Time-domain method of lines applied to a partially filled waveguide

A time-domain method for the analysis of guided-wave propagation and scattering on planar microwave transmission-line structures is developed. In this method an analytical process is incorporated along one of the three dimensions in space, so that the problem is effectively reduced in a two-dimensional one. The process entails discretization of the structure by a number of lines perpendicular to the substrate surface. At the specified time, the field distribution at each intersection of these lines with the substrate surface is calculated by Maxwell's equations discretized only in the x and z directions, which are parallel to the substrate surface. The field information in the y direction is obtained analytically at each point and time. From the inverse Fourier transform of the solution of the frequency-domain Helmholtz equation in the y direction. A simple numerical example is presented as a demonstration of the method.<>