Second-harmonic generation in metallic nanoparticles: Clarification of the role of the surface

Abstract

We present a numerical investigation of the second-order nonlinear optical properties of metal-based metamaterial nanoresonators. The nonlinear optical response of the metal is described by a hydrodynamic model, with the effects of electron pressure in the electron gas also taken into account. We show that as the pressure term tends to zero the amount of converted second-harmonic field tends to an asymptotic value. In this limit it becomes possible to rewrite the nonlinear surface contributions as functions of the value of the polarization vector inside the bulk region. Nonlocality thus can be incorporated into numerical simulations without actually utilizing the nonlocal equation of motion or solving for the rapidly varying fields that occur near the metal surface. We use our model to investigate the second-harmonic generation process with three-dimensional gold nanoparticle arrays and show that nanocrescents can easily attain conversion efficiencies of $\ensuremath{\sim}$$6.0\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}8}$ for pumping peak intensities of a few tens of MW/cm${}^{2}$.