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.

We compare detailed spatio-temporal propagation simulations with experiments on generation of terahertz (THz) pulses in single filaments with two-color optical excitation, which elucidates the mechanism whereby positively chirped optical pulses lead to the maximum THz yield. The long-wavelength components in the leading edge of the positively chirped 2ω-pulse preserve the overlap with the ω-pulse. The THz yield is extremely sensitive to the temporal overlap: for a 35-fs ω-pulse, the yield decreases by an order of magnitude upon a ω–2ω pulse shift of only 5 fs.

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.

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 $\sim 85°$ 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.

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.

Through numerical simulations we reveal the scenario of $3.9-\mu \mathrm{m}$ filament spectrum enrichment in the atmosphere in the cases of linear and circular polarization of the incident pulse. The discrete spectrum of odd harmonics transforms into the two-octave plateau in the case of linear polarization. In contrast, in the case of circular polarization of the incident pulse, the harmonic-free flat supercontinuum appears with the plasma onset, reaching the tenth harmonic of the input radiation. We identify the energy balance specific to the filamentation near 4 $\mu \mathrm{m}$: the absorption on ${\mathrm{CO}}_2$ lines in the atmosphere is accelerated by the self-phase modulation in the Kerr nonlinearity early before the plasma channel is formed. This nonlinearly enhanced linear absorption overwhelms the plasma losses and conversion of the input pulse energy to the higher harmonics as well as the plateau.