# Negative Nonlinear Refractive Index

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:

$$n_{2E} = \frac{3\chi_{1111}}{8n_0}\label{nonlinear_ref}$$

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?