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

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Abstract
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 self-focusing 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.