The mid-infrared OPCPA-based laser facilities have recently reached the critical power for self-focusing in air . This ensures the demonstration of the major difference between the mid- and near-infrared filamentation in air: the odd optical harmonics, harshly suppressed by the material dispersion and phase-mismatch in the near-infrared (800 nm), gain reliable energies in the mid-infrared (3.9 µm) filament [1,2].
Another issue that makes mid-infrared filamentation different from the near-infrared one is a lot of molecular vibrational lines belonging to atmospheric constituents and located in the mid-infrared range . As the result the mid-infrared region of interest becomes subdivided into the bands of normal and anomalous dispersion, the former of which leads to the pulse splitting in temporal domain, while the latter produces the confined light bullet.
We simulate the 3.9-µm filamentation using Forward Maxwell equation. We include the tunnel ionization and transient photocurrent as the collapse arresting mechanism, which balances dynamically the instantaneous third-order medium response (similarly to 800-nm filamentation). The key feature that allows us to quantify the losses due to absorption bands is the accurate account of the complex linear absorption index. The absorption index obtained from Mathar model  is interpolated to the fine frequency grid (step of about 0.1 THz), and the refractive index is matched according to Kramers-Krönig relations .
If the initial Gaussian pulse has a center wavelength of 3.9 µm and a duration of 80 fs FWHM, the energy loss in the carbon dioxide (CO_2) absorption band at 4.3 µm is about 1% in the linear propagation regime. But when we take the 80-mJ pulse (about 3 critical powers for self-focusing), the Kerr-induced spectral broadening develops significantly before the clamping level of intensity is reached. In the collimated beam geometry about 2% of the initial pulse energy is absorbed on the CO_2 band before the filament is formed. In the developed filament all the partial losses due to plasma, harmonic generation and absorption on vibrational lines grow up rapidly with the propagation distance, and the absorption on vibrational lines overwhelms all the rest ones. Indeed the new mechanism is revealed – the linear absorption is enhanced by the nonlinear spectral broadening. Thus, the nonlinearly enhanced linear absorption (NELA) is formed. The rotational transitions are estimated to consume as much energy as the free electron generation mechanism , which is less than NELA for 3.9-µm filament.
In conclusion, in the 3.9-µm filament the excitations of molecular absorption lines are estimated to provide the major optical losses in the atmosphere as compared with plasma and high-frequency conversion.
 A. V. Mitrofanov et al., Sci. Rep. 5, 8368 (2015).
 P. Panagiotopoulos et al., Nat. Photonics 9, 543 (2015).
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 N. A. Panov et al., Phys. Rev. A 94, 041801 (2016).
 S. Zahedpour et al., Phys. Rev. Lett. 112, 143601 (2014).
We develop the model of the acoustic wave emission by the femtosecond filament and the model of optical nanosecond pulse guiding in the transient waveguide created as a result of interference of acoustic waves diverging from the filaments array. The numerical algorithms and appropriate solvers are created. In the simulation we identify two regions of time delays between the femtosecond pulse launching the acoustic waves and the nanosecond guided pulse, where the optical guiding is achieved with the high and moderate quality.
Spatio-spectral distribution of THz radiation generated by two-color femtosecond laser breakdown in air is investigated theoretically. The theoretical model is based on the fast oscillating light field propagation and self-consistent free electron generation process. We find that the THz emission spectrum has both the low-frequency component related to the transient photocurrent with the maximum spectral intensity at ~1 THz, and the high-frequency component at ~10 THz related to the nonlinear response of bound electrons.
The possibility of single-cycle infrared pulses generation by for-wave mixing of visible seed radiation with high power
femtosecond filament field with central wavelength of 800 nm is shown. It is determined that phase synchronism does
not play a significant role in this ultrafast nonlinear optical process.
We have demonstrated the possibility to control filamentation in the turbulent atmosphere by means of introduction of regular wavefront perturbations into the initial beam. Statistical processing of simulation results has shown that the spatial position of filaments in turbulence deviates from the similar spatial positions in the regular medium within 10% of the initial perturbation period.
We have shown that control of stochastic multiple filamentation may be performed with either large - scale spatial modifications of the beam, such as squeezing the whole beam, or relatively small-scale periodic light field perturbations introduced into the transverse beam distribution. We have found that the average conversion efficiency to the supercontinuum grows according to the similar law in both small beam and large beam cases, starting from the point of the parent filament formation. Stability of the supercontinuum signal grows essentially with decreasing initial beam size. Periodic intensity and phase perturbations are used to control stochastic filamentation arising in atmospheric turbulence. Regular phase fluctuations are introduced into the beam in the form of a lens array. With decreasing array period the spatial arrangement is attained earlier in the propagation distance. In addition, the amplitude of multiple filaments has smaller fluctuations relatively to the propagation in the regular medium. In the case of periodic intensity perturbations, control of stochastic filaments is more pronounced as compared with the phase perturbations of the same period. However, introduction of amplitude perturbations leads to the energy loss from the initial pulse.