  The filamentational instability of spatially broadband femtosecond optical
pulses in air is investigated by means of a kinetic wave equation for spatially
incoherent photons. An explicit expression for the spatial amplification rate
is derived and analyzed. It is found that the spatial spectral broadening of
the pulse can lead to stabilization of the filamentation instability. Thus,
optical smoothing techniques could optimize current applications of ultra-short
laser pulses, such as atmospheric remote sensing.
