, B. Meers, E. D. Brook, Y. Gürsel, “Gravitational wave detectors using laser interferometers and optical cavities,” in Quantum Optics, Experimental Gravity and Measurement Theory, P. Meystre, M. O. Scully, eds. (Plenum, New York, 1983).
[CrossRef]

Raab, F.

A. Gillespie, F. Raab, “Thermally excited vibrations of the mirrors of laser interferometer gravitational-wave detectors,” Phys. Rev. D 52, 577–585 (1995).
[CrossRef]

Raab, F. J.

A. Abramovici, W. Althouse, R. W. P. Drever, Y. Gursel, S. Kawamura, F. J. Raab, D. Shoemaker, L. Sievers, R. E. Spero, R. E. Vogt, R. Weiss, S. E. Whitcomb, M. E. Zucker, “LIGO: the Laser Interferometer Gravitational Wave Observatory,” Science 256, 325–333 (1992).
[CrossRef] [PubMed]

Rizzo, C.

P. Micossi, F. Valle, E. Milotti, E. Zavattini, C. Rizzo, G. Ruoso, “Measurement of the birefringence properties of the reflecting surface of an interferential mirror,” Appl. Phys. B 57, 95–98 (1993).
[CrossRef]

Robertson, N. A.

R. W. P. Drever, J. Hough, A. J. Munley, S.-A. Lee, R. Spero, S. E. Whitcomb, H. Ward, G. M. Ford, M. Hereld, N. A. Robertson, I. Kerr, J. R. Pugh, G. P. Newton, B. Meers, E. D. Brook, Y. Gürsel, “Gravitational wave detectors using laser interferometers and optical cavities,” in Quantum Optics, Experimental Gravity and Measurement Theory, P. Meystre, M. O. Scully, eds. (Plenum, New York, 1983).
[CrossRef]

Rudiger, A.

W. Winkler, A. Rudiger, R. Schilling, K. Strain, K. Danzmann, “Birefringence-induced losses in interferometers,” Opt. Commun. 112, 245–252 (1994).
[CrossRef]

Ruoso, G.

P. Micossi, F. Valle, E. Milotti, E. Zavattini, C. Rizzo, G. Ruoso, “Measurement of the birefringence properties of the reflecting surface of an interferential mirror,” Appl. Phys. B 57, 95–98 (1993).
[CrossRef]

Schilling, R.

W. Winkler, A. Rudiger, R. Schilling, K. Strain, K. Danzmann, “Birefringence-induced losses in interferometers,” Opt. Commun. 112, 245–252 (1994).
[CrossRef]

Seckold, J.

Shoemaker, D.

A. Abramovici, W. Althouse, R. W. P. Drever, Y. Gursel, S. Kawamura, F. J. Raab, D. Shoemaker, L. Sievers, R. E. Spero, R. E. Vogt, R. Weiss, S. E. Whitcomb, M. E. Zucker, “LIGO: the Laser Interferometer Gravitational Wave Observatory,” Science 256, 325–333 (1992).
[CrossRef] [PubMed]

Sievers, L.

A. Abramovici, W. Althouse, R. W. P. Drever, Y. Gursel, S. Kawamura, F. J. Raab, D. Shoemaker, L. Sievers, R. E. Spero, R. E. Vogt, R. Weiss, S. E. Whitcomb, M. E. Zucker, “LIGO: the Laser Interferometer Gravitational Wave Observatory,” Science 256, 325–333 (1992).
[CrossRef] [PubMed]

Spero, R.

R. W. P. Drever, J. Hough, A. J. Munley, S.-A. Lee, R. Spero, S. E. Whitcomb, H. Ward, G. M. Ford, M. Hereld, N. A. Robertson, I. Kerr, J. R. Pugh, G. P. Newton, B. Meers, E. D. Brook, Y. Gürsel, “Gravitational wave detectors using laser interferometers and optical cavities,” in Quantum Optics, Experimental Gravity and Measurement Theory, P. Meystre, M. O. Scully, eds. (Plenum, New York, 1983).
[CrossRef]

Spero, R. E.

A. Abramovici, W. Althouse, R. W. P. Drever, Y. Gursel, S. Kawamura, F. J. Raab, D. Shoemaker, L. Sievers, R. E. Spero, R. E. Vogt, R. Weiss, S. E. Whitcomb, M. E. Zucker, “LIGO: the Laser Interferometer Gravitational Wave Observatory,” Science 256, 325–333 (1992).
[CrossRef] [PubMed]

Strain, K.

W. Winkler, A. Rudiger, R. Schilling, K. Strain, K. Danzmann, “Birefringence-induced losses in interferometers,” Opt. Commun. 112, 245–252 (1994).
[CrossRef]

K. Strain, University of Glasgow (personal communication, 2000).

Taylor, C. T.

