The heart of topological photonics lies at topological invariants, which are deeply related to singular points. In this report, we take up three examples in topological photonics—photonic topological insulators, polarization singular states, and exceptional points in non-Hermitian photonic crystals, and show the definition of the topological invariant (charge), and its topological properties. Owing to the conservation of the topological invariant, one can control various optical properties of Hermitian and non-Hermitian photonic crystals simply by tuning their crystal symmetry. Such intriguing concepts and unique tunability may pave the way to novel photonic devices and processing.
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