In most of our discussions about the nonlinear refractive index in both the “Nonlinear Optics” section as well as the “Fiber Optics” section, the materials that we dealt with had a positive nonlinear refractive index. However, some of you may be asking yourselves (as I was asking myself as well), is it possible to have a *negative* nonlinear refractive index? If so, what will physically happen in this case? Can you have solitons form with positive dispersion and a negative nonlinear refractive index? All great questions! In the following article, I have compiled all that I know/can find on the negative nonlinear refractive index, so we can answer these questions together.

**WHAT IS THE NEGATIVE NONLINEAR REFRACTIVE INDEX, AND WHERE DOES IT COME FROM?**

As a reminder, the nonlinear refractive index is given by the following equation:

\begin{equation} n_{2E} = \frac{3\chi_{1111}}{8n_0}\label{nonlinear_ref}\end{equation}

where $\chi_{1111}$ is the susceptibility in third-order material, and $n_0$ is the refractive index of the material in the absence of an intense light wave. In order for the nonlinear refractive index to be negative, the susceptibility must carry a negative value. According to [1], the sign of the susceptibility has to do with the transitions between the ground state, excited state, and two-photon excited state. When the two photon state dominates, the susceptibility is positive while when the absorption dominates, the susceptibility is negative.

**WHICH MATERIALS HAVE A NEGATIVE NONLINEAR REFRACTIVE INDEX?**

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Thanks for the update on negative nonlinear refractive index! What kind of properties do materials with these negative indexes exhibit? I’m looking forward to reading more with your next update!