  We investigated a multilayer graphene-dielectric composite material,
comprising graphene sheets separated by subwavelength-thick dielectric spacer,
and found it to exhibit hyperbolic isofrequency wavevector dispersion at far-
and mid-infrared frequencies allowing propagation of waves that would be
otherwise evanescent in a dielectric. Electrostatic biasing was considered for
tunable and controllable transition from hyperbolic to elliptic dispersion. We
explored the validity and limitation of the effective medium approximation
(EMA) for modeling wave propagation and cutoff of the propagating spatial
spectrum due to the Brillouin zone edge. We found that EMA is capable of
predicting the transition of the isofrequency dispersion diagram under certain
conditions. The graphene-based composite material allows propagation of
backward waves under the hyperbolic dispersion regime and of forward waves
under the elliptic regime. Transition from hyperbolic to elliptic dispersion
regimes is governed by the transverse epsilon-near-zero (TENZ) condition, which
implies a flatter and wider propagating spectrum with higher attenuation, when
compared to the hyperbolic regime. We also investigate the tunable transparency
of the multilayer at that condition in contrast to other materials exhibiting
ENZ phenomena.
