Spikes formation in the dispersion relation for dielectric–graphene photonic crystal

Abstract

In this article we report a novel characteristic in the dispersion relation for dielectric–graphene photonic crystal, resulting from the modulation of the chemical potential (μg,j) of the graphene sheets in the unit cell that form the entire optical structure. The photonic dispersion relation of the system is obtained employing the transfer matrix formalism taking into account the intra and interband contributions of the optical conductivity of graphene. The chemical potential of each graphene sheet is distributed with discrete values following envelope functions such as Gaussian, linear, Lorentzian and Pöschl–Teller. We found that this kind of dielectric–graphene photonic crystal shows the formation of spikes in the dispersion relation due to the discrete values of chemical potential in its unit cell. The spikes are located in the frequency positions which correspond to 2μg,j for each distribution and can be modulated by optical and geometric parameters.