Variational analysis and angular bistability in layered nonlinear Kerr media with phase conjugation

The calculus of variations is applied to electromagnetic fields in a layered nonlinear structure supporting a guided wave. The system also includes a phase-conjugate mirror (PCM). By introducing a variational dimension and using a collection of plane waves as a trial function, we approximate the exact solution of the nonlinear Kerr-Maxwell equation. The formalism is new, and it involves the nonlinear interference of multiple plane waves. A simple analytical expression for the nonlinear field in the presence of the PCM is derived, and the fact that the scattered intensities may become bistable when the angle of incidence is varied is demonstrated. In particular, our theory predicts the angular bistability in the backscattering direction, where the effect of the guided waves is subtle. Our numerical results are also in good agreement with other theoretical approaches and with the experimental data. (C) 2000 Optical Society of America [S0740-3224(00)00106-5].