Interplay between anisotropy and spatial dispersion in metamaterial waveguides

We analyze the spectrum of waveguide modes of an arbitrary uniaxial anisotropic metamaterial slab with nonlocal electromagnetic response whose permittivity tensor could be described within the Drude approximation. Spatial dispersion was introduced within the hydrodynamical model. By considering both anisotropy and spatial dispersion as perturbations, we distinguish their effect on the spectrum of the slab and analyze lifting of the degeneracy of eigenmodes at plasma frequency in detail. Spatial dispersion is shown to result in a break of the singularity in the density of optical states in the hyperbolic regime and in suppression of negative dispersion induced by anisotropy. We demonstrate that the interplay of spatial dispersion and anisotropy can bring light to a complete stop at certain frequencies.