Electromagnetic wave propagation along a thin wire over an arbitrary isotropic interface

The problem of a transmission line formed by an infinitely long and thin metal wire over a realistic ground surface (ground return effect) has been studied since the 20s of the last century. Solution to the problem implies determination of a complex propagation constant of a traveling wave, that is localized between the wire and the ground. However, analytical solutions were obtained only for a number of particular simplified models of the ground (e.g. an impedance surface or a lossy dielectric half-space). In this work, we introduce a new full-wave approach, which is suitable for determination of the propagation constant in the case of a thin infinite wire over an arbitrary isotropic interface. The interface is characterized by its reflection coefficients with respect to incident TE- and TM-polarized plane waves as functions of the normal component of the incident wave vector. We show that the propagation constant can be found as a root of the general characteristic equation, which is derived based on the Exact Image Theory and the Integral Equation technique. In order to verify the equation we study its asymptotic solutions for particular instances of an interface, for which the propagation constant is given by closed-form equations known from the literature.