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.

提出了一种用于模拟探测光穿过等离子体通道后衍射成像过程的分段衍射模型，该模型考虑了等离子体对探测光的散焦效应。将分段衍射模型与现有计算模型进行对比，并将模拟结果与基于纵向衍射测量法的实验结果进行拟合，获得了不同衍射环结构下的电子密度分布。结果表明：分段衍射模型可以拓展探测范围，实现对较高电子密度等离子体的测量。基于分段衍射模型测量电子密度和光丝尺寸的方法为精确诊断光丝提供了一种新思路。

The temporal evolutions of electron density and plasma diameter of 1 kHz femtosecond laser filament in air are experimentally investigated by utilizing a pump-probe longitudinal diffraction method. A model based on scalar diffraction theory is proposed to extract the spatial phase shift of the probe pulse from the diffraction patterns by the laser air plasma channel. The hydrodynamic effect on plasma evolution at 1 kHz filament is included and analyzed. The measured initial peak electron density of ∼1018cm-3 in our experimental conditions decays rapidly by nearly two orders of magnitude within 200 ps. Moreover, the plasma channel size rises from 90 µm to 120 µm as the delay time increases. The experimental observation is in agreement with numerical simulation results by solving the rate equations of the charged particles.

Laser polarization and its intensity inside a filament core play an important role in filament-based applications. However, polarization dependent clamping intensity inside filaments has been overlooked to interpret the polarization-related filamentation phenomena. Here, we report on experimental and numerical investigations of polarization dependent clamping intensity inside a femtosecond filament in air. By adjusting the initial polarization from linear to circular, the clamping intensity is increased by 1.36 times when using a 30 cm focal length lens for filamentation. The results indicate that clamping intensity inside the filament is sensitive to laser polarization, which has to be considered to fully understand polarization-related phenomena.