Evaluation of Unsteady Non-Harmonic Fields in Microwave Devices. III. Decomposition in the Regular Modes

Abstract

Decomposition of electrodynamic line field in so-called regular modes is described. Comparing with the partial modes, series of the regular modes ensures less "truncation" errors (caused by the Gibbs' phenomenon) at the same number of the terms. A generalized wave equation for a regular dispersive and dissipative electrodynamic line of arbitrary geometry and dispersion characteristic is derived. The classic wave equation, the Klein-Gorgon equation, and the Telegraphist’s equation are subsets of one. The advantages of using the four-vector potential, inherently taking into account the Lorenz gauge, is discussed. A full set of regular modes of the potential four-vector in a rectangular waveguide is written.