A numerical strategy for evaluating the array Green´s function for a class of planar problems

The array Green´s function (AGF) represents the basic constituent for the full wave description of electromagnetic radiation from rectangular periodic arrays and scattering from periodic surfaces. In modeling the performance of such structures: one of the main objectives is the reduction of the often prohibitive numerical effort that accompanies the full-wave analysis based on an integral equation, which is structured around the ordinary individual element Green´s function. For a periodic array, this array Green´s function is composed of the sum of the individual dipole radiations. Under certain assumptions the integral equation can be restructured around the active Green´s function, which is the field collectively radiated by an array of elementary dipoles. A series of papers have investigated the description of the AGF in terms of propagating and evanescent Floquet waves (FWs) together with corresponding FW-modulated diffracted fields which arise from FW scattering at the array edges and vertices. The above mentioned formulation, being based on an asymptotic evaluation of the constituent radiation integrals, fails when observing too close to the edge and vertices. The present work is intended to illustrate a complementary strategy for treating the observation point also close to the array contour, as implicated by a full-wave scheme.