Lateral wave propagation in a wedge shaped region

Lateral wave propagation in a wedge shaped region is examined. The geometry consists of two media, the lower one of which is bounded from below by a conducting plate. The plate intersects the interface between the two media from below at an oblique angle. The transmitting antenna is an infinite, time harmonic, electric line source located close to the interface between the two media, and oriented to make the problem two dimensional. The wavenumber of the upper medium has a magnitude which is much greater than that of the lower medium. The lateral wave travels downward from the source into the second medium, along the interface, and back up to the point of observation in the first medium. The problem cannot be easily solved in closed form as the boundary conditions at the interface do not permit solution by separation of variables techniques. An approximate analytical method is therefore used in which the two media are separated from one another at each step of an iterative procedure using impedance boundary conditions. The simpler single medium problems which result are more amenable to analysis. The lateral wave field is expressed either as a modal series or image series depending on the angle the plate makes with the interface and on the location of the source and receiver. The decay of the wave in the direction parallel to the interface is shown to be algebraic, even in the presence of the plate. The results are valid subject to the restrictions that the source and receiver are close to the interface and are not too close to each other or the edge of the plate. There will be other waves present which are not considered in this paper if the upper region is not conducting, although the expression for the lateral wave remains valid.