Despite the fact that metal is the most common conducting constituent element in
the fabrication of metamaterials, one of the advantages of graphene over metal is that its
conductivity can be controlled by the Fermi energy. Here, we theoretically investigate
multilayer structures comprising alternating graphene and dielectric layers as a class of
hyperbolic metamaterials for THz frequencies based on a general simple model of the
graphene and the dielectric layers. By employing a method of matching the tangential
components of the electrical and magnetic fields, we derive the relevant dispersion relations
and demonstrate that tuning can be achieved by modifying the Fermi energy. Moreover,
tunability of the graphene-dielectric heterostructures can be enhanced further by changing
either the thickness of the dielectric layers or the number of graphene sheets employed.
Calculated dispersion relations, propagation lengths of plasmon modes in the system are
presented. This allows us to characterize and categorize the modes into two groups: FerrelBerreman
modes and surface plasmon polaritons.