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arXiv:patt-sol/9908004 · Physical Review Letters

Bilateral Symmetry Breaking in a Nonlinear Fabry-Pérot Cavity Exhibiting Optical Tristability

Juan P. Torres, Jack Boyce, R. Y. Chiao

Published Nov 22, 1999• 26 citations
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Abstract

We show the existence of a region in the parameter space that defines the field dynamics in a Fabry-P\'erot cylindrical cavity, where three output stable stationary states of the light are possible for a given localized incident field. Two of these states do not preserve the bilateral (i.e., left-right) symmetry of the entire system. These broken-symmetry states are the high-transmission nonlinear modes of the system. We also discuss how to excite these states.

DOI
10.1103/physrevlett.83.4293

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We show the existence of a region in the parameter space that defines the field dynamics in a Fabry-P'erot cylindrical cavity, where three output stable stationary states of the light are possible for a given localized incident field. Two of these states do not preserve the bilateral (i.e., left-right) symmetry of the entire system. These broken-symmetry states are the high-transmission nonlinear modes of the system. We also discuss how to excite these states.
It is predicted with use of a simplified model that a Fabry-Perot cavity filled with atoms with Zeeman sublevels in the ground state should exhibit optical tristability via optical pumping. For linearly polarized incident light, three stable states appear in the polarization of the transmitted light; ${\ensuremath{\sigma}}_{+}$ dominant, ${\ensuremath{\sigma}}_{\ensuremath{-}}$ dominant, and linear polarizations. This optical tristability is discussed in the context of a butterfly catastrophe.
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 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.
A semiclassical theoretical model is described under the plane-wave and mean-field approximations on the transmission characteristics of a system of two-level atoms with large permanent dipole moments contained in a Fabry-Perot cavity and driven by two coherent two-photon resonant fields. In the steady-state situation, the coupled field equations are solved by eliminating one of the field variables to obtain the state equation. This state equation is numerically analyzed in detail, thus providing the regions on two-dimensional maps corresponding to one, three, and five stationary states of the system. The linear stability analysis is also carried out for the case when the length of the cavity is such that the medium-relaxation times are much shorter than the cavity-photon life times for both the waves. The simple stability criterion that the negative-slope regions of the transmission curves are unstable holds, but only the lowest positive-slope branches show stability in all of the cases we tested numerically.