Multiple filamentation of terawatt laser pulses in air

Stabilization and correction of aberrated laser beams via plasma channelling

High-power laser applications, and especially laser wakefield acceleration, continue to draw attention through various research topics, and may bring many industrial applications based on compact accelerators, from ultrafast imaging to cancer therapy. However, one main step towards this is the arch issue of stability. Indeed, the interaction of a complex, aberrated laser beam with plasma involves a lot of physical phenomena and non-linear effects, such as self-focusing and filamentation. Different outcomes can be induced by small laser instabilities (i.e. laser wavefront), therefore harming any practical solution. One promising path to be explored is the use of a plasma channel to possibly guide and correct aberrated beams. Complex and costly experimental facilities are required to investigate such topics. However, one way to quickly and efficiently explore new solutions is numerical simulations, especially Particle-In-Cell (PIC) simulations if, and only if, one is confidently implementing such aberrated beams which, contrary to a Gaussian beam, do not have analytical solutions. In this research, we propose two new advancements: the correct implementation of aberrated laser beams inside a 3D PIC code, showing a great consistency, under vacuum, compared to the calculations with Fresnel theory); and the correction of their quality via the propagation inside a plasma channel. We demonstrate improvements in the beam pattern, becoming closer to a single plasma mode with less distortions, and thus suggesting a better stability for the targeted application. Through this confident calculation technique for distorted laser beams, we are now expecting to proceed with more accurate PIC simulations, closer to experimental conditions, and obtained results with plasma channels indicate promising future research.

Volume plasma grating by noncollinear interaction of femtosecond filament arrays

Stable propagation of multifilament arrays in transparent bulk media with adjustable separation distances between adjacent child filaments has always been desired for advanced manufacturing. Here, we report on the generation of an ionization-induced volume plasma grating (VPG) by the interaction of two batches of noncollinearly propagating arrays of multiple filaments (AMF). The VPG can externally arrange the propagation of the pulses along regular plasma waveguides via spatial reconstruction of electrical fields, which is compared with the self-formation of randomly distributed multiple filamentation originated from noises. The separation distances of filaments in VPG are controllable by readily changing the crossing angle of the excitation beams. In addition, an innovative method to efficiently fabricate multidimensional grating structures in transparent bulk media through laser modification using VPG was demonstrated.

Generation of multiple obstruction-free channels for free space optical communication

Multi-filament structures produced by vortical high-power femtosecond pulses propagating through clouds and fog can simultaneously clear two channels with cylindrical and annular profile. We present a method to achieve Free Space Optical (FSO) communications through such highly scattering media by propagating appropriately shaped laser modes through these channels. As a proof of concept, we implemented a Laguerre-Gaussian beam as information signal carrier to demonstrate transmission of 543-nm CW laser beam through a 1-m long cloud chamber using both channels. The low power of the information signal in this experiment allows considering applications in Earth-satellite FSO communication.

Ultrafast laser filament-induced fluorescence for detecting uranium stress in Chlamydomonas reinhardtii

Plants and other photosynthetic organisms have been suggested as potential pervasive biosensors for nuclear nonproliferation monitoring. We demonstrate that ultrafast laser filament-induced fluorescence of chlorophyll in the green alga Chlamydomonas reinhardtii is a promising method for remote, in-field detection of stress from exposure to nuclear materials. This method holds an advantage over broad-area surveillance, such as solar-induced fluorescence monitoring, when targeting excitation of a specific plant would improve the detectability, for example when local biota density is low. After exposing C. reinhardtii to uranium, we find that the concentration of chlorophyll a, chlorophyll fluorescence lifetime, and carotenoid content increase. The increased fluorescence lifetime signifies a decrease in non-photochemical quenching. The simultaneous increase in carotenoid content implies oxidative stress, further confirmed by the production of radical oxygen species evidence in the steady-state absorption spectrum. This is potentially a unique signature of uranium, as previous work finds that heavy metal stress generally increases non-photochemical quenching. We identify the temporal profile of the chlorophyll fluorescence to be a distinguishing feature between uranium-exposed and unexposed algae. Discrimination of uranium-exposed samples is possible at a distance of [Formula: see text]35 m with a single laser shot and a modest collection system, as determined through a combination of experiment and simulation of distance-scaled uncertainty in discriminating the temporal profiles. Illustrating the potential for remote detection, detection over 125 m would require 100 laser shots, commensurate with the detection time on the order of 1 s.

