OSA's Digital Library

Applied Optics

Applied Optics


  • Vol. 31, Iss. 9 — Mar. 20, 1992
  • pp: 1185–1198

Eigenmodes of misaligned unstable optical resonators with circular mirrors

Mark S. Bowers  »View Author Affiliations

Applied Optics, Vol. 31, Issue 9, pp. 1185-1198 (1992)

View Full Text Article

Enhanced HTML    Acrobat PDF (1465 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



It is shown numerically that the diffractive transverse (Fox–Li) eigenmodes supported by an unstable cavity with tilted end mirrors can be computed by expanding these modes in terms of the fully aligned (aberration-free) eigenmodes of the same cavity. Circular mirror resonators are considered in which the aligned cavity eigenmodes can be decomposed into different azimuthal components. The biorthogonality property of the aligned cavity eigenmodes is used to obtain the coefficients in the modal expansion of the misaligned modes. Results are given for two different resonators: a conventional hard-edge unstable cavity with a small tilt of the output coupler and one that uses a graded reflectivity output mirror with a small tilt of the primary mirror. It is shown that the series expansion of the misaligned modes in terms of the aligned modes converges, and the converged eigenvalues are virtually identical to those computed by using the Prony method. Symmetry considerations and other new insights into the effects of a mirror tilt on the modes of a resonator are also discussed.

© 1992 Optical Society of America

Original Manuscript: March 6, 1991
Published: March 20, 1992

Mark S. Bowers, "Eigenmodes of misaligned unstable optical resonators with circular mirrors," Appl. Opt. 31, 1185-1198 (1992)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. K. E. Oughstun, “Aberration sensitivity of unstable-cavity geometries,” J. Opt. Soc. Am. A 3, 1113–1141 (1986). [CrossRef]
  2. K. E. Oughstun, “Intracavity adaptive optic compensation of phase aberrations. II: Passive cavity study for a small Neq resonator,” J. Opt. Soc. Am. 71, 1180–1192 (1981). [CrossRef]
  3. K. E. Oughstun, “Intracavity adaptive optic compensation of phase aberrations. III: Passive and active cavity study for a large Neq resonator.” J. Opt. Soc. Am. 73, 282–302 (1983). [CrossRef]
  4. R. Hauck, N. Hodgson, H. Weber, “Misalignment sensitivity of unstable resonators with spherical mirrors,” J. Mod. Opt. 35, 165–176 (1988). [CrossRef]
  5. M. E. Smithers, “Transverse-mode control in unstable optical resonators,” J. Opt. Soc. Am. 73, 1894 (1983).
  6. W. F. Krupke, W. R. Sooy, “Properties of an unstable confocal resonator CO2 laser system,” IEEE J. Quantum Electron. QE-5, 575–586 (1969). [CrossRef]
  7. A. N. Chester, “Mode selectivity and mirror misalignment effects in unstable laser resonators,” Appl. Opt. 11, 2584–2590 (1972). [CrossRef] [PubMed]
  8. A. G. Fox, T. Li, “Modes in a maser interferometer with curved and tilted mirrors,” Proc. IEEE 51, 80–89 (1963). [CrossRef]
  9. A. E. Siegman, H. Y. Miller, “Unstable optical resonator loss calculations using the Prony method,” Appl. Opt. 9, 1729–2736 (1970). [CrossRef]
  10. W. P. Latham, G. G. Dente, “Matrix methods for bare resonator eigenvalue analysis,” Appl. Opt. 19, 1618–1621 (1980). [CrossRef] [PubMed]
  11. W. D. Murphy, M. L. Bernabe, “Numerical procedures for solving nonsymmetric eigenvalue problems associated with optical resonators,” Appl. Opt. 17, 2358–2365 (1978). [CrossRef] [PubMed]
  12. E. A. Sziklas, A. E. Siegman, “Mode calculations in unstable resonators with flowing saturable gain. 2: Fast Fourier transform method,” Appl. Opt. 14, 1874–1889 (1975). [CrossRef] [PubMed]
  13. A. E. Siegman, Lasers (University Science Books, Mill Valley, Calif., 1986), Chap. 21.
  14. A. E. Siegman, “A canonical formulation for analyzing multielement unstable resonators,” IEEE J. Quantum Electron. QE-12, 35–40 (1976). [CrossRef]
  15. K. E. Oughstun, “Unstable resonator modes,” in Progress in Optics XXIV, E. Wolf, ed. (North-Holland, Amsterdam, 1987), pp. 165–387. [CrossRef]
  16. A. E. Siegman, “Orthogonality properties of optical resonator eigenmodes,” Opt. Commun. 31, 369–373 (1979). [CrossRef]
  17. B. T. Smith, J. M. Boyle, J. J. Dongarra, B. S. Garbow, Y. Ikebe, V. C. Klema, C. B. Moler, Matrix Eigensystem Routines—EISPACK Guide (Springer-Verlag, New York, 1976). [CrossRef]
  18. M. S. Bowers, S. E. Moody, “Numerical solution of the exact cavity equations of motion for an unstable optical resonator,” Appl. Opt. 29, 3905–3915 (1990). [CrossRef] [PubMed]
  19. N. McCarthy, M. Morin, “High-order transverse modes of misaligned laser resonators with Gaussian reflectivity mirrors,” Appl. Opt. 28, 2189–2191 (1989). [CrossRef] [PubMed]

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited