Probing Phase Transition of Band Topology via Radiation Topology

Abstract: Topological photonics has received extensive attention from researchers because it provides brand new physical principles to manipulate light. Band topology of optical materials is characterized using the Berry phase defined by Bloch states. Until now, the criteria for experimentally probing the topological phase transition of band topology has always been relatively lacking in topological physics. Moreover, radiation topology can be aroused by the far-field polarizations of the radiating Bloch states, which is described by the Stokes phase. Although such two types of topologies are both related to Bloch states on the band structure, it is rather surprising that their development is almost independent. Here, we reveal that the phase transition of band topology can be probed by the radiation topology. We theoretically design and experimentally demonstrate such an intriguing phenomenon by constructing photonic crystals that support optical analogs of quantum spin Hall effects. The results show that the topological charge of the far-field polarization vortex changes from +1 to -2 or from -2 to +1 when the band topology changes from trivial to non-trivial, which provides a new criterion to probe the phase transition of band topology using radiation topology. Our findings not only provide an insightful understanding of band topology and radiation topology, but also can serve as a novel route to manipulate the near and far fields of light.