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Applied Optics

Applied Optics


  • Editor: James C. Wyant
  • Vol. 47, Iss. 15 — May. 20, 2008
  • pp: 2840–2851

Modal frequency degeneracy in thermally loaded optical resonators

Amber L. Bullington, Brian T. Lantz, Martin M. Fejer, and Robert L. Byer  »View Author Affiliations

Applied Optics, Vol. 47, Issue 15, pp. 2840-2851 (2008)

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We observe power coupling from the fundamental mode to frequency-degenerate higher-order spatial modes in optical resonators illuminated with a 30 W laser. Thermally-induced modal frequency degeneracy facilitates power transfer from the fundamental mode to higher-order modes, reduces power coupling into the cavity, and triggers power fluctuations. Modeling thermoelastic deformation of a mirror’s surface shows predicted modal frequency degeneracy to be in reasonable agreement with experimental observations. Predictions for the Laser Interferometer Gravitational-wave Observatory (LIGO) show that the circulating fundamental-mode power necessary for gravitational-wave detection is compromised at coating absorptions of 3.8 and 0.44 ppm for Enhanced and Advanced LIGO Fabry–Pérot cavities, respectively.

© 2008 Optical Society of America

OCIS Codes
(140.0140) Lasers and laser optics : Lasers and laser optics
(140.4780) Lasers and laser optics : Optical resonators
(140.6810) Lasers and laser optics : Thermal effects
(230.5750) Optical devices : Resonators
(260.5740) Physical optics : Resonance

ToC Category:
Lasers and Laser Optics

Original Manuscript: December 4, 2007
Revised Manuscript: April 11, 2008
Manuscript Accepted: April 18, 2008
Published: May 14, 2008

Amber L. Bullington, Brian T. Lantz, Martin M. Fejer, and Robert L. Byer, "Modal frequency degeneracy in thermally loaded optical resonators," Appl. Opt. 47, 2840-2851 (2008)

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  1. T. Kimura and K. Otsuka, “Thermal effects of a continuously pumped Nd3+:YAG laser,” IEEE J. Quantum Electron. 7, 403-407 (1971). [CrossRef]
  2. T. Kimura, K. Otsuka, and M. Saruwatari, “Spatial hole-burning effects in a Nd3+:YAG laser,” IEEE J. Quantum Electron. 7, 225-230 (1971). [CrossRef]
  3. T. Klaassen, J. de Jong, M. van Exter, and J. P. Woerdman, “Transverse mode coupling in an optical resonator,” Opt. Lett. 30, 1959-1961 (2005). [CrossRef] [PubMed]
  4. P. Fritschel, “The second generation LIGO interferometers,” in Proceedings of Astrophysical Sources for Ground-Based Gravitational Wave Detectors, J. M. Centrella, ed. (American Institute of Physics, 2001), pp. 15-23.
  5. R. Adhikari, P. Fritschel, and S. Waldman, “Enhanced LIGO,” http://www.ligo.caltech.edu/docs/T/T060156-01.pdf.
  6. E. D'Ambrosio, LIGO Laboratory, California Institute of Technology, MS 18-34, Pasadena, CA 91125, USA, and A. M. Gretarsson, V. Frolov, B. O'Reilly, and P. K. Fritschel, are preparing a manuscript to be called “Effects of mode degeneracy in the LIGO Livingston Observatory recycling cavity.”
  7. V. Loriette and C. Boccara, “Absorption of low-loss optical materials measured at 1064 nm by a position-modulated collinear photothermal detection technique,” Appl. Opt. 42, 649-656(2003). [CrossRef] [PubMed]
  8. C. Janke, “Thermal loading of optical components in interferometric systems,” presented at the LIGO Scientific Collaboration Conference, Baton Rouge, Louisiana, (March 2001).
  9. A. E. Siegman, Lasers (University Science, 1986). Errata URL: http://www.stanford.edu/siegman/lasers_book_errata.pdf.
  10. R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, “Laser phase and frequency stabilization using an optical resonator,” Appl. Phys. B, Laser Opt. 31, 97-105 (1983). [CrossRef]
  11. W. Winkler, K. Danzmann, A. Rudiger, and R. Schilling, “Heating by optical absorption and the performance of interferometric gravitational-wave detectors,” Phys. Rev. A 44, 7022-7036 (1991). [CrossRef] [PubMed]
  12. N. Uehara and K. Ueda, “Accurate measurement of the radius of curvature of a concave mirror and the power dependence in a high-finesse Fabry-Pérot interferometer,” Appl. Opt. 34, 5611-5619 (1995). [CrossRef] [PubMed]
  13. R. Paschotta, “Beam quality deterioration of lasers caused by intracavity beam distortions,” Opt. Express 14, 6069-6074(2006). [CrossRef] [PubMed]
  14. P. T. Beyersdorf, S. Zappe, M. M. Fejer, and M. Burkhardt, “Cavity with a deformable mirror for tailoring the shape of the eigenmode,” Appl. Opt. 45, 6723-6728 (2006). [CrossRef] [PubMed]
  15. H. Kogelnik, “Coupling and conversion coefficients for optical modes,” in Proceedings of the Symposium on Quasi-Optics, (Polytechnic Press, 1964), pp. 333-347.
  16. S. Saraf, R. L. Byer, and P. J. King, “High-extinction-ratio resonant cavity polarizer for quantum-optics measurements,” Appl. Opt. 46, 3850-3855 (2007). [CrossRef] [PubMed]
  17. N. Uehara, E. K. Gustafson, M. M. Fejer, and R. L. Byer, “Modeling of efficient mode matching and thermal-lensing effect on a laser-beam coupling into a mode-cleaner cavity,” Proc. SPIE 2989, 57-68 (1997). [CrossRef]
  18. K. An, B. A. Sones, C. Fang-Yen, R. R. Dasari, and M. S. Feld, “Optical bistability induced by mirror absorption: measurement of absorption coefficients at the sub-ppm level,” Opt. Lett. 22, 1433-1435 (1997). [CrossRef]
  19. D. Tanner, Department of Physics, University of Florida, P.O. Box 118440, Gainesville, Florida, 32611 (personal communication, 2007).
  20. R. Adhikari, Department of Physics, California Institute of Technology, Physics Department 103-33, Pasadena, California, 91125 (personal communication, 2007).
  21. P. Fritschel, “Advanced LIGO interferometer parameters,” http://emvogil3.mit.edu/~pf/advligo/SYS/ALparameters.htm.
  22. K. X. Sun and R. L. Byer, “All-reflective Michelson, Sagnac, and Fabry-Pérot interferometers based on grating beam splitters,” Opt. Lett. 23, 567-569 (1998). [CrossRef]
  23. P. T. Beyersdorf, R. L. Byer, and M. M. Fejer, “Results from the Stanford 10 m Sagnac interferometer,” Class. Quantum Grav. 19, 1585-1589 (2002). [CrossRef]
  24. S. Rowan, J. Hough, and D. R. M. Crooks, “Thermal noise and material issues for gravitational wave detectors,” Phys. Lett. A 347, 25-32 (2005). [CrossRef]

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