Spurious modes of the TLM-condensed node formulation

The TLM (transmission line matrix) method is based on temporal and spatial sampling of electromagnetic fields. As with he FDTD (finite-difference-time-domain) method, this results in dispersive effects and propagating spurious modes that corrupt the field solution. The general dispersion relation for the TLM condensed node is used to quantify the propagation attributes of these spurious modes. The propagating and evanescent spurious modes of the condensed TLM node formulation are derived. When the condensed node mesh is applied to problems involving scattering or source structures that have feature dimensions of several lattice spacings, high-order spatial modes are generated. These modes suffer significant dispersion effects. If the spatial frequency of the mode is sufficiently high, it will propagate as a spurious node with an incorrect propagation constant and in some cases with no loss. Spurious modes may have positive or negative group velocities.<>