The dispersion properties of an anisotropic metamaterial
composed of periodic stacking of graphene-liquid crystal layers are
investigated in the far-infrared region. It is represented that this
structure is able to show both the elliptic and hyperbolic dispersions
using the tunable properties of the graphene and liquid crystal.
The switching between two dispersion phases via control of the
temperature, voltage and external electric field is studied. It is shown
that this switching can be used to control of the transmission and
reflection at the interface of the metamaterial and air.