  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.
