Tunable band gap near the Dirac point in nonlinear negative-zero-positive index metamaterial waveguide

We make theoretical investigations of the nonlinear guided modes near the Dirac point (DP) in nonlinear negative-zero-positive index metamaterial (NZPIM) waveguide. When the nonlinearity is self-focusing, an asymmetric forbidden band exists near the DP that can be modulated by the strength of the nonlinearity. However, the self-defocusing nonlinearity can completely eliminate the asymmetric band gap. We also study the nonlinear surface waves in such nonlinear NZPIM waveguide. These results may predict analogous phenomena in nonlinear graphene.