Spectral methods applied to the characterization of stationary guided waves in nonlinear optical slabs

Two spectral methods for the analysis of monochromatic stationary TE-polarized waves propagating in nonlinear optical slabs are presented. Both methods are based on a Fourier series expansion but the first one is directly applied to the nonlinear wave equation while the second one makes use of a nonlinear mapping of the spatial coordinate. A suitable numerical strategy to solve the resultant system of equations is also presented, which uses the FFT to link the spatial and frequency domains and efficiently calculates the Jacobian elements. The spectral methods are applied to find the fields of an optical slab with a nonlinear Kerr type substrate and their performance is compared