Multimode Propagation in 2-D Filters and Metamaterials

Abstract

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.