The transient response of a dielectric layer

Abstract

The transient response of an atmospheric surface duct will be studied when the distance between receiving and transmitting end is arbitrarily chosen. The duct model used is that of Kahan and Eckart, consisting of a layer of relative permittivity ε₁ overlying an infinitely conducting plane earth. At heighth, this permittivity decreases discontinuously to the value ε₂. The source of the electromagnetic field is assumed to be a vertical magnetic dipole at the height ξ (ξ<h) above the surface of the earth with arbitrary time varying moment. The application of two integral transforms to the wave equation for the Fitzgerald vector — a Laplace transform in time and a two-dimensional Fourier transform in the horizontal coordinates in space — leads, under consideration of initial, boundary and transition conditions, to an integral representation of the solution of the wave equation in transform space. A series expansion with respect to the images of the primary source permits us to extend a method of Cagniard, de Hoop and Frankena to the case where the position of the source is in the medium of greater permittivity. Thus we get the step-function solution of the problem as an infinite sum of definite integrals over finite intervals by distinguishing between cases where the distance between receiving and transmitting end is greater or less than the total reflection distance. Thus we can give a physically intuitive description of the pulse propagation in a dielectric layer.