In this paper, we review and discuss how nanoantennas may be used to largely enhance the nonlinear response of optical materials. For single nanoantennas, there have been tremendous advancements in understanding how to exploit the local field enhancement to boost the nonlinear susceptibility at the surface or sharp edges of plasmonic metals. After an overview of the work in this area, we discuss the possibility of controlling the optical nonlinear response using nanocircuit concepts and of significantly enhancing various nonlinear optical processes using planar arrays of plasmonic nanoantennas loaded with χ(2) or χ(3) nonlinear optical materials, forming ultrathin, nanometer-scale nonlinear metasurfaces, as optical nanodevices. We describe how this concept may be used to boost the efficiency of nonlinear wave mixing and optical bistability, due to the large local field enhancement at the nonlinear nanoloads associated with the plasmonic features of suitably tailored nanoantenna designs. We finally discuss three exciting applications of the proposed nonlinear metasurface: dramatically-enhanced frequency conversion efficiency, efficient phase-conjugation for super-resolution imaging and large optical bistabilities.
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