Lattice Sums for an Electromagnetic Scattering Problem

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Abstract
We consider the problem of the diffraction of a plane electromagnetic wave by a square array of perfectly conducting cylinders of finite length. We outline a method of generating a modal solution of this problem. The finding of modes necessitates the evaluation of a set of dynamic lattice sums over the square array. We consider two methods of evaluating the lattice sums, which do not converge absolutely. The first of these methods is that of Ewald summation, while the second relies on a set of identities among the lattice sums. We show that the results of the two methods agree, and that the second method is both the easier of the two to implement, and is capable of generating accurately the values of a large set of lattice sums.