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

In this paper, we provide an efficient numerical procedure for evaluating t he field scattered by two-dimensional (2-D) photonic crystals when they are illuminated by Gaussian beams, In particular, the incident Gaussian beam i s interpreted as a spectrum of both homogeneous and inhomogeneous plane wav es, The scattering of each plane wave is analyzed by resorting to a hybrid technique combining the finite-element method (FEM) with a Floquet modal ex pansion. Moreover, by applying the standard saddle point method, the evalua tion of the held at a specific point of the exterior medium is reduced to t he contribution of the fundamental Floquet mode of a single plane wave belo nging to the incident spectrum, strongly enhancing numerical efficiency.