The characteristics of plasmas play an important role in femtosecond laser filament-based applications. Spectroscopic analysis is used to experimentally investigate the plasma density and its temperature of the air filament under different pulse repetition rates. In our experiments, the measured average plasma density of the filament is 1.54×1017cm-3 and the temperature of the plasma is about 5100 K under 100 Hz pulse repetition rate. The plasma density decreases to 1.43×1017cm-3 and the temperature increases to 6230 K as the pulse repetition rate increases to 1000 Hz. The experimental observation agrees with the numerical simulation by solving the nonlinear Schrödinger equations with repetition rate related “low density hole” correction.

Nonlinear compression has become an obligatory technique along with the development of ultrafast lasers in generating ultrashort pulses with narrow pulse widths and high peak power. In particular, techniques of nonlinear compression have experienced a rapid progress as ytterbium (Yb)-doped lasers with pulse widths in the range from hundreds of femtoseconds to a few picoseconds have become mainstream laser tools for both scientific and industrial applications. Here, we report a simple and stable nonlinear pulse compression technique with high efficiency through cascaded filamentation in air followed by dispersion compensation. Pulses at a center wavelength of 1040 nm with millijoule pulse energy and 160 fs pulse width from a high-power Yb:CaAlGdO₄ regenerative amplifier are compressed to 32 fs, with only 2.4% loss from the filamentation process. The compressed pulse has a stable output power with a root-mean-square variation of 0.2% over 1 hour.

The effects of turbulence intensity and turbulence region on the distribution of femtosecond laser filaments are experimentally elaborated. Through the ultrasonic signals emitted by the filaments, it is observed that increasing turbulence intensity and an expanding turbulence active region cause an increase in the start position of the filament and a decrease in filament length, which can be well explained by theoretical calculation. It is also observed that the random perturbation of the air refractive index caused by atmospheric turbulence expands the spot size of the filament. Additionally, when the turbulence refractive index structure constant reaches 8.37×10-12m-2/3, multiple filaments are formed. Furthermore, the standard deviation of the transverse displacement of filament is found to be proportional to the square root of the turbulent structure constant under the experimental turbulence parameters in this paper. These results contribute to the study of femtosecond laser propagation mechanisms in complex atmospheric turbulence conditions.

As intense, ultrashort, kHz-repetition-rate laser systems become commercially available, pulse cumulative effects are critical for laser filament-based applications. In this work, the pulse repetition-rate effect on femtosecond laser filamentation in air was investigated both numerically and experimentally. The pulse repetition-rate effect has negligible influence at the leading edge of the filament. Clear intensity enhancement from a high-repetition pulse is observed at the peak and tailing edge of the laser filament. As the repetition rate of the laser pulses increases from 100 to 1000 Hz, the length of the filament extends and the intensity inside the filament increases. A physical picture based on the pulse repetition-rate dependent ‘low-density hole’ effect on filamentation is proposed to explain the obtained results well.

It was shown experimentally that for a 65-fs 17-J pulse, the effect of filamentation instability, also known as small-scale self-focusing, is much weaker than that predicted by stationary and nonstationary theoretical models for high B-integral values. Although this discrepancy has been left unexplained at the moment, in practice no signs of filamentation may allow a breakthrough in nonlinear pulse post-compression at high laser energy.