Arbitrary-order non-linear contribution to self-steepening

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.Comment: 10 pages, 3 figures (14 panels

Effect of a plasma grating on pump-probe experiments near the ionization threshold in gases

Calculations are performed of the phase shift caused by the spatial modulation in the plasma density due to interference between a strong pump pulse and a weak probe pulse. It is suggested that a recent experiment [Loriot et al., Opt. Express v. 17, 13429 (2009)] observed an effective birefringence from this plasma grating rather than from the higher-order Kerr effect.Comment: 3 pages, 1 figure. Fix typos and correct number

Multimodal unidirectional pulse propagation equation

International audienceIn this paper, after a brief recall of the derivation of the unidirectional pulse propagation equation generalized to structured media, a fast modal transform linking the spatiotemporal representation of the field and its modal distribution is presented. This transform is used for solving the propagation equation by using a split-step algorithm in an efficient way. As an example, we present, to the best of our knowledge, the first numerical evidence of the generation of conical waves in highly multimodes waveguides

Resonantly enhanced filamentation in gases

In this Letter, a low-loss Kerr-driven optical filament in Krypton gas is experimentally reported in the ultraviolet. The experimental findings are supported by ab initio quantum calculations describing the atomic optical response. Higher-order Kerr effect induced by three-photon resonant transitions is identified as the underlying physical mechanism responsible for the intensity stabilization during the filamentation process, while ionization plays only a minor role. This result goes beyond the commonly-admitted paradigm of filamentation, in which ionization is a necessary condition of the filament intensity clamping. At resonance, it is also experimentally demonstrated that the filament length is greatly extended because of a strong decrease of the optical losses

Energy conservation in self-phase modulation

Spectral broadening of ultrashort laser pulses is simultaneously described by either self-phase modulation (SPM) or four-wave mixing (FWM). The latter implies the instantaneous conservation of both the photon number and energy, while the former describes a time-dependent frequency shift, implying a violation of the energy conservation if the number of photons is to be conserved in each time slice. We resolve this paradox by considering the transient energy storage in the propagation medium, that can be calculated in the SPM formalism via the dephasing between the incident pulse and the medium polarization leading to an effective imaginary part in the third-order susceptibility. In parallel, considering the temporal variation of the incident intensity in FWM offsets the instantaneous frequency.Comment: 6 page

Transition from plasma- to Kerr-driven laser filamentation

While filaments are generally interpreted as a dynamic balance between Kerr focusing and plasma defocusing, the role of the higher-order Kerr effect (HOKE) is actively debated as a potentially dominant defocusing contribution to filament stabilization. In a pump-probe experiment supported by numerical simulations, we demonstrate the transition between two distinct filamentation regimes at 800\,nm. For long pulses (1.2 ps), the plasma substantially contributes to filamentation, while this contribution vanishes for short pulses (70 fs). These results confirm the occurrence, in adequate conditions, of filamentation driven by the HOKE rather than by plasma.Comment: 6 pages, 4 figures. Accepted for publication in Physical Review Letter