Hyperbolic-metamaterial waveguides for long-range propagation

We study optical waveguides that include layers of materials and metamaterials with hyperbolic dispersion (HMM). We consider long-range regime at the dielectric-HMM interface in different waveguide geometries (single interface or symmetric cladding with different layers). In contrast to the traditional analysis of geometrical parameters, we make emphasis on optical properties of constituent materials, and by solving dispersion equations, analyze how dielectric and HMM permittivities affect propagation length and mode size. We derive a figure of merits that should be used for each waveguide in a broad range of permittivity values as well as compare them with plasmonic waveguides. We show conventional plasmonic quality factor, which is the ratio of real to imaginary parts of permittivity, is not applicable to the case of waveguides with complex structure. Both telecommunication wavelengths and mid-infrared spectral ranges are of interest considering recent advances in van der Waals materials such as hexagonal boron nitride. Finally, we evaluate the performance of the waveguides with hexagonal boron nitride in the range where it possesses hyperbolic dispersion (6.2-7.3 um), and we identify the optimum wavelength for each type of the waveguide.