Topological slow light enhanced second harmonic generation in double-resonant topological photonic crystal

Generally, the second-harmonic generation and slow light of multi-band topological edge states (TESs) have been studied separately. Therefore, the influence of simultaneous slow light and topology protection on second-harmonic generation (SHG) is deficient. Here, we propose a high-efficiency SHG using dual-frequency TESs in topological photonic crystals (TPCs) with slow-light conditions. The wave vector matching condition and energy conservation condition (frequency doubling) can be achieved by adequately adjusting the overall structural parameters of TPCs. The double-resonant nonlinear interaction between two TESs is enabled using a square lattice TPC. Due to the topological localization of the TES and the long interaction time of slow-light effect, the energy densities of the fundamental wave and SHG are significantly increased. Consequently, the high intrinsic efficiency of SHG can be obtained in the order of 7.40 x 10(-4). Our work opens new avenues for using topological protected and slow light enhanced nonlinear frequency conversion in a TPC system.