Abstract

We present a signal extraction scheme for longitudinal sensing and control of an interferometric gravitational-wave detector based on a multiple-frequency heterodyne detection technique. Gravitational-wave detectors use multiple-mirror resonant optical systems where resonance conditions must be satisfied for multiple degrees of freedom that are optically coupled. The multiple-carrier longitudinal-sensing technique provides sensitive signals for all interferometric lengths to be controlled and successfully decouples them. The feasibility of the technique is demonstrated on a tabletop-scale power-recycled Michelson interferometer with Fabry–Perot arm cavities, and the experimentally measured values of the length-sensing signals are in good agreement with theoretical calculations.

© 1998 Optical Society of America

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  1. See, for example, K. S. Thorne, “Gravitational radiation,” in 300 Years of Gravitation, S. W. Hawking, W. Israel, eds. (Cambridge U. Press, Cambridge, UK, 1987), pp. 330–458.
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  3. A. Giazotto, “The VIRGO experiment: status of the art,” in First Edoardo Amaldi Conference on Gravitational Wave Experiments, E. Coccia, G. Pixella, F. Ronga, eds. (World Scientific, Singapore, 1995), pp. 86–99.
  4. K. Danzmann, “GEO600—600 m laser interferometric gravitational wave antenna,” in First Edoardo Amaldi Conference on Gravitational Wave Experiments, E. Coccia, G. Pixell, F. Ronga, eds. (World Scientific, Singapore, 1995), pp. 100–111.
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    [CrossRef] [PubMed]
  8. 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), pp. 503–524.
    [CrossRef]
  9. H. Billing, K. Maischberger, A. Rüdiger, R. Schilling, L. Schnupp, W. Winkler, “The Munich Gravitational Wave Detector using laser interferometry,” in Quantum Optics, Experimental Gravity, and Measurement Theory, P. Meystre, M. O. Scully, eds. (Plenum, New York, 1983), pp. 525–566.
    [CrossRef]
  10. D. Schnier, J. Mizuno, G. Heinzel, H. Lück, A. Rüdiger, R. Schilling, M. Schrempel, W. Winkler, K. Danzmann, “Power recycling in the Garching 30 m prototype interferometer for gravitational-wave detection,” Phys. Lett. A 225, 210–216 (1997).
    [CrossRef]
  11. A. Schenzle, R. DeVoe, G. Brewer, “Phase-modulation laser spectroscopy,” Phys. Rev. A 25, 2606–2621 (1982).
    [CrossRef]
  12. 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]
  13. L. Schnupp, Max Planck Institute for Quantum Optics, D-85748 Garching, Germany (personal communication, 1986).
  14. M. W. Regehr, F. J. Raab, S. E. Whitcomb, “Demonstration of a power-recycled Michelson interferometer with Fabry–Perot arms by frontal modulation,” Opt. Lett. 20, 1507–1509 (1995).
    [CrossRef] [PubMed]
  15. A. Giaime, “Studies of laser interferometric design and a vibration isolation system for interferometric gravitational wave detectors,” Ph.D. dissertation (Massachusetts Institute of Technology, Cambridge, Mass., 1995).
  16. N. Mavalvala, “Alignment issues in laser interferometric gravitational-wave detectors,” Ph.D. dissertation (Massachu-setts Institute of Technology, Cambridge, Mass., 1997), p. 23.
  17. A. E. Siegman, Lasers (University Science, Mill Valley, Calif., 1986), p. 423.
  18. Y. Hefetz, N. Mavalvala, D. Sigg, “Principles of calculating alignment signals in complex resonant optical interferometers,” J. Opt. Soc. Am. B 14, 1597–1605 (1997).
    [CrossRef]
  19. N. Mavalvala, D. Sigg, D. Shoemaker, “Experimental test of an alignment sensing scheme for a gravitational-wave interferometer,” Appl. Opt. (to be published).
  20. C. N. Man, D. Shoemaker, M. Pham Tu, D. Dewey, “External modulation technique for sensitive interferometric detection of displacements,” Phys. Lett. A 148, 8–16 (1990).
    [CrossRef]
  21. B. J. Meers, “Recycling in laser-interferometric gravitational-wave detectors,” Phys. Rev. D 38, 2317–2326 (1988).
    [CrossRef]

1997 (2)

D. Schnier, J. Mizuno, G. Heinzel, H. Lück, A. Rüdiger, R. Schilling, M. Schrempel, W. Winkler, K. Danzmann, “Power recycling in the Garching 30 m prototype interferometer for gravitational-wave detection,” Phys. Lett. A 225, 210–216 (1997).
[CrossRef]

