Pulse repetition rate effect on the intensity inside femtosecond laser filament in air

Fig.1. Maximal on-axis intensities of femtosecond laser pulses as a function of propagation distance for 100 Hz and 1000Hz repetition rates with different pulse energies of (a) 0.1mJ, (b) 0.2mJ, (c) 0.7mJ, (d) 1.2mJ. The geometric focus position is defined as 0 of the propagation distance and negative value is before the focus. The inset of (a) shows the enlargement of the shadow region of (a)Fig.2. Experimental setupFig.2. The typical spectrum images and intensity plots captured by the ICCD mounted on the spectrometer. (a) is in non-divided imaging mode. (b) and (c) are centered at the wavelengths of 337nm and 391nm. Laser pulse energy and repetition rate are 1.2 mJ and 1000 Hz, respectively.Fig.4. The laser peak intensities with different incident laser pulse energies (a) 0.1mJ, (b) 0.2mJ, (c) 0.7mJ, (d) 1.2mJ, under different laser repetition rates (black line:100Hz, red line:1kHz ) as determined by Eq (10). Fig.5. Longitudinal distribution of the nitrogen 337nm and 391nm fluorescence signal along filaments under filament repetition rates of (a) 100 Hz and (b) 1000Hz. The geometric focus position is defined as 0 of the propagation position and the negative values are before the focus. Laser pulse energy is 1.2mJ for filamentation.Fig.6. Experimentally measured average intensity of the filament as a function of (a) incident energy, (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 filamentation zone as a function of incident energy for laser repetition rates of 100 Hz and 1000 Hz. (d) Numerically obtained average intensity of filamentation zone as a function of laser repetition rates for incident energy of 1.2mJ. (e) The radial distributions of the gas density hole generated by 100 Hz and 1000 Hz repetition rate lasers.