High-frequency Green's function for planar periodic phased arrays with skewed grid and polygonal contour

The derivation of an uniform high-frequency asymptotic representation of the array Green's function (AGF) for finite planar periodic phased arrays with arbitrary polygonal contour and skewed grid is presented. This result generalizes those obtained, in a series of recent papers, in the case of rectangular phased arrays with rectangular grid. For the treatment of the high-frequency phenomena, the actual finite array is rigorously decomposed in terms of canonical constituents, i.e., infinite, semi-infinite and sectoral arrays. The final result is a representation of the AGF in terms of spatially truncated Floquet waves (FWs) and FW-induced diffracted fields arising from the edges and vertices of the polygonal rim of the array. Consequently, the number of field contributions necessary to reconstruct the total field is independent of the number of elements of the array, leading to a very efficient algorithm. A series of numerical results is provided to demonstrate the effectiveness of the high-frequency representation.