Tensor Transmission-Line Metamaterials

Transmission-line (TL) metamaterials possessing effective material parameters that are diagonal in the Cartesian basis have been previously studied. In this paper, TL metamaterials with arbitrary full tensors are introduced and analyzed. An approximate tensor analysis of the proposed metamaterials is first developed. Bloch analysis is then used to verify the approximate analysis and derive exact dispersion equations and impedance relations. Finally, simulation results are presented that validate the analysis and show the utility of this new class of metamaterials. The ability to design tensor metamaterials such as these is crucial to the practical implementation of novel devices derived through transformational optics/electromagnetics.