Sensitivity of propagation and energy deposition in femtosecond filamentation to the nonlinear refractive index

The axial dependence of femtosecond filamentation in air is measured under conditions of varying laser pulsewidth, energy, and focusing f-number. Filaments are characterized by the ultrafast z-dependent absorption of energy from the laser pulse and diagnosed by measuring the local single cycle acoustic wave generated. Results are compared to 2D+1 simulations of pulse propagation, whose results are highly sensitive to the instantaneous (electronic) part of the nonlinear response of $N_2$ and $O_2$. We find that recent measurements of the nonlinear refractive index ($n_2$) in [J.K. Wahlstrand et al., Phys. Rev. A. 85, 043820 (2012)] provide the best match and an excellent fit between experiments and simulations.