Nonlinear topological photonics, which explores topics common to the fields of topological phases and nonlinear optics, is expected to open up a new paradigm in topological photonics. Here, we demonstrate second-harmonic generation (SHG) via nonlinear interaction of double topological valley-Hall kink modes in all-dielectric photonic crystals (PhCs). We first show that two topological frequency band gaps can be created around a pair of frequencies, ${\omega }_0$ and $2{\omega }_0$, by gapping out the corresponding Dirac points in two-dimensional honeycomb PhCs. 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, we 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 particular, by using Stokes parameters associated with the magnetic part of the valley-Hall kink modes, we introduce the concept of SHG directional dichroism, which is employed to characterize optical probes for sensing chiral molecules. Our work opens up avenues toward topologically protected nonlinear frequency mixing and active photonic devices implemented in all-dielectric material platforms.

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• Nonlinear optics
• Photonic crystals
• Second order nonlinear optical processes
• Topological effects in photonic systems