Nonlinear nanophotonics is a rapidly developing field of research with many potential applications for the design of
nonlinear nanoantennas, light sources, nanolasers, and ultrafast miniature metadevices. A tight confinement of the
local electromagnetic fields in resonant photonic nanostructures can boost nonlinear optical effects, thus offering
versatile opportunities for the subwavelength control of light. To achieve the desired functionalities, it is essential
to gain flexible control over the near- and far-field properties of nanostructures. To engineer nonlinear scattering from
resonant nanoscale elements, both modal and multipolar control of the nonlinear response are widely exploited for
enhancing the near-field interaction and optimizing the radiation directionality. Motivated by the recent progress of
all-dielectric nanophotonics, where the electric and magnetic multipolar contributions may become comparable, here
we review the advances in the recently emerged field of multipolar nonlinear nanophotonics, starting from earlier
relevant studies of metallic and metal–dielectric structures supporting localized plasmonic resonances to then
discussing the latest results for all-dielectric nanostructures driven by Mie-type multipolar resonances and optically
induced magnetic response. These recent developments suggest intriguing opportunities for a design of nonlinear
subwavelength light sources with reconfigurable radiation characteristics and engineering large effective optical
nonlinearities at the nanoscale, which could have important implications for novel nonlinear photonic devices operating beyond the diffraction limit.
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