Y. Hefetz, N. Mavalvala, D. Sigg, “Principles of calculating alignment signals in complex resonant optical interferometers,” J. Opt. Soc. Am. B 14, 1597–1605 (1997).
[CrossRef]

1995 (1)

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, M. E. Zucker, “LIGO: the Laser Interferometer Gravitational-wave Observatory,” Science 256, 325–333 (1992).
[CrossRef] [PubMed]

1990 (1)

C. N. Man, D. Shoemaker, M. Pham Tu, D. Dewey, “External modulation technique for sensitive interferometric detection of displacements,” Phys. Lett. A 148, 8–16 (1990).
[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, H. Ward, “Laser phase and frequency stabilization using an optical resonator,” Appl. Phys. B 31, 97–105 (1983).
[CrossRef]

1982 (1)

A. Schenzle, R. DeVoe, G. Brewer, “Phase-modulation laser spectroscopy,” Phys. Rev. A 25, 2606–2621 (1982).
[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, M. E. Zucker, “LIGO: the Laser Interferometer Gravitational-wave Observatory,” Science 256, 325–333 (1992).
[CrossRef] [PubMed]

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, M. E. Zucker, “LIGO: the Laser Interferometer Gravitational-wave Observatory,” Science 256, 325–333 (1992).
[CrossRef] [PubMed]

Billing, H.

H. Billing, K. Maischberger, A. Rüdiger, R. Schilling, L. Schnupp, W. Winkler, “The Munich Gravitational Wave Detector using laser interferometry,” in Quantum Optics, Experimental Gravity, and Measurement Theory, P. Meystre, M. O. Scully, eds. (Plenum, New York, 1983), pp. 525–566.
[CrossRef]

Brewer, G.

A. Schenzle, R. DeVoe, G. Brewer, “Phase-modulation laser spectroscopy,” Phys. Rev. A 25, 2606–2621 (1982).
[CrossRef]

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), pp. 503–524.
[CrossRef]

Danzmann, K.

D. Schnier, J. Mizuno, G. Heinzel, H. Lück, A. Rüdiger, R. Schilling, M. Schrempel, W. Winkler, K. Danzmann, “Power recycling in the Garching 30 m prototype interferometer for gravitational-wave detection,” Phys. Lett. A 225, 210–216 (1997).
[CrossRef]

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

DeVoe, R.

A. Schenzle, R. DeVoe, G. Brewer, “Phase-modulation laser spectroscopy,” Phys. Rev. A 25, 2606–2621 (1982).
[CrossRef]

Dewey, D.

C. N. Man, D. Shoemaker, M. Pham Tu, D. Dewey, “External modulation technique for sensitive interferometric detection of displacements,” Phys. Lett. A 148, 8–16 (1990).
[CrossRef]

Drever, R. W. P.

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, 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), pp. 503–524.
[CrossRef]

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), pp. 503–524.
[CrossRef]

Giaime, A.

A. Giaime, “Studies of laser interferometric design and a vibration isolation system for interferometric gravitational wave detectors,” Ph.D. dissertation (Massachusetts Institute of Technology, Cambridge, Mass., 1995).

Giazotto, A.

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

Gürsel, Y.

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, 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), pp. 503–524.
[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]

Hefetz, Y.

Heinzel, G.

D. Schnier, J. Mizuno, G. Heinzel, H. Lück, A. Rüdiger, R. Schilling, M. Schrempel, W. Winkler, K. Danzmann, “Power recycling in the Garching 30 m prototype interferometer for gravitational-wave detection,” Phys. Lett. A 225, 210–216 (1997).
[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), pp. 503–524.
[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), pp. 503–524.
[CrossRef]

Kawamura, 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, 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), pp. 503–524.
[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), pp. 503–524.
[CrossRef]

Lück, H.

D. Schnier, J. Mizuno, G. Heinzel, H. Lück, A. Rüdiger, R. Schilling, M. Schrempel, W. Winkler, K. Danzmann, “Power recycling in the Garching 30 m prototype interferometer for gravitational-wave detection,” Phys. Lett. A 225, 210–216 (1997).
[CrossRef]

Maischberger, K.

H. Billing, K. Maischberger, A. Rüdiger, R. Schilling, L. Schnupp, W. Winkler, “The Munich Gravitational Wave Detector using laser interferometry,” in Quantum Optics, Experimental Gravity, and Measurement Theory, P. Meystre, M. O. Scully, eds. (Plenum, New York, 1983), pp. 525–566.
[CrossRef]

Man, C. N.

