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.