Recurrence in the high-order nonlinear Schr\"odinger equation: a low dimensional analysis

We study a three-wave truncation of the high-order nonlinear Schr\"odinger equation for deepwater waves (HONLS, also named Dysthe equation). We validate our approach by comparing it to numerical simulation, distinguish the impact of the different fourth-order terms and classify the solutions according to their topology. This allows us to properly define the temporary spectral upshift occurring in the nonlinear stage of Benjamin-Feir instability and provides a tool for studying further generalizations of this model

Spin-Glass Model Governs Laser Multiple Filamentation

We show that multiple filamentation patterns in high-power laser beams, can be described by means of two statistical physics concepts, namely self-similarity of the patterns over two nested scales, and nearest-neighbor interactions of classical rotators. The resulting lattice spin model perfectly reproduces the evolution of intense laser pulses as simulated by the Non-Linear Schr\"odinger Equation, shedding a new light on multiple filamentation. As a side benefit, this approach drastically reduces the computing time by two orders of magnitude as compared to the standard simulation methods of laser filamentation.Comment: 8 pages, 4 figure

Laser filamentation as a new phase transition universality class

We show that the onset of laser multiple filamentation can be described as a critical phenomenon that we characterize both experimentally and numerically by measuring a set of seven critical exponents. This phase transition deviates from any existing universality class, and offers a unique perspective of conducting two-dimensional experiments of statistical physics at a human scale.Comment: 8 pages, 9 figure

Nonlinear stage of Benjamin-Feir instability in forced/damped deep water waves

We study a three-wave truncation of a recently proposed damped/forced high-order nonlinear Schr\"odinger equation for deep-water gravity waves under the effect of wind and viscosity. The evolution of the norm (wave-action) and spectral mean of the full model are well captured by the reduced dynamics. Three regimes are found for the wind-viscosity balance: we classify them according to the attractor in the phase-plane of the truncated system and to the shift of the spectral mean. A downshift can coexist with both net forcing and damping, i.e., attraction to period-1 or period-2 solutions. Upshift is associated with stronger winds, i.e., to a net forcing where the attractor is always a period-1 solution. The applicability of our classification to experiments in long wave-tanks is verified.Comment: 8 pages, 4 figure

Reversibility of laser filamentation

We investigate the reversibility of laser filamentation, a self-sustained, non-linear propagation regime including dissipation and time-retarded effects. We show that even losses related to ionization marginally affect the possibility of reverse propagating ultrashort pulses back to the initial conditions, although they make it prone to finite-distance blow-up susceptible to prevent backward propagation.Comment: 12 pages, 3 figure

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

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