Finite Difference Scheme for Nonlinear Finite Grating without and with Defect

Abstract

We present a simple numerical scheme based on finite difference method (FDM) with different boundary treatments to study the nonlinear optical response of finite one-dimensional grating with Kerr medium. For linear and nonlinear case, we use the second order numerical scheme for interior with different treatments of boundary conditions. The resulting of nonlinear system of equations is solved using Newton method with continuation method. To illustrate this method, we consider a periodic medium with and without defect. As the result, this method is able to show the bandgap and optical bistability phenomena for both mediums.