Sk. Chin et al., GREENS-FUNCTION AND LATTICE SUMS FOR ELECTROMAGNETIC SCATTERING BY A SQUARE ARRAY OF CYLINDERS, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics, 49(5), 1994, pp. 4590-4602
A method is given to represent in terms of absolutely convergent serie
s the lattice sums involved in solving problems of electromagnetic dif
fraction by two-dimensional periodic arrays of obstacles. The expressi
ons of the lattice sums are used to express the Green's function of th
e problem as a Neumann series. These results lead to very efficient al
gorithms for numerical calculations of the Green's function.