Nonlinear Dielectric Nanoantennas and Metasurfaces: Frequency Conversion and Wavefront Control

High-index dielectric nanostructures can support optical resonances of electric and magnetic character with ultralow linear absorption. In contrast to plasmonics, they can be engineered to confine electromagnetic fields inside the resonator, amplifying intrinsic nonlinearities of the dielectric. In this Review I examine the ability of dielectric nanoantennas and metasurfaces for efficient harmonic generation and wave-mixing processes, as well as nonlinear wavefront manipulation of the incident and radiated light. A detailed comparison is made between the many nanoscopic dielectric configurations reported in the literature, evaluating the influence of the material, crystal symmetry, structure geometry, and the different resonances involved (electric and magnetic Mie modes, Fano resonances, and quasi-nonradiative states, including anapoles and quasi-bound states in the continuum). The nonlinear performance of the nanosystems is analyzed, with emphasis on frequency conversion efficiency and emission directionality control, also discussing recent advances in nonlinear imaging, nonlinear holography, and all-optical switching. The role of topology in nonlinear nanophotonics is reviewed in the end, and potential future directions in the field are laid out.