Array scattering resonance in the context of Foldy’s approximation

This article provides an overview of resonance phenomena in wave scattering by infinite and semi-infinite periodic arrays of small cylindrical scatterers, in the context of Foldy’s approximation. It briefly summarizes well-known results from the literature. Moreover, for infinite arrays, the asymptotics of the resonant wave amplitudes in the double resonance case is investigated. This leads to the rediscovery of non-uniqueness of the solution in this context, and to a discussion of the validity of Foldy’s approximation for double resonance. For semi-infinite arrays, a new and improved uniform far-field approximation is derived, uniqueness issues are considered and the validity of Foldy’s approximation is discussed.