Optimization of a femtosecond pulse self-compression region along a filament in air

We have identified the pulse self-compression region in a filament produced by 55 fs, 4 mJ, 805 nm radiation propagating in air without geometrical focusing. In our experiment the pulse self-compression region is attained by the propagation distance, where the shortest wavelength in the supercontinuum blue wing reaches a minimum, and the growing conversion efficiency to white light has a large gradient. Numerical tracking of the pulse along the filament shows a single-peak 9 fs pulse with a flat spectral phase at the optimum compression distance.