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

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