BROKEN SYMMETRY AND TOPOLOGY IN PHOTONIC ANALOG OF GRAPHENE

We review how broken symmetries affect optical properties in photonic analog of graphene, namely, honeycomb-lattice photonic crystals (PhCs). The spatial symmetry of the honeycomb lattice yields Dirac spectra at Brillouin zone corners without fine tuning of physical parameters. In addition, the Dirac-mass gap can be introduced by breaking the time-reversal symmetry and/or the space-inversion symmetry. These two symmetries are closely related to the topology of radiation fields in momentum space, and are linked with nontrivial edge states if the system has edges. We show that an effective Hamiltonian for photon obtained with the aid of group theory predicts a modulation of chiral edge states that are hardly implemented in electronic graphene. Numerical simulation of the honeycomb-lattice PhCs of infinitely-long cylinders, confirms the prediction fairly well.