Asymptotic high-frequency Green´s function for a large rectangular planar periodic phased array of dipoles with weakly tapered excitation in two dimensions

This paper deals with the derivation and physical interpretation of a uniform high-frequency representation of the Green\´s function for a large planar rectangular phased array of dipoles with weakly varying excitation. Thereby, our earlier published results, valid for equiamplitude excitation, and those for tapered illumination in one dimension are extended to tapering along both dimensions, including dipole amplitudes tending to zero at the edges. As previously, the field obtained by direct summation over the contributions from the individual radiators is restructured into a double spectral integral whose high-frequency asymptotic reduction yields a series of propagating and evanescent Floquet waves (FWs) together with corresponding FW-modulated diffracted fields, which arise from FW scattering at the array edges and vertexes. To accommodate the weak amplitude tapering, new generalized periodicity-modulated edge and vertex "slope" transition functions are introduced, accompanied by a systematic procedure for their numerical evaluation. Special attention is given to the analysis and physical interpretation of the complex vertex diffracted ray fields. A sample calculation is included to demonstrate the accuracy of the asymptotic algorithm. The resulting array Green\´s function forms the basic building block for the full-wave analysis of planar weakly amplitude-tapered phased array antennas, and for the description of electromagnetic radiation and scattering from weakly amplitude-tapered rectangular periodic structures