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This paper presents a theoretical analysis on bulk and edge states inhoneycomb lattice photonic crystals with and without time-reversal and/orspace-inversion symmetries. Multiple Dirac cones are found in the photonic bandstructure and the mass gaps are controllable via symmetry breaking. The zigzagand armchair edges of the photonic crystals can support novel edge states thatreflect the symmetries of the photonic crystals. The dispersion relation andthe field configuration of the edge states are analyzed in detail in comparisonto electronic edge states. Leakage of the edge states to free space is inherentin photonic systems and is fully taken into account in the analysis. Atopological relation between bulk and edge, which is analogous to that found inquantum Hall systems, is also verified.

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