Abstract
This paper deals with the construction, physical interpretation and application of a uniform high-frequency representation of array Green’s functions (AGFs) for planar rectangular phased arrays of dipoles. An AGF is the basic constituent for the full-wave description of electromagnetic radiation from large periodic structures. For efficient treatment of high-frequency phenomena, the AGF obtained by direct summation over the contributions from the individual radiators is globally restructured via the Poisson sum formula into a series of propagating and evanescent Floquet waves (FWs) together with corresponding FW-modulated diffracted waves, which arise from FW scattering at the array edges and vertexes. These results are obtained by high-frequency uniform asymptotics applied to the wave integrals generated by Poisson summation in the spatial or spectral domains. The final algorithm is physically appealing, numerically accurate, and efficient, owing to the rapid convergence of both the FW series and the series of corresponding FW-modulated diffracted fields away from the array plane. The use of the asymptotic AGF in the full-wave analysis of large slot arrays is discussed, with the inclusion of numerical results.
Highlights
Periodic structures are of interest in many current engineering applications, which include phased array antennas [1,2,3,4,5,6,7,8,9,10]
Applying high-frequency asymptotics, the radiation from, or scattering by, finite phased arrays is interpreted as the radiation from a superposition of continuous equivalent Floquet wave (FW)-matched source distributions extending over the entire finite array aperture, from which the Floquet waves (FWs)-based array Green’s functions (AGFs) can be calculated efficiently
A high-frequency formulation for the AGF of a periodic rectangular array of linearly phased parallel dipoles has been developed and utilized as the base for an array-matched generalized geometrical theory of diffraction (GTD) which extends the concepts of conventional GTD for smooth configurations
Summary
Periodic structures are of interest in many current engineering applications, which include phased array antennas [1,2,3,4,5,6,7,8,9,10]. We explore replacement of the element-by-element Green’s function by a global AGF which is constructed via Poisson summation and represents, in terms of the resulting Poisson-transformed integrals, the collective field radiated by the elementary dipoles. Applying high-frequency asymptotics, the radiation from, or scattering by, finite phased arrays is interpreted as the radiation from a superposition of continuous equivalent Floquet wave (FW)-matched source distributions extending over the entire finite array aperture, from which the FW-based AGF can be calculated efficiently. This approach has been applied successfully to various prototypical configurations, such as linear arrays of dipoles [3], arrays of line sources. The FW-based asymptotic treatment of rectangular AGF is presented and applied to practical array problems
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