Photonic analog of graphene model and its extension: Dirac cone, symmetry, and edge states

This paper investigates the topological phase transition in honeycomb lattice photonic crystals with and without time-reversal and space-inversion symmetries through extensive analysis on bulk and edge states. In the system with both the symmetries, there appear multiple Dirac cones in the photonic band structure, and the mass gaps are controllable via symmetry breaking. The zigzag and armchair edges of the photonic crystals can support novel edge states that reflect the symmetries of the photonic crystals. The dispersion relation and the field configuration of the edge states are analyzed in detail in comparison to electronic edge states. Leakage of the edge states to free space, which is inherent in photonic systems, is fully taken into account in the analysis. A topological relation between bulk and edge states, which has been discussed in the context of electronic quantum Hall effect, is also examined in the photonic system with leaky edge states.