Spectral Transmission Line Analysis of a Composite Right/Left-Handed Uniaxially Anisotropic Meta-substrate

The TM spectral transmission line model of a grounded meta-substrate with uniaxially anisotropic properties, corresponding to a composite right/left-handed sub-wavelength mushroom-type structure, is computed. The dispersion relation is found by the transverse resonance technique. It is analyzed and compared with the particular case of an isotropic grounded slab. The study is limited to the left-handed region of the meta-substrate, which corresponds to the frequency band where the permittivity and permeability are negative and most dispersive. The work considers only TM modes, for which the effects of dispersion and anisotropy are most significant. The leaky-modes in the anisotropic left-handed meta-substrate are shown to exhibit a leakage factor which may be conveniently designed to very low values for super highly directive leaky-wave antennas.