3.1 Introduction

This chapter is concerned with the field analysis of the dielectric rod waveguide shown in Fig. 3.1. Such a structure has found its applications in the areas of dielectric rod antennas and optical fiber waveguides, to name a few. The analysis is later specialized to the parallel-plate dielectric resonator shown in Fig. 3.2. The use of the resonator in measuring dielectric constants is also discussed.

Figure 3.1: The dielectric rod waveguide

Figure 3.2: The parallel-plate dielectric resonator

A familiarity with electromagnetic waves in dielectric rod waveguides is very helpful in understanding the operation of dielectric resonators. Just as a truncated hollow waveguide becomes a resonant cavity, so the dielectric rod waveguide when truncated becomes a dielectric resonator.

The topics considered are classical electromagnetic field problems. Many of the concepts and formulas established in this chapter form a basis for some of the simple as well as rigorous models of dielectric resonators discussed in later chapters. The presentation here is, therefore, rather detailed. In the first two sections, the basic electromagnetic equations used and the method of separation of variables for solving the scalar Helmholtz equation in cylindrical coordinates are introduced. A field analysis then shows that the dielectric rod waveguide, for any given frequency and rod material and radius, is capable of supporting different field configurations, called the modes of the rod, at certain discrete values called the characteristic values, or eigenvalues, of the rod. An equation whose zeros are the eigenvalues...