A Direct Method for Bloch Wave Excitation by Scattering at the Edge of a Lattice. Part I: Point Scatterer Problem

A new method for determining the reflection and transmission properties of lattices is developed. The method uses multipole expansions, and certain transformations of the algebraic equation systems that appear when boundary conditions are applied. It is more direct, and much simpler, than earlier approaches based on integral transforms and the Wiener–Hopf technique. The method is demonstrated for the case of a semi-infinite lattice of sound soft acoustic point scatterers, but can easily be generalised to account for finite size effects, and more general boundary conditions.