Dispersion properties of lossy, dispersive, and anisotropic left-handed material slab waveguide

An asymmetric three-layer slab waveguide with air as a substrate, lossless dielectric medium as a guiding layer, and lossy, dispersive, and anisotropic left-handed material (LHM) as a cladding was investigated. The LHM cladding layer was assumed to exhibit positive permittivity and permeability in the transverse directions and negative ones along the longitudinal direction (z-axis). The dispersion equations were derived and corresponding dispersion curves were plotted and studied for TE and TM polarized light. The dispersion properties were studied with different parameters of the proposed structure. A set of interesting features were observed such as the existence of the fundamental mode in a narrow frequency range, positive group velocity which becomes faster as the frequency increases, and crucial dependence of the dispersion curves on the anisotropy of the LHM cladding.