Resonant effects in scattering by periodic arrays

This paper is concerned with resonant effects caused by the scattering of a plane wave by a periodic array of vertical circular cylinders. The scattered field is known to consist of a finite set of plane waves, and an infinite number of evanescent modes which decay exponentially as the perpendicular distance between array and observer is increased. The problem is said to be resonant when the direction of propagation of a scattered plane wave is exactly parallel to the array. An efficient method for computing the solution in this special case is presented. No such method appears to exist in the literature; other authors have derived only asymptotic results as the resonant state is approached (see Twersky [1], for example).