Investigations of nonlinear femtosecond pulse propagation with the inclusion of Raman, shock, and third-order phase effects

The propagation of intense femtosecond pulses in a nonlinear, dispersive bulk medium is investigated numerically in the regime where the combined effects of diffraction, normal dispersion, and cubic nonlinearity lead to pulse splitting. We present numerical solutions of a modified $(3+1)$-dimensional nonlinear Schr\"odinger equation, accounting for the Raman effect, linear and nonlinear shock terms, third-order dispersion, and initial temporal third-order phase modulation. The calculated results are found to be in good agreement with experimental measurements.