Nonlinear FDTD formulations using Z transforms

Abstract

An implementation of the FDTD method for nonlinear optical simulation is described, This method draws on ideas from digital filtering theory by formulating the nonlinearities using Z transforms, This provides a means of directly calculating the nonlinear polarizations in a straightforward manner, Further, an analytic expression for the reflection coefficient from a nonlinear dielectric is described and used to confirm the accuracy of the nonlinear FDTD formulation. Finally, a one-dimensional nonlinear FDTD simulation is used to calculate soliton propagation in nonlinear media.