General method for solving nonlinear optical scattering problems using fix point iterations

In this paper we introduce a new fix point iteration scheme for solving nonlinear electromagnetic scattering problems. The method is based on a spectral formulation of Maxwell's equations called the Bidirectional Pulse Propagation Equations. The scheme can be applied to a wide array of slab-like geometries, and for arbitrary material responses. We derive the scheme and investigated how it performs with respect to convergence and accuracy by applying it to the case of light scattering from a simple slab whose nonlinear material response is a sum a very fast electronic vibrational response, and a much slower molecular vibrational response.