# Metal nanospheres under intense continuous wave illumination - a unique case of non-perturbative nonlinear nanophotonics

## TL;DR

This paper investigates the nonlinear thermal response of metal nanospheres under intense continuous wave illumination, highlighting the limitations of perturbative models and emphasizing the need for non-perturbative descriptions in certain cases.

## Contribution

It demonstrates the inadequacy of cubic nonlinear models for small metal nanospheres at high temperatures and explores when higher-order or full non-perturbative models are necessary.

## Key findings

- Cubic models are insufficient beyond small temperature rises.
- A cubic-quintic model often suffices, but sometimes full non-perturbative analysis is needed.
- Differences between gold and silver nanospheres are identified.

## Abstract

We show that the standard perturbative (i.e., cubic) description of the thermal nonlinear response of small metal nanospheres to intense continuous wave illumination is insufficient already beyond temperature rises of a few tens of degrees. In some cases, a cubic-quintic nonlinear response is sufficient to describe accurately the intensity dependence of the temperature, permittivity and field, while in other cases, a full non-perturbative description is required. We further analyze the relative importance of the various contributions to the thermal nonlinearity, identify a qualitative difference between Au and Ag, and show that the thermo-optical nonlinearity of the host typically plays a minor role, but its thermal conductivity is important.