  Rapid progress in nonlinear plasmonic metasurfaces enabled many novel optical
characteristics for metasurfaces, with potential applications in frequency
metrology, timing characterization and quantum information. However, the
spectrum of nonlinear optical response was typically based upon the linear
optical resonance. In this work, a wavelength-multiplexed nonlinear
plasmon-MoS2 hybrid metasurface with suppression phenomenon was proposed, where
multiple nonlinear signals could to be simultaneously processed and optionally
tuned. A clear physical picture to depict the nonlinear plasmonic bound states
in the continuum (BICs) was presented, from the perspective of both classical
and quantum approaches. Particularly, beyond the ordinary plasmon-polariton
effect, we numerically demonstrated a giant BIC-inspired second-order nonlinear
susceptibility $10^{-5}$~$m/V$ of MoS2 in the infrared band. The novelty in our
study lies in the presence of a quantum oscillator that can be adopted to both
suppress and enhance the nonlinear quasi BICs. This selectable nonlinear
BIC-based suppression and enhancement effect can optionally block undesired
modes, resulting in narrower linewidth as well as smaller quantum decay rates,
which is also promising in slow-light-associated technologies.
