Observation of Berry curvature in non-Hermitian system from far-field radiation

Berry curvature that describes local geometrical properties of energy bands can elucidate many fascinating phenomena in solid-state, photonic, and phononic systems, given its connection to global topological invariants such as the Chern number. Despite its significance, the observation of Berry curvature poses a substantial challenge since wavefunctions are deeply embedded within the system. Here, we theoretically propose a correspondence between the geometry of far-field polarization and the underneath band topology in non-Hermitian systems, thus providing a general method to fully capture the Berry curvature without strongly disturbing the eigenstates. We further experimentally observe the Berry curvature in a honeycomb photonic crystal slab from polarimetry measurements and quantitatively obtain the nontrivial valley Chern number. Our work reveals the feasibility of retrieving the bulk band topology from escaping photons and paves the way to exploring intriguing topological landscapes in non-Hermitian systems.