Band structure of one-dimensional photonic crystal with graphene layers using the Fresnel coefficients method

In this paper, we have calculated the band structure of an instance of one-dimensional photonic crystal (1DPC) composed of double-layered dielectrics via the Fresnel coefficients method. Then, we supposed the addition of a thin layer of graphene to each dielectric layer and the given photonic crystal (PC) composed of dielectric–graphene composites. The effects of graphene layers on the PC band structure were evaluated. We found out that according to the effective medium theory unlike the TE polarization, the electric permittivity of the dielectric layers changed at TM polarization. As such, the band structure of PC for TM polarization changed, too. Moreover, instead of bandgap related to “zero averaged refractive index” an approximately omnidirectional bandgap appeared and a related bandgap to “𝜀 = 0” disappeared. In addition, a new angular gap branch appeared at a new frequency at TM polarization in which the width of gap increased as the angle increased.