Semi-classical approximation for the second harmonic generation in nanoparticles

TL;DR

This paper introduces a semi-classical method to calculate second harmonic generation in nanoparticles from first principles, using electronic density from density-functional theory, enabling efficient analysis of large systems.

Contribution

It presents a novel semi-classical approach based on quantum sum-over-states for second harmonic generation, reducing reliance on experimental dielectric and susceptibility data.

Findings

Efficient numerical solution for second harmonic generation in nanoparticles.

Application to Na2869 cluster demonstrating the method's effectiveness.

First-principles approach capturing non-linear optical response.

Abstract

Second harmonic generation by spherical nanoparticles is a non-local optical process that can also be viewed as the result of the non-linear response of the thin interface layer. The classical electrodynamic description, based e.g. on the non-linear Mie theory, entails the knowledge of the dielectric function and the surface non-linear 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 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 the 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 Na2869 cluster.