Electromagnetic field of transient signals above a dielectric layer

The polarization of the primary source, whose moment varies arbitrarily in time, is chosen in such a way that it allows the exact determination of the electric field strength at some field point above the duct layer. Two integral transform, a Laplace transform in time and a two-dimensional Fourier transform in the horizontal coordinates in space are applied. This leads to an integral representation of the solution of the wave equation in transform space. Saddle point and residue methods are used to compute the integral. The problem is evaluated mathematically using the residue and saddle point methods.