C. N. Man, D. Shoemaker, M. Pham Tu, D. Dewey, “External modulation technique for sensitive interferometric detection of displacements,” Phys. Lett. A 148, 8–16 (1990).
[CrossRef]

Mavalvala, N.

Y. Hefetz, N. Mavalvala, D. Sigg, “Principles of calculating alignment signals in complex resonant optical interferometers,” J. Opt. Soc. Am. B 14, 1597–1605 (1997).
[CrossRef]

N. Mavalvala, D. Sigg, D. Shoemaker, “Experimental test of an alignment sensing scheme for a gravitational-wave interferometer,” Appl. Opt. (to be published).

N. Mavalvala, “Alignment issues in laser interferometric gravitational-wave detectors,” Ph.D. dissertation (Massachu-setts Institute of Technology, Cambridge, Mass., 1997), p. 23.

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), pp. 503–524.
[CrossRef]

Meers, B. J.

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

Mizuno, J.

D. Schnier, J. Mizuno, G. Heinzel, H. Lück, A. Rüdiger, R. Schilling, M. Schrempel, W. Winkler, K. Danzmann, “Power recycling in the Garching 30 m prototype interferometer for gravitational-wave detection,” Phys. Lett. A 225, 210–216 (1997).
[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), pp. 503–524.
[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), pp. 503–524.
[CrossRef]

Pham Tu, M.

C. N. Man, D. Shoemaker, M. Pham Tu, D. Dewey, “External modulation technique for sensitive interferometric detection of displacements,” Phys. Lett. A 148, 8–16 (1990).
[CrossRef]

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), pp. 503–524.
[CrossRef]

Raab, F. J.

M. W. Regehr, F. J. Raab, S. E. Whitcomb, “Demonstration of a power-recycled Michelson interferometer with Fabry–Perot arms by frontal modulation,” Opt. Lett. 20, 1507–1509 (1995).
[CrossRef] [PubMed]

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, M. E. Zucker, “LIGO: the Laser Interferometer Gravitational-wave Observatory,” Science 256, 325–333 (1992).
[CrossRef] [PubMed]

F. J. Raab, “The LIGO project: progress and prospects,” in First Edoardo Amaldi Conference on Gravitational Wave Experiments, E. Coccia, G. Pixella, F. Ronga, eds. (World Scientific, Singapore, 1995), pp. 70–85.

Regehr, M. W.

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), pp. 503–524.
[CrossRef]

Rüdiger, A.

D. Schnier, J. Mizuno, G. Heinzel, H. Lück, A. Rüdiger, R. Schilling, M. Schrempel, W. Winkler, K. Danzmann, “Power recycling in the Garching 30 m prototype interferometer for gravitational-wave detection,” Phys. Lett. A 225, 210–216 (1997).
[CrossRef]

H. Billing, K. Maischberger, A. Rüdiger, R. Schilling, L. Schnupp, W. Winkler, “The Munich Gravitational Wave Detector using laser interferometry,” in Quantum Optics, Experimental Gravity, and Measurement Theory, P. Meystre, M. O. Scully, eds. (Plenum, New York, 1983), pp. 525–566.
[CrossRef]

Schenzle, A.

A. Schenzle, R. DeVoe, G. Brewer, “Phase-modulation laser spectroscopy,” Phys. Rev. A 25, 2606–2621 (1982).
[CrossRef]

Schilling, R.

D. Schnier, J. Mizuno, G. Heinzel, H. Lück, A. Rüdiger, R. Schilling, M. Schrempel, W. Winkler, K. Danzmann, “Power recycling in the Garching 30 m prototype interferometer for gravitational-wave detection,” Phys. Lett. A 225, 210–216 (1997).
[CrossRef]

H. Billing, K. Maischberger, A. Rüdiger, R. Schilling, L. Schnupp, W. Winkler, “The Munich Gravitational Wave Detector using laser interferometry,” in Quantum Optics, Experimental Gravity, and Measurement Theory, P. Meystre, M. O. Scully, eds. (Plenum, New York, 1983), pp. 525–566.
[CrossRef]

Schnier, D.

D. Schnier, J. Mizuno, G. Heinzel, H. Lück, A. Rüdiger, R. Schilling, M. Schrempel, W. Winkler, K. Danzmann, “Power recycling in the Garching 30 m prototype interferometer for gravitational-wave detection,” Phys. Lett. A 225, 210–216 (1997).
[CrossRef]

Schnupp, L.

H. Billing, K. Maischberger, A. Rüdiger, R. Schilling, L. Schnupp, W. Winkler, “The Munich Gravitational Wave Detector using laser interferometry,” in Quantum Optics, Experimental Gravity, and Measurement Theory, P. Meystre, M. O. Scully, eds. (Plenum, New York, 1983), pp. 525–566.
[CrossRef]

L. Schnupp, Max Planck Institute for Quantum Optics, D-85748 Garching, Germany (personal communication, 1986).

Schrempel, M.

