Filamentational Instability of Partially Coherent Femtosecond Optical   Pulses in Air
  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. 
M. Marklund and P. K. Shukla