# Beyond the perturbative description of the nonlinear optical response of low-index materials

## TL;DR

This paper demonstrates that in epsilon-near-zero and low-index materials, standard nonlinear optics approximations break down, requiring a non-perturbative approach to accurately describe their optical response.

## Contribution

It reveals the failure of conventional perturbative models in low-index media and shows the nonlinear response can dominate linear effects without divergence issues.

## Key findings

- Nonlinear response surpasses linear in low-index materials
- Standard $n(I) = n_0 + n_2 I$ approximation fails
- No divergence found in polarization power series

## Abstract

We show that standard approximations in nonlinear optics are violated for situations involving a small value of the linear refractive index. Consequently, the conventional equation for the intensity-dependent refractive index, $n(I) = n_0 + n_2 I$, becomes inapplicable in epsilon-near-zero and low-index media, even in the presence of only third-order effects. For the particular case of indium tin oxide, we find that the $\chi^{(3)}$, $\chi^{(5)}$ and $\chi^{(7)}$ contributions to refraction eclipse the linear term; thus, the nonlinear response can no longer be interpreted as a perturbation in these materials. Although the response is non-perturbative, we find no evidence that the power series expansion of the material polarization diverges.