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Article

Original Solution of Coupled Nonlinear Schrödinger Equations for Simulation of Ultrashort Optical Pulse Propagation in a Birefringent 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, Rep. Tatarstan 420111, Russia
2
Department of Communication Lines, Povozhskiy State University of Telecommunications and Informatics, 23, Lev Tolstoy street, Samara 443010, Russia
3
JSC “Scientific Production Association State Optical Institute Named after Vavilov S.I.”, 36/1, Babushkin street, Saint Petersburg 192171, Russia
*
Author to whom correspondence should be addressed.
Fibers 2020, 8(6), 34; https://doi.org/10.3390/fib8060034
Received: 4 May 2020 / Revised: 25 May 2020 / Accepted: 28 May 2020 / Published: 3 June 2020
(This article belongs to the Special Issue Optical Fibers as a Key Element of Distributed Sensor Systems)
This paper discusses approaches to the numerical integration of the coupled nonlinear Schrödinger equations system, different from the generally accepted approach based on the method of splitting according to physical processes. A combined explicit/implicit finite-difference integration scheme based on the implicit Crank–Nicolson finite-difference scheme is proposed and substantiated. It allows the integration of a nonlinear system of equations with a choice of nonlinear terms from the previous integration step. The main advantages of the proposed method are: its absolute stability through the use of an implicit finite-difference integration scheme and an integrated mechanism for refining the numerical solution at each step; integration with automatic step selection; performance gains (or resolutions) up to three or more orders of magnitude due to the fact that there is no need to produce direct and inverse Fourier transforms at each integration step, as is required in the method of splitting according to physical processes. An additional advantage of the proposed method is the ability to calculate the interaction with an arbitrary number of propagation modes in the fiber.
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Keywords: nonlinear Schrödinger equations system; birefringent fiber; few-mode propagation; Kerr effect; Raman scattering; dispersion; implicit/explicit Crank–Nicolson scheme nonlinear Schrödinger equations system; birefringent fiber; few-mode propagation; Kerr effect; Raman scattering; dispersion; implicit/explicit Crank–Nicolson scheme
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MDPI and ACS Style

Zhavdatovich Sakhabutdinov, A.; Ivanovich Anfinogentov, V.; Gennadievich Morozov, O.; Alexandrovich Burdin, V.; Vladimirovich Bourdine, A.; Mudarrisovich Gabdulkhakov, I.; Anatolievich Kuznetsov, A. Original Solution of Coupled Nonlinear Schrödinger Equations for Simulation of Ultrashort Optical Pulse Propagation in a Birefringent Fiber. Fibers 2020, 8, 34. https://doi.org/10.3390/fib8060034

AMA Style

Zhavdatovich Sakhabutdinov A, Ivanovich Anfinogentov V, Gennadievich Morozov O, Alexandrovich Burdin V, Vladimirovich Bourdine A, Mudarrisovich Gabdulkhakov I, Anatolievich Kuznetsov A. Original Solution of Coupled Nonlinear Schrödinger Equations for Simulation of Ultrashort Optical Pulse Propagation in a Birefringent Fiber. Fibers. 2020; 8(6):34