Nonlinear Propagation and Filamentation on 100 Meter Air Path of Femtosecond Beam Partitioned by Wire Mesh

High-intensity (∼1 TW/cm2 and higher) region formed in the propagation of ∼60 GW, 90 fs Ti:Sapphire laser pulse on a ∼100 m path in air spans for several tens of meters and includes a plasma filament and a postfilament light channel. The intensity in this extended region is high enough to generate an infrared supercontinuum wing and to initiate laser-induced discharge in the gap between the electrodes. In the experiment and simulations, we delay the high-intensity region along the propagation direction by inserting metal-wire meshes with square cells at the laser system output. We identify the presence of a high-intensity region from the clean-spatial-mode distributions, appearance of the infrared supercontinuum wing, and occurrence of the laser-induced discharge. In the case of free propagation (without any meshes), the onset of the high-intensity zone is at 40-52 m from the laser system output with ∼30 m extension. Insertion of the mesh with 3 mm cells delays the beginning of the high-intensity region to 49-68 m with the same ∼30 m extension. A decrease in the cell size to 1 mm leads to both delay and shrinking of the high-intensity zone to 71-73 m and 6 m, respectively. Three-dimensional simulations in space confirm the mesh-induced delay of the high-intensity zone as the cell size decreases.

Iterative wavefront optimization of ultrafast laser beams carrying orbital angular momentum

Structured intense laser beams offer degrees of freedom that are highly attractive for high-field science applications. However, the performance of high-power laser beams in these applications is often hindered by deviations from the desired spatiotemporal profile. This study reports the wavefront optimization of ultrafast Laguerre-Gaussian beams through the synergy of adaptive optics and genetic algorithm-guided feedback. The results indicate that the intensity fluctuations along the perimeter of the target ring-shaped profile can be reduced up to ∼15%. Furthermore, the radius of the ring beam profile can be tailored to a certain extent by establishing threshold fitting criteria. The versatility of this approach is experimentally demonstrated in conjunction with different focusing geometries.

Experimental study of high-intensity light channels produced on an extended air path by phase and amplitude modulated femtosecond laser pulses

We present the results of our experimental study of the propagation dynamics of high-power femtosecond laser radiation in air with initially imposed amplitude and/or phase modulations. Depending on the modulation type and magnitude, the laser pulse upon nonlinear propagation breaks up into several high-intensity spatially localized light channels, which may or may not contain air plasma and thus are referred to as laser filaments, post-filaments, or plasmaless channels. The pulse modulations are implemented by means of control of the phase or amplitude front using a bimorph deformable mirror or amplitude masks, respectively. We show that the distance of formation and spatial length of high-intensity light channels along a propagation path strongly depend on the shapes and spatial positions of the inhomogeneities created in the transverse phase/amplitude pulse profile, but weakly depend on their sizes.

Generation of radio frequency radiation by femtosecond filaments

Recent experiments have shown that femtosecond filamentation plasmas generate ultrabroadband radio frequency radiation (RF). We show that a combination of plasma dynamics is responsible for the RF: A plasma wake field develops behind the laser pulse, and this wake excites (and copropagates with) a surface wave on the plasma column. The surface wave proceeds to detach from the end of the plasma and propagates forward as the RF pulse. We have developed a four-stage model of these plasma wake surface waves and find that it accurately predicts the RF from a wide range of experiments, including both 800-nm and 3.9-μm laser systems.

