Optical properties of one-dimensional photonic crystals containing graphene-based hyperbolic metamaterials

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 normal to 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.