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Journal of the Optical Society of America A

Journal of the Optical Society of America A

| OPTICS, IMAGE SCIENCE, AND VISION

  • Vol. 16, Iss. 7 — Jul. 1, 1999
  • pp: 1730–1739

Method for analyzing multiple-mirror coupled optical systems

Jun Mizuno and Ichirou Yamaguchi  »View Author Affiliations


JOSA A, Vol. 16, Issue 7, pp. 1730-1739 (1999)
http://dx.doi.org/10.1364/JOSAA.16.001730


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Abstract

A general method of analyzing Michelson-based, multiple-mirror optical systems, such as interferometers designed as gravitational-wave detectors, is described. Assuming that phase-modulated light is injected, signals that will be generated by demodulation of the photocurrent anywhere in the system, together with their frequency dependences, can be evaluated. Since this method is based on the manipulation of matrices, it is appropriate for computerization.

© 1999 Optical Society of America

OCIS Codes
(000.3860) General : Mathematical methods in physics
(120.2230) Instrumentation, measurement, and metrology : Fabry-Perot
(120.3180) Instrumentation, measurement, and metrology : Interferometry
(120.4570) Instrumentation, measurement, and metrology : Optical design of instruments
(120.5050) Instrumentation, measurement, and metrology : Phase measurement
(120.5060) Instrumentation, measurement, and metrology : Phase modulation

History
Original Manuscript: October 22, 1998
Revised Manuscript: February 24, 1999
Manuscript Accepted: February 24, 1999
Published: July 1, 1999

Citation
Jun Mizuno and Ichirou Yamaguchi, "Method for analyzing multiple-mirror coupled optical systems," J. Opt. Soc. Am. A 16, 1730-1739 (1999)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-16-7-1730


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References

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  16. The use of the algorithm described in this paper, however, is not limited to these assumptions. For instance, if the east and south paths are regarded as the two arms and the north path is used for detection, the response of (non-Michelson-based) synchronous recycling (Ref. 14) can be analyzed.
  17. These matrices are often used in analyzing multilayer dielectric coatings, as can be found in, e.g., Ref. 18. We, however, adopted a slightly modified definition of Eq. (4) that does not distinguish the direction of incidence. (The results are identical except for constant offsets in the definition of detunings.)
  18. M. V. Klein, T. E. Furtak, Optics, 2nd ed. (Wiley, New York, 1986), Sec. 5.4.
  19. To be exact, this expression must be rewritten as “these sidebands work mainly as the local oscillators” because there is actually no clear distinction between the carrier and the local oscillator in such a system in which the two are modulated by the signal simultaneously (like the example discussed in this paper). The signal sidebands induced on the carrier light interfere with the local oscillator light, whereas the signal sidebands induced on the local oscillator light interfere with the carrier light in contributing the signal, as is described in Section 4. Nevertheless, we adopt the naming in the text in view of the “main” signal generation.
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  21. Evaluating the frequency response of a coupled optical system was initially explored by Vinet et al. (Ref. 22) to obtain the detector’s response to gravitational waves (i.e., not for the control purpose). The analysis adopted in this paper is similar to theirs but has a slightly different viewpoint, and it is modified and extended for generality. In their approach the signal-induced sidebands are produced from the carrier in each transit inside a cavity, whereas in our approach they are produced from the summed amplitude of the carrier. The results should be identical, and the choice is a matter of preference.
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  23. Actually there will be a slight difference due to the nonstationary shot-noise effect discussed in, e.g., Refs. 24 and 25. It is, in principle, possible to extend the present analysis to include such effects. In practice, however, the difference is less than a few decibels and can be ignored in almost any applications (excepting, probably, the most sensitive gravitational-wave readout).
  24. T. M. Niebauer, R. Schilling, K. Danzmann, A. Rüdiger, W. Winkler, “Nonstationary shot noise and its effect on the sensitivity of interferometers,” Phys. Rev. A 43, 5022–5029 (1991). [CrossRef] [PubMed]
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  28. G. Heinzel, K. A. Strain, J. Mizuno, K. D. Skeldon, B. Willke, W. Winkler, R. Schilling, A. Rüdiger, K. Danzmann, “Experimental demonstration of a suspended dual recycling interferometer,” Phys. Rev. Lett. 81, 5493–5496 (1998). [CrossRef]

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