Laser-plasma coupling for enhanced ablation of GaAs with combined femtosecond and nanosecond pulses

The laser-plasma interactions that occur during the ablation of solid materials by a femtosecond filament superimposed with a lower-intensity nanosecond pulse are investigated. Pulses of 50 fs duration with intensities of ∼10¹⁴ W/cm² centered at 800 nm are combined with 8 ns pulses at 1064 nm with ∼10¹⁰ W/cm² intensity with delays of ±40 ns on crystalline GaAs targets in air. For each delay, the volume of material removed by a single femtosecond-nanosecond dual-pulse is compared to the laser-plasma interactions that are captured with ultrafast shadowgraph imaging of the plasma and shockwave generated by each pulse. Sedov-Taylor analysis of the shockwaves provides insight on the coupling of energy from the second pulse to the plasma. These dynamics are corroborated with radiation-hydrodynamics simulations. The interaction of the secondary pulse with the pre-existent plasma is shown to play a critical role in enhancing the material removal.

Nanosecond laser coupling for increased filament ablation

Laser filaments can project intensities sufficient to ablate materials at long ranges, but the clamping of a filament's intensity to ∼10¹⁴  W/cm² limits the effective ablation of targets with which the laser pulses interact. We seek to identify regimes in which auxiliary radiation can be used to augment the ablation created by single filaments. In this work, the combination of an 800 nm, 50 fs beam at single filament intensity and a 1064 nm, 8 ns laser pulse is studied. The ablation of GaAs is quantitatively evaluated for varying interpulse delays. Under optimum conditions, an ∼threefold increase in the ablation is observed. The metrology and surface features of the resultant ablation craters are examined to gain insight on the mechanisms of ablation in the dual-pulse cases.

Controlling TW-laser pulse long-range filamentation in air by a deformable mirror

The results of experiments and theoretical modeling of the multiple filamentation of terawatt-power femtosecond laser pulses on a 137 m long air path are presented. We use a multielement optical setup consisting of a Galilean telescope and a deformable bimorph mirror, which allows construction for the desired pulse wavefront at the optical path entrance. By introducing controlled aberrations of the pulse phase profile, we demonstrate the wide-ranging manipulations on the position and spatial structure of the filamentation region. For the first time, to the best of our knowledge, the stable wide-aperture (5 cm in diameter) ring-shaped spatial lattice of high-intense light channels is experimentally realized, which can persist over hundreds of meters in air.

Optical emission from ultrafast laser filament-produced air plasmas in the multiple filament regime

We perform optical emission spectroscopy of ultrafast laser filament-produced air plasmas in the multiple filament regime at driving wavelengths of 400 nm and 800 nm. The spatiotemporal structure of the emission from the plasmas are observed and the emission spectra are used to estimate plasma temperature and density for a range of laser parameters. Plasma temperatures are determined from the molecular nitrogen fluorescence, while the electron densities are estimated from Stark broadening of the oxygen-I 777.19-nm line. Electron temperatures are determined to be in the range of 5000-5200 K and they do not vary significantly along the length of the filament, nor are they sensitive to incident laser energy or wavelength. Electron densities are on order of 10¹⁶ cm^-3 and show a greater variation with axial position, laser energy, and laser wavelength. We discuss mechanisms responsible for spatial localization of emitting species within the filament. Optical emission spectroscopy offers a simple, non-perturbing method to measure filament properties, that allows the information on the associated molecular transitions and excitation/ionization mechanisms to be extracted.

Ultrafast Laser Filament-induced Fluorescence Spectroscopy of Uranyl Fluoride

Uranyl fluoride (UO2F2) is a compound which forms in the reaction between water and uranium hexafluoride, a uranium containing gas widely used for uranium enrichment. Uranyl fluoride exhibits negligible natural background in atmosphere; as a result, its observation implies the presence and active operation of nearby enrichment facilities and could be used as a tracer for treaty verification technologies. Additionally, detection of UO2F2 has a potential application in guiding remediation efforts around enrichment facilities. Laser-induced fluorescence (LIF) has been proposed in the past as a viable technique for the detection and tracking of UO2F2. We demonstrate that ultrafast laser filamentation coupled with LIF extends the capabilities of standard LIF to enable remote detection of UO2F2. An intense femtosecond laser pulse propagated in air collapses into a plasma channel, referred to as a laser filament, allowing for the extended delivery of laser energy. We first investigate the luminescence of UO2F2 excited by the second harmonic of an ultrafast Ti:sapphire laser and subsequently excite it using the conical emission that accompanies ultrafast laser filamentation in air. We measure the decay rates spanning 4.3-5.6 × 104 s-1 and discuss the characteristics of the luminescence for both ultrafast- and filament-excitation. Larger decay rates than those observed using standard LIF are caused by a saturated component of prompt decay from annihilation of dense excited states upon excitation with an ultrafast source. The reproducibility of such decay rates for the given range of incident laser intensities 1.0-1.6 × 1011 W cm-2 is promising for the application of this technique in remote sensing.

