Transient diffraction on a permittivity step in a waveguide: Closed-form solution in time domain

Abstract

The paper deals with impulse solutions to Klein-Gordon equation that describes in Time Domain (TD) propagation of waves in a waveguide, plane waves in plasma, and wave beams in free space. We consider the basic problem of transient diffraction on a permittivity step in a waveguide. Generalized scattering matrix in TD approach is used to present the solution in the form of convolution type transmission and reflection operators. Closed-form expressions for these operators are obtained by Laplace transform method for TE- and TM-waves both. Some consideration of transient wave propagation in a regular waveguide is given as well. Time-back propagation operator is introduced. The solution is illustrated with energy flow diagrams.