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Multistability, Self-Oscillation and Chaos in Nonlinear Optics

  • H. J. Carmichael
  • C. M. Savage
  • D. F. Walls
Conference paper

Abstract

We describe a system comprising two circularly polarized ring-cavity modes coupled via a J=½ to J=½ transition. Both modes are equally excited by a linearly polarized incident laser. The steady-state transmission of the cavity shows optical tristability and polarization switching as predicted by Kitano et al.[1] and recently observed[2]. We generalise the model of Kitano et al. with the inclusion of saturation and absorption. In addition to optical tri-stability we find quadrastability (four stable output configurations for the same input intensity), self-oscillation and chaos[3]. We have studied the chaotic region numerically as the incident laser intensity and the detuning of the cavity modes is varied. The outes to chaos appear to be analogous to those in the Lorenz equations. For a decreasing incident intensity the passage to chaos involves a new period-doubling sequence of periodic windows embedded in chaos, where in each periodic window conventional period-doubling of the Feigenbaum type is observed. We have estimated the experimental parameters required to observe chaos in this system and find that power requirements are modest, although the limitations imposed by the adiabatic elimination and single-mode assumptions used in our theory cause some difficulties — chaos may well remain, however, when these theoretical restrictions are relaxed.

References

  1. 1.
    M. Kitano, T. Yabuzaki and T. Ogawa, Phys. Rev. Lett. 46, 926 (1981).ADSCrossRefMathSciNetGoogle Scholar
  2. 2.
    S. Cecchi, G. Giusfredi, E. Petriella and P. Salieri, Phys. Rev. Lett. 49,1928 (1982); W. Sandle and M. Hamilton., in Proceedings of the Third New Zealand Symposium on Laser Physics (Springer), to be published.Google Scholar
  3. 3.
    C. M. Savage, H. J. Carmichael and D. F. Walls, Opt. Commun. 42, 211 (1982); H. J. Carmichael, C. M. Savage and D. F. Walls, Phys. Rev. Lett. 50, 163 (1983).MathSciNetGoogle Scholar
  4. 4.
    K. J. McNeil, P. D. Drummond and D. F. Walls, Opt. Commun. 27, 292 (1978).ADSCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 1984

Authors and Affiliations

  • H. J. Carmichael
    • 1
  • C. M. Savage
    • 2
  • D. F. Walls
    • 2
  1. 1.University of ArkansasFayettevilleUSA
  2. 2.University of WaikatoHamiltonNew Zealand

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