A generalized perturbative approach for the computation of nonlinear scattering problems

We developed a perturbative approach for the resolution of nonlinear scattering electromagnetic problems for arbitrary polarizations and incident angles. The modeling of the scattering of light by nonlinear materials leads, even for a monochromatic source, to a system of coupled nonlinear partial differential equations. Two main approaches are commonly employed to solve these equations. The first consists in directly solving the coupled nonlinear system through iterative methods; however this approach is very time-consuming. The second approach relies on perturbation theory. Assuming that the field amplitudes are sufficiently small, the coupled nonlinear system can be decoupled into a set of linear equations that are solved sequentially. In this work, we generalize this approach to the n-th order for the full system of nonlinear equations describing light scattering in the harmonic domain, and compare it in several test cases with the solution obtained from a previously reported iterative approach.