Direct measurement of the plasma density of a femtosecond laser induced-filament in air

The long-range filamentary propagation of an intense femtosecond laser pulse in atmosphere [1] results from the interplay between laser-induced plasma and nonlinear optical response of air molecules. To study the filamentation process in detail, it is crucial to determine the electron density in the transversely confined filament (typical diameter $<$ 100 $\mu $m), which is a challenging task due to the weak ionization (n$_{e}\sim $10$^{14}$-10$^{16}$ cm$^{-3})$. The previously developed techniques, for example, longitudinal spectral interferometry [2], shadowgraphy and optical diffraction [3], electron conductivity [4], and fluorescence spectroscopy [5] can only give crude estimations because they are either lack of spatial resolution or heavily model-dependent. Here we present the direct, radially and axially space-resolved measurement of electron density along an optical filament extending over $\sim $1 m in air. \\[4pt] [1] A. Braun et al., Opt. Lett. 20, 73(1995). \\[0pt] [2] B. La Fontaine et al., Phys. Plasmas 6, 1615 (1999). \\[0pt] [3] S. Tzortzakis et al., Opt. Commun. 181,123 (2000). \\[0pt] [4] R. P. Fischer et al., IEEE Trans. Plasma Sci. 35, 1430 (2007). \\[0pt] [5] J. Bernhardt et al., Opt. Commun. 281, 1268 (2008).