Nonlinear processes in multi-quantum-well plasmonic metasurfaces: Electromagnetic response, saturation effects, limits, and potentials

Nonlinear metasurfaces based on coupling a locally enhanced plasmonic response to intersubband transitions of n-doped multi-quantum-wells (MQWs) can provide 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.