Polarization-orthogonal filament array induced by birefringent crystals in air

We demonstrate the generation of filament array with orthogonal polarizations in air by using specifically designed wedge-type birefringent quartz plates. Experimental results show that the number of the generated filaments can be expressed as N = 2n wherenis the number of quartz plates inserted in the laser propagation path. By manipulating the optic axis of the quartz plates with respect to the polarization direction of the input laser pulse, the generated filaments can be separated into two parts with the polarization directions perpendicular with each other. The separation distance between the adjacent filaments is found to be linearly dependent on the focal length of external focusing lens. Our results provide a simple and efficient way to generate regular and reproductive femtosecond filament array in air.

Transition of Femtosecond-Filament-Solid Interactions from Single to Multiple Filament Regime

High-peak-power fs-laser filaments offer unique characteristics attractive to remote sensing via techniques such as remote laser-induced breakdown spectroscopy (R-LIBS). The dynamics of several ablation mechanisms following the interaction between a filament and a solid determines the emission strength and reproducibility of target plasma, which is of relevance for R-LIBS applications. We investigate the space- and time-resolved dynamics of ionic and atomic emission from copper as well as the surrounding atmosphere in order to understand limitations of fs-filament-ablation for standoff energy delivery. Furthermore, we probe the shock front produced from filament-target interaction using time-resolved shadowgraphy and infer laser-material coupling efficiencies for both single and multiple filament regimes through analysis of shock expansion with the Sedov model for point detonation. The results provide insight into plasma structure for the range of peak powers up to 30 times the critical power for filamentation P cr . Despite the stochastic nucleation of multiple filaments at peak-powers greater than 16 P cr , emission of ionic and neutral species increases with pump beam intensity, and short-lived nitrogen emission originating from the ambient is consistently observed. Ultimately, results suggest favorable scaling of emission intensity from target species on the laser pump energy, furthering the prospects for use of filament-solid interactions for remote sensing.

Coupling nonlinear optical waves to photoreactive and phase-separating soft matter: Current status and perspectives

Nonlinear optics and polymer systems are distinct fields that have been studied for decades. These two fields intersect with the observation of nonlinear wave propagation in photoreactive polymer systems. This has led to studies on the nonlinear dynamics of transmitted light in polymer media, particularly for optical self-trapping and optical modulation instability. The irreversibility of polymerization leads to permanent capture of nonlinear optical patterns in the polymer structure, which is a new synthetic route to complex structured soft materials. Over time more intricate polymer systems are employed, whereby nonlinear optical dynamics can couple to nonlinear chemical dynamics, opening opportunities for self-organization. This paper discusses the work to date on nonlinear optical pattern formation processes in polymers. A brief overview of nonlinear optical phenomenon is provided to set the stage for understanding their effects. We review the accomplishments of the field on studying nonlinear waveform propagation in photopolymerizable systems, then discuss our most recent progress in coupling nonlinear optical pattern formation to polymer blends and phase separation. To this end, perspectives on future directions and areas of sustained inquiry are provided. This review highlights the significant opportunity in exploiting nonlinear optical pattern formation in soft matter for the discovery of new light-directed and light-stimulated materials phenomenon, and in turn, soft matter provides a platform by which new nonlinear optical phenomenon may be discovered.

