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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. 12 — Dec. 1, 1999
  • pp: 2990–3002

Spatiotemporal model of the LIGO interferometer

R. G. Beausoleil and D. Sigg  »View Author Affiliations


JOSA A, Vol. 16, Issue 12, pp. 2990-3002 (1999)
http://dx.doi.org/10.1364/JOSAA.16.002990


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Abstract

We develop a detailed spatiotemporal model in the adiabatic approximation of the optical response of the Laser Interferometer Gravitational-Wave Observatory (LIGO) optical system to environmental perturbations. We begin by deriving a first-order linear time-dependent evolution equation that models the electromagnetic field as a function of position within a Fabry–Perot interferometer. This model allows both the length of the resonator and the misalignment angles of the end mirrors to vary in time and describes both resonant and nonresonant phenomena. After defining a biorthogonality relation that must be satisfied by general unperturbed spatial eigenfunctions of the Fabry–Perot interferometer, we expand the intracavity field as a linear combination of these functions and convert the spatiotemporal evolution equation into a linear system of coupled time-dependent iteration and/or differential equations. We then calculate the adiabatic connection equations that link the two LIGO Fabry–Perot interferometers through the power recycling cavity, which comprises two mirrors (the power recycling input mirror and the beam splitter) that have the same mechanical degrees of freedom as those in the Fabry–Perot arm cavities. We develop a detailed instance of this model for the evolution of the intracavity field within a resonator with sufficiently small misalignment angles that a Hermite–Gauss basis set can be used. We develop a detailed general approach to signal demodulation for simulation of servo-control systems and describe its implementation in the Hermite–Gauss approximation for Cartesian split-plane detectors. Finally, we demonstrate the use of this small-angle model to simulate the effect of angular misalignment on the longitudinal response function.

© 1999 Optical Society of America

OCIS Codes
(030.4070) Coherence and statistical optics : Modes
(120.2230) Instrumentation, measurement, and metrology : Fabry-Perot
(120.3180) Instrumentation, measurement, and metrology : Interferometry
(220.1140) Optical design and fabrication : Alignment

Citation
R. G. Beausoleil and D. Sigg, "Spatiotemporal model of the LIGO interferometer," J. Opt. Soc. Am. A 16, 2990-3002 (1999)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-16-12-2990


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References

  1. A. Abramovici, W. Althouse, J. Camp, J. A. Giaime, A. Gillespie, S. Kawamura, A. Kuhnert, T. Lyons, F. J. Raab, R. L. Savage, Jr., D. Shoemaker, L. Sievers, R. Spero, R. Vogt, R. Weiss, S. Whitcomb, and M. Zucker, “Improved sensitivity in a gravitational wave interferometer and implications for LIGO,” Phys. Lett. A 218, 157–163 (1996).
  2. A. Giazotto, “The VIRGO experiment: status of the art,” in First Edoardo Amaldi Conference on Gravitational Wave Experiments, E. Coccia, G. Pizella, and F. Ronga, eds. (World Scientific, Singapore, 1995), p. 86.
  3. K. Danzmann, “GEO 600—A 600-m Laser Interferometric Gravitational Wave Antenna,” in First Edoardo Amaldi Conference on Gravitational Wave Experiments, E. Coccia, G. Pizella, and F. Ronga, eds. (World Scientific, Singapore, 1995), p. 100.
  4. K. Tsubono, “300-m Laser Interferometric Gravitational Wave Detector (TAMA300) in Japan,” in First Edoardo Amaldi Conference on Gravitational Wave Experiments, E. Coccia, G. Pizella, and F. Ronga, eds. (World Scientific, Singapore, 1995), p. 112.
  5. J.-Y. Vinet, B. J. Meers, C. N. Man, and A. Brillet, “Optimization of long-baseline optical interferometers for gravitational-wave detection,” Phys. Rev. D 38, 433–447 (1988).
  6. M. W. Regehr, F. J. Raab, and S. E. Whitcomb, “Demonstration of a power-recycled Michelson interferometer with Fabry–Perot arms by frontal modulation,” Opt. Lett. 20, 1507–1509 (1995).
  7. J.-Y. Vinet, P. Hello, C. N. Man, and A. Brillet, “A highaccuracy method for the simulation of non-ideal optical cavities,” J. Phys. (Paris) I 2, 1287–1303 (1992).
  8. P. Saha, “Fast estimation of transverse fields in high-finesse optical cavities,” J. Opt. Soc. Am. A 14, 2195–2202 (1997).
  9. B. Bochner, “Modelling the performance of interferometric gravitational-wave detectors with realistically imperfect optics,” Ph.D. thesis (Massachusetts Institute of Technology, Cambridge, Mass., 1998).
  10. D. Z. Anderson, “Alignment of resonant optical cavities,” Appl. Opt. 23, 2944–2949 (1984).
  11. E. Morrison, B. J. Meers, D. I. Robertson, and H. Ward, “Automatic alignment of optical interferometers,” Appl. Opt. 33, 5041–5049 (1994).
  12. Y. Hefetz, N. Mavalvala, and D. Sigg, “Principles of calculating alignment signals in complex resonant optical interferometers,” J. Opt. Soc. Am. B 14, 1597–1605 (1997).
  13. J. Camp, L. Sievers, R. Bork, and J. Heefner, “Guided lock acquisition in a suspended Fabry–Perot cavity,” Opt. Lett. 20, 2463–2465 (1995).
  14. K. E. Oughstun, in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1987), Vol. 24, pp. 165–387.
  15. A. E. Siegman, Lasers (University Science, Mill Valley, Calif., 1986).
  16. A. Gerrard and J. M. Burch, Introduction to Matrix Methods in Optics (Wiley, New York, 1975).
  17. P. M. Morse and H. Feshbach, Methods of Theoretical Physics (McGraw-Hill, New York, 1953), p. 904.
  18. K. An, C. Yang, R. R. Dasari, and M. S. Feld, “Cavity ring-down technique and its application to the measurement of ultraslow velocities,” Opt. Lett. 20, 1068–1070 (1995).
  19. M. J. Lawrence, B. Willke, M. E. Husman, E. K. Gustafson, and R. L. Byer, “The dynamic response of a Fabry–Perot interferometer,” J. Opt. Soc. Am. B 16, 523–532 (1999).
  20. W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in C: The Art of Scientific Computing (Cambridge U. Press, Cambridge, UK, 1992).
  21. L. Schnupp, Max Planck Institut für Quantenoptik, D-85748 Garching, Germany (personal communication, 1986).
  22. R. G. Beausoleil, D. Sigg, and M. R. Zwikel, “Initial alignment tolerance of the LIGO interferometer,” available from D. Sigg, LIGO Hanford Observatory, P.O. Box 1970 S9–02, Richland, Wash. 99352.

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