Multimode Propagation in 2-D Filters and Metamaterials

Metamaterials are characterized using a modal technique for the analysis of 2N-port 2-D 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 multiwire 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-low-pass filter. This demonstrates that there are always N modes even when the transverse network is infinite in extent.