Near-Earth wave propagation characteristics of electric dipole in presence of vegetation or snow layer

The problem of near-earth wave propagation in the presence of a dielectric layer such as a vegetation or snow covering is considered in this paper by modeling the propagation environment as a homogeneous two-layer medium (air/dielectric/ground). A number of studies have demonstrated the relevancy of the lateral wave for the case when both the transmitter and receiver are located within a simple half-space dielectric medium . Unfortunately, for the generalized two-layer model, for configurations in which the transmitter or receiver (or both) is located above the dielectric layer, far-field analytical expressions that include all propagation features do not exist. In this paper, in order to arrive at a computational efficient solution for the two-layer model, a second-order asymptotic evaluation for the electric fields of an arbitrarily oriented, infinitesimal electric dipole-for source and observation points located in the vicinity of the air/dielectric interface-is carried out through the method of steepest descents. The formulations are valid in the far field, with the limitation that the exponentially decaying pole and branch cut contributions have been ignored. It is observed that the Norton wave, though it is highly localized near the air/dielectric interface, is a significant contribution either when the dipole and observation points are both located above the dielectric layer or when one is above and the other is within the layer.