D. Schnier, J. Mizuno, G. Heinzel, H. Lück, A. Rüdiger, R. Schilling, M. Schrempel, W. Winkler, K. Danzmann, “Power recycling in the Garching 30 m prototype interferometer for gravitational-wave detection,” Phys. Lett. A 225, 210–216 (1997).
[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, M. E. Zucker, “LIGO: the Laser Interferometer Gravitational-wave Observatory,” Science 256, 325–333 (1992).
[CrossRef] [PubMed]

C. N. Man, D. Shoemaker, M. Pham Tu, D. Dewey, “External modulation technique for sensitive interferometric detection of displacements,” Phys. Lett. A 148, 8–16 (1990).
[CrossRef]

N. Mavalvala, D. Sigg, D. Shoemaker, “Experimental test of an alignment sensing scheme for a gravitational-wave interferometer,” Appl. Opt. (to be published).

Siegman, A. E.

A. E. Siegman, Lasers (University Science, Mill Valley, Calif., 1986), p. 423.

Sievers, L.

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, M. E. Zucker, “LIGO: the Laser Interferometer Gravitational-wave Observatory,” Science 256, 325–333 (1992).
[CrossRef] [PubMed]

Sigg, D.

Y. Hefetz, N. Mavalvala, D. Sigg, “Principles of calculating alignment signals in complex resonant optical interferometers,” J. Opt. Soc. Am. B 14, 1597–1605 (1997).
[CrossRef]

N. Mavalvala, D. Sigg, D. Shoemaker, “Experimental test of an alignment sensing scheme for a gravitational-wave interferometer,” Appl. Opt. (to be published).

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), pp. 503–524.
[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, M. E. Zucker, “LIGO: the Laser Interferometer Gravitational-wave Observatory,” Science 256, 325–333 (1992).
[CrossRef] [PubMed]

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, M. E. Zucker, “LIGO: the Laser Interferometer Gravitational-wave Observatory,” Science 256, 325–333 (1992).
[CrossRef] [PubMed]

See, for example, K. S. Thorne, “Gravitational radiation,” in 300 Years of Gravitation, S. W. Hawking, W. Israel, eds. (Cambridge U. Press, Cambridge, UK, 1987), pp. 330–458.

Tsubono, K.

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

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, M. E. Zucker, “LIGO: the Laser Interferometer Gravitational-wave Observatory,” Science 256, 325–333 (1992).
[CrossRef] [PubMed]

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), pp. 503–524.
[CrossRef]

Weiss, R.

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, M. E. Zucker, “LIGO: the Laser Interferometer Gravitational-wave Observatory,” Science 256, 325–333 (1992).
[CrossRef] [PubMed]

R. Weiss, “Electromagnetically coupled broadband gravitational antenna,” MIT Res. Lab. Electron. Q. Prog. Rep.105, 54–76 (1972).

Whitcomb, S. E.

M. W. Regehr, F. J. Raab, S. E. Whitcomb, “Demonstration of a power-recycled Michelson interferometer with Fabry–Perot arms by frontal modulation,” Opt. Lett. 20, 1507–1509 (1995).
[CrossRef] [PubMed]

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, 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), pp. 503–524.
[CrossRef]

Winkler, W.

D. Schnier, J. Mizuno, G. Heinzel, H. Lück, A. Rüdiger, R. Schilling, M. Schrempel, W. Winkler, K. Danzmann, “Power recycling in the Garching 30 m prototype interferometer for gravitational-wave detection,” Phys. Lett. A 225, 210–216 (1997).
[CrossRef]

H. Billing, K. Maischberger, A. Rüdiger, R. Schilling, L. Schnupp, W. Winkler, “The Munich Gravitational Wave Detector using laser interferometry,” in Quantum Optics, Experimental Gravity, and Measurement Theory, P. Meystre, M. O. Scully, eds. (Plenum, New York, 1983), pp. 525–566.
[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, M. E. Zucker, “LIGO: the Laser Interferometer Gravitational-wave Observatory,” Science 256, 325–333 (1992).
[CrossRef] [PubMed]

Appl. Phys. B (1)

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]

J. Opt. Soc. Am. B (1)

Opt. Lett. (1)

Phys. Lett. A (2)

C. N. Man, D. Shoemaker, M. Pham Tu, D. Dewey, “External modulation technique for sensitive interferometric detection of displacements,” Phys. Lett. A 148, 8–16 (1990).
[CrossRef]

