Trade-Off between Second- and Third-Order Nonlinearities, Ultrafast Free Carrier Absorption and Material Damage in Silicon Nanoparticles

Reaching the optimal second- and third-order nonlinear conversion efficiencies while avoiding undesirable free carrier absorption losses and material damage in ultrashort laser-excited nanostructures is a challenging obstacle in all-dielectric ultrafast nanophotonics. In order to elucidate the main aspects of this problem, a multi-physical model is developed, coupling nonlinear Maxwell equations supplied by surface and bulk nonlinearities with free carrier hydrodynamic equations for electron–hole plasma kinetics and electron-ion transfer for silicon. The maximum feasible efficiencies for a single spherical particle supporting different electric and magnetic resonances are compared, and the harmonic yields are further optimized by tuning lattice resonances in a periodic arrangement of nanoparticles. Results support the dominant role of magnetic dipole and quadrupole contributions in the enhancement of the third harmonic and the electric dipole for the second harmonic, as well as the possibility to further improve the conversion of both harmonics simultaneously at least by two orders of magnitude by designing properly the resonant metasurface.