In-situ visualization of multiple filament competition dynamic during nonlinear propagation of femtosecond laser

In this work, multiple filamentation competition of femtosecond pulse in methanol is studied both experimentally and numerically. The visualization of multiple filamentation competition has been realized in the experiment performing the three-photon fluorescence of Coumarin 440. The random changes of multiple filamentation stemmed from the jitter of the peak laser intensity ratio of initial hot spots are first observed directly and visually, which can be well explained by a simplified (2D+1)-dimensional model.

Inhibition of multi-filamentation of high-power laser beams

We experimentally demonstrate the control and complete elimination of multi-filamentation in condensed matter by varying the focusing geometry. In particular, increasing the input beam power enables the extension of the filament length without generating multi-filaments up to 1400 times the critical power in fused silica at an 800 nm wavelength. Furthermore, the generated single filament exhibits spatial solitary wave behavior.

White-light generation control with crossing beams of femtosecond laser pulses

We investigated the variations in generated white-light when crossing two femtosecond laser beams in a Kerr medium. By changing the relative delay of two interacting intense femtosecond laser pulses, we show that white-light generation can be enhanced or suppressed. With a decrease of the relative delay an enhancement of the white-light output was observed, which at even smaller delays was reverted to a suppression of white-light generation. Under choosen conditions, the level of suppression resulted in a white-light output lower than the initial level corresponding to large delays, when the pulses do not overlap in time. The enhancement of the white-light generation takes place in the pulse that is lagging. We found that the effect of the interaction of the beams depends on their relative orientation of polarization and increases when the polarizations are changed from perpendicular to parallel. The observed effects are explained by noting that at intermediate delays, the perturbations introduced in the path of the lagging beam lead to a shortening of the length of filament formation and enhancement of the white-light generation, whereas at small delays the stronger interaction and mutual rescattering reduces the intensity in the central part of the beams, suppressing filamentation and white-light generation.

Spatiotemporal rogue events in optical multiple filamentation

The transient appearance of bright spots in the beam profile of optical filaments formed in xenon is experimentally investigated. Fluence profiles are recorded with high-speed optical cameras at the kilohertz repetition rate of the laser source. A statistical analysis reveals a thresholdlike appearance of heavy-tailed fluence distributions together with the transition from single to multiple filamentation. The multifilament scenario exhibits near-exponential probability density functions, with extreme events exceeding the significant wave height by more than a factor of 10. The extreme events are isolated in space and in time. The macroscopic origin of these experimentally observed heavy-tail statistics is shown to be local refractive index variations inside the nonlinear medium, induced by multiphoton absorption and subsequent plasma thermalization. Microscopically, mergers between filament strings appear to play a decisive role in the observed rogue wave statistics.

Plasma-assisted coherent backscattering for standoff spectroscopy

We show that an intense coherent backward signal can be generated through a Raman-type four-wave-mixing process using forward propagating fields only. Phase matching for this process is achieved through a plasma modulation of the refractive index. Applications to standoff spectroscopy are discussed.

Characteristics of micro air plasma produced by double femtosecond laser pulses

Dynamic characteristics of air plasma generated by focused double collinear femtosecond laser pulses with a time interval of 10 ns are experimentally investigated. The air plasma emission changes significantly when altering the energy ratio between the two laser pulses. Time-resolved shadowgraphic measurements reveal that a small volume of transient vacuum is formed inside the air shock wave produced by the first laser pulse, which causes the second laser pulse induced ionization zone to present as two separate sections in space. Also recorded is strong scattering of the second laser pulse by the ionized air just behind the ionization front of the first laser pulse produced shock wave. Due to the high intensity of the scattered light, coherent Thomson scattering enhanced by plasma instabilities is believed to be the main scattering mechanism in this case.

Loss of phase of collapsing beams

We experimentally investigate the phase of an optical field after it has undergone wave collapse. We confirm the theoretical prediction that it acquires a large cumulative nonlinear phase shift that is highly sensitive to small fluctuations of the laser input power. This results in an effective postcollapse "loss of phase," whereby the phase of the transmitted beam shows a significant increase in sensitivity to the input fluctuations of the pulse energy. We also investigate interactions between two beams that each undergoes collapse and observe large fluctuations in the output mode profiles, which are due to the postcollapse loss of their relative phase difference. Such effects should occur in all systems that exhibit wave collapse.

