Theory and Computation of Electromagnetic Fields, 2nd Edition

Chapter 5Fields and Waves in Rectangular Coordinates

Starting with this chapter, we discuss how to solve a variety of electromagnetic boundary-value problems in the three most commonly used coordinate systems: rectangular, cylindrical, and spherical. In this chapter, we deal with problems best described with rectangular coordinates. Those include wave propagation in rectangular waveguides and dielectric slab waveguides, resonances in rectangular cavities, and fields due to sources in a planar multilayered medium. However, since this is the first time we consider waveguides and cavities, we also discuss the general properties of waveguides and cavities of an arbitrary cross section. These properties are also applicable to other types of waveguides and cavities, such as those treated in the next two chapters.

5.1 Uniform Waveguides

In general, any structure that can guide electromagnetic waves from one end to the other end can be called a waveguide. Under this general definition, parallel-wire transmission lines, coaxial cables, microstrip lines, coplanar slotlines, hollow metallic pipes of various cross sections, and dielectric slabs or cylinders can all be called waveguides. In a certain sense, even free space can be considered a waveguide because it allows a wave to propagate from one place to another. In microwave engineering, the term waveguide usually refers to either a hollow or a partially filled metallic pipe of a rectangular, circular, or elliptical cross section. It ...