Graphene-based hyperbolic metamaterial

We introduce a graphene-based composite multilayer structure that exhibits hyperbolic-like wavevector dispersion at terahertz and mid-infrared frequencies. The multilayer structure comprises graphene sheets separated by dielectric layers. We formulate the effective permittivity tensor of the multilayer using a simple homogenization scheme. In addition, we employ Bloch theory for evaluating the wavevector dispersion for a propagation mode inside the HM, and show that the homogenization scheme is in good agreement with Bloch theory in a very wide spatial spectrum. We report the tunability of transition from elliptic to hyperbolic iso-frequency wavevector dispersion by varying the chemical potential of graphene sheets.