Optical properties of a semi-infinite medium consist of graphene based hyperbolic meta-materials with tilted optical axis

In this paper, the  optical properties of a semi-infinite medium composed of graphen-based hyperbolic meta-materials with the optical axis were tilted with respect to its boundary with air, by using the  Maxwell equations; then  the homogeneous effective medium approximation method was  studied. The results showed that the orientation of the structure layers (geometric induced anisotropy) affected the magnetic transverse polarization spectra in the region, such that the structure exhibited the hyperbolic dispersion. Also, in the large frequency range, in which the medium had hyperbolic dispersion, due to the presence of  graphene nanolayer, the transmission of the structure was vanished; by increasing tilt angle of layers with respect to the boundary, it was gradually decreased and finally disappeared