Instabilities in the Propagation of Arbitrarily Polarized Counterpropagating Waves in a Nonlinear Kerr Medium
The stability of strong optical waves counterpropagating in a nonlinear optical material has important implications for nonlinear optical processes such as optical bistability and phase conjugation. Nonlinear Kerr media are perhaps the simplest nonlinear optical material to model, yet the interaction of light waves in these materials can exhibit very rich and complicated behavior [1–5]. SILBERBERG and BAR-JOSEPH  have predicted that the output intensities of two strong waves with parallel polarization, counterpropagating in a nonlinear Kerr medium with finite response time, can show oscillatory as well as chaotic behavior. KAPLAN and LAW  have recently demonstrated that multistable polarization states are possible in the steady-state outputs of two counterpropagating vector fields in a nonlinear Kerr medium with an infinitely fast response time. This complicated steady-state behavior has motivated us to study the time dependence of the output polarizations of counterpropagating vector fields in a nonlinear Kerr medium. The inclusion of temporal effects enables us to study theoretically the stability of the polarization of the transmitted waves in order to determine whether oscillatory, hysteretic, or chaotic behavior occurs. In this paper, we present numerical results that demonstrate the existence of hysteretic bistability in the output polarizations.
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