TABLE OF CONTENTS Periodic structures are used in various waveguide designs. For example, a metal ground plane with periodic corrugations is used to guide slow waves. A microstrip line periodically loaded with inter-digit capacitors and stub inductors is designed to support backward waves. In this section, the FDTD/PBC algorithm is used to analyze several typical waveguides and their dispersion relations are illustrated.
A fundamental question in waveguide analysis is how to accurately characterize the dispersion relation of the structure [29]. Assume an electromagnetic wave propagates along the x direction in a periodic waveguide. At a given frequency ?, the propagation constants k x (or ?) of guided waves need to be identified. The results are usually plotted in the k x-frequency plane, and are known as the dispersion curves. For example, Fig. 2.7 shows the dispersion curves of a dielectric slab waveguide. There are four curves in this figure and each represents a specific surface wave mode. At the frequency 25 GHz, the corresponding propagation constants are 539 radian/m, 575 radian/m, 736 radian/m, and 771 radian/m, respectively. It is observed that cutoff frequencies exist for higher-order modes, such as the TM 1 and TE 1 modes in Fig. 2.7.
An alternative way to state the question is at a given propagation constant k x find the corresponding...
