Green's Function of an Infinite Slot Printed Between Two Homogeneous Dieletrics—Part II: Uniform Asymptotic Solution

Abstract

This second part of a two-paper sequence deals with the uniform asymptotic description of the Green's function of an infinite slot printed between two different homogeneous dielectric media. Starting from the magnetic current derived in Part I, the dyadic Green's function is first formulated in integral form in both spectral and spatial domains; next, the asymptotic solution for the vector potential is evaluated asymptotically. The asymptotic ray-field is structured in three contributions: a spherical wave radiated by the source (space wave), a conical leaky wave, and a lateral wave. These contributions are first introduced by the stationary phase method applied to the space-domain radiation integral. From this approach it is seen that the lateral wave contribution is negligible in actual configurations. Next, a rigorous uniform asymptotic evaluation of the radiated field is formulated in the spectral domain by using a steepest descent path deformation which accounts for the vicinity of the pole to the saddle point. Through this rigorous asymptotics, the domain of existence of the leaky-wave is found to be limited by a conical shadow boundary which deviates from that defined by the stationary phase regime. Along this conical shadow boundary, phase matching occurs between space and leaky wave, which facilitates the transition mechanism between the two wave types. This transition occurs inside a conical transition region with elliptical cross section. The interference between space and leaky waves from the near to the far zone are discussed by means of illustrative examples, which also confirm the accuracy of the asymptotics.