Properties of the Time-Domain Waveguide Modes

Abstract

The time-domain problem is solved within the framework of the evolutionary approach to electrodynamics. The procedure is decomposed onto solving two autonomous problems. The first one is standard solving a boundary-eigenvalue problem for transverse Laplacian what yields a configurational basis in the waveguide cross section. Elements of this basis depend on transverse coordinates only. At the last step, we extract from Maxwell's equations with partial derivative(t) a system of the evolutionary equations for the modal amplitudes dependent on axial coordinate, z; and time, t. Klein-Gordon equation (KGE) plays the main role herein. Solving KGE yields an evolutionary basis for analysis of the modal amplitudes in Minkowski plane (z, ct).