Terahertz beam with radial or orthogonal to laser polarization from a single-color femtosecond filament.

At the selected frequencies from 0.3 to 10 THz we measured the two-dimensional (2D) distributions of fluence and polarization of terahertz (THz) emission from a single-color femtosecond filament. At the majority of frequencies studied, the THz beam has a donut-like shape with azimuthal modulations and radial polarization. At the maximal modulation, THz beam takes the form of the two lobes and polarization of the THz field degenerates into orthogonal to the laser pulse polarization direction. Violation of the radially polarized donut beam shape is due to destructive interference of THz waves driven by light pressure directed along the laser beam propagation axis and ponderomotive force parallel to the laser polarization.

Observation of conical emission from DC-biased filament at 10 THz.

The terahertz (THz) radiation emitted by an air-based femtosecond filament biased by a static electric field is known to have on-axis shape and relatively low frequency spectrum in contrast to the unbiased single-color and two-color schemes. Here, we measure the THz emission of a 15-kV/cm-biased filament in air produced by a 740-nm, 1.8-mJ, 90-fs pulse and demonstrate that a flat-top on-axis THz angular distribution of the emission at 0.5-1 THz transforms into a contrast ring-shaped one at 10 THz.

Flat-top THz directional diagram of a DC-biased filament.

In the experiment, the laser pulse (744 nm, 0.5 mJ, 90 fs) focused into the air gap between the plane electrodes biased by a 10 kV/cm field (DC-biased filament) produced terahertz (THz) radiation. At the selected frequencies of ν=0.3, 0.5, 1 THz, a wide flat-top angular distribution was measured by a bolometer rotating in the plane of the electrodes. The simulations based on the unidirectional pulse propagation equation with fine 0.01 THz resolution and 3 PHz frequency domain showed the transition of the THz directional diagram from the flat-top at ν≲1THz to the conical one at ν>8THz due to the destructive interference of THz waves from the ionization front propagating with the superluminal velocity. Refraction on the plasma is not the major factor in ring formation.

Postfilament supercontinuum on 100 m path in air.

Pulses at 744 nm with 90 fs duration, 6 mJ energy, and a weakly divergent wavefront propagate for more than 100 m and generate a filament followed by an unprecedently long high intensity (≥1TW/cm2) light channel. Over a 20 m long sub-section of this channel, the pulse energy is transferred continuously to the infrared wing, forming spectral humps that extend up to 850 nm. From 3D+time carrier-resolved simulations of 100 m pulse propagation, we show that spectral humps indicate the formation of a train of femtosecond pulses appearing at a predictable position in the propagation path.

Tight focusing of electromagnetic fields by large-aperture mirrors.

We derive nonparaxial input conditions for simulations of tightly focused electromagnetic fields by means of unidirectional nonparaxial vectorial propagation equations. The derivation is based on the geometrical optics transfer of the incident electric field from significantly curved reflecting surfaces such as parabolic and conical mirrors to the input plane, with consideration of the finite thickness of the focusing element and large convergence angles, making the propagation vectorial and nonparaxial. We have benchmarked numerical solutions of propagation equations initiated with the nonparaxial input conditions against the solutions of Maxwell equations obtained by vectorial diffraction integrals. Both transverse and longitudinal components of the electric field obtained by these methods are in excellent agreement.

Ring and unimodal angular-frequency distribution of THz emission from two-color femtosecond plasma spark.

We study angular and frequency-angular distributions of the terahertz (THz) emission of the low-frequency region (0.3-3 THz) from a two-color femtosecond plasma spark experimentally and in three-dimensional numerical simulations. We investigate the dependence of the angular shapes of the THz radiation on focusing conditions and pulse durations by using two laser facilities (pulse durations 35 and 150 fs) for different focusing geometries. Our experiments and simulations show that decrease in the numerical aperture from NA ≈0.2 to NA ≈0.02 results simultaneously in (I) squeezing of the THz angular distribution and (II) formation of the bright conical emission in the THz range. The moderate focusing NA ≈0.05, which forms the relatively narrow unimodal THz angular distribution, is identified as optimal in terms of angular divergence. Numerical simulations with carrier wave resolved show that bright THz ring structures appear at the frequencies ≥2 THz for longer focuses (NA ≈0.02), while for optimal focusing conditions NA ≈0.05 the conical emission develops at THz frequencies higher than 10 THz.

Polarization control of terahertz radiation from two-color femtosecond gas breakdown plasma.

We individually control polarizations of 800 and 400 nm beams, which form a two-color femtosecond plasma filament in air irradiating a linear-to-elliptical THz signal. We detected a threshold-like appearance of THz ellipticity at the angle of ∼85° between the fundamental and second-harmonic field polarization directions. The simulations confirm the abrupt change of THz polarization and reveal that the weak ellipticity of the second harmonic is sufficient to generate essentially elliptical THz radiation.

Fifteen meter long uninterrupted filaments from sub-terawatt ultraviolet pulse in air.

A technique is presented to create uninterrupted long ultraviolet filaments in air using appropriately structured transmission mesh. The mesh with different cell sizes was inserted into 10-cm parallel beam of 0.2-J, 248-nm, and 870-fs pulse propagating along ~100-m corridor. Transverse positions of multiple filaments formed by the optimum size cells were reproducible within at least 15 m along the propagation path. 3D+time simulations confirmed uninterrupted plasma channels with fixed positions in the transverse space similar to the experiment. Unoptimized cell size resulted in filaments shifting towards the cell center and destruction of uninterrupted filaments.

Ultrabroad Terahertz Spectrum Generation from an Air-Based Filament Plasma.

We have solved the long-standing problem of the mechanism of terahertz (THz) generation by a two-color filament in air and found that both neutrals and plasma contribute to the radiation. We reveal that the contribution from neutrals by four-wave mixing is much weaker and higher in frequency than the distinctive plasma lower-frequency contribution. The former is in the forward direction while the latter is in a cone and reveals an abrupt down-shift to the plasma frequency. Ring-shaped spatial distributions of the THz radiation are shown to be of universal nature and they occur in both collimated and focusing propagation geometries. Experimental measurements of the frequency-angular spectrum generated by 130-fs laser pulses agree with numerical simulations based on a unidirectional pulse propagation model.

Propagation equation for tight-focusing by a parabolic mirror.

Part of the chain in petawatt laser systems may involve extreme focusing conditions for which nonparaxial and vectorial effects have high impact on the propagation of radiation. We investigate the possibility of using propagation equations to simulate numerically the focal spot under these conditions. We derive a unidirectional propagation equation for the Hertz vector, describing linear and nonlinear propagation under situations where nonparaxial diffraction and vectorial effects become significant. By comparing our simulations to the results of vector diffraction integrals in the case of linear tight-focusing by a parabolic mirror, we establish a practical criterion for the critical f -number below which initializing a propagation equation with a parabolic input phase becomes inaccurate. We propose a method to find suitable input conditions for propagation equations beyond this limit. Extreme focusing conditions are shown to be modeled accurately by means of numerical simulations of the unidirectional Hertz-vector propagation equation initialized with suitable input conditions.