Optical Interactions in Nonlinear Topological Photonic Nanostructures

In this talk, I will review some of our recent results regarding nonlinear optical interactions in certain topological photonic systems. In particular, I will present a detailed analysis of the band topology of 2D photonic crystals (PhCs) with hexagonal symmetry and demonstrate that nonlinear optical processes, such as second- and third-harmonic generation (SHG, THG) can be readily implemented via one-way edge modes of this setup. I will also demonstrate SHG via nonlinear interaction of double topological valley-Hall kink modes in such PhCs. I will first show that two topological frequency band gaps can be created around a pair of frequencies, ω0 and 2ω0, by gapping out the corresponding Dirac points. Valley-Hall kink modes along a kink-type domain wall interface between two PhCs placed together in a mirror-symmetric manner are generated within the two frequency band gaps. Importantly, through full-wave simulations and mode dispersion analysis, I demonstrate that tunable, bidirectional phase-matched SHG via nonlinear interaction of the valley-Hall kink modes inside the two band gaps can be achieved. In the second part of my talk, I will illustrate how bound states in the continuum (BICs) of certain PhC slabs, engineered to possess sharp resonances with high quality factors at both the fundamental frequency (FF) and second-harmonic (SH), can be used to achieve an orders-of-magnitude enhancement of the SHG. Thus, I will first show that PhCs operating at telecommunication wavelengths support a pair of at- resonances. This double-resonance phenomenon is subsequently used to significantly enhance the SHG from the PhC slabs. The peak values of the SHG signal are several orders of magnitude larger than those corresponding to homogeneous slabs with the same thickness.