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.

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.

Real-time and spatially resolved assessment of pathogens in crops for site-specific pesticide reduction strategies

We deploy a network of autonomous stations measuring meteorological and soil parameters, as well as the airborne particle size distribution with a focus on the size ofPlasmapora Viticola(PV). They provide early warning and detection of PV spore outbursts with high spatial and temporal resolution. We evidence the high spatial inhomogeneity of this pathogen, potentially allowing to limit treatments to the specific times and locations where infection risk is detected.

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.

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.

Ultraviolet-visible conical emission by multiple laser filaments

We characterized the angular distribution of the supercontinuum emission from multiple infrared laser filaments propagating in air over long distances, from the infrared (1080 nm) to ultraviolet (225 nm). These experimental data suggest that the X-Waves modeling or Cerenkov emission, rather than phase matching of four-wave mixing, could explain the conical emission. We also estimate the total light conversion efficiency from the original laser wavelength into the white-light continuum.

Ultrafast gaseous "half-wave plate"

We demonstrate that filaments generated by ultrashort laser pulses can induce a remarkably large birefringence in Argon over its whole length, resulting in an ultrafast "half-wave plate" for a copropagating probe beam. This birefringence originates from the difference between the nonlinear refractive indices induced by the filament on the axes parallel and orthogonal to its polarization. An angle of 45 degrees between the filament and the probe polarizations allows the realization of ultrafast Kerr-gates, with a switching time ultimately limited by the duration of the filamenting pulse.

Laser filaments generated and transmitted in highly turbulent air

The initiation and propagation of a filament generated by ultrashort laser pulses in turbulent air is investigated experimentally. A filament can be generated and propagated even after the beam has propagated through strongly turbulent regions, with structure parameters C(n)2 as many as 5 orders of magnitude larger than those encountered in the usual atmospheric conditions. Moreover, the filament's position within the beam is not affected by the interaction with a turbulent region. This remarkable stability is allowed by the strong Kerr refractive-index gradients generated within the filament, which exceed the turbulence-induced refractive-index gradients by 2 orders of magnitude.

Multifilamentation transmission through fog

The influence of atmospheric aerosols on the filamentation patterns created by TW laser beams over 10 m propagation scales is investigated, both experimentally and numerically. From the experimental point of view, it is shown that dense fogs dissipate quasi-linearly the energy in the beam envelope and diminish the number of filaments in proportion. This number is strongly dependent on the power content of the beam. The power per filament is evaluated to about 5 critical powers for self-focusing in air. From the theoretical point of view, numerical computations confirm that a dense fog composed of micrometric droplets acts like a linear dissipator of the wave envelope. Beams subject to linear damping or to collisions with randomly-distributed opaque droplets are compared.

Supercontinuum emission and enhanced self-guiding of infrared femtosecond filaments sustained by third-harmonic generation in air

The long-range propagation of two-colored femtosecond filaments produced by an infrared (IR) ultrashort pulse exciting third harmonics (TH) in the atmosphere is investigated, both theoretically and experimentally. First, it is shown that the coupling between the pump and TH components is responsible for a wide spectral broadening, extending from ultraviolet (UV) wavelengths (220 nm) to the mid-IR (4.5 microm). Supercontinuum generation takes place continuously as the laser beam propagates, while TH emission occurs with a conversion efficiency as high as 0.5%. Second, the TH pulse is proven to stabilize the IR filament like a saturable quintic nonlinearity through four-wave mixing and cross-phase modulation. Third, the filamentation is accompanied by a conical emission of the beam, which becomes enlarged at UV wavelengths. These properties are revealed by numerical simulations and direct experimental observations performed from the Teramobile laser facility.

Filamentation of femtosecond light pulses in the air: turbulent cells versus long-range clusters

The filamentation of ultrashort pulses in air is investigated theoretically and experimentally. From the theoretical point of view, beam propagation is shown to be driven by the interplay between random nucleation of small-scale cells and relaxation to long waveguides. After a transient stage along which they vary in location and in amplitude, filaments triggered by an isotropic noise are confined into distinct clusters, called "optical pillars," whose evolution can be approximated by an averaged-in-time two-dimensional (2D) model derived from the standard propagation equations for ultrashort pulses. Results from this model are compared with space- and time-resolved numerical simulations. From the experimental point of view, similar clusters of filaments emerge from the defects of initial beam profiles delivered by the Teramobile laser facility. Qualitative features in the evolution of the filament patterns are reproduced by the 2D reduced model.

Multiple filamentation of terawatt laser pulses in air

The filamentation of femtosecond light pulses in air is numerically and experimentally investigated for beam powers reaching several TW. Beam propagation is shown to be driven by the interplay between intense, robust spikes created by the defects of the input beam and random nucleation of light cells. Evolution of the filament patterns can be qualitatively reproduced by an averaged-in-time (2D+1)-dimensional model derived from the propagation equations for ultrashort pulses.

