Non-perturbative Hydrodynamic Model for Multiple Harmonics Generation in   Metallic Nanostructures
  Optical response of free-electron gas leads to inherent nonlinear optical behaviour of nanostructured plasmonic materials enabled via both strong local field enhancements and inherent complex electron dynamics. We present a comprehensive treatment of microscopic polarization of conduction electrons in the time-domain using full hydrodynamic description which allows self-consistent modelling of linear and nonlinear response and multiple harmonics generation. The effects of convective acceleration, magnetic contribution of the Lorenz force, quantum electron pressure, and nanostructures boundaries have been taken into account leading to simultaneous appearance of second and third harmonics. The developed method provides an ultimate approach to investigate nonlinear responses of arbitrarily-shaped complex nano-scale plasmonic structures and enables addressing their self-consistent nonlinear dynamics. 
Pavel Ginzburg, Alexey V. Krasavin, Gregory A.Wurtz, and Anatoly V.   Zayats
physics.optics