Hybrid Numerical/Asymptotic approach for the Analysis of Rectangular Array Greens Function in a Multilayered Dielectric Slab

Abstract

This paper illustrates a formulation to evaluate the array Green's function (AGF) of large finite planar phased array for observation points on the array plane. The procedure is based on the AGF representation in terms of different terms, namely space wave (SP) and surface wave (SW) contributions. This two terms are calculated by using different approaches. The space wave contribution is obtained through a hybrid numerical/asymptotic algorithm. In fact, the diffraction integral, associated with the finiteness of the actual array, is evaluated numerically for point close to the array edges while an asymptotic treatment is proposed far from the edges and vertexes. This latter comprises higher order contributions. Thanks to this convergence properties, the final algorithm is numerically accurate, stable and more efficient with respect to the individual element summation for large arrays. The procedure can be also applied for array in multilayered environment by resorting to a complex source expansion method. The surface waves contribution can be calculated fully asymptotically, through a suitable uniform saddle point evaluation