Green's function for a planar phased sectoral array of dipoles: synthesis via canonical constituents

The EM modeling of large phased arrays is a topic of increasing interest. One objective is to reduce the numerical effort that accompanies an element-by-element full-wave analysis based on integral equations which are structured around the ordinary free space Green's function; when applied to a periodic array this array Green's function is composed of the sum over the individual dipole radiations. As an alternative, we explore replacement of the element-by-element Green's function by the array Green's function (AGF) which represents the collective field radiated by the elementary dipoles. The efficient calculation of the AGF is accomplished via a Floquet wave (FW) representation. With this representation, the wave radiation from, or scattering by, finite phased arrays is interpreted as the radiation from a superposition of continuous equivalent FW-matched source distributions extending over the entire finite array aperture. The asymptotic treatment of each FW sectoral aperture distribution leads to a FW that is truncated at the array edges, plus FW-modulated diffracted contributions from the edges and vertex of the array. This approach is extended here to a right-angle sectoral planar phased array of dipoles which is the basic constituent for the treatment of planar rectangular arrays.