OSA's Digital Library

Applied Optics

Applied Optics


  • Vol. 26, Iss. 17 — Sep. 1, 1987
  • pp: 3710–3716

Stability of planar ring lasers with mirror misalignment

H. R. Bilger and G. E. Stedman  »View Author Affiliations

Applied Optics, Vol. 26, Issue 17, pp. 3710-3716 (1987)

View Full Text Article

Enhanced HTML    Acrobat PDF (910 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



We consider an active cavity defined by a geometrically symmetric ring of N mirrors, each of which may have an arbitrary radius. The beam steering imposed by all possible mirror misalignment parameters is shown to diverge if the radii of curvature Ri of the mirrors satisfy two constraints of the form |κN({Ri})| = 2. By comparison, the standard conditions for the stability of rays departing from the design path in a perfectly aligned ring have the form |κN({Ri})| ≤ 2, so that only approximately half of the critical radii for the latter stability conditions is also critical radii for the former. The detailed solutions identify the most sensitive misalignment parameters regarding beam steering. Certain beam steering effects vanish for resonators with κN = −2; this can be of practical importance, as, for example, the N = 2 confocal resonator.

© 1987 Optical Society of America

Original Manuscript: November 24, 1986
Published: September 1, 1987

H. R. Bilger and G. E. Stedman, "Stability of planar ring lasers with mirror misalignment," Appl. Opt. 26, 3710-3716 (1987)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. W. F. Krupke, W. R. Sooy, “Properties of an Unstable Confocal Resonator CO2 Laser System,” IEEE J. Quantum Electron. QE-5575 (1969). [CrossRef]
  2. R. J. Freiberg, A. S. Halsted, “Properties of Low Order Transverse Modes in Ar+ Lasers,” Appl. Opt. 8, 355 (1969). [CrossRef] [PubMed]
  3. N. Yamauchi, “Resonant Modes in a Ring Laser Resonator and their Deformations by Mirror Rearrangements,” Electron. Commun. Jpn. 57-C, 92 (1974).
  4. R. Hauck, H. P. Kortz, H. Weber, “Misalignment Sensitivity of Optical Resonators,” Appl. Opt. 19, 598 (1980). [CrossRef] [PubMed]
  5. A. D. Schnurr, “Unstable Resonator Misalignment in Ring and Linear Toroidal Resonators,” Appl. Opt. 22, 298 (1983). [CrossRef] [PubMed]
  6. V. Magni, “Resonators for Solid State Lasers with Large-Volume Fundamental Mode and High Alignment Stability,” Appl. Opt. 25, 107 (1986). [CrossRef] [PubMed]
  7. E. F. Ishchenko, E. F. Reshetin, “Sensitivity to Misalignment of an Optical Ring Resonator,” Opt. Spektrosk. 46, 202 (1979)[Opt. Spectrosc. USSR 46, 366 (1979)].
  8. I. W. Smith, “Optical Resonator Axis Stability and Instability from First Principles,” Proc. Soc. Photo-Opt. Instrum. Eng. 412, 203 (1983).
  9. T. Habib, M.Sc. Thesis, Oklahoma State U. (1986).
  10. A. E. Siegman, Lasers (University Science Books, Mill Hill Valley, CA, 1986), p. 607.
  11. J. A. Arnaud, “Degenerate Optical Cavities. 2: Effect of Misalignments,” Appl. Opt. 8, 1909 (1969). [CrossRef] [PubMed]
  12. J. T. Verdeyen, Laser Electronics (Prentice-Hall, Englewood Cliffs, N.J., 1981).
  13. S. A. Collins, “Analysis of Optical Resonators Involving Focusing Elements,” Appl. Opt. 3, 1263 (1964). [CrossRef]
  14. H. R. Bilger, “Modelling a Large Ring Resonator Gyroscope,” Report: AFOSR grant 84-0058 (1985).
  15. T. F. Ewanizky, “Ray Transfer Matrix Approach to Unstable Resonator Analysis,” Appl. Opt. 18, 724 (1979). [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.


Fig. 1 Fig. 2 Fig. 3

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited