Photonic moiré 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 moiré 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 and at the fundamental intensity of 30 kW/m2, respectively, in the moiré superlattice of near flat band formed by the twist angle 6.01o. The results indicate the photonic moiré superlattice of a high-quality factor and flatbands is a promising platform for efficient nonlinear processes and advanced photonic devices.

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