Topologically protected second harmonic generation via doubly resonant high-order photonic modes

Topology-driven nonlinear light-matter effects open up new paradigms for both topological photonics and nonlinear optics. Here, we propose to achieve high-efficiency second harmonic generation in a second-order photonic topological insulator. Such a system hosts highly localized topological corner states with large quality factors for both fundamental and second harmonic waves, which could be matched perfectly in frequency by simply tuning the structural parameters. Through the nonlinear interaction of the doubly resonant topological corner states, unprecedented frequency conversion efficiency is predicted. In addition, the robustness of the nonlinear process against defects is also demonstrated. Our work opens up avenues toward topologically protected nonlinear frequency conversion using high-order photonic topological modes.