Diffraction by a truncated planar array of dipoles: a Wiener-Hopf approach

Abstract

We present a rigorous solution to the problem of scattering of a semi-infinite planar array of dipoles, i.e., infinite in one direction and semi-infinite in the other direction, thus presenting an edge truncation, when illuminated by a plane wave. Such an arrangement represents the canonical problem to investigate the di raction occurring at the edge-truncation of a planar array. By applying the Wiener-Hopf technique to the Z-transformed system of equations derived from the electric field integral equation, we provide rigorous close form expressions for the dipoles’ currents. We find that such currents are represented as the superposition of the infinite array solution plus a perturbation, which comprises both edge di raction and bound surface waves excited by the edge truncation. Furthermore, we provide an analytical approximation for the double-infinite sum involved in the calculation which drastically reduces the computational e ort of this approach and also provides physically-meaningful asymptotics for the di racted currents.