Topological photonics aims to utilize topological photonic bands and corresponding edge modes to implement robust light manipulation. Importantly, topological photonics provide an ideal platform to study nonlinear interactions. In this talk, I will review some recent results regarding nonlinear interactions of one-way edge-modes in frequency mixing processes in topological photonic nanostructures. More specifically, I will discuss the band topology of 2D photonic crystals with hexagonal symmetry and demonstrate that SHG and THG can be implemented via one-way edge modes. Moreover, I will demonstrate that more exotic phenomena, such as slow-light enhancement of nonlinear interactions and harmonic generation upon interaction of backward-propagating edge modes can also be realized. Finally, FWM of topological plasmon modes of graphene plasmonic crystals and SHG upon interaction of valley-Hall topological modes of all-dielectric photonic crystals will be discussed.
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