Corner States in C 6 Symmetric Photonic Crystals: Origins and Properties

ABSTRACT Based on 2D C₆ symmetric photonic crystals (PCs), different photonic finite structures possessing overall C 6 , C 3 , and C 2 symmetries are designed. By implementing Perfect Electric Conductor (PEC) boundary, several typical corner configurations with angles 2π/3, π/3, 4π/3, and 5π/3 are constructed, and the corresponding CSs are detailedly investigated. With help of filling anomaly analysis, local density of states (LDOS) calculation and eigenmode simulation, the frequency distribution, field localization, fractional corner charge, topological origin and robustness of these CSs are demonstrated. These results reveal that in 2D PCs finite structures, the corner charges at corners with conjugate angles θ and 2π‐ θ fundamentally have deterministic relationship ( Q θ + Q 2π ‐ θ = 0 mod 1), and CSs can exist even at corners without fractional corner charge which is different from cases in acoustic, mechanical, optical waveguide, and other resonator systems. Especially, at corners with large angles, such as at angle 4π/3, topological CSs with nonzero fractional corner charge are also susceptive to the defects adjacent to the corner cells. These results reveal topological origins and properties of CSs in PCs systems, and provide insights for designing higher‐order CSs and photonic micro‐nano devices based on PCs. Furthermore, these methodologies can also be extended to other 2D and 3D PCs systems and photonic metamaterial platforms.