Fields in planar anisotropic transmission-line metamaterials

An electromagnetic analysis of wave propagation in planar anisotropic transmission-line metamaterials is presented. It is shown that a planar square-celled grid, series-loaded with orthogonal inductors and capacitors and positioned over a ground plane, is magnetically anisotropic and may be described in terms of a diagonal permeability tensor. Resonance cone field concentrations form when two of the three diagonal elements of the permeability tensor are opposite in sign and the dispersion surface becomes hyperbolic. A theoretical treatment of an electric line current source excitation shows that the formation of resonance cones is a consequence of the singularity associated with the characteristic surface of a hyperbolic equation. The resonance cone angle, which also describes the direction of local power flow in the region between the grid and the ground plane, can be predicted to a good degree of accuracy. To the authors' best knowledge, the present work also verifies experimentally for the first time that current flow reverses direction across the resonance cone. Experiments, simulations, and analytical calculations of the cone angle are in good agreement.