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Multi-Parameter Universal Route to Chaos in Nonlinear Resonators: Observation of Period-Doubling in Ammonia Gas

  • E. Abraham
  • W. J. Firth
  • R. G. Harrison
Conference paper

Abstract

The ever increasing interest in chaos and related phenomena in the context of optical bistability1, has emerged from the predictions by Ikeda and Ikeda et al2 and subsequent observations by Gibbs et al3 in a hybrid system. As Ikeda et al treated systems with a delayed feedback, e.g. a ring cavity, it seemed an ‘open question’ the existence of chaos in a Fabry-Perot cavity. Firth4 was the first to show that a standing-wave resonator containing a cubic non-linearity with relaxation time τ = 0, exhibited Ikeda-type instabilities; Firth’s calculations were extended by Abraham et al5 to the case where τ≠ 0 and strong diffusion (to obliterate standing-wave effects).

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References

  1. 1.
    For a review with a tutorial approach see E. Abraham and S.D. Smith, Rep. Prog. Phys. 45, 815 (1982).ADSCrossRefGoogle Scholar
  2. 2.
    K. Ikeda, Opt. Comm. 30, 257 (1979); K. Ikeda, H. Daido andGoogle Scholar
  3. O. Akimoto, Phys. Rev. Lett. 45, 709 (1980).CrossRefGoogle Scholar
  4. 3.
    H.M. Gibbs, F.A. Hopf, D.L. Kaplan and R.L. Shoemaker, Phys. Rev. Lett. 46, 474 (1981).ADSCrossRefGoogle Scholar
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    W.J. Firth, Opt. Comm. 39, 343 (1981).ADSCrossRefGoogle Scholar
  6. 5.
    E. Abraham, W.J. Firth and J. Carr, Phys. Lett. 91A, 47 (1982); E. Abraham and W.J. Firth, Optica Acta (to appear).Google Scholar
  7. 6.
    R.G. Harrison, C.A. Emshary and I.A. Al-Saidi, in Optical Bistability ed. C. Bowden (Plenum, New York) to appear.Google Scholar
  8. 7.
    J.S. Garing, H.H. Nielsen and K. Narahari Row, J. Mol. Spect. 3, 496 (1959).ADSCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 1984

Authors and Affiliations

  • E. Abraham
    • 1
  • W. J. Firth
    • 1
  • R. G. Harrison
    • 1
  1. 1.Department of PhysicsHeriot-Watt UniversityEdinburghUK

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