Edge diffracted Floquet waves at a truncated array of dipoles

A rigorous element by element method of moments (MoM) becomes too complex and computationally inefficient when the size increases, so that large arrays are usually studied by supposing the structure as infinite. A technique which was proposed previously, accounts for the edge effects by a windowing approach, which is based on a physical optics (PO)-type approximation and on the active Green´s function concept. This latter terminology denotes the near-field radiated by a finite array of elementary sources. To efficiently calculate the active free-space Green´s function, a Floquet waves (FWs) representation may be used. This representation allows one to interpret the radiation (or scattering) of a finite phased array as a superposition of FW distributions on the global aperture of the array. Consequently, each FW radiation integral can be asymptotically represented by the FWs themselves plus ray contributions from the edge of the array. In this paper the Green´s function of an array of dipoles which is truncated in one dimension and infinite in the other is formulated. The dipoles are considered of uniform amplitude and linearly phased for including a scan beam description. By invoking the locality of the high-frequency phenomena, the actual finite distribution may be treated by using local edges. The problem is firstly formulated by superimposing the near field contributions of each source. Next, the global radiation from the structure is represented in terms of a spectral integral which is asymptotically evaluated.