Topological aspects of periodic and aperiodic photonic crystals

Topological properties of Bloch modes have been demonstrated in purely dielectric photonic crystals at high symmetry points where a hidden time reversal-like symmetry can be exhibited. So far, the topological properties that have been shown are essentially due to these symmetries. For one dimensional structure, we define a topological invariant that can be extended to lossy or aperiodic structures.