TABLE OF CONTENTS In this section we discuss the way to evaluate the electromagnetic field components in linear waveguides. Without any restriction in general we assume the waveguides to be oriented in the z-direction. Furthermore, we assume that the cross-section of the waveguide may be subdivided into subsections and that each of these subsections is either empty or filled by conducting material or homogeneous isotropic lossless dielectric material. One strategy to solve Maxwell's equations for such structures is to seek the partial solutions for every subsection and to match the solution along the boundaries. If the metallic conductors are considered to be perfectly conducting, we do not need to solve the field equation inside the metallic regions. By superposition of partial solutions the boundary conditions may be fulfilled. The mathematical effort may be reduced considerably, if we can choose a cylindric coordinate system in which boundary surfaces of the waveguide may be defined by setting constant one coordinate. In this case a single partial solution may already represent the field distribution of a mode.
We may derive transverse magnetic modes from the electric Hertz form ? e and the transverse electric modes from the magnetic Hertz form ? m. We can choose an electric Hertz form ? e or a magnetic Hertz form ? m, which exhibits only a longitudinal field component ? ez or ? mz, respectively. The electric and magnetic Hertz forms and the scalar wave equation for...
