Abstract
We present the suitability of two optimized split-step methods for validating the femtosecond pulse propagation problem in the nonlinear fiber optics formalism that is governed by an extended nonlinear Schrödinger equation. In particular, the embedded split-step Fourier method (embedded-SSFM) and the embedded symmetrized split-step Fourier method (embedded-SymSSFM), which are optimized by the implementation of a step size control algorithm, are tested in terms of the femtosecond soliton fission phenomenology to analyze the numerical stability. As a result, it is possible to validate that these numerical methods introduce the appropriate resolution as function of the accuracy order that is needed at different stages of the soliton fission dynamics, which involves very large spectral shifts driven by the interaction between the nonlinear response and the high-order dispersion contribution of the optical fiber. Thus, the presented numerical methods can be used to validate accurately complex processes such as the development of supercontinuum spectra in the current formalism.
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