Mathematical studies of optical bistability

Abstract

Efficient numerical methods are developed to analyze optical bistability in a multilayer structure with Kerr nonlinearity. It corresponds to computing multiple solutions of the one-dimensional nonlinear Helmholtz equation for a range of frequencies and incident intensities. The input-output characteristics is calculated as a simple initial value problem without any iterations. Bistability intervals of the incident intensity are determined directly without using a continuation scheme. The complete transmission spectrum at a fixed incident intensity and a varying frequency is obtained including both stable and unstable solutions. For the multilayer structure, we also study the effect of random perturbations in the thickness of the layers. The perturbations are assumed to follow a normal distribution. For the linear case, the study is concentrated on the resonant transmission. Approximate distributions for the maximum transmission coefficient and the corresponding wavenumber are obtained. For nonlinear multilayer structure, we study the effect of the random perturbations on the bistability interval. Approximate distributions for the lower and upper ends of the bistability interval are obtained.