Chinese Optics Letters, Volume. 20, Issue 9, 093201(2022)

Time-resolved measurements of electron density and plasma diameter of 1 kHz femtosecond laser filament in air

Hengyi Zheng1,2, Fukang Yin1,2, Tie-Jun Wang1,2,*, Yaoxiang Liu1, Yingxia Wei1, Bin Zhu3, Kainan Zhou3, and Yuxin Leng1,2
Author Affiliations
  • 1State Key Laboratory of High Field Laser Physics, Shanghai Institute of Optics and Fine Mechanics and CAS Center for Excellence in Ultra-intense Laser Science, Chinese Academy of Sciences, Shanghai 201800, China
  • 2Center of Materials Science and Optoelectronics Engineering, University of Chinese Academy of Sciences, Beijing 100049, China
  • 3Laser Fusion Research Center and Science & Technology on Plasma Physics Laboratory, China Academy of Engineering Physics, Mianyang 621999, China
  • show less

    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 1018 cm-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.


    1. Introduction

    Filamentation refers to the phenomenon of the plasma channel generated by the dynamic balance between the optical Kerr self-focusing effect and the plasma defocusing effect caused by the ionization of neutral molecules when an ultrashort pulsed high-intensity laser propagates in a transparent medium such as air[14]. Femtosecond laser filamentation opens up many potential applications involving lightning control[5,6], atmospheric condensation and precipitation[7,8], remote sensing[911], THz emission[12,13], spectral broadening, and pulse compression[14]. Thus, the diagnosis of the filament, such as plasma channel size and electron density, is of great significance for understanding nonlinear propagation and applications of femtosecond laser pulses. The electron density inside the filament depends on external focusing and pulse energy[15]. There have been a variety of methods to experimentally characterize the electron density. Some methods, such as plasma electrical conductivity measurements[16,17], plasma acoustic wave probing[18], and nitrogen fluorescence detection[15], are simple and practicable but need to be calibrated. The other group includes interferometry[1922], holography[2325], and diffractometry[2628], which are based on the pump-probe scheme. For these approaches, the wavefront spatial phase of the probe beam is modulated when it passes through the plasma channel due to the difference of the refractive index between the filamentation region and ambient background. The electron density information can be unveiled through the phase change. Thus, time-resolved measurement can be achieved using time delay between the filamenting pulse and probe pulse. Typical interferometry provides more information, especially on axially resolved electron density distribution. In an interferometric scheme, the probe is typically split into two beams to record the interference fringes on the CCD. The spatiotemporal synchronization of the two beams is required. Longitudinal diffractometry is much simpler with the sacrifice of the axially resolved information. The ionized plasmas produced by ultrafast laser pulse recombine to neutrals in a time range of a few nanoseconds with their energy repartition into molecules in translational, rotational, and vibrational energies[29]. The localized energy deposition subsequently launches an acoustic wave along the radial direction. As a consequence, a low-density air channel is established. After a few microseconds, the air pressure forms a quasi-equilibrium. The temperature decreases radially, and the gas density changes inversely to the temperature. Then, the density depression decay is dominated by thermal diffusion on millisecond timescales[2933]. Hence, there exists a low-density air channel generated by the cumulative effect of a high repetition rate pulse train. The phenomenon of femtosecond filaments that generate long-lived underdense channels was observed by Cheng et al.[29] experimentally using 0.7 mJ pump pulse energy at a repetition rate of kilohertz. Following the study, Point et al.[32] proved that the low-density channel could last more than 90 ms after filamentation in the case of 5 mJ laser pulse energy under tight focusing. After many pulses pass through, the low air density channel will stabilize when every following pump pulse comes for the laser repetition higher than 10 Hz. Previous studies using longitudinal diffractometry[15,26,34] considered that the effect of the low-density electrons on the probe only contributes the additional phase shift term of the complex amplitude at the exit of the plasma channel. The defocusing effect on the intensity distribution was assumed to be negligible. But, the intensity of the probe does experience defocusing effects, especially at the electron density in air filament. Moreover, the previous works ignored the existence of the long-lived underdense air channels under the experimental conditions of high repetition rate, which would affect the accuracy of the measurement results.


    Get Citation

    Copy Citation Text

    Hengyi Zheng, Fukang Yin, Tie-Jun Wang, Yaoxiang Liu, Yingxia Wei, Bin Zhu, Kainan Zhou, Yuxin Leng. Time-resolved measurements of electron density and plasma diameter of 1 kHz femtosecond laser filament in air[J]. Chinese Optics Letters, 2022, 20(9): 093201

    Download Citation

    EndNote(RIS)BibTexPlain Text
    Save article for my favorites
    Paper Information

    Category: Ultrafast Optics and Attosecond/High-field Physics

    Received: Apr. 25, 2022

    Accepted: May. 20, 2022

    Posted: May. 23, 2022

    Published Online: Jun. 16, 2022

    The Author Email: Tie-Jun Wang (



    Please enter the answer below before you can view the full text.