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Communications in Theoretical Physics

Bifurcation and Chaos in Two-Photon Optical Multistability

Ying-Hai Wang, Huawei Yin

Published Jul 1, 1993• 0 citations
Publisher

Abstract

Investigation of the two-photon optical multistability (tristability and double-bistability) has revealed the existence of the spontaneous oscillation and chaotic motion. By the information obtained from the time-dependent solution, power spectra, Lyapunov exponents and phase trajectory, we proved evidence of the bifurcation structure for tristability, and show the existence of two coexisting at tractors for the double-bistability.

DOI
10.1088/0253-6102/20/1/49

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Investigation of the two-photon optical multistability (tristability and double-bistability) has revealed the existence of the spontaneous oscillation and chaotic motion. By the information obtained from the time-dependent solution, power spectra, Lyapunov exponents and phase trajectory, we proved evidence of the bifurcation structure for tristability, and show the existence of two coexisting at tractors for the double-bistability.
The theory of the optical multistability by two-photon resonant interaction is investigated. The nonlinear medium inside a Fabry-Perot cavity is in two-photon resonance with the laser beam. The two-photon equation of state including dynamical Stark shift and relaxation parameters is obtained and studied under mean-field approximation. The equations for both Fabry-Perot cavity and ring cavity take basically the same form. The physics mechanisms resulting in optical multistability are also studied. It has been shown that the combined effects of Kerr switching and saturation absorption switching can lead to two-photon optical double-bistability, tristability as well as bistability. Furthermore, the criterion conditions under which double-bistability or tristability can occur are given and discussed. Finally, the phase-conjugated reflectivity by two-photon four-wave mixing is also shown to exhibit multistability as well as hysteresis.
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 tristability 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 routes 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.
The distributions, in parameter space, of subcritical Hopf bifurcations and the various attractors of time-dependent motions of optical bistable systems are investigated systematically. The main emphasis is placed on the influence of the variations of the control parameters on the distributions. We have observed the tristability of large-amplitude regular or chaotic motions, periodic pulsations, and the stationary state for the parameters where no instability of the stationary solution exists at all over the complete range of the external field. The problem of how to find the various attractors and how to reveal chaotic motions by adjusting the control parameters is discussed according to the numerical results.
We consider an intracavity nonlinear medium interacting with two modes of the electromagnetic field via a two-photon process. The cavity is coherently driven at the frequencies of the two modes. We consider as the intracavity medium (a) a two-photon absorber, and (b) NNN three-level atoms. These systems display a new class of bifurcations, and, in the case of the two-photon absorber, optical tristability is possible.