Routes to Optical Turbulence in a Dispersive Ring Bistable Cavity Containing Saturable Nonlinearities

  • J. V. Moloney
  • H. M. Gibbs
  • F. A. Hopf

Abstract

Using a plane wave analysis we show that co-existent attractors, representing distinct routes to optical turbulence, appear on a single branch of a dispersive ring bistable cavity. Some of these routes appear to arise via a tangent (saddle-node) bifurcation and are not found in the logistic map analyzed by Feigenbaum. When transverse variations in the beam profile are accounted for, a new transition sequence arises which is consistent with recent observations in a fluid dynamical experiment.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    “Nonlinear Dynamics”, ed. R.H.G. Helleman, in Annals of the New York Academy of Sciences, 357, (1980).Google Scholar
  2. 2.
    J.V. Moloney, F.A. Hopf and H.M. Gibbs, Phys. Rev. A 25, 3442 (1982).ADSCrossRefGoogle Scholar
  3. 3.
    W.J. Firth, E. Abraham and E.M. Wright, Appl. Phys. B 28, 170 (1982).CrossRefGoogle Scholar
  4. 4.
    J.V. Moloney, to be published.Google Scholar
  5. 5.
    D. Ruelle and F. Takens, Commun. Math. Phys. 20 ,167 (1971).MathSciNetADSMATHCrossRefGoogle Scholar
  6. 6.
    J.P. Gollub and S.V. Benson, J. Fluid Mech. 100, 449 (1980).ADSCrossRefGoogle Scholar
  7. 7.
    The arguments of the exponents in equation (1) should really involve integrals over the nonlinear medium (to account for propagation effects) corresponding to the formal solution to Maxwell’s equation. In the map given by equation (1), inclusion of propagation effects just rescales the argument of the exponent but does not effect the global parameter space picture in Figure 1 beyond a slight shift of the boundaries.Google Scholar
  8. 8.
    K. Ikeda, Opt. Commun. 30, 257 (1979)ADSCrossRefGoogle Scholar
  9. 8a.
    K. Ikdea, H. Daido and O. Akimoto, Phys. Rev. Lett. 45, 709 (1980).ADSCrossRefGoogle Scholar
  10. 9.
    R.R. Snapp, H.J. Carmichael and W.C. Schieve, Opt. Commun. 40, 68 (1981).ADSCrossRefGoogle Scholar
  11. 10.
    J.V. Moloney, S. Hammell and C.R.T. Jones, to be published.Google Scholar

Copyright information

© Plenum Press, New York 1984

Authors and Affiliations

  • J. V. Moloney
    • 1
  • H. M. Gibbs
    • 1
  • F. A. Hopf
    • 1
  1. 1.Optical Sciences CenterUniversity of ArizonaTucsonUSA

Personalised recommendations