Electromagnetic Surface-Wave Propagation Along a Dielectric Cylinder of Elliptical Cross Section

Abstract

The problem of electromagnetic wave propagation along a dielectric rod of elliptical cross section is considered. The field components and the dispersion relations of the principal modes are obtained. The principal modes degenerate to the well known HE_(mn) modes of the circular dielectric rod as the eccentricity of the elliptical rod approaches zero. It is found that there are two non-degenerate principal modes which possess no cut off frequencies. They are called the dominant principal modes. In contrast to the case of a circular dielectric rod, the boundary conditions for the elliptical rod cannot be satisfied by using a single product term consisting of a radial and a periodic Mathieu function of a specific order to describe the field components in both regions (the region inside the rod and the region outside the rod). It is generally believed that an infinite series of such product terms must be used to describe the field components in both regions. In the present investigation, it is shown that the boundary conditions may be fulfilled if the field components in one of the two regions are represented by a single product term consisting of a radial and a periodic Mathieu function of a specific order. The field components in the other region are then represented by an infinite series of such product terms. The problem is therefore sufficiently simplified to permit analysis. The propagation characteristics (the propagation constant, the field distribution and the attenuation constant) of the dominant principal modes are given theoretically and experimentally. It is found that the analytic and experimental results are in very good agreement. The Q's of a dielectric rod cavity resonator supporting the dominant principal modes are also given.