Fig. 1. Maximal on-axis intensities of femtosecond laser pulses as a function of propagation distance for 100 and 1000 Hz repetition rates with different pulse energies of (a) 0.1 mJ, (b) 0.2 mJ, (c) 0.7 mJ and (d) 1.2 mJ. The geometric focus position is defined as 0 of the propagation distance and the negative values are before the focus. The inset of (a) shows the enlargement of the shadow region of (a).

Fig. 2. Experimental setup.

Fig. 3. The typical spectrum images and intensity plots captured by the ICCD mounted on the spectrometer: (a) is in non-divided imaging mode, while (b) and (c) are centered at the wavelengths of 337 and 391 nm, respectively. The laser pulse energy and repetition rate are 1.2 mJ and 1000 Hz, respectively.

Fig. 4. Longitudinal distribution of the nitrogen 337 and 391 nm fluorescence signal along the filaments under filament repetition rates of (a) 100 Hz and (b) 1000 Hz. The geometric focus position is defined as 0 of the propagation position and the negative values are before the focus. The laser pulse energy is 1.2 mJ for filamentation.

Fig. 5. The laser peak intensities with different incident laser pulse energies of (a) 0.1 mJ, (b) 0.2 mJ, (c) 0.7 mJ and (d) 1.2 mJ under different laser repetition rates (black line, 100 Hz; red line, 1 kHz), as determined by Equation (10).

Fig. 6. Experimentally measured average intensity of the filament as a function of (a) incident energy and (b) laser repetition rate (the incident energy is 1.2 mJ). The filament range is defined by specifying the filamentation initiation and termination when the total fluorescence intensity approaches 1/e of the maximum intensity. (c) Numerically obtained average intensity of the filamentation zone as a function of incident energy for laser repetition rates of 100 and 1000 Hz. (d) Numerically obtained average intensity of the filamentation zone as a function of laser repetition rates for incident energy of 1.2 mJ. (e) The radial distributions of the gas density hole generated by 100 and 1000 Hz repetition-rate lasers.