Towards Floquet Chern insulators of light.

Topological photonics explores photonic systems that exhibit robustness against defects and disorder, enabled by protection from underlying topological phases. These phases are typically realized in linear optical systems and characterized by their intrinsic photonic band structures. Here we experimentally study Floquet Chern insulators in periodically driven nonlinear photonic crystals, where the topological phase is controlled by the polarization and the frequency of the driving field. Our transient sum-frequency generation measurements reveal strong hybridization of the Floquet photonic bands. The measured spectrum remains gapless under a linearly polarized drive but becomes gapped under a circularly polarized drive. Theoretical analysis confirms that the Floquet gap is topological, characterized by a non-zero Chern number-a consequence of time-reversal symmetry breaking induced by the circularly polarized driving field. This work offers opportunities to explore the role of classical optical nonlinearity in topological phases and their applications in nonlinear optoelectronics.