  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.
