Nonlinear light generation in topological nanostructures.

Topological photonics has emerged as a route to robust optical circuitry protected against disorder1,2 and now includes demonstrations such as topologically protected lasing3-5 and single-photon transport6. Recently, nonlinear optical topological structures have attracted special theoretical interest7-11, as they enable tuning of topological properties by a change in the light intensity7,12 and can break optical reciprocity13-15 to realize full topological protection. However, so far, non-reciprocal topological states have only been realized using magneto-optical materials and macroscopic set-ups with external magnets4,16, which is not feasible for nanoscale integration. Here we report the observation of a third-harmonic signal from a topologically non-trivial zigzag array of dielectric nanoparticles and the demonstration of strong enhancement of the nonlinear photon generation at the edge states of the array. The signal enhancement is due to the interaction between the Mie resonances of silicon nanoparticles and the topological localization of the electric field at the edges. The system is also robust against various perturbations and structural defects. Moreover, we show that the interplay between topology, bi-anisotropy and nonlinearity makes parametric photon generation tunable and non-reciprocal. Our study brings nonlinear topological photonics concepts to the realm of nanoscience.