  Topological photonics aims to utilize topological photonic bands and
corresponding edge modes to implement robust light manipulation, which can be
readily achieved in the linear regime of light-matter interaction. Importantly,
unlike solid state physics, the common test bed for new ideas in topological
physics, topological photonics provide an ideal platform to study wave mixing
and other nonlinear interactions. These are well-known topics in classical
nonlinear optics but largely unexplored in the context of topological
photonics. Here, we investigate nonlinear interactions of one-way edge-modes in
frequency mixing processes in topological photonic crystals. We present a
detailed analysis of the band topology of two-dimensional photonic crystals
with hexagonal symmetry and demonstrate that nonlinear optical processes, such
as second- and third-harmonic generation can be conveniently implemented via
one-way edge modes of this setup. Moreover, we demonstrate that more exotic
phenomena, such as slow-light enhancement of nonlinear interactions and
harmonic generation upon interaction of backward-propagating (left-handed) edge
modes can also be realized. Our work opens up new avenues towards
topology-protected frequency mixing processes in photonics.
