Finite element analysis of optical bistability in one-dimensional nonlinear photonic band gap structures with a defect

We present a new approach based on the recently reported finite element scheme16 to study the optical response of a finite one-dimensional nonlinear grating. Using the transmitted wave amplitude as a numerical input parameter, we are able to find all stable and unstable solutions related to a specific incident wave which build up the complete bistability curve. The method is applied to investigate the optical bistability in a nonlinear quarter-wave reflector with a defect. With a proper choice of the incident light frequency, a very low bistability threshold is predicted for an optimized defect structure