Multi-mode Propagation in 2D filters and Metamaterials

Meta-materials are characterised using a modal technique for the analysis of 2N- port two dimensional filter networks. It will be shown that in general, all such networks support N modes of propagation each with different propagation constants unless as with the TEM multi-wire transmission line, the inductance matrix is the inverse of the capacitance matrix. Furthermore a simple equivalent circuit for these 2N port networks is derived, enabling complete network analysis for any combination of modal excitations. An explicit formula is derived for the propagation constants of a quasi lowpass filter. This demonstrates that there are always N modes even when the transverse network is infinite in extent.