Hysteresis in the complex nonlinear refractive index of a homogeneous and isotropic medium

TL;DR

This paper models a medium with quadratic electro-optic effects as a Duffing oscillator, revealing hysteresis in its nonlinear refractive index and absorption coefficient when varying light intensity and frequency.

Contribution

It introduces a novel approach to analyze hysteresis in nonlinear optical properties using a Duffing oscillator model for a homogeneous, isotropic medium.

Findings

Hysteresis observed in nonlinear refractive index and absorption coefficient.

Negative nonlinear refractive index near resonances.

Hysteresis depends on light intensity and frequency variations.

Abstract

We calculate the permittivity, $\epsilon(\omega)$, for a medium with a quadratic electro-optic effect, modeling it as a Duffing oscillator. The nonlinear refractive index $n(\omega, E(\omega))$ and the nonlinear absorption coefficient $\alpha(\omega, E(\omega))$ exhibit hysteresis when the light intensity is varied [here $E(\omega)$ is the electric field strength at angular frequency $\omega$], and when the light frequency is varied. $n(\omega, E(\omega))$ can be negative when the resonances in the permittivity and permeability are close to one another.