We use a phase-retrieval cross-correlation technique to analyze the spatiot
emporal field evolution of self-focused ultrashort pulses. The technique fe
atures a new phase-retrieval algorithm based on functional differentiation.
Its sensitivity, rapid convergence, and temporal nonreciprocality enable r
eliable three-dimensional waveform reconstruction. At less than the critica
l power, the experiments verify conventional description of self-focusing a
nd give a direct proof of the Kerr-lens mode-locking mechanism. In contrast
, for pulses with peak power much more than the critical power, nearly unif
orm self-focusing and quasi-stable single-filament trapping to a universal
beam diameter were observed. The trapping can be explained by the saturatio
n of the nonlinear refractive-index change at Delta n similar to 7 x 10(-5)
. The saturation is verified by an independent cross-polarization modulatio
n measurement. (C) 2000 Optical Society of America [S0740-3224(00)02108-1].