Band Inversion Flips the Winding of Bound States in the Continuum

Bound states in the continuum (BICs) in photonic slabs and metasurfaces appear as polarization singularities in momentum space, characterized by an integer winding number. This winding is widely treated as a robust topological label, preserved under smooth deformations of the structure. Here we show that this robustness fails under band inversion. Using a general two-band theory of open periodic photonic structures, we prove that a band inversion at a band-edge BIC reverses the local far-field polarization map and flips the BIC winding, $w_{\mathrm{B}\mathrm{I}\mathrm{C}}\to -w_{\mathrm{B}\mathrm{I}\mathrm{C}}$, \emph{without} any defect dynamics in momentum space. We verify the prediction in a tunable subwavelength grating, where polarization tomography directly images the reversal, and confirm it numerically in multiband rectangular and triangular photonic lattices. Band inversion thus emerges as a key mechanism governing polarization-singularity topology in non-Hermitian photonic band structures.