# Nonlinear Optical Properties and Self-Kerr Effect of Rydberg Excitons in Cu$_2$O

## TL;DR

This paper develops analytical methods to compute nonlinear optical properties of Rydberg excitons in Cu$_2$O, demonstrating agreement with experiments and exploring self-Kerr effects for potential optical applications.

## Contribution

It introduces an analytical framework using the Real Density Matrix Approach to model nonlinear optical functions in Rydberg excitons, including Kerr nonlinearity effects.

## Key findings

- Analytical expressions for nonlinear optical functions are derived.
- Numerical results align well with experimental data.
- Self-phase modulation due to Kerr nonlinearity is feasible in Rydberg excitons.

## Abstract

We show how to compute the nonlinear optical functions (absorption, reflection, and transmission) for a medium with Rydberg excitons, including the effect of the coherence between the electron-hole pair and the electromagnetic field. Using the Real Density Matrix Approach the analytical expressions for nonlinear optical functions are obtained and numerical calculations for Cu$_2$0 crystal are performed. We report a good agreement with recently published experimental data. Propagation of the electromagnetic waves in Rydberg excitons media with nonliner effect is also discussed and the possibility of obtainig self-phase modulation due to Kerr nonlinearity is investigated.