Toy model of harmonic and sum frequency generation in 2D nanostructures

TL;DR

This paper presents a toy oscillator model demonstrating that collective nonlinear optical responses can emerge in 2D dielectric nanoparticles due to Coulomb interactions, even when individual atoms are linear.

Contribution

It introduces a simple model showing how collective nonlinearities arise from atomic interactions in 2D nanostructures, highlighting multipole contributions and scaling behaviors.

Findings

Nonlinear response can originate from Coulomb interactions in atomic arrays.

Odd and even order nonlinear electric dipoles scale with area and perimeter.

Collective effects can induce nonlinearities absent in individual atoms.

Abstract

Optical nonlinearities of matter are often associated with the response of individual atoms. Here, using a toy oscillator model, we show that in the confined geometry of a two-dimensional dielectric nanoparticle a collective nonlinear response of the atomic array can arise from the Coulomb interactions of the bound optical electrons, even if the individual atoms exhibit no nonlinearity. We determine the multipole contributions to the nonlinear response of nanoparticles and demonstrate that the odd order and even order nonlinear electric dipole moments scale with the area and perimeter of the nanoparticle, respectively.