  Strongly enhanced third-harmonic generation (THG) by the topological
localization of an edge mode in a Su-Schrieffer-Heeger (SSH) chain of silicon
photonic crystal nanocavities is demonstrated. The edge mode of the nanocavity
chain not only naturally inherits resonant properties of the single nanocavity,
but also exhibits the topological feature with mode robustness extending well
beyond individual nanocavity. By engineering the SSH nanocavities with
alternating strong and weak coupling strengths on a silicon slab, we observe
the edge mode formation that entails a THG signal with three orders of
magnitude enhancement compared with that in a trivial SSH structure. Our
results indicate that the photonic crystal nanocavity chain could provide a
promising on-chip platform for topology-driven nonlinear photonics.
