Free-electron Optical Nonlinearities in Plasmonic Nanostructures: A Review of the Hydrodynamic Description

Requirements of integrated photonics and miniaturisation of optical devices demand efficient nonlinear components not constrained by conventional macroscopic nonlinear crystals. Intrinsic nonlinear response of free carriers in plasmonic materials provides opportunities to design both second- and third-order nonlinear optical properties of plasmonic nanostructures and control light with light using Kerr-type nonlinearities as well as achieve harmonic generation. This review summarises principles of free-carrier nonlinearities in the hydrodynamic description in both perturbative and non-perturbative regimes, considering also contribution of nonlocal effects. Engineering of harmonic generation, solitons, nonlinear refraction and ultrafast all-optical switching in plasmonic nanostructures and metamaterials are discussed. The full hydrodynamic consideration of nonlinear dynamics of free carriers reveals key contributions to the nonlinear effects defined by the interplay between a topology of the nanostructure and nonlinear response of the fermionic gas at the nanoscale, allowing design of high effective nonlinearities in a desired spectral range. Flexibility and unique features of free-electron nonlinearities are important for nonlinear plasmonic applications in free-space as well as integrated and quantum nanophotonic technologies.