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 via nonlinear interaction of double topological valley-Hall kink
modes in all-dielectric photonic crystals. We first show that two topological
frequency bandgaps can be created around a pair of frequencies, ω0 and
2ω0, by gapping out the corresponding Dirac points in two-dimensional
honeycomb photonic crystals. Valley-Hall kink modes along a kink-type domain
wall interface between two photonic crystals placed together in a
mirror-symmetric manner are generated within the two frequency bandgaps.
Importantly, through full-wave simulations and mode dispersion analysis, we
demonstrate that tunable, bi-directional phase-matched second-harmonic
generation via nonlinear interaction of the valley-Hall kink modes within the
two frequency bandgaps could be achieved. Our work opens up new avenues towards
topologically protected nonlinear frequency mixing in optics using
all-dielectric materials.Comment: 5 pages, 4 figure