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The use of Z-transforms in TLM with non uniform meshes

The use of Z-transforms in electromagnetic simulations using TLM when dispersive media are present, has been described by Christopoulos [Christopoulos-99] and its efficiency proven. This description concerned cubic meshes. This paper describes a generalization to non uniform meshes. We give the general formulation in this case. To validate our results we apply the algorithm to a gyromagnetic media where a Polder magnetic tensor is used and when this media is included in a rectangular waveguide to obtain non reciprocal effects (isolator). A comparison with experimental results obtained by Gardiol [2] is made. Introduction In order to model generalized materials, Paul et al. solve Maxwell's equations using TLM method in vacuum, considering the material wave interaction as voltage and current sources applied in the media.