Modeling dispersive dielectrics for the 2-D TLM method

The transition line matrix (TLM) method, since it is a time-domain method, cannot deal directly with dispersive media. We propose a way for modeling such media, starting from the causality relationship between field vectors D and E, which is discretized over the same space-time mesh as the two-dimensional TLM mesh. This leads to adding a voltage source at each node, its value depending on the previous instants. The method is validated by computing the reflection coefficient at an air-water interface and the cutoff frequencies of a rectangular waveguide containing a Debye dielectric.