Abstract
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
Highlights
I N A systematic sequence of previous studies [1]–[5], we have explored methods to reduce the often prohibitive numerical effort that accompanies an element-by-element full-wave analysis of large truncated plane periodic phased arrays
The element-by-element array Green’s function (AGF) formed by a planar periodic phased array of dipoles is restructured into an alternative “collective” formulation that represents the field radiated from the elementary
Our new extension in this paper addresses planar rectangular arrays with slowly varying excitation profiles that are separable in the two orthogonal variables
Summary
I N A systematic sequence of previous studies [1]–[5], we have explored methods to reduce the often prohibitive numerical effort that accompanies an element-by-element full-wave analysis of large truncated plane periodic phased arrays. The element-by-element array Green’s function (AGF) formed by a planar periodic phased array of dipoles is restructured into an alternative “collective” formulation that represents the field radiated from the elementary. For the canonical finite planar phased array of dipoles with tapered excitation, the AGF is constructed by plane wave spectral decomposition in the two-dimensional complex wavenumber domain corresponding to the array-plane coordinates. This is followed by manipulations and contour deformations that prepare the integrands for subsequent efficient and physically incisive asymptotics parameterized by critical spectral points, i.e., saddle points and points at which the spectral amplitude function exhibits highly peaked characteristics very similar to those of poles (denoted later on as “quasi-poles”). The numerical DFT procedure can be applied to a wider class of taperings, our results here are in analytical closed form and can be rapidly computed for the considered class of applications [7]–[9]
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