Modal interactions in lossy dielectric metamaterial slabs

In recent years, the study of modal propagation in planar waveguides including one or more metamaterial layers has been addressed by various research groups, and a number of peculiar effects have been reported. Both surface (bound) and leaky (radiating) modes have been considered. Regarding the analysis of metamaterial layers, homogenized and isotropic models have mainly been used, with frequency-dispersive constitutive parameters, although interesting propagation phenomena have also been found, e.g., in wire-medium slabs, by adopting more sophisticated anisotropic and spatially-dispersive models. In this work, we study the effect of electric and magnetic losses on the dispersion properties of modes supported by a grounded metamaterial slab. The metamaterial is assumed to be constituted by an arrangement of small spherical dielectric or magneto-electric inclusions embedded in a host dielectric medium. Such a medium is particularly interesting one since it allows for homogenization via scalar constitutive parameters (so the homogenized medium is isotropic) whose real parts may take negative values, thus supporting backward-wave propagation. Appropriate frequency-dispersive models are adopted for both the electric permittivity and magnetic permeability of the resulting homogenized medium, including the presence of losses. Different kinds of modal interactions are reported for both the TE and TM modes. As in ordinary dielectric slabs, qualitative changes occurring in modal interaction regions are found to be related to the migration of suitable complex frequency-plane branch points, parameterized by the level of losses in the medium.