Influence of self-steepening effect on focusing property of femtosecond pulsed beam

The influence of nonlinear shock on the focusing property of femtosecond pulsed beams was studied through numerical simulation by using the modified(3+1)-dimensional nonlinear Schrodinger equation,taking into account of diffraction effects,space-time coupling,normal dispersion,and cubic nonlinearity.The self-focusing properties of the 90fs pulsed beam were analyzed and discussed in the absence and in presence of shock effect respectively.The results show:The space-time coupling,dispersion,and Kerr effect together will cause the pulse filament,amplitude descending and its width broadening.As implied by the functional form,space-time coupling relates to the dispersion will produce a time shift.The shift increases with distance and dispersion,and that the self-steepening effect will result in the peak power decreasing greatly,moreover it will weak the pulse self-focusing effect.