A Perfectly Matched Layer for the Nonlinear Dispersive Finite-Element Time-Domain Method

A novel implementation of a perfectly matched layer (PML) is presented for the truncation of finite-element time-domain (FETD) meshes containing electrically complex materials, exhibiting any combination of linear dispersion, instantaneous nonlinearity, and dispersive nonlinearity. Based on the complex coordinate stretching formulation of the PML, the presented technique yields an artificial absorbing layer whose matching condition is independent of material parameters. Moreover, by virtue of only modifying spatial derivatives, the incorporation of the PML into existing solvers for complex media is simple and straightforward. The resulting material-independent PML is incorporated into a nonlinear dispersive method for the vector wave equation, which leverages the z transform and Newton-Raphson techniques to yield an implementation free from recursive convolutions, auxiliary differential equations, and linearizations. This permits the unprecedented truncation and attenuation of nonlinear phenomena, such as spatial and temporal solitons, within the FETD method.