Arbitrary-order non-linear contribution to self-steepening

TL;DR

This paper derives the spectral dependence of higher-order non-linear indices' contributions to group velocity, revealing their sign alternation and importance in laser filamentation, emphasizing the need to consider dispersion in calculations.

Contribution

It introduces a generalized formula for the spectral dependence of arbitrary-order non-linear indices' contributions to group velocity, applicable to laser filamentation.

Findings

Higher-order non-linear indices have alternating signs and similar magnitudes.

Dispersion of non-linear indices significantly affects group velocity calculations.

All experimentally accessible orders up to the 11th are relevant in gases like air and argon.

Abstract

Based on the recently published generalized Miller formula, we derive the spectral dependence of the contribution of arbitrary-order non-linear indices to the group-velocity index. We show that in the context of laser filamentation in gases all experimentally-accessible orders (up to the $9^{th}$-order non-linear susceptibility $\chi^{(9)}$ in air and $\chi^{(11)}$ in argon) have contributions of alternative signs and similar magnitudes. Moreover, we show both analytically and numerically that the dispersion term of the non-linear indices must be considered when computing the intensity-dependent group velocity.