Mode matching in time domain

Abstract—A new method is presented for analysis of transient electromagnetic fields in regular structures with abrupt discontinuities. The method is based on mode expansion of the fields in the Time Domain. The modes propagate independently in the regular parts of the structure and are coupled at the discontinuity. The main idea consists in solving 1D FDTD equations for each independent mode channel in the regular waveguides and using mode-matching at the junction cross-section in order to relate the mode amplitudes in all the channels at the same time instant via imposing boundary conditions. As examples the problems of pulse signal diffraction at a step discontinuity in a parallel-plate waveguide, diffraction at a junction of circular and coaxial waveguides, and pulse radiation of a bi-conical antenna are considered. The latter problem is treated as a junction of two conical lines (one of which is the free space) that are regular in spherical coordinates. 1