Spectral statistics of light in one-dimensional graphene-based photonic crystals

The optical properties and spectral statistics of light in one-dimensional photonic crystals in the representative classes of (AB)^{N} (composed of dielectric layers) and (AGBG)^{N} (composed of periodic stacking of graphene-dielectric layers) have been investigated using the transfer matrix method and random matrix theory. The proposed method provides new predictions to determine the chaos and regularity of the optical systems. In this analysis, the chaoticity parameter with q=0 for Poisson distribution and q→1 for Wigner distribution is determined based on the random matrix theory. It has been shown that two kinds of chaos and regularity modes can be found with Brody distribution. Also, as a part of this work, we found out the regular pattern in both classes of (AB)^{N} and (AGBG)^{N} when results were fit to a Brody distribution. Moreover, the effects of different parameters such as the number of unit cells, incident angle, state of polarization, and chemical potential of the graphene nanolayers on the structures' regularity are discussed. It is found that the regular patterns are seen in the band gaps. The results show that the structure (AGBG)^{N} has an extra photonic band gap compared to (AB)^{N}, which is tunable by changing the chemical potential of the graphene nanolayers. Therefore, the possibility of external control of the regularity using a gate voltage in the graphene-based photonic crystals is obtained. Finally, comparing of TE and TM waves based on the random matrix theory, which interpolates between regular and chaotic systems, indicates that the Poisson statistics well describes the TE waves.