White-light filaments for atmospheric analysis

Most long-path remote spectroscopic studies of the atmosphere rely on ambient light or narrow-band lasers. High-power femtosecond laser pulses have been found to propagate in the atmosphere as dynamically self-guided filaments that emit in a continuum from the ultraviolet to the infrared. This white light exhibits a directional behavior with enhanced backward scattering and was detected from an altitude of more than 20 kilometers. This light source opens the way to white-light and nonlinear light detection and ranging applications for atmospheric trace-gas remote sensing or remote identification of aerosols. Air ionization inside the filaments also opens promising perspectives for laser-induced condensation and lightning control. The mobile femtosecond-terawatt laser system, Teramobile, has been constructed to study these applications.

Triggering and guiding megavolt discharges by use of laser-induced ionized filaments

We have demonstrated the ability to trigger and guide high-voltage discharges with ionized filaments generated by femtosecond terawatt laser pulses. The plasma filaments extended over the whole gap, providing a direct ohmic connection between the electrodes. Laser-guided straight discharges have been observed for gaps of as much as 3.8 m at a high voltage reduced to 68% of the natural breakdown voltage. The triggering efficiency was found to depend critically on the spatial connection of the laser filaments to the electrode as well as on the temporal coincidence of the laser with the peak of the high voltage.

Microtubule structure at improved resolution

Microtubule architecture can vary with eukaryotic species, with different cell types, and with the presence of stabilizing agents. For in vitro assembled microtubules, the average number of protofilaments is reduced by the presence of sarcodictyin A, epothilone B, and eleutherobin (similarly to taxol) but increased by taxotere. Assembly with a slowly hydrolyzable GTP analogue GMPCPP is known to give 96% 14 protofilament microtubules. We have used electron cryomicroscopy and helical reconstruction techniques to obtain three-dimensional maps of taxotere and GMPCPP microtubules incorporating data to 14 A resolution. The dimer packing within the microtubule wall is examined by docking the tubulin crystal structure into these improved microtubule maps. The docked tubulin and simulated images calculated from "atomic resolution" microtubule models show tubulin heterodimers are aligned head to tail along the protofilaments with the beta subunit capping the microtubule plus end. The relative positions of tubulin dimers in neighboring protofilaments are the same for both types of microtubule, confirming that conserved lateral interactions between tubulin subunits are responsible for the surface lattice accommodation observed for different microtubule architectures. Microtubules with unconventional protofilament numbers that exist in vivo are likely to have the same surface lattice organizations found in vitro. A curved "GDP" tubulin conformation induced by stathmin-like proteins appears to weaken lateral contacts between tubulin subunits and could block microtubule assembly or favor disassembly. We conclude that lateral contacts between tubulin subunits in neighboring protofilaments have a decisive role for microtubule stability, rigidity, and architecture.

Backward supercontinuum emission from a filament generated by ultrashort laser pulses in air

Backward emission of the supercontinuum from a light filament induced by high-intensity femtosecond laser pulses propagating in air has been observed to be enhanced compared with linear Rayleigh-Mie scattering. This enhancement is interpreted as a nonlinear scattering process onto longitudinal refractive-index changes induced by the laser pulse itself. The spectral dependence of the supercontinuum angular distribution is also investigated.

Infrared extension of the super continuum generated by femtosecond terawatt laser pulses propagating in the atmosphere

We investigated the spectral behavior of a white-light continuum generated in air by 2-TW femtosecond laser pulses at 800 nm. The spectrum extends at least from 300 nm to 4.5 mum. From 1 to 1.6 mum the continuum's intensity increases strongly with the laser energy and depends on the initial chirp.

Three-Dimensional Analysis of Urban Aerosols by use of a Combined Lidar, Scanning Electron Microscopy, and X-Ray Microanalysis

We present a novel method of characterizing urban aerosols that combines scanning-electron microscopy, x-ray microanalysis, and lidar measurements. Inversion algorithms, based on fractal aerosol models, allowed us to compute the scattering coefficients of the measured size distribution. The alpha and beta coefficients were used to invert lidar data, yielding what to our knowledge are the first quantitative three-dimensional measurements of the aerosol mass concentrations in urban conditions. The combined method was used during an extensive experiment in Lyon in the summer of 1996. Size distributions exhibit two main modes, at 0.1 and 0.9 mum, the composition of which was determined by x-ray microanalysis. The first mode is soot, and the second is composed of 60% coarse soot particles and 40% silica particles. Lidar measurements showed a homogeneous aerosol concentration within the mixing layer and a steep gradient above. Measurements made over 24 h also showed loads that were due to traffic rush hours and the dynamics of the height of the planetary boundary layer.