Elementary Floquet wave diffraction by an arbitrarily contoured planar phased array

The development of novel techniques capable of accelerating the analysis of large finite arrays is a subject of current interest for a large variety of engineering applications. Recently, a uniform high-frequency formulation of the Green's function (GF) for semi-infinite or sectoral arrays of dipoles relying on a Floquet wave diffraction theory has been introduced. These results can be exploited for the analysis of large finite phased array; indeed, the GF of such arrays can be efficiently expressed in terms of a series of propagating and evanescent FWs augmented by the relevant diffracted waves arising from the scattering at the edges and vertices of the array. However, this formulation becomes cumbersome for arrays with irregular contour, due to the intrinsic ambiguity in defining edges and tips. This contribution proposes a more general representation, in which the array GF is obtained as the sum of spherical diffracted wave contributions arising from the actual array rim and conical wave contributions coming from the array surface. This is obtained by regarding the planar distribution of sources as the superposition of parallel suitably excited finite linear arrays, and next by asymptotically evaluating the contributions of each linear array. These latter consist of the sum of truncated single-indexed FWs relevant to the infinite linear array plus the corresponding diffracted waves at the two end-points.