OSA's Digital Library

Journal of the Optical Society of America B

Journal of the Optical Society of America B


  • Vol. 2, Iss. 4 — Apr. 1, 1985
  • pp: 552–564

Global dynamical behavior of the optical field in a ring cavity

S. M. Haramel, C. K. R. T. Jones, and J. V. Moloney  »View Author Affiliations

JOSA B, Vol. 2, Issue 4, pp. 552-564 (1985)

View Full Text Article

Acrobat PDF (1680 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



A new class of instabilities for a plane-wave intracavity field in an optical ring resonator is identified. Dynamical systems techniques are explained and applied to the map. A bifurcation diagram is given that organizes the important information, and global pictures are developed that describe the evolution of the attractor and its basin boundary. Anomalous behavior observed in earlier numerical studies is explained.

© 1985 Optical Society of America

S. M. Haramel, C. K. R. T. Jones, and J. V. Moloney, "Global dynamical behavior of the optical field in a ring cavity," J. Opt. Soc. Am. B 2, 552-564 (1985)

Sort:  Author  |  Journal  |  Reset


  1. A comprehensive review of chaos in optical bistability can be found in C. M. Bowden, H. M. Gibbs, and S. L. McCall, eds. Optical Bistability II (Plenum, New York, 1984).
  2. H. Haken, Phys. Lett. 53A, 77 (1975).
  3. K. Ikeda, Opt. Commun. 30, 257 (1979); K. Ikeda, H. Daido, and 0. Akimoto, Phys. Rev. Lett. 45, 709 (1980).
  4. F. T. Arrechi, R. Meucci, G. Puccioni, and J. Tredicce, Phys. Rev. Lett. 49, 1217 (1982); R. S. Gioggia and N. B. Abraham, Phys. Rev. Lett. 51, 650 (1983); K. Otsuka and H. Kawaguchi, Phys. Rev. A 29, 2953 (1984).
  5. R. G. Harrison, W. J. Firth, C. A. Emshary, and I. A. Al-Saidi, Phys. Rev. Lett. 51, 562 (1983); R. G. Harrison, W. J. Firth, and I. A. Al-Saidi, Phys. Rev. Lett. 53, 258 (1984).
  6. M. LeBerre, E. Ressayre, A. Tallet, K. Tai, F. A. Hopf, H. M. Gibbs, and J. V. Moloney, "Optical bistability and instabilities via diffraction-free-encoding and a single feedback mirror," presented at International Conference on Quantum Electronics, Los Angeles, California, 1984. The first reported observation of period-2 oscillations in a cw experiment was described.
  7. J. V. Moloney, F. A. Hopf, and H. M. Gibbs, Phys. Rev. A 25, 3442 (1982); J. V. Moloney, Phys. Rev. Lett, (to be published).
  8. W. J. Firth and E. M. Wright, Phys. Lett. 92A, 211 (1982).
  9. R. R. Snapp, H. J. Carmichael, and W. C. Schieve, Opt. Commun. 40, 68 (1981); Phys. Rev. A 26, 3408 (1982).
  10. J. V. Moloney, Opt. Commun. 48, 435 (1984).
  11. C. Grebogi, E. Ott, and J. A. Yorke, Phys. Rev. Lett. 48, 1507 (1982); Phys. D 7, 181 (1983).
  12. J. Guckenheimer and P. Holmes, Nonlinear Oscillations, Dynamical Systems and Bifurcation of Vector Fields (Springer-Verlag, New York, 1983).
  13. W. J. Firth, Opt. Commun. 39, 343 (1981); E. Abraham, W. J. Firth, and J. Carr, Phys. Lett. 69A, 47 (1982); E. Abraham and W. J. Firth, Opt. Acta, 30, 1541 (1983).
  14. J. Carr and J. C. Eilbeck, "One dimensional approximations for a quadratic Ikeda map," Los Alamos National Laboratory Tech. Notes (1984).
  15. P. Holmes and D. Whitley, Phys. D, 7, 111 (1983), and references therein.
  16. S. Smale, Bull Am. Math. Soc. 73, 747 (1967).
  17. Y. Ueda, Ann. N. Y. Acad. Sci. 357, 422 (1980).
  18. J. D. Cresser and P. Meystre, in Optical Bistability, C. M. Bowden, M. Ciftan, and H. R. Robl, eds. (Plenum, New York, 1981), p. 265 and references therein.
  19. N. K. Gavrilov and L. P. Silnikov, Mat. Sb. 88, 467 (1972); 90, 139 (1973).
  20. S. E. Newhouse, Progress in Mathematics (Birkhauser, Boston, Mass., 1980), Vol. 8, pp. 1–114.
  21. J. A. Yorke, Institute for Physical Science and Technology, Department of Mathematics, University of Maryland, College Park, Maryland 20742 (personal communication).
  22. K. T. Alligood and J. A. Yorke, "Period doubling cascades of attractors: a prerequisite for horseshoes," Department of Mathematics, Michigan State University, East Lansing, Michigan 48824 (personal communication).
  23. J. V. Moloney, Phys. Rev. Lett. 51, 556 (1984).

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