6.1 Introduction

In practical applications a dielectric resonator is expected to operate within a given frequency range and the electromagnetic field in the vicinity of the resonator is expected to exhibit behavior particular to the desired mode of operation (often TE _{01 ?}). One of the disadvantages associated with the use of dielectric resonators, however, is that one may find resonant frequencies of undesired modes in proximity to the resonant frequency of the desired mode. It is, therefore, of great practical importance to be able to determine the resonant frequencies and field patterns of the unwanted modes of a resonator, as well as those of the desired mode, so that proper operation of, and coupling to, the resonator can be obtained. The proximity of the resonant frequencies and the field patterns of the various modes are, of course, influenced by the surroundings of the resonator, such as metal cavity walls, metal tuning screws, or dielectric tuning rods. If the resonant frequencies and field patterns of the resonator structure can be reliably and accurately computed, it should be possible to determine the most appropriate way to modify the environment of the resonator so as to alter the resonant frequencies of the interfering modes or to suppress the excitation of these modes.

One approach to the analysis of dielectric resonators that has the potential to provide such information under a wide variety of circumstances is a surface integral equation (SIE) approach. In this chapter we present a description...