Tsubono, K.

K. Tsubono, “300-m laser interferometer gravitational wave detector (TAMA300) in Japan,” in First Edoardo Amaldi Conference on Gravitational Wave Experiment, E. Coccia, G. Pizella, F. Ronga, eds. (World Scientific, Singapore, 1995), pp. 112–114.

Valle, F.

P. Micossi, F. Valle, E. Milotti, E. Zavattini, C. Rizzo, G. Ruoso, “Measurement of the birefringence properties of the reflecting surface of an interferential mirror,” Appl. Phys. B 57, 95–98 (1993).
[CrossRef]

Vallet, M.

Vogt, R. E.

A. Abramovici, W. Althouse, R. W. P. Drever, Y. Gursel, S. Kawamura, F. J. Raab, D. Shoemaker, L. Sievers, R. E. Spero, R. E. Vogt, R. Weiss, S. E. Whitcomb, M. E. Zucker, “LIGO: the Laser Interferometer Gravitational Wave Observatory,” Science 256, 325–333 (1992).
[CrossRef] [PubMed]

Vyatchanin, S.

V. Braginsky, M. Gorodetsky, S. Vyatchanin, “Thermodynamical fluctuations and photo-thermal shot noise in gravitational antennae,” Phys. Lett. A 264, 1–10 (1999).
[CrossRef]

Walsh, C.

Ward, H.

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

R. W. P. Drever, J. Hough, A. J. Munley, S.-A. Lee, R. Spero, S. E. Whitcomb, H. Ward, G. M. Ford, M. Hereld, N. A. Robertson, I. Kerr, J. R. Pugh, G. P. Newton, B. Meers, E. D. Brook, Y. Gürsel, “Gravitational wave detectors using laser interferometers and optical cavities,” in Quantum Optics, Experimental Gravity and Measurement Theory, P. Meystre, M. O. Scully, eds. (Plenum, New York, 1983).
[CrossRef]

Weiss, R.

A. Abramovici, W. Althouse, R. W. P. Drever, Y. Gursel, S. Kawamura, F. J. Raab, D. Shoemaker, L. Sievers, R. E. Spero, R. E. Vogt, R. Weiss, S. E. Whitcomb, M. E. Zucker, “LIGO: the Laser Interferometer Gravitational Wave Observatory,” Science 256, 325–333 (1992).
[CrossRef] [PubMed]

Whitcomb, S. E.

A. Abramovici, W. Althouse, R. W. P. Drever, Y. Gursel, S. Kawamura, F. J. Raab, D. Shoemaker, L. Sievers, R. E. Spero, R. E. Vogt, R. Weiss, S. E. Whitcomb, M. E. Zucker, “LIGO: the Laser Interferometer Gravitational Wave Observatory,” Science 256, 325–333 (1992).
[CrossRef] [PubMed]

R. W. P. Drever, J. Hough, A. J. Munley, S.-A. Lee, R. Spero, S. E. Whitcomb, H. Ward, G. M. Ford, M. Hereld, N. A. Robertson, I. Kerr, J. R. Pugh, G. P. Newton, B. Meers, E. D. Brook, Y. Gürsel, “Gravitational wave detectors using laser interferometers and optical cavities,” in Quantum Optics, Experimental Gravity and Measurement Theory, P. Meystre, M. O. Scully, eds. (Plenum, New York, 1983).
[CrossRef]

Winkler, W.

W. Winkler, A. Rudiger, R. Schilling, K. Strain, K. Danzmann, “Birefringence-induced losses in interferometers,” Opt. Commun. 112, 245–252 (1994).
[CrossRef]

Wong, E. K.

Zavattini, E.

P. Micossi, F. Valle, E. Milotti, E. Zavattini, C. Rizzo, G. Ruoso, “Measurement of the birefringence properties of the reflecting surface of an interferential mirror,” Appl. Phys. B 57, 95–98 (1993).
[CrossRef]

Zucker, M. E.

A. Abramovici, W. Althouse, R. W. P. Drever, Y. Gursel, S. Kawamura, F. J. Raab, D. Shoemaker, L. Sievers, R. E. Spero, R. E. Vogt, R. Weiss, S. E. Whitcomb, M. E. Zucker, “LIGO: the Laser Interferometer Gravitational Wave Observatory,” Science 256, 325–333 (1992).
[CrossRef] [PubMed]

Appl. Opt.

Appl. Phys. B

P. Micossi, F. Valle, E. Milotti, E. Zavattini, C. Rizzo, G. Ruoso, “Measurement of the birefringence properties of the reflecting surface of an interferential mirror,” Appl. Phys. B 57, 95–98 (1993).
[CrossRef]

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

Opt. Commun.

