  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.
