Mode symmetries required for creating photonic Dirac cones in the Brillouin-zone center

摘要

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 C4v and C6v 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 C4v symmetry and the combination of A1g and T1u modes of the simple cubic lattice of Oh symmetry create isotropic Dirac cones [3], while the combination of E1 and E2 modes of the triangular lattice of C6v symmetry leads to isotropic double Dirac cones [4].