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.

Grating diffraction and Wood's anomalies at two-dimensionally periodic impedance surfaces.

We address the problem of plane-wave scattering and Wood's anomalies at two-dimensional (2-D) periodic surfaces by employing a simplified grating model given by a planar surface whose impedance varies sinusoidally along two orthogonal directions. We obtain a rigorous solution to the corresponding boundary-value problem in terms of an infinite set of coupled recurrence equations. When truncated for computational purposes, this solution is in the form of a banded matrix, which we solve by direct methods and also by a highly efficient iterated matrix procedure. Numerical results are presented for symmetric and nonsymmetric incidence cases, and we show that certain diffracted fields do not depolarize in the former case. The expected Wood's anomalies of both Rayleigh and leaky-wave types are confirmed, and their location in wavelength space is numerically demonstrated for 2-D periodic configurations.

Modal transmission-line theory of three-dimensional periodic structures with arbitrary lattice configurations.

The scattering of waves by multilayered periodic structures is formulated in three-dimensional space by using Fourier expansions for both the basic lattice and its associated reciprocal lattice. The fields in each layer are then expressed in terms of characteristic modes, and the complete solution is found rigorously by using a transmission-line representation to address the pertinent boundary-value problems. Such an approach can treat periodic arbitrary lattices containing arbitrarily shaped dielectric components, which may generally be absorbing and have biaxial properties along directions that are parallel or perpendicular to the layers. We illustrate the present approach by comparing our numerical results with data reported in the past for simple structures. In addition, we provide new results for more complex configurations, which include multiple periodic regions that contain absorbing uniaxial components with several possible canonic shapes and high dielectric constants.