FDTD analysis of modes in arbitrarily shaped waveguides

The analysis of waveguide discontinuities has traditionally been solved using mode matching. However, mode matching does not provide a flexible solution applicable to arbitrary cross-sections. For example, a barline T-junction is a different problem to a rectangular waveguide T-junction and requires a different approach. Waveguide discontinuity problems can be solved using FDTD by exciting the problem with a hard source, which must be placed far enough from the discontinuity to allow the propagating mode to establish. An alternative method, "bootstrapping", was referred to by Taflove (1995), where two problems are analysed, one with and one without the discontinuity, and the fields in the problem without the discontinuity are used to "bootstrap" or excite the other problem. This method has been extended here to excite arbitrary modes, and can also be run in reverse to act as a selective mode absorber. This technique reduces the size of the problem, since the established mode can be excited at the discontinuity. Coupling to higher order modes can also be predicted.