Spectral dependence of purely-Kerr-driven filamentation in air and argon

Based on numerical simulations, we show that higher-order nonlinear indices (up to $n_8$ and $n_{10}$, respectively) of air and argon have a dominant contribution to both focusing and defocusing in the self-guiding of ultrashort laser pulses over most of the spectrum. Plasma generation and filamentation are therefore decoupled. As a consequence, ultraviolet wavelength may not be the optimal wavelength for applications requiring to maximize ionization.

Figure 1

Maximum on-axis intensity (a), (b), electron density (c), (d), spectral broadening (e), (f), and pulse-averaged ratio $\overline{\xi }$ of the on-axis pulse-averaged contributions of the higher-order Kerr and plasma contributions to the nonlinear refractive index [(g), (h), see text for details], as a function of the wavelength and propagation distance in air (a), (c), (e), (g) and argon (b), (d), (f), (h).

Figure 2

Wavelength dependence close to 800 nm of the electron density generated by a 30-fs pulse of constant intensity 50 TW.

Figure 3

Wavelength dependence of the clamping intensity canceling the Kerr effect $I_{\Delta n_{\mathrm{Kerr}}=0}$, in ${\mathrm{O}}_2$, ${\mathrm{N}}_2$, air, and Ar, based on the dispersion of the higher-order Kerr indices from Eq. (6).

Figure 4

Wavelength dependence of ionization in laser filamentation. (a) Peak electron density; (b) total number of electrons; (c), (d) transverse-integrated longitudinal electron density in air and argon, representative of the electric conductivity of the filament. Note the difference with Figs. 1c and 1d, which is due to the larger filament diameter in the IR.