Wavelength scaling of terahertz pulse energies delivered by two-color air plasmas.

We address the long-standing problem of anomalous growth observed in the terahertz (THz) energy yield from air plasmas created by two-color laser pulses, as the fundamental wavelength λ0 is increased. Using two distinct optical parametric amplifiers (OPAs), we report THz energies scaling like λ0α with large exponents 5.6≤α≤14.3, which departs from the growth in λ02 expected from photocurrent theory. By means of comprehensive 3D simulations, we demonstrate that the changes in the laser beam size, pulse duration, and phase-matching conditions in the second-harmonic generation process when tuning the OPA's carrier wavelength can lead to these high scaling powers. The value of the phase angle between the two colors reached at the exit of the doubling crystal turns out to be crucial and even explains non-monotonic behaviors in the measurements.

Creating Complex Optical Longitudinal Polarization Structures.

In this Letter, we show that it is possible to structure the longitudinal polarization component of light. We illustrate our approach by demonstrating linked and knotted longitudinal vortex lines acquired upon nonparaxially propagating a tightly focused subwavelength beam. The remaining degrees of freedom in the transverse polarization components can be exploited to generate customized topological vector beams.

Spectral dynamics of THz pulses generated by two-color laser filaments in air: the role of Kerr nonlinearities and pump wavelength.

We theoretically and numerically study the influence of both instantaneous and Raman-delayed Kerr nonlinearities as well as a long-wavelength pump in the terahertz (THz) emissions produced by two-color femtosecond filaments in air. Although the Raman-delayed nonlinearity induced by air molecules weakens THz generation, four-wave mixing is found to impact the THz spectra accumulated upon propagation via self-, cross-phase modulations and self-steepening. Besides, using the local current theory, we show that the scaling of laser-to-THz conversion efficiency with the fundamental laser wavelength strongly depends on the relative phase between the two colors, the pulse duration and shape, rendering a universal scaling law impossible. Scaling laws in powers of the pump wavelength may only provide a rough estimate of the increase in the THz yield. We confront these results with comprehensive numerical simulations of strongly focused pulses and of filaments propagating over meter-range distances.

Self-Organization of Light in Optical Media with Competing Nonlinearities.

We study the propagation of light beams through optical media with competing nonlocal nonlinearities. We demonstrate that the nonlocality of competing focusing and defocusing nonlinearities gives rise to self-organization and stationary states with stable hexagonal intensity patterns, akin to transverse crystals of light filaments. Signatures of this long-range ordering are shown to be observable in the propagation of light in optical waveguides and even in free space. We consider a specific form of the nonlinear response that arises in atomic vapor upon proper light coupling. Yet, the general phenomenon of self-organization is a generic consequence of competing nonlocal nonlinearities, and may, hence, also be observed in other settings.

Boosting terahertz generation in laser-field ionized gases using a sawtooth wave shape.

Broadband ultrashort terahertz (THz) pulses can be produced using plasma generation in a noble gas ionized by femtosecond two-color pulses. Here we demonstrate that, by using multiple-frequency laser pulses, one can obtain a waveform which optimizes the free electron trajectories in such a way that they acquire the largest drift velocity. This allows us to increase the THz conversion efficiency to 2%, an unprecedented performance for THz generation in gases. In addition to the analytical study of THz generation using a local current model, we perform comprehensive 3D simulations accounting for propagation effects which confirm this prediction. Our results show that THz conversion via tunnel ionization can be greatly improved with well-designed multicolor pulses.

Direct Observation of the Injection Dynamics of a Laser Wakefield Accelerator Using Few-Femtosecond Shadowgraphy.

We present few-femtosecond shadowgraphic snapshots taken during the nonlinear evolution of the plasma wave in a laser wakefield accelerator with transverse synchronized few-cycle probe pulses. These snapshots can be directly associated with the electron density distribution within the plasma wave and give quantitative information about its size and shape. Our results show that self-injection of electrons into the first plasma-wave period is induced by a lengthening of the first plasma period. Three-dimensional particle-in-cell simulations support our observations.

Air-photonics terahertz platform with versatile micro-controller based interface and data acquisition.

We present a terahertz (THz) platform employing air plasma produced by an ultrashort two-color laser pulse as a broadband THz source and air biased coherent detection (ABCD) of the THz field. In contrast to previous studies, a simple peak detector connected to a micro-controller board acquires the ABCD-signal coming from the avalanche photodiode. Numerical simulations of the whole setup yield temporal and spectral profiles of the terahertz electric field in both source and detection area. The latter ones are in excellent agreement with our measurements, confirming THz electric fields with peak amplitude in the MV/cm range. We further illustrate the capabilities of the platform by performing THz spectroscopy of water vapor and a polystyrene reference sample.

Phase-matched high-order harmonic generation in pre-ionized noble gases.

One of the main difficulties of efficiently generating high-order harmonics in long neutral-gas targets is to reach the phase-matching conditions. The issue is that the medium cannot be sufficiently ionized by the driving laser due to plasma defocusing. We propose a method to improve the phase-matching by pre-ionizing the gas using a weak capillary discharge. We have demonstrated this mechanism, for the first time, in absorption-limited XUV generation by an 800 nm femtosecond laser in argon and krypton. The ability to control phase-mismatch is confirmed by an analytical model and numerical simulations of the entire generation process. Our method allows to increase the efficiency of the harmonic generation significantly, paving the way towards photon-hungry applications of these compact short-wavelength sources.

