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Applied Optics

Applied Optics


  • Vol. 42, Iss. 7 — Mar. 1, 2003
  • pp: 1269–1282

Signal extraction and optical design for an advanced gravitational-wave interferometer

James E. Mason and Phil A. Willems  »View Author Affiliations

Applied Optics, Vol. 42, Issue 7, pp. 1269-1282 (2003)

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We present an experimental demonstration of a locking and control scheme for an interferometer using a power-recycled resonant sideband extraction configuration and show that the measured response to mirror vibrations matches an optical model. We discuss some aspects of resonant sideband extraction that are relevant to gravitational-wave detection.

© 2003 Optical Society of America

OCIS Codes
(120.2230) Instrumentation, measurement, and metrology : Fabry-Perot
(120.3180) Instrumentation, measurement, and metrology : Interferometry
(120.5050) Instrumentation, measurement, and metrology : Phase measurement
(350.1270) Other areas of optics : Astronomy and astrophysics

Original Manuscript: July 5, 2002
Revised Manuscript: November 14, 2002
Published: March 1, 2003

James E. Mason and Phil A. Willems, "Signal extraction and optical design for an advanced gravitational-wave interferometer," Appl. Opt. 42, 1269-1282 (2003)

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  1. J. Mizuno, K. A. Strain, P. G. Nelson, J. M. Chen, R. Schilling, A. Rüdiger, W. Winkler, K. Danzmann, “Resonant sideband extraction: a new configuration for interferometric gravitational-wave detectors,” Phys. Lett. A 175, 273–276 (1993). [CrossRef]
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  7. K. A. Strain, G. Müller, T. Delker, D. H. Reitze, D. B. Tanner, J. E. Mason, P. A. Willems, D. A. Shaddock, M. B. Gray, C. Mow-Lowry, D. E. McClelland, “Sensing and control in dual-recycling laser interferometer gravitational-wave detectors,” Appl. Opt. 42, 1244–1256 (2003). [CrossRef] [PubMed]
  8. L. Schnupp, “Internal modulation schemes,” presented at the European Collaboration Meeting on Interferometric Detection of Gravitational Waves, Sorrento, Italy, 2 Oct. 1988.
  9. M. Regehr, “Signal extraction and control for an interferometric gravitational wave detector,” Ph.D. dissertation (California Institute of Technology, Pasadena, Calif., 1995).
  10. J. Mizuno, “Comparison of optical configurations for laser-interferometric gravitational-wave detectors,” Ph.D. dissertation (Max-Planck-Institute fur Quantenoptik, Garching, Germany, 1995).
  11. There is no useful heterodyne signal in or beyond the arm cavities because there is no sufficient rf sideband amplitude present in the arm cavities to heterodyne against. The light amplitudes at the dark port are just those inside the signal extraction cavity, reduced by the SEM transmission; thus there is no useful additional information about the interferometer degrees of freedom inside the signal extraction cavity.
  12. P. Fritschel, R. Bork, G. González, N. Mavalvala, D. Ouimette, H. Rong, D. Sigg, M. Zucker, “Readout and control of a power-recycled interferometric gravitational-wave antenna,” Appl. Opt. 40, 4988–4998 (2001). [CrossRef]
  13. The alert reader may have asked about demodulation at 2f1. This approach is tricky because the approximation of only first-order PM sidebands is not strictly accurate in practice.
  14. A. Freise, G. Heinzel, K. A. Strain, J. Mizuno, K. D. Skeldon, H. Lück, B. Willke, R. Schilling, A. Rüdinger, W. Winkler, K. Danzmann, “Demonstration of detuned dual recycling at the Garching 30m laser interferometer,” Phys. Lett. A 277, 135–142 (2000). [CrossRef]
  15. Once again, this is important only in a broadband interferometer. In a detuned interferometer, it does not matter because the relative phases are not preserved when the frequencies are off resonant.
  16. J. Mason, “Signal extraction and optical design for an advanced gravitational wave detector,” Ph.D. dissertation (California Institute of Technology, Pasadena, Calif., 2001).
  17. Twiddle is a Mathematica-based program that solves the self-consistent optical field equations for an interferometer given a set of mirror parameters and spacings and then evaluates transfer functions from mirror motion to output optical sideband fields. See M. Regehr, J. Mason, H. Yamamoto, O. Miyakawa, http://www.phys.ufl.edu/LIGO/LIGO/STAIC.html#9 .
  18. D. Sigg, N. Mavalvala, J. Giaime, P. Fritschel, D. Shoemaker, “Signal extraction in a power-recycled Michelson interferometer with Fabry-Perot arm cavities by use of a multiple-carrier frontal modulation scheme,” Appl. Opt. 37, 5687–5693 (1998). [CrossRef]
  19. G. Heinzel, J. Mizuno, R. Schilling, A. Rüdiger, K. Danzmann, “An experimental demonstration of resonant sideband extraction for laser-interferometric gravitational wave detectors,” Phys. Lett. A 217, 305–314 (1996). [CrossRef]

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