  Nonlinear metasurfaces based on coupling a locally enhanced plasmonic
response to intersubband transitions of n-doped multi-quantum-wells (MQWs) have
recently provided second-order susceptibilities orders of magnitude larger than
any other nonlinear flat structure measured so far. Here, we present a
comprehensive theory to characterize the electromagnetic response of nonlinear
processes occurring in ultrathin MQW-based plasmonic metasurfaces, providing a
homogeneous model that takes phase-matching at the unit-cell level and the
influence of saturation and losses into account. In addition, the limits
imposed by saturation of the MQW transitions on the nonlinear response of these
metasurfaces are analytically derived, revealing useful guidelines to design
devices with enhanced performance. Our approach is first validated using
experimental data and then applied to theoretically investigate novel designs
able to achieve significant second-harmonic generation efficiency in the
infrared frequency band.
