Space–time focusing of femtosecond pulses in a Ti:sapphire laser

We present what is to our knowledge the first three-dimensional model of a femtosecond pulse propagating in a Ti:sapphire laser crystal, which 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 catastrophic selffocusing and self-steepening of the pulse, even though the peak power of the pulse is much greater than the critical power for self-focusing filamentation. Extrapolation of these results to shorter-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.