  We study nonlinear effects in two-dimensional photonic metasurfaces
supporting topologically-protected helical edge states at the nanoscale. We
observe strong third-harmonic generation mediated by optical nonlinearities
boosted by multipolar Mie resonances of silicon nanoparticles. Variation of the
pump-beam wavelength enables independent high-contrast imaging of either bulk
modes or spin-momentum-locked edge states. We demonstrate topology-driven
tunable localization of the generated harmonic fields and map the
pseudospin-dependent unidirectional waveguiding of the edge states bypassing
sharp corners. Our observations establish dielectric metasurfaces as a
promising platform for the robust generation and transport of photons in
topological photonic nanostructures.
