Abstract

The linear dispersion relation around certain points in the Brillouin zone of optical periodic structures, which is often called (photonic) Dirac cones, has been attracting considerable interest during the last five years [1], since it can realize interesting optical phenomena such as unidirectional propagation of surface modes, optical simulation of Zitterbewegung, pseudo-diffusive transmission of optical waves, scatter-free waveguides, and lenses of arbitrary shapes. In particular, Huang et al. [2] clarified that isotropic Dirac cones in the Brillouin-zone center can be created by accidental degeneracy of two modes for two-dimensional square and triangular dielectric photonic crystals of C_4v and C_6v symmetries. On the other hand, we showed for metamaterials characterized by well-defined electromagnetic resonant states localized in their unit structures that the combination of A₁ and E modes of the square lattice of C_4v symmetry and the combination of A_1g and T_1u modes of the simple cubic lattice of O_h symmetry create isotropic Dirac cones [3], while the combination of E₁ and E₂ modes of the triangular lattice of C_6v symmetry leads to isotropic double Dirac cones [4].

© 2013 IEEE