Numerical Method for Coupled Nonlinear Schrödinger Equations in Few-Mode Fiber
| Autor: | Airat Zh. Sakhabutdinov, Ildaris M. Gabdulkhakov, Vladimir I. Anfinogentov, Oleg G. Morozov, A. Kuznetsov, Vladimir A. Burdin, Vladimir Ivanov, Anton V. Bourdine, M. I. Ryabova, V. V. Ovchinnikov, Dmitry Ivanov |
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| Rok vydání: | 2021 |
| Předmět: |
Raman scattering
Computer science Wave propagation pulse chirping MathematicsofComputing_NUMERICALANALYSIS 02 engineering and technology 01 natural sciences Schrödinger equation 010309 optics Biomaterials symbols.namesake Kerr effect lcsh:TP890-933 implicit/explicit Crank–Nicolson scheme lcsh:TP200-248 ComputingMethodologies_SYMBOLICANDALGEBRAICMANIPULATION 0103 physical sciences Applied mathematics pulse collapse third-order dispersion lcsh:QH301-705.5 Nonlinear Schrödinger equation Civil and Structural Engineering second-order dispersion Independent equation Numerical analysis lcsh:Chemicals: Manufacture use etc Mathematics::Spectral Theory 021001 nanoscience & nanotechnology lcsh:QC1-999 few-mode propagation Numerical integration Nonlinear system nonlinear Schrödinger equation system Fourier transform lcsh:Biology (General) optical pulse compression Mechanics of Materials Ceramics and Composites symbols chirp pulse lcsh:Textile bleaching dyeing printing etc dispersion 0210 nano-technology lcsh:Physics |
| Zdroj: | Fibers Volume 9 Issue 1 Fibers, Vol 9, Iss 1, p 1 (2021) |
| ISSN: | 2079-6439 |
| DOI: | 10.3390/fib9010001 |
| Popis: | This paper discusses novel approaches to the numerical integration of the coupled nonlinear Schrö dinger equations system for few-mode wave propagation. The wave propagation assumes the propagation of up to nine modes of light in an optical fiber. In this case, the light propagation is described by the non-linear coupled Schrö dinger equation system, where propagation of each mode is described by own Schrö dinger equation with other modes&rsquo interactions. In this case, the coupled nonlinear Schrö dinger equation system (CNSES) solving becomes increasingly complex, because each mode affects the propagation of other modes. The suggested solution is based on the direct numerical integration approach, which is based on a finite-difference integration scheme. The well-known explicit finite-difference integration scheme approach fails due to the non-stability of the computing scheme. Owing to this, here we use the combined explicit/implicit finite-difference integration scheme, which is based on the implicit Crank&ndash Nicolson finite-difference scheme. It ensures the stability of the computing scheme. Moreover, this approach allows separating the whole equation system on the independent equation system for each wave mode at each integration step. Additionally, the algorithm of numerical solution refining at each step and the integration method with automatic integration step selection are used. The suggested approach has a higher performance (resolution)&mdash up to three times or more in comparison with the split-step Fourier method&mdash since there is no need to produce direct and inverse Fourier transforms at each integration step. The key advantage of the developed approach is the calculation of any number of modes propagated in the fiber. |
| Databáze: | OpenAIRE |
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