Nonlinear topological photonics: nested frequency combs and novel phase-matching schemes

Topology manifests across physical systems, from single-particle phenomena to strongly correlated, topologically ordered states hosting anyons. The intermediate regime of classical or mean-field nonlinear systems, however, has remained comparatively less explored. In this talk, we focus on nonlinear topological effects in photonic platforms that operate in this regime. We experimentally demonstrate how incorporating optical nonlinearity gives rise to distinct bosonic phenomena with no direct electronic analogs, including topological frequency combs and harmonic generation. In particular, we show that topological design enables capabilities not accessible in conventional non-topological architectures, such as harmonic generation without post-fabrication tuning. Despite this progress, nonlinear topological states still lack a systematic topological-invariant classification. These results point toward classical and quantum optical devices with intrinsic robustness, advancing next-generation optoelectronic, optical-computing, and quantum technologies.