D. Schnier, J. Mizuno, G. Heinzel, H. Lück, A. Rüdiger, R. Schilling, M. Schrempel, W. Winkler, K. Danzmann, “Power recycling in the Garching 30 m prototype interferometer for gravitational-wave detection,” Phys. Lett. A 225, 210–216 (1997).
[CrossRef]

Phys. Rev. A (1)

A. Schenzle, R. DeVoe, G. Brewer, “Phase-modulation laser spectroscopy,” Phys. Rev. A 25, 2606–2621 (1982).
[CrossRef]

Phys. Rev. D (1)

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

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, M. E. Zucker, “LIGO: the Laser Interferometer Gravitational-wave Observatory,” Science 256, 325–333 (1992).
[CrossRef] [PubMed]

Other (13)

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), pp. 503–524.
[CrossRef]

H. Billing, K. Maischberger, A. Rüdiger, R. Schilling, L. Schnupp, W. Winkler, “The Munich Gravitational Wave Detector using laser interferometry,” in Quantum Optics, Experimental Gravity, and Measurement Theory, P. Meystre, M. O. Scully, eds. (Plenum, New York, 1983), pp. 525–566.
[CrossRef]

See, for example, K. S. Thorne, “Gravitational radiation,” in 300 Years of Gravitation, S. W. Hawking, W. Israel, eds. (Cambridge U. Press, Cambridge, UK, 1987), pp. 330–458.

F. J. Raab, “The LIGO project: progress and prospects,” in First Edoardo Amaldi Conference on Gravitational Wave Experiments, E. Coccia, G. Pixella, F. Ronga, eds. (World Scientific, Singapore, 1995), pp. 70–85.

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

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

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

R. Weiss, “Electromagnetically coupled broadband gravitational antenna,” MIT Res. Lab. Electron. Q. Prog. Rep.105, 54–76 (1972).

L. Schnupp, Max Planck Institute for Quantum Optics, D-85748 Garching, Germany (personal communication, 1986).

A. Giaime, “Studies of laser interferometric design and a vibration isolation system for interferometric gravitational wave detectors,” Ph.D. dissertation (Massachusetts Institute of Technology, Cambridge, Mass., 1995).

N. Mavalvala, “Alignment issues in laser interferometric gravitational-wave detectors,” Ph.D. dissertation (Massachu-setts Institute of Technology, Cambridge, Mass., 1997), p. 23.

A. E. Siegman, Lasers (University Science, Mill Valley, Calif., 1986), p. 423.

N. Mavalvala, D. Sigg, D. Shoemaker, “Experimental test of an alignment sensing scheme for a gravitational-wave interferometer,” Appl. Opt. (to be published).

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Figures (3)

Fig. 1
Fig. 1

Optical layout of an interferometric gravitational-wave detector to be used by the LIGO. RM, power-recycling mirror; BS, beam splitter; ITM, input test mass; and ETM, end test mass.

Fig. 2
Fig. 2

Amplitude of the fields (relative to the input power) as a function of frequency offset from the double resonance of the carrier (in units of f 0, the half-FSR of the power-recycling cavity) in (a) the power-recycling cavity and (b) at the antisymmetric port. The narrow carrier double resonance occurs at f = 0 and again at f = ±13.3f 0, the FSR of the arm cavity. The field amplitude in the power-recycling cavity at f = 0 is lower than the one at f = 20f 0 (the subcarrier resonance) because the carrier sees additional losses in the arm cavities. The sinusoidal envelop is due to the Michelson transmissivity corresponding to the asymmetry. The interferometer parameters used in this calculation are given in Table 1.

Fig. 3
Fig. 3

Schematic overview of the fixed-mirror interferometer, including the input optics train.

Tables (2)

Tables Icon

Table 1 Interferometer Parameters for the Fixed-Mirror Interferometer Experiment

Tables Icon

Table 2 Measured Values (with their experimental errors in parentheses) and Calculated Values of the Length Sensitivity Matrixa

Equations (9)

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

f 0 = c 4 l C ,
Δ ν CSB f CSB = ± 2 m + 1 f 0 ,
T RM sin 2 4 π f CSB c   l D .
f SC = n + 1 2 FSR ARM = n + 1 2 c L 1 + L 2 ,
r M     cos 4 π f c   l D .
Δ ν SC f SC = 2 pf 0 ,
Δ ν SCSB f SC - f SCSB = ± 2 qf 0 ,
c f SC = 2 l D .
S i t ,   δ l = 2 J 0 Γ i J 1 Γ i P i j   L ij δ l j   cos Ω i t + ϕ ij ,

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