TABLE OF CONTENTS In 1897 Lord Rayleigh in his paper "On the passage of electric waves through tubes, or the vibrations of dielectric cylinders" suggested that electromagnetic waves could propagate through metallic tubes or dielectric cylinders [26]. A hollow waveguide exhibits a single connected metallic boundary. Figure 7.20 shows the schematic drawing of a cylindric hollow waveguide. Since electrostatic fields cannot occur inside closed hollow tubes TEM modes will not exist. However, electromagnetic wave solutions with either a longitudinal electric field or a longitudinal magnetic field exist. Hollow waveguides play an important role in microwave technology, especially for low attenuation and high power applications and as basic elements of microwave circuits. In the following we discuss the general properties of TE-, and TM modes. For a first reading the reader may directly proceed to Section 7.9.
Consider a closed uniform general cylindric hollow waveguide with cross-section A and bounded by perfectly conducting walls at ?A as depicted in Figure 7.20. Let the waveguide be filled with a lossless dielectric. To represent the electromagnetic field in the waveguide we choose a general cylindric coordinate system with the coordinates u, v, z where z is a linear coordinate and u, v are orthogonal curvilinear coordinates transverse to z. Furthermore, we choose the transverse coordinates such that the wall of the waveguide is a boundary surface (i.e., a surface defined by setting one of the transverse coordinates...
