WIAS Preprint No. 2975, (2022)

Spurious four-wave mixing processes in generalized nonlinear Schrödinger equations


Authors

  • Severing, Fenja
  • Bandelow, Uwe
    ORCID: 0000-0003-3677-2347
  • Amiranashvili, Shalva
    ORCID: 0000-0002-8132-882X

2020 Mathematics Subject Classification

  • 78A40 78A60 91G60

Keywords

  • Nonlinear fibers, numerical analysis, modulation instability (MI), four-wave mixing (FWM), non-linear Schrödinger equation (NLSE), generalized nonlinear Schrödinger equation (GNLSE), split-step Fourier method (SSFM), supercontinuum generation

Abstract

Numerical solutions of a nonlinear Schödinger equation, e.g., for pulses in optical fibers, may suffer from the spurious four-wave mixing processes. We study how these nonphysical resonances appear in solutions of a much more stiff generalized nonlinear Schödinger equation with an arbitrary dispersion operator and determine the necessary restrictions on temporal and spatial resolution of a numerical scheme. The restrictions are especially important to meet when an envelope equation is applied in a wide spectral window, e.g., to describe supercontinuum generation, in which case the appearance of the numerical instabilities can occur unnoticed.

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