W. Winkler, A. Rudiger, R. Schilling, K. Strain, K. Danzmann, “Birefringence-induced losses in interferometers,” Opt. Commun. 112, 245–252 (1994).
[CrossRef]

Opt. Lett.

Phys. Lett. A

V. Braginsky, M. Gorodetsky, S. Vyatchanin, “Thermodynamical fluctuations and photo-thermal shot noise in gravitational antennae,” Phys. Lett. A 264, 1–10 (1999).
[CrossRef]

Phys. Rev. D

A. Gillespie, F. Raab, “Thermally excited vibrations of the mirrors of laser interferometer gravitational-wave detectors,” Phys. Rev. D 52, 577–585 (1995).
[CrossRef]

Science

A. Abramovici, W. Althouse, R. W. P. Drever, Y. Gursel, S. Kawamura, F. J. Raab, D. Shoemaker, L. Sievers, R. E. Spero, R. E. Vogt, R. Weiss, S. E. Whitcomb, M. E. Zucker, “LIGO: the Laser Interferometer Gravitational Wave Observatory,” Science 256, 325–333 (1992).
[CrossRef] [PubMed]

Other

A. Giazotto, “The Virgo experiment: status of the art,” in First Edoardo Amaldi Conference on Gravitational Wave Experiments, E. Coccia, G. Pizella, F. Ronga, eds. (World Scientific, Singapore, 1995), pp. 86–99.

K. Tsubono, “300-m laser interferometer gravitational wave detector (TAMA300) in Japan,” in First Edoardo Amaldi Conference on Gravitational Wave Experiment, E. Coccia, G. Pizella, F. Ronga, eds. (World Scientific, Singapore, 1995), pp. 112–114.

K. Danzmann, “GEO600—a 600 m laser interferometric gravitational wave antenna,” in First Edoardo Amaldi Conference on Gravitational Wave Experiment, E. Coccia, G. Pizella, F. Ronga, eds. (World Scientific, Singapore, 1995), pp. 100–111.

R. W. P. Drever, J. Hough, A. J. Munley, S.-A. Lee, R. Spero, S. E. Whitcomb, H. Ward, G. M. Ford, M. Hereld, N. A. Robertson, I. Kerr, J. R. Pugh, G. P. Newton, B. Meers, E. D. Brook, Y. Gürsel, “Gravitational wave detectors using laser interferometers and optical cavities,” in Quantum Optics, Experimental Gravity and Measurement Theory, P. Meystre, M. O. Scully, eds. (Plenum, New York, 1983).
[CrossRef]

K. Strain, University of Glasgow (personal communication, 2000).

The coating was provided by Research Electro-Optics, Inc., Boulder, Colo.

W. Driscoll, ed., Handbook of Optics (McGraw-Hill, New York, 1978), pp. 10–107.

A. Alexandrovski, Ginzton Laboratory, Stanford University, Stanford, California 94305 (personal communication, 2000).

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Figures (8)

Fig. 1
Fig. 1

Schematic diagram of the LIGO detector. ITM, input test mass; ETM, end test mass; RM, recycling mirror; BS, beam splitter.

Fig. 2
Fig. 2

Schematic diagram of apparatus. FI, Faraday isolator; λ/2, half-wave plate; RFPD, radio-frequency photodetector.

Fig. 3
Fig. 3

Transmitted power versus input polarization of light for the substrate inside the cavity.

Fig. 4
Fig. 4

Eigenfrequencies for the substrate inside the cavity. The sapphire substrate birefringence causes a splitting of the cavity TEM01 resonance.

Fig. 5
Fig. 5

Frequency spectrum for the substrate outside the cavity. The coating birefringence is too small to resolve the splitting of the TEM01 resonances.

Fig. 6
Fig. 6

Transmitted power versus input polarization for the substrate outside the cavity. The depth of the minima gives the magnitude of the coating birefringence, whereas the location of the minima gives the birefringence direction. Also shown is the orientation of the c-axis of the crystal.

Fig. 7
Fig. 7

Experimental setup used to determine the sapphire substrate optical axes. P, polarizer; PD, photodetector.

Fig. 8
Fig. 8

Transmitted power versus input polarization for one pass through the substrate. At each point the polarizer before the detector was adjusted for maximum transmission.

Equations (6)

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Δϕ=2Garmθ sin α cos α,
0.1Grc>4Garmθα2.
Δν1000=c2πlcos-1g1g21/2,
ϕ=n2-n1t+θwx,
II0=cos2Φ+Φ0+sin2Φ+Φ01+δνΔνHWHM2,
θ=22πδνcl,

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