Two statistical regimes in the transition to filamentation.

We experimentally investigate fluctuations in the spectrum of ultrashort laser pulses propagating in air, close to the critical power for filamentation. Increasing the laser peak power broadens the spectrum while the beam approaches the filamentation regime. We identify two regimes for this transition: In the center of the spectrum, the output spectral intensity increases continuously. In contrast, on the edges of the spectrum the transition implies a bimodal probability distribution function for intermediate incident pulse energies, where a high-intensity mode appears and grows at the expense of the original low-intensity mode. We argue that this dual behavior prevents the definition of a univoquial threshold for filamentation, shedding a new light on the long-standing lack of explicit definition of the boundary of the filamentation regime.

Paradoxical effects of altruism on efforts to mitigate climate change.

It is common wisdom that altruism is a crucial element in addressing climate change and other public good issues. If individuals care about the welfare of others (including future generations) they can be expected to unilaterally adapt their behaviour to preserve the common good thus enhancing the wellbeing of all. We introduce a network game model featuring both altruism and a public good (e.g. climate) whose degradation affects all players. As expected, in an idealistic fully connected society where all players care about each other, increasing altruism results in a better protection of the public good. However, in more realistic networks where people are not all related to each other, we highlight an intrinsic trade-off between the effects of altruism on reducing inequality and the preservation of a global public good: the consumption redistribution generated by a higher altruism is partly achieved by lowering income transfers towards protection of the public good. Therefore, it increases overall consumption and is thereby detrimental to the public good. These results suggest that altruism, although good from a welfarist point of view, is not in itself sufficient to simultaneously solve public good and inequality issues.

Nonlinear wave evolution with data-driven breaking.

Wave breaking is the main mechanism that dissipates energy input into ocean waves by wind and transferred across the spectrum by nonlinearity. It determines the properties of a sea state and plays a crucial role in ocean-atmosphere interaction, ocean pollution, and rogue waves. Owing to its turbulent nature, wave breaking remains too computationally demanding to solve using direct numerical simulations except in simple, short-duration circumstances. To overcome this challenge, we present a blended machine learning framework in which a physics-based nonlinear evolution model for deep-water, non-breaking waves and a recurrent neural network are combined to predict the evolution of breaking waves. We use wave tank measurements rather than simulations to provide training data and use a long short-term memory neural network to apply a finite-domain correction to the evolution model. Our blended machine learning framework gives excellent predictions of breaking and its effects on wave evolution, including for external data.

Separatrix crossing and symmetry breaking in NLSE-like systems due to forcing and damping.

We theoretically and experimentally examine the effect of forcing and damping on systems that can be described by the nonlinear Schrödinger equation (NLSE), by making use of the phase-space predictions of the three-wave truncation. In the latter, the spectrum is truncated to only the fundamental frequency and the upper and lower sidebands. Our experiments are performed on deep water waves, which are better described by the higher-order NLSE, the Dysthe equation. We therefore extend our analysis to this system. However, our conclusions are general for NLSE systems. By means of experimentally obtained phase-space trajectories, we demonstrate that forcing and damping cause a separatrix crossing during the evolution. When the system is damped, it is pulled outside the separatrix, which in the real space corresponds to a phase-shift of the envelope and therefore doubles the period of the Fermi-Pasta-Ulam-Tsingou recurrence cycle. When the system is forced by the wind, it is pulled inside the separatrix, lifting the phase-shift. Furthermore, we observe a growth and decay cycle for modulated plane waves that are conventionally considered stable. Finally, we give a theoretical demonstration that forcing the NLSE system can induce symmetry breaking during the evolution.

Single-spectrum prediction of kurtosis of water waves in a nonconservative model.

We study statistical properties after a sudden episode of wind for water waves propagating in one direction. A wave with random initial conditions is propagated using a forced-damped higher-order nonlinear Schrödinger equation. During the wind episode, the wave action increases, the spectrum broadens, the spectral mean shifts up, and the Benjamin-Feir index (BFI) and the kurtosis increase. Conversely, after the wind episode, the opposite occurs for each quantity. The kurtosis of the wave height distribution is considered the main parameter that can indicate whether rogue waves are likely to occur in a sea state, and the BFI is often mentioned as a means to predict the kurtosis. However, we find that while there is indeed a quadratic relation between these two, this relationship is dependent on the details of the forcing and damping. Instead, a simple and robust quadratic relation does exist between the kurtosis and the bandwidth. This could allow for a single-spectrum assessment of the likelihood of rogue waves in a given sea state. In addition, as the kurtosis depends strongly on the damping and forcing coefficients, by combining the bandwidth measurement with the damping coefficient, the evolution of the kurtosis after the wind episode can be predicted.

Gas-Solid Phase Transition in Laser Multiple Filamentation.

While propagating in transparent media, near-infrared multiterawatt (TW) laser beams break up in a multitude of filaments of typically 100-200 um diameter with peak intensities as high as 10 to 100 TW/cm^{2}. We observe a phase transition at incident beam intensities of 0.4 TW/cm^{2}, where the interaction between filaments induce solidlike two-dimensional crystals with a 2.7 mm lattice constant, independent of the initial beam diameter. Below 0.4 TW/cm^{2}, we evidence a mixed phase state in which some filaments are closely packed in localized clusters, nucleated on inhomogeneities (seeds) in the transverse intensity profile of the beam, and other are sparse with almost no interaction with their neighbors, similar to a gas. This analogy with a thermodynamic gas-solid phase transition is confirmed by calculating the interaction Hamiltonian between neighboring filaments, which takes into account the effect of diffraction, Kerr self-focusing, and plasma generation. The shape of the effective potential is close to a Morse potential with an equilibrium bond length close to the observed value.