Broadband supercontinuum generation in air using tightly focused femtosecond laser pulses

Supercontinuum generation in air using tightly focused femtosecond laser pulses was investigated experimentally. Broadband white-light emission covering the whole visible spectral region was generated. Spectral broadening extended only to the blue side of the fundamental frequency due to the phase modulation induced by the strong ionization of air. Numerical simulation was also performed to confirm the spectral broadening mechanism. A constant UV cutoff wavelength close to 400 nm was observed in the supercontinuum spectrum. This phenomenon indicated that intensity clamping still plays a role in tight focusing geometry.

Tightly focused femtosecond laser pulse in air: from filamentation to breakdown

The propagation of tightly focused femtosecond laser pulse with numerical aperture of 0.12 in air is investigated experimentally. The formation and evolution of the filament bunch are recorded by time-resolved shadowgraph with laser energy from 2.4 mJ to 47 mJ. The distribution of electron density in breakdown area is retrieved using Nomarski interferometer. It is found that intensity clamping during filamentation effect still play a role even under strong external focusing. The electron density in some interaction zones is higher than 3 × 10(19) cm(-3), which indicates that each air molecule there is ionized.

Femtosecond multi-filamentation control by mixture of gases: towards synthesised nonlinearity

We have investigated femtosecond multi-filamentation process in a mixture of gases controlling the concentration of atoms versus molecules in the gas cell. The experimental results show that this control could provide a new freedom degree to deterministic spatial distribution control of the multiple filaments. Our simulation indicates surprisingly that only difference of the gases nonlinearity (referred to as "synthesised nonlinearity") is sufficient to be responsible for this control. This study opens the way to provide few-cycle pulses spatial distributed source for spatially encoded measurements and experiments.

Transverse-mode dependence of femtosecond filamentation

We theoretically investigate the transverse-mode dependence of femtosecond filamentation in Ar gas. Three different transverse modes, Bessel, Gaussian, and Laguerre modes, are considered for incident laser pulses. By solving the extended nonlinear Schrödinger equation coupled with the electron density equation, we find that the lengths of the filament and the plasma channel induced by the Bessel incident beam is much longer than the other transverse modes with the same peak intensity, pulse duration, and beam diameter. Moreover we find that the temporal profile of the pulse with the Bessel incident mode is nearly undistorted during the propagation. Since the pulse energy that the Bessel beam can carry is more than one order of magnitude larger than the other modes for the same peak intensity, pulse duration, and beam diameter, the Bessel beam can be a very powerful tool in ultrafast nonlinear optics involving propagation in a Kerr medium.

Characteristics of multiple filaments generated by femtosecond laser pulses in air: prefocused versus free propagation

The characteristics of the multiple filaments formed by prefocused and freely propagating femtosecond laser pulses are investigated and compared. It is shown in our experiments that the diameter, length, stability, and interaction for the two cases can be quite different. The filaments formed by prefocused beam indicate dynamic spatial evolution with higher laser intensity and electron density. They have a typical diameter of 100 microm are of shorter length. In the free propagation case, the filaments exhibit interesting properties such as hundred-meter propagation distance and mm-size diameter. Moreover, only the interaction of the filaments with the energy background affects the evolution of the filaments. Filament-filament interactions such as the filament splitting and merging were not observed in this case.

Modulational instability of spatially broadband nonlinear optical pulses in four-state atomic systems

The modulational instability of broadband optical pulses in a four-state atomic system is investigated. In particular, starting from a recently derived generalized nonlinear Schrödinger equation, a wave-kinetic equation is derived. A comparison between coherent and random-phase wave states is made. It is found that the spatial spectral broadening can contribute to the nonlinear stability of ultrashort optical pulses. In practical terms, this could be achieved by using random-phase plate techniques.

