Nanoscale dielectric-graphene-dielectric tunable infrared waveguide with ultrahigh refractive indices.

We propose in this paper a dielectric-graphene-dielectric tunable infrared waveguide based on multilayer metamaterials with ultrahigh refractive indices. The waveguide modes with different orders are systematically analyzed with numerical simulations based on both multilayer structures and effective medium approach. The waveguide shows hyperbolic dispersion properties from mid-infrared to far-infrared wavelength, which means the modes with ultrahigh mode indices could be supported in the waveguide. Furthermore, the optical properties of the waveguide modes could be tuned by the biased voltages on graphene layers. The waveguide may have various promising applications in the quantum cascade lasers and bio-sensing.