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 nonlinear Schrödinger equation, shedding new light on multiple filamentation. As a side benefit, this approach drastically reduces the computing time by 2 orders of magnitude as compared to the standard simulation methods of laser filamentation.

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.

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.

Mid-infrared laser filamentation in molecular gases.

We observed the filamentation of mid-infrared ultrashort laser pulses (3.9 µm, 80 fs) in molecular gases. It efficiently generates a broadband supercontinuum over two octaves in the 2.5-6 µm spectral range, with a red-shift up to 500 nm due to the Raman effect, which dominates over the blue shift induced by self-steepening and the gas ionization. As a result, the conversion efficiency into the Stokes region (4.3-6 µm) 65% is demonstrated.

High-field quantum calculation reveals time-dependent negative Kerr contribution.

The exact quantum time-dependent optical response of hydrogen under strong-field near-infrared excitation is investigated and compared to the perturbative model widely used for describing the effective atomic polarization induced by intense laser fields. By solving the full 3D time-dependent Schrödinger equation, we exhibit a supplementary, quasi-instantaneous defocusing contribution missing in the weak-field model of polarization. We show that this effect is far from being negligible, in particular when closures of ionization channels occur and stems from the interaction of electrons with their parent ions. It provides an interpretation of the higher-order Kerr effect recently observed in various gases.

Higher-order Kerr improve quantitative modeling of laser filamentation.

We test numerical filamentation models against experimental data about the peak intensity and electron density in laser filaments. We show that the consideration of the higher-order Kerr effect improves the quantitative agreement without the need of adjustable parameters.

Ultrafast laser spectroscopy and control of atmospheric aerosols.

We review applications of ultrafast laser pulses for aerosol analysis via linear and non-linear spectroscopy, including the most advanced techniques like coherent control of molecular excited states. We also discuss the capability of such pulses to influence the nucleation of atmospheric aerosols by assisting condensation of water in air.

Conical emission from laser filaments and higher-order Kerr effect in air.

We numerically investigate the conical emission (CE) from ultrashort laser filaments, both considering and disregarding the higher-order Kerr effect (HOKE). While the consideration of HOKE has almost no influence on the predicted CE from collimated beams, differences arise for tightly focused beams. This difference is attributed to the different relative contributions of the nonlinear focus and of the modulational instability over the whole filament length.

Modelling of HNO3-mediated laser-induced condensation: a parametric study.

Based on both static (extended Köhler) and dynamic modelling, we investigate the influence of temperature, humidity, HNO(3) initial concentration, as well as of the particle concentration, on the efficiency of HNO(3)-mediated laser-induced condensation. This mechanism is most efficient for low temperatures, high HNO(3) concentration, and relative humidities. It is, however, still active up to 30 °C, down to 70% relative humidity, and below the ppm level of HNO(3). Furthermore, lower particle concentration minimizing the depletion of both HNO(3) and water vapor is more favourable to particle growth.

Field measurements suggest the mechanism of laser-assisted water condensation.

Because of the potential impact on agriculture and other key human activities, efforts have been dedicated to the local control of precipitation. The most common approach consists of dispersing small particles of dry ice, silver iodide, or other salts in the atmosphere. Here we show, using field experiments conducted under various atmospheric conditions, that laser filaments can induce water condensation and fast droplet growth up to several µm in diameter in the atmosphere as soon as the relative humidity exceeds 70%. We propose that this effect relies mainly on photochemical formation of p.p.m.-range concentrations of hygroscopic HNO(3), allowing efficient binary HNO(3)-H(2)O condensation in the laser filaments. Thermodynamic, as well as kinetic, numerical modelling based on this scenario semiquantitatively reproduces the experimental results, suggesting that particle stabilization by HNO(3) has a substantial role in the laser-induced condensation.

Transition from plasma-driven 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.

From higher-order Kerr nonlinearities to quantitative modeling of third and fifth harmonic generation in argon.

The recent measurement of negative higher-order Kerr effect (HOKE) terms in gases has given rise to a controversial debate, fed by its impact on short laser pulse propagation. By comparing the experimentally measured yield of the third and fifth harmonics, with both an analytical and a full comprehensive numerical propagation model, we confirm the absolute and relative values of the reported HOKE indices.

Generalized Miller formulae.

We derive the spectral dependence of the non-linear susceptibility of any order, generalizing the common form of Sellmeier equations. This dependence is fully defined by the knowledge of the linear dispersion of the medium. This finding generalizes the Miller formula to any order of non-linearity. In the frequency-degenerate case, it yields the spectral dependence of non-linear refractive indices of arbitrary order.

Higher-order Kerr terms allow ionization-free filamentation in gases.

We show that higher-order nonlinear indices (n(4), n(6), n(8), n(10)) provide the main defocusing contribution to self-channeling of ultrashort laser pulses in air and argon at 800 nm, in contrast with the previously accepted mechanism of filamentation where plasma was considered as the dominant defocusing process. Their consideration allows us to reproduce experimentally observed intensities and plasma densities in self-guided filaments.