NONLINEAR FDTD FORMULATIONS USING Z-TRANSFORMS

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 straig htforward manner, Further, an analytic expression for the reflection c oefficient from a nonlinear dielectric is described and used to confir m the accuracy of the nonlinear FDTD formulation. Finally, a one-dimen sional nonlinear FDTD simulation is used to calculate soliton propagat ion in nonlinear media.