Hyperbolic metamaterials based on graphene sheets with different values of chemical potentials

Abstract

In this paper possibility of creating a medium based on graphene-dielectric structures with the hyperbolic shape wave number dispersion is considered for the case when two types of graphene sheets with different chemical potentials periodically alternate. Using the Bloch theorem and the transfer matrix method, dispersion relations for the light wave numbers are derived for the layered structure and the possibility is demonstrated to manipulate the light propagation. The optical conductivity of graphene sheets is known to be frequency dependent and in the present scrutiny it is estimated via Kubo formula which simultaneously accounts for both the inter band and the intraband transitions of electrons. To apply the transfer matrix method we routinely express the amplitudes of the incident and reflected radiation at the input to the layered structure in terms of the amplitudes of electromagnetic waves at the output. The transmission spectrum of the layered dielectric medium which is sliced by two types of graphene sheets with different chemical potentials have a staircase behavior. It is demonstrated that the jump points in the transmission spectrum are simply controlled by adjusting the values of chemical potentials of graphene sheets.