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Open AccessArticle

Numerical Method for Coupled Nonlinear Schrödinger Equations in Few-Mode Fiber

1
Department of Radiophotonics and Microwave Theory, Kazan National Research State University Named after A.N. Tupolev-KAI, 31/7, Karl Marx street, Kazan, 420111 Rep. Tatarstan, Russia
2
Department of Communication Lines, Povozhskiy State University of Telecommunications and Informatics, 23, Lev Tolstoy street, 443010 Samara, Russia
3
JSC “Scientific Production Association State Optical Institute Named after Vavilov S.I.”, 36/1, Babushkin street, 192171 Saint Petersburg, Russia
4
Volga State University of Technology, 3, Lenin Sq., Yoshkar-Ola, 424000 Rep. Mari El, Russia
*
Author to whom correspondence should be addressed.
Fibers 2021, 9(1), 1; https://doi.org/10.3390/fib9010001
Received: 9 December 2020 / Revised: 24 December 2020 / Accepted: 28 December 2020 / Published: 2 January 2021
(This article belongs to the Special Issue Optical Fibers as a Key Element of Distributed Sensor Systems)
This paper discusses novel approaches to the numerical integration of the coupled nonlinear Schrödinger 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 Schrödinger equation system, where propagation of each mode is described by own Schrödinger equation with other modes’ interactions. In this case, the coupled nonlinear Schrödinger 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–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)—up to three times or more in comparison with the split-step Fourier method—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. View Full-Text
Keywords: nonlinear Schrödinger equation system; Raman scattering; Kerr effect; dispersion; implicit/explicit Crank–Nicolson scheme; pulse chirping; few-mode propagation; second-order dispersion; third-order dispersion; chirp pulse; optical pulse compression; pulse collapse nonlinear Schrödinger equation system; Raman scattering; Kerr effect; dispersion; implicit/explicit Crank–Nicolson scheme; pulse chirping; few-mode propagation; second-order dispersion; third-order dispersion; chirp pulse; optical pulse compression; pulse collapse
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MDPI and ACS Style

Sakhabutdinov, A.Z..; Anfinogentov, V.I.; Morozov, O.G.; Burdin, V.A.; Bourdine, A.V.; Kuznetsov, A.A.; Ivanov, D.V.; Ivanov, V.A.; Ryabova, M.I.; Ovchinnikov, V.V. Numerical Method for Coupled Nonlinear Schrödinger Equations in Few-Mode Fiber. Fibers 2021, 9, 1. https://doi.org/10.3390/fib9010001

AMA Style

Sakhabutdinov AZ, Anfinogentov VI, Morozov OG, Burdin VA, Bourdine AV, Kuznetsov AA, Ivanov DV, Ivanov VA, Ryabova MI, Ovchinnikov VV. Numerical Method for Coupled Nonlinear Schrödinger Equations in Few-Mode Fiber. Fibers. 2021; 9(1):1. https://doi.org/10.3390/fib9010001

Chicago/Turabian Style

Sakhabutdinov, Airat Z..; Anfinogentov, Vladimir I.; Morozov, Oleg G.; Burdin, Vladimir A.; Bourdine, Anton V.; Kuznetsov, Artem A.; Ivanov, Dmitry V.; Ivanov, Vladimir A.; Ryabova, Maria I.; Ovchinnikov, Vladimir V. 2021. "Numerical Method for Coupled Nonlinear Schrödinger Equations in Few-Mode Fiber" Fibers 9, no. 1: 1. https://doi.org/10.3390/fib9010001

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