On the Saturation of the Nonlinear Refractive Index in Atomic Gases

TL;DR

This paper investigates the nonlinear index saturation in atomic gases during femtosecond filamentation, using quantum simulations to compare models and confirm that free electron contributions are the main cause of saturation.

Contribution

The study provides a quantum mechanical analysis comparing the HOKE and Standard models, clarifying the physical origin of nonlinear index saturation in atomic gases.

Findings

HOKE model does not match quantum results at clamping intensities

Standard models with charge contributions align well with quantum simulations

Saturation mainly caused by free or nearly free electron contributions

Abstract

Motivated by the ongoing controversy on the origin of the nonlinear index saturation and subsequent intensity clamping in femtosecond filaments, we study the atomic nonlinear polarization induced by a high-intensity and ultrashort laser pulse in hydrogen by numerically solving the time dependent Schr\"odinger equation. Special emphasis is given to the efficient modeling of the nonlinear polarization at central laser frequency corresponding to 800 nm wavelength. Here, the recently proposed model of the Higher-Order Kerr Effect (HOKE) and two versions of the Standard model for femtosecond filamentation, including either a multi-photon or tunnel ionization rate, are compared. We find that around the clamping intensity the instantaneous HOKE model does not reproduce the temporal structure of the nonlinear response obtained from the quantum mechanical results. In contrast, the non-instantaneous charge contributions included in the Standard models ensure a reasonable quantitative agreement. Therefore, the physical origin for the observed saturation of the overall electron response is confirmed to mainly result from contributions of free or nearly free electrons.