Anomalous spatial modifications of beams diffracted by two-dimensional periodic media

By using a rigorous plane-wave representation, we examine the diffracted fields generated by a Gaussian beam incident onto the planar upper boundary of a 2D periodic structure. We first determine a geometric profile for every diffracted beam by neglecting the amplitude variation of its plane-wave spectrum. We then account for the spectral variation and show that, with respect to that geometric profile, every actual diffracted beam exhibits spatial modifications in the form of 2D lateral displacements, focal shifts, angular deviations, and beam-width alterations. These effects are relatively large if the incidence conditions tend to generate grating resonances. The magnitudes of the beam modifications are illustrated by using a canonic grating model that consists of a planar surface whose impedance varies sinusoidally along its two orthogonal directions. We also develop accurate analytical expressions for the spatial modifications by expressing the spectral amplitude functions in terms of Padé approximants. We thus find that the 2D spatial effects exhibit greater complexity and include features that are absent in previously reported cases involving 1D periodic surfaces.