Directionality of terahertz emission from photoinduced gas plasmas.

Forward and backward terahertz emission by ionizing two-color laser pulses in gas is investigated by means of a simple semianalytical model based on Jefimenko's equations and rigorous Maxwell simulations in one and two dimensions. We find the emission in the backward direction has a much smaller spectral bandwidth than in the forward direction and explain this by interference effects. Forward terahertz radiation is generated predominantly at the ionization front and is thus almost not affected by the opacity of the plasma, in excellent agreement with results obtained from a unidirectional pulse propagation model.

Rydberg-induced solitons: three-dimensional self-trapping of matter waves.

We propose a scheme for the creation of stable three-dimensional bright solitons in Bose-Einstein condensates, i.e., the matter-wave analog of so-called spatiotemporal "light bullets." Off-resonant dressing to Rydberg nD states is shown to provide nonlocal attractive interactions, leading to self-trapping of mesoscopic atomic clouds by a collective excitation of a Rydberg atom pair. We present detailed potential calculations and demonstrate the existence of stable solitons under realistic experimental conditions by means of numerical simulations.

Generation of terahertz radiation from ionizing two-color laser pulses in Ar filled metallic hollow waveguides.

The generation of THz radiation from ionizing two-color femtosecond pulses propagating in metallic hollow waveguides filled with Ar is numerically studied. We observe a strong reshaping of the low-frequency part of the spectrum. More precisely, after several millimeters of propagation the spectrum is extended from hundreds of GHz up to approximately 150 THz. For longer propagation distances, nearly single-cycle near-infrared pulses with wavelengths around 4.5 microm are obtained by appropriate spectral filtering, with an efficiency of 0.1-1%.

Ultrafast spatiotemporal dynamics of terahertz generation by ionizing two-color femtosecond pulses in gases.

We present a combined theoretical and experimental study of spatiotemporal propagation effects in terahertz (THz) generation in gases using two-color ionizing laser pulses. The observed strong broadening of the THz spectra with increasing gas pressure reveals the prominent role of spatiotemporal reshaping and of a plasma-induced blueshift of the pump pulses in the generation process. Results obtained from (3+1)-dimensional simulations are in good agreement with experimental findings and clarify the mechanisms responsible for THz emission.

Rotating soliton solutions in nonlocal nonlinear media.

We discuss generic properties of rotating nonlinear wave solutions, the so called azimuthons, in nonlocal media. Variational methods allow us to derive approximative values for the rotating frequency, which is shown to depend crucially on the nonlocal response function. Further on, we link families of azimuthons to internal modes of classical non-rotating stationary solutions, namely vortex and multipole solitons. This offers an exhaustive method to identify azimuthons in a given nonlocal medium.

Stability of two-dimensional spatial solitons in nonlocal nonlinear media.

We discuss the existence and stability of two-dimensional solitons in media with spatially nonlocal nonlinear response. We show that such systems, which include thermal nonlinearity and dipolar Bose-Einstein condensates, may support a variety of stationary localized structures, including rotating dipole solitons. We also demonstrate that the stability of these structures critically depends on the spatial profile of the nonlocal response function.

Theory of terahertz emission from femtosecond-laser-induced microplasmas.

We present a theoretical investigation of terahertz (THz) generation in laser-induced gas plasmas. The work is strongly motivated by recent experimental results on microplasmas, but our general findings are not limited to such a configuration. The electrons and ions are created by tunnel ionization of neutral atoms, and the resulting plasma is heated by collisions. Electrons are driven by electromagnetic, convective, and diffusive sources and produce a macroscopic current which is responsible for THz emission. The model naturally includes both ionization current and transition-Cherenkov mechanisms for THz emission, which are usually investigated separately in the literature. The latter mechanism is shown to dominate for single-color multicycle laser pulses, where the observed THz radiation originates from longitudinal electron currents. However, we find that the often discussed oscillations at the plasma frequency do not contribute to the THz emission spectrum. In order to predict the scaling of the conversion efficiency with pulse energy and focusing conditions, we propose a simplified description that is in excellent agreement with rigorous particle-in-cell simulations.

Self-channeling of ultrashort laser pulses in materials with anomalous dispersion.

The nonlinear dynamics of femtosecond optical pulses propagating in solid media with anomalous group-velocity dispersion (GVD) is investigated. A map fixing the boundaries of collapse or noncollapse regimes for high-power beams versus the relative strength of GVD is first established. Next, from a nonlinear Schrödinger model accounting for higher-order dispersion, self-steepening, and plasma generation, the possibility of producing extended collapse events that promote a long self-guiding is confirmed, in agreement with recent experiments [K.D. Moll and A.L. Gaeta, Opt. Lett. 29, 995 (2004)]. Three-dimensional collapsing pulses are shown to propagate by emitting quasiperiodically bursts of temporally compressed light bullets, with durations close to the single cycle limit.

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.

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.

Stability of weakly nonlinear localized states in attractive potentials.

We analyze the stability of bound states to the nonlinear Schrödinger equation with an "attractive" linear potential and a cubic nonlinearity of arbitrary sign. A sufficient stability criterion is derived, which only requires knowledge of the linear modes of the potential. The results are double-checked numerically for the step-index optical fiber. An estimate of the growth rate versus nonlinearity is established in the limit of weak power.

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.