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

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)=n₀+n₂I, 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 χ⁽³⁾, χ⁽⁵⁾, and χ⁽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.