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.<>