Effect of nonlinear cap layer on TM-polarized surface waves in a graphene-based photonic crystal

In this paper, we investigated the effect of nonlinear cap layer and the chemical potential of the graphene on the p-polarized surface waves (SWs) in a one-dimensional graphene-based photonic crystal (GBPC). Three different cases were considered for the dielectric tensor of the nonlinear cap layer: (1) perpendicular uniaxial approximation, (2) parallel uniaxial approximation and (3) generic case. The results of the study indicated that the effect of nonlinear cap layer on TM SWs may be neglected due to the perpendicular approximation. On the other hand, in parallel approximation as well as generic form of dielectric function, the frequency of the TM SWs within the graphene-induced band gap (GIPBG) may be controlled by the nonlinear cap layer and the chemical potential of the graphene. Moreover, according to the results, in the GIPBG of GBPC with self-defocusing cap layer, enhancing chemical potential and optical nonlinearity shift the frequency of the SWs in the same direction. However, with respect to the self-focusing cap layer, enhancing chemical potential and optical nonlinearity shift the frequency of the SWs in the opposite direction. Consequently, by adjusting the chemical potential in the self-defocusing cap layer, the tunability range of the SW frequency may be extended and in the case of self-focusing, optical nonlinear effects may be eliminated.