On negative higher-order Kerr effect and filamentation
V. Loriot, P. B\'ejot, W. Ettoumi, Y. Petit, J. Kasparian, S.~Henin,, E. Hertz, B. Lavorel, O. Faucher, J.-P.~Wolf

TL;DR
This paper investigates the role of the higher-order Kerr effect in laser filamentation, clarifying experimental protocols, addressing potential artifacts, and discussing conditions where HOKE or plasma defocusing dominate.
Contribution
It provides a detailed protocol for inferring HOKE indices, analyzes potential experimental artifacts, and discusses the conditions influencing HOKE versus plasma effects in filamentation.
Findings
Experimental measurements of birefringence are consistent and reliable.
The inclusion of HOKE in filamentation models is justified based on the analysis.
The dominance of HOKE or plasma effects depends on wavelength and pulse duration.
Abstract
As a contribution to the ongoing controversy about the role of higher-order Kerr effect (HOKE) in laser filamentation, we first provide thorough details about the protocol that has been employed to infer the HOKE indices from the experiment. Next, we discuss potential sources of artifact in the experimental measurements of these terms and show that neither the value of the observed birefringence, nor its inversion, nor the intensity at which it is observed, appear to be flawed. Furthermore, we argue that, independently on our values, the principle of including HOKE is straightforward. Due to the different temporal and spectral dynamics, the respective efficiency of defocusing by the plasma and by the HOKE is expected to depend substantially on both incident wavelength and pulse duration. The discussion should therefore focus on defining the conditions where each filamentation regime…
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