2025/09/10 by Ze Tao, Tao, Ze, Fujun Liu +1
Physics and Astronomy · #Computational Physics (physics.comp-ph) #FOS: Physical sciences #Materials Science (cond-mat.mtrl-sci) #Mathematical Physics (math-ph) #Optics (physics.optics) #Photonic Crystals and Applications #Photorefractive and Nonlinear Optics #Topological Materials and Phenomena
paper · pdf · doi:10.48550/arxiv.2509.08620
openalex publication_date 2025/09/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The lack of a unified theoretical framework for characterizing band inversions across different crystal symmetries hinders the rapid development of topological photonic band engineering. To address this issue, we have constructed a framework constrained by symmetry k ⋅ p that universally models bands near high-symmetry points for symmetric photonic crystals C6, C4, C3, and C2. This framework enables a coefficient-free quantitative diagnosis of band topology. We have demonstrated the power of this framework by systematically engineering band inversions. In C6 crystals, we induce a reopening of the linear gap at Γ. In C4 systems, mirror symmetry enforces a characteristic quadratic coupling leading to distinct spectral features. Our analysis further reveals that a lone E doublet prevents inversion at the Γ point in C3 symmetry, while C2 symmetry facilitates a unique inversion of Y pointsints with anisotropic gap. This symmetry-first, fit-free approach establishes a direct link between experimental band maps and the extraction of fundamental topological parameters. It offers a universal tool for inversion and coupling-order identification.