Rapidly convergent quasi-periodic Green functions for scattering by arrays of cylinders---including Wood anomalies

TL;DR

This paper introduces a rapid, highly accurate Green function method for scattering problems involving periodic arrays of cylinders, effective even at Wood-anomaly frequencies, with applications to various electromagnetic array configurations.

Contribution

The paper develops a full-spectrum Green function approach that handles Wood anomalies using shifted Green functions and Woodbury-Sherman-Morrison formulas, ensuring fast convergence and high accuracy.

Findings

Method achieves full-spectrum validity including Wood anomalies.

Converges rapidly, providing solutions in milliseconds.

High accuracy with minimal computational resources.

Abstract

This paper presents a full-spectrum Green function methodology (which is valid, in particular, at and around Wood-anomaly frequencies) for evaluation of scattering by periodic arrays of cylinders of arbitrary cross section-with application to wire gratings, particle arrays and reflectarrays and, indeed, general arrays of conducting or dielectric bounded obstacles under both TE and TM polarized illumination. The proposed method, which, for definiteness is demonstrated here for arrays of perfectly conducting particles under TE polarization, is based on use of the shifted Green-function method introduced in the recent contribution (Bruno and Delourme, Jour. Computat. Phys. pp. 262--290 (2014)). A certain infinite term arises at Wood anomalies for the cylinder-array problems considered here that is not present in the previous rough-surface case. As shown in this paper, these infinite terms can be treated via an application of ideas related to the Woodbury-Sherman-Morrison formulae. The resulting approach, which is applicable to general arrays of obstacles even at and around Wood-anomaly frequencies, exhibits fast convergence and high accuracies. For example, a few hundreds of milliseconds suffice for the proposed approach to evaluate solutions throughout the resonance region (wavelengths comparable to the period and cylinder sizes) with full single-precision accuracy.