Efficient high harmonic generation in nonlinear photonic moir\'e superlattice

Photonic moir\'e superlattice as an emerging platform of flatbands can tightly confine the light inside the cavity and has important applications not only in linear optics but also in nonlinear optics. In this paper, we numerically investigate the third- and fifth-order harmonic generation (THG and FHG) in photonic moir\'e superlattices fabricated by the nonlinear material silicon. The high conversion efficiency of THG and FHG is obtained at a relatively low intensity of fundamental light, e.g., the maximum conversion efficiency of THG and FHG arrives even up to be $10^{-2}$ and $10^{-9}$ at the fundamental intensity of 30 kW/m2, respectively, in the moir\'e superlattice of near flat band formed by the twist angle 6.01o. The results indicate the photonic moir\'e superlattice of a high-quality factor and flatbands is a promising platform for efficient nonlinear processes and advanced photonic devices.