The transmission properties of a one-dimensional photonic crystal made of alternate layers of an isotropic
ordinary dielectric and a graphene-based hyperbolic metamaterial are studied theoretically using the
transfer matrix method. The metamaterial layers show hyperbolic dispersion in certain frequency range
and are considered as an anisotropic effective medium in which the optical axis is normalto the graphene
layers. It is shown that the structure has some photonic band gaps in both the hyperbolic and elliptical
frequency regions of the hyperbolic metamaterial layers, which are tunable by changing the chemical
potential of the graphene monolayers. Moreover, the characteristics of the transverse-magnetic (TM)-
polarized photonic band gaps remarkably depend on the orientation of the optical axis of the hyperbolic
metamaterial layers. It is found that the electric field intensity of the propagating modes from the hyperbolic
metamaterial frequency region is concentrated in the high-index isotropic layers and the electric
field intensity of the propagating modes from the elliptical frequency region is concentrated in the
low-index anisotropic layers.