A hybrid FEM-based procedure for the scattering from photonic crystals illuminated by a Gaussian beam

We provide an efficient numerical procedure for evaluating the field scattered by two-dimensional (2-D) photonic crystals when they are illuminated by Gaussian beams. In particular, the incident Gaussian beam is interpreted as a spectrum of both homogeneous and inhomogeneous plane waves. The scattering of each plane wave is analyzed by resorting to a hybrid technique combining the finite-element method (FEM) with a Floquet modal expansion. Moreover, by applying the standard saddle point method, the evaluation of the field at a specific point of the exterior medium is reduced to the contribution of the fundamental Floquet mode of a single plane wave belonging to the incident spectrum, strongly enhancing the numerical efficiency.