We present nonlinear optical four-wave mixing in a silicon nanodisk dimer metasurface. Under the oblique incident plane waves, the designed metasurface exhibits a multi-resonant feature with simultaneous excitations of three quasi-bound states in the continuum (BIC). Through employing these quasi-BICs with maximizing electric field energy at the input bump wavelengths, significant enhancement of third-order nonlinear processes including third-harmonic generation, degenerate and non-degenerate four-wave mixing are demonstrated, giving rise to ten new frequencies in the visible wavelengths. This work may lead to a new frontier of ultracompact optical mixer for applications in optical circuitry, ultrasensitive sensing, and quantum nanophotonics.

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