The common practice is to derive in the time domain the equations for the nonlinear propagation of ultrashort pulses and to solve them by the split-step Fourier method. When fields at different frequencies propagate and interact in a fiber, it is also usual to write a distinct equation for each of these fields. This implicitly assumes that the spectra of these various fields do not overlap, which may no longer be the case for femtosecond pulses. It then becomes necessary to consider the propagation of the total field as a whole. Moreover, for such broad field spectra the dispersion of higher orders must be taken into account, which can be dealt with in the frequency domain without any difficulty. It is shown that writing the equations for the total field presents many advantages, and an alternative to the split-step Fourier method is proposed, based on an integration rule of higher order.
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