Femtosecond filamentation in air and higher-order nonlinearities

Abstract

According to a recent experiment, the instantaneous electronic Kerr effect in air exhibits a strong intensity dependence, the nonlinear refractive index switching sign and crossing over from a self-focusing to a de-focusing nonlinearity. A subsequent theoretical work has demonstrated that this has paradigm-changing consequences for the understanding of filamentation in air, so it is important to subject the idea of higher-order nonlinearities to stringent tests. Here we use numerical modeling to propose an experiment capable of discriminating between the standard and the new intensity-dependent Kerr-effect models. c 2018 Optical Society of America OCIS codes: 320.2250, 320.7110.Over the last sesquidecade research into femtosecond filamentation in air has produced a widely accepted picture in which a dilute plasma, generated in the highintensity optical field, is a major determinant of the light pulse dynamics. For gaseous media, this scenario is based on the notion of a dynamical balance between the Kerrinduced self-focusing and the counteracting de-focusing caused by the free electrons [1]. Higher-order nonlinearities have previously been considered before as an additional mechanism regularizing the self-focusing collapse. In particular, phenomenological Kerr-effect saturation at high intensities (see e.g. [2-4] and Sec 3.4. of [5]) was explored in filament modeling. In several papers quantummechanical simulations of the electronic polarization response (e.g. [6] and references therein) were used to study the interplay of the saturated Kerr and plasma contributions. Nevertheless, in the absence of experimental evidence for these effects, the consensus in the filamentation community was that the standard self-focusing Kerr effect was sufficient to describe the electronic nonlinearity. Moreover, many experiments clearly showed the presence of plasma in filaments, and this was accepted as the mechanism clamping the intensity [7].Recent experimental results by Loriot et al. [8,9] have the potential to change this long-standing paradigm. They found that the instantaneous Kerr nonlinearity exhibits a strong intensity dependence, and that it not only saturates, but even changes from self-focusing to de-focusing at large enough intensity. As a consequence, the plasma is not necessary for the arrest of the selffocusing collapse, because the Kerr-induced de-focusing at high intensity can alone be sufficient. Inspired by these findings, the recent modeling work of Ref. [10] proposed that contrary to our current belief, ionization-free filamentation is possible in gases.This has been a surprising development to say the least, and one which poses many questions. The first one is of course, why the earlier experiments did not detect such a strong intensity dependence of the Kerr effect? Further, is it just an accident that the cross-over from self-focusing to de-focusing occurs in the vicinity of the intensity range where plasma starts to form, or is there a connection between the two? In particular, central to the interpret...

Saturation of the All-Optical Kerr Effect

“…This analysis supports the experimental results in Ref. [8], indicating that we may have in fact a paradigm shift in explaining femtosecond filamentation [10].…”

“…Recently, this accepted picture was challenged by measurements [8,9] that indicate yet again a strong influence of higher-order nonlinearities to the extent that filament formation is explained in the complete absence of plasma formation. These results have been controversially discussed [10,11]. In the following, we provide an independent and previously unreported approach towards computing Kerr saturation.…”

Interaction of ultrashort-laser pulses with induced undercritical plasmas in fused silica

“…[37][38][39][40][41]) will reduce the need to assumeg an initial field with no spatiotemporal dependences or to use apertured FROG traces. Additionally, recent investigations into the possible role of high-order nonlinear optical effects [42][43][44], ionization by multichromatic pulses [45], and the influence of phenomenological parameters (such as the free-carrier collision time and the effective electron mass) [46] may also allow for further improvements in predamage calculations.…”

Optical Nonlinearity in Ar andN2near the Ionization Threshold

“…It would overturn the picture most have of the mechanism behind long-range filamentary propagation of intense ultrashort pulses -as arising from an interplay between self-focusing due to the positive optical nonlinearity from bound electrons and defocusing due to the plasma generated by ionization. The existence of a higher-order Kerr effect would also have implications for the general nonlinear susceptibility in transparent media [7,8], including harmonic generation [9][10][11].Subsequent experimental studies of light filaments [12][13][14][15] have not supported the higher-order Kerr model, with one exception [16]. One measurement [13] found that the electron density was two orders of magnitude higher than predicted by a calculation including higher-order nonlinearities, but agreed with a simulation based on plasma defocusing alone [5].…”