We present what is to our knowledge the first three-dimensional model
of a femtosecond pulse propagating in a Ti:sapphire laser crystal, whi
ch includes dispersion, self-focusing, and finite response time of the
medium and does not assume the slowly varying envelope approximation.
The combined action of material dispersion and phase modulation leads
to a dramatic space-time focusing on the pulse. Dispersion prevents c
atastrophic self-focusing and self-steepening of the pulse, even thoug
h the peak power of the pulse is much greater than the critical power
for self-focusing filamentation. Extrapolation of these results to sho
rter-pulse durations shows that this space-time focusing mechanism can
operate even for pulses with durations close to the response time of
the Kerr nonlinearity.