Spectral statistics of a 1D photonic crystal containing an anisotropic graphene-based hyperbolic metamaterial defect layer

Abstract

A simple photonic crystal is a periodic and regular nanostructure. Breaking the periodicity of a photonic crystal by a defect layer can be an interesting pattern. We study the spectral statistics of eigenfrequency spacings (the so-called level spacing statistics) for TM-polarized waves in the one-dimensional (1D) defective photonic crystal containing graphene-based hyperbolic metamaterial as a defect layer. The localization of light in the proposed structure has been investigated using the transfer matrix method. Moreover, the effects of different parameters, such as the number of graphene cells and the defect layer's optical axis orientation, are discussed. The performance of the ratios of nearest neighbor level spacings has become a Wigner distribution at the localized phases which are introduced by inserting a defect layer. The spectral statistics are found to approach the Wigner distribution for different repeat numbers of graphene layers. In contrast, in the absence of graphene layers, the level spacing statistics follow the Poisson distribution.