Filamentational instability of partially coherent femtosecond optical pulses in air

The filamentational instability of spatially broadband femtosecond optical pulses in air is investigated by means of a kinetic wave equation for spatially incoherent photons. An explicit expression for the spatial amplification rate is derived and analyzed. It is found that the spatial spectral broadening of the pulse can lead to stabilization of the filamentation instability. Thus optical smoothing techniques could optimize current applications of ultrashort laser pulses, such as atmospheric remote sensing.

Collisional absorption in aluminum

The interaction of ultrashort laser pulses with matter is a topic of growing interest. In particular, recent developments on free-electron lasers have opened an unexplored field in which many interesting physical phenomena are to be expected. Since hydrodynamic descriptions of the interaction process need a microscopic "input," a quantum statistical theory of energy absorption by matter is required. We present a kinetic theory of collisional absorption in dense plasmas and analyze the electron-ion collision frequency in warm dense aluminum in dependence on laser frequency and temperature.

Interaction of light filaments generated by femtosecond laser pulses in air

The interaction of two light filaments propagating in air is simulated. Simulations show that the interaction of the two light filaments displays interesting features such as attraction, fusion, repulsion, and spiral propagation, depending on the relative phase shift and the crossing angle between them. A long and stable channel can be formed by fusing two in-phase light filaments. The channel becomes unstable with the increase of the crossing angle and phase shift. The interaction of two light filaments in different planes is studied and the spiral propagation is observed.

Femtosecond optical vortices in air

We examine the robustness of ultrashort optical vortices propagating freely in the atmosphere. We first approximate the stability regions of femtosecond spinning pulses as a function of their topological charge. Next, we numerically demonstrate that atmospheric optical vortices are capable of conveying high power levels in air over hundreds of meters before they break up into filaments.

Self-organization of spatial solitons

We present experimental results on the transverse modulation instability of an elliptical beam propagating in a bulk nonlinear Kerr medium, and the formation and self-organization of spatial solitons. We have observed the emergence of order, self organization and a transition to an unstable state. Order emerges through the formation of spatial solitons in a periodic array. If the initial period of the array is unstable the solitons will tend to self-organize into a larger (more stable) period. Finally the system transitions to a disordered state where most of the solitons disappear and the beam profile becomes unstable to small changes in the input energy.

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.

Femtosecond pulse propagation in nitrogen: numerical study of (3 + 1)-dimensional extended nonlinear Schrödinger equation with shock-term correction

We develop an accurate and efficient method for calculating evolution due to the extended nonlinear Schrödinger equation, which describes the propagation behavior of a femtosecond light pulse in a nonlinear medium. Applying Suzuki's exponential operator expansion to the evolution operator based on the finite-differential formulation, we realize the accurate and fast calculation that can be performed without large-scale computing systems even for (3 + 1)-dimensional problems. To study the correspondence between experiments and calculations, we calculate the propagation behavior of a femtosecond light pulse that is weakly focused in nitrogen gas of various pressures and compare the calculation results to the experimental ones. The calculation results reproduce the relative behavior of the spatial light pattern observed during the propagation. Additionally, the multiple-cone formation and interaction between two collimated pulses in nitrogen gas are also demonstrated as applications of the developed method.

Stability and transient effects in nanosecond ultraviolet light filaments in air

We investigate the transient behavior and stability of nanosecond duration ultraviolet pulses propagating in air. Both the transient behavior arising from the finite pulse duration and the modulational instability, are found to cause pulses to fragment over lengths on the scale of meters. We discuss the theoretical and experimental implications of the instability and transient effects for long duration pulse propagating in air and generating filaments. In particular, our results imply that continuous-wave models are very limited when used to predict dynamical properties of pulse propagation.

Postionization regimes of femtosecond laser pulses self-channeling in air

An optical self-guiding of femtosecond filaments in air is identified in a regime where plasma generation ceases to support the self-channeling process. Group-velocity dispersion is shown to keep the beam temporally and spatially localized upon a few meters by taking over the ionization of air molecules, once the pulse peak power becomes close to the self-focusing threshold. In this regime, the pulse undergoes slow splitting events that maintain a residual self-guiding with light intensities as high as 10 TW/cm2, as soon as the electron plasma density has fallen down below 10(15) cm(-3).

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.