The thermo-optic nonlinearity of single metal nanoparticles under intense continuous-wave illumination

TL;DR

This study systematically analyzes the thermal nonlinear response of metal nanoparticles under continuous-wave illumination, revealing complex dependencies on size and material properties, and demonstrating a significantly higher nonlinearity than other systems.

Contribution

It provides a comprehensive thermal model explaining the nonlinear response of metal nanoparticles, clarifies the dependence on various parameters, and aligns well with experimental data.

Findings

Nonlinearity coefficients depend on particle size and material properties.

The nonlinear response can be up to 1000 times higher than in other systems.

The model matches experimental scattering measurements.

Abstract

Over the last few decades, extensive previous studies of the nonlinear response of metal nanoparticles report a wide variation of nonlinear coefficients, thus, revealing a highly confused picture of the underlying physics. This naturally prevents rational design of these systems for practical devices. Here, we provide a systematic study of the nonlinear response of metal spheres under continuous wave illumination within a purely thermal model. We characterize the strong dependence of the temperature rise and overall thermo-optic nonlinear response on the particle size and permittivity, on the optical and thermal host properties, as well as on the thermo-derivatives of these properties. This dependence on the non-intrinsic parameters explains why it is inappropriate to extract an intrinsic nonlinear coefficient from a specific system. Despite the revealed complex multi-parameter dependence, we managed to uncover a rather simple behaviour of the nonlinear response. In particular, we show that the nonlinearity coefficients exhibit a dependence on the illumination intensity which mimics the dependence of the temperature itself on the illumination intensity, namely, it grows for small nanoparticle sizes, reaches a maximum and then decreases monotonically for larger nanoparticles. The improved modelling allows us to demonstrate an overall nonlinear response which is about a 1000 times higher than in other strongly nonlinear systems (e.g., $\epsilon$-near-zero systems); it also provides an excellent match to experimental measurements of the scattering from a single metal nanoparticles, thus, confirming the dominance of the thermal nonlinear mechanism. Our work lays the foundations for an overall evaluation of previous studies of the nonlinear response of metal-dielectric system under general conditions.