Guided modes near the Dirac point in negative-zero-positive index metamaterial waveguide.

Motivated by the realization of the Dirac point (DP) with a double-cone structure for optical field in the negative-zero-positive index metamaterial (NZPIM), we make theoretical investigations of the guided modes in the NZPIM waveguide near the DP by using the graphical method. Due to the linear Dirac dispersion, the fundamental mode is absent when the angular frequency is smaller than the DP, while the behaviors of NZPIM waveguide are similar to the conventional dielectric waveguide when the angular frequency is larger than the DP. The unique properties of the guided modes are analogous to the propagation of electron waves in graphene waveguide [Appl. Phys. Lett., 94, 212105 (2009)], corresponding to the classical motion and the Klein tunneling. These results suggest that many exotic phenomena in graphene can be simulated by the relatively simple optical NZPIM.