Lateral wave propagation in a three‐layered medium

Abstract

The effect of an intervening layer on a lateral wave which propagates along the interface between two different electrical media is considered. The lateral wave travels down from a time‐harmonic electric dipole source in the upper region, through the middle region, and parallel to the interface between the middle and lower regions. It is assumed that the magnitude of the wavenumber in the upper medium is much greater than that of the middle, which in turn is much greater than that of the lower. The middle layer affects the lateral wave in two ways. It multiplies the usual lateral wave results by an overall factor which depends on the thickness of the slab and the electrical properties of the three media. It also changes at what distance the transition from intermediate to far field behavior occurs. Typically, the presence of the slab increases the magnitude of the fields near the transmitter, but leads to smaller field strengths in the far field region. The formulas are derived in two ways. The first utilizes an iterative procedure based on impedance boundary conditions and boundary layer theory. The second uses the more traditional steepest descent evaluation of the exact integrals available for the problem.