Unified Phase Criterion for Band Crossings in One‐Dimensional Topological Photonics

ABSTRACT One‐dimensional photonic crystals (1DPCs) provide a simple and versatile platform for exploring topological photonics. Topological effects in these layered systems have enabled a range of applications in robust light confinement, lasing, modulation, and disorder‐tolerant optical devices. Among their underlying band features, band crossings are of particular interest because they represent critical degeneracies associated with topological phase transitions in periodic media. However, although band crossings in one‐dimensional topological photonics have been extensively studied, a unified theoretical criterion for their occurrence remains unclear. In this work, a unified phase criterion for band crossings that applies to both TE and TM polarizations from normal to oblique incidence was derived based on transfer‐matrix method and Bloch theory. Notably, for TM polarization, besides the generic band crossings satisfying the integer‐phase criterion, the Brewster condition enables additional crossings without the phase constraint, forming a straight trajectory in momentum space. These results establish a direct connection between classical interface optics and band‐crossing formation in periodic media, and provide a unified framework for understanding and engineering band crossings in layered photonic structures. These findings provide design guidelines for multilayer photonic devices: Brewster‐angle transmission improves fabrication tolerance, whereas polarization‐independent band crossings enable robust polarization‐insensitive optical responses.