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