Semi-classical approximation for second-harmonic generation in nanoparticles

Abstract

Second-harmonic generation by spherical nanoparticles is a non-local optical process that can also be viewed as the result of the nonlinear response of the a interface layer. The classical electrodynamic description, based e.g. on the nonlinear Mie theory, entails the knowledge of the dielectric function and the surface nonlinear optical susceptibility; both quantities are usually assumed to be predetermined, for instance from experiment. We propose here an approach based on the semi-classical approximation for the quantum sum-over-states expression that allows one to capture the second-order optical process from first principles. A key input is the electronic density, which can be obtained from effective single particle approaches such as density-functional theory in the local density implementation. We show that the resulting integral equations can be solved very efficiently rendering thus the treatment of macroscopic systems. As an illustration we present numerical results for the magic Na cluster.