The Effect of a Grounded Slab on the Radiation from a Line Source

A theoretical investigation, based upon the method of fourier transforms, is made of the effect of a grounded dielectric slab on the radiation from a line source. It is shown that the principal part of the electric field above the dielectric slab can be found either by evaluating the resultant contour integral, using the saddle-point method of integration, or by evaluating the integral containing the tangential H-field along the interface. The radiation pattern of the principal field is found to be identical with the resultant field of a direct ray and a reflected ray that can be obtained by a simple consideration of geometrical optics. The condition of the existence of propagating modes in the dielectric slab has been discussed in detail. When the slab is thick enough to support a propagating mode, in addition to the space wave, a surface wave will appear in the neighborhood of the interface. The latter attenuates rapidly as the point of observation is moved away from the interface. The deformation of the path of integration corresponding to different angles of observation has been displayed graphically both in the original h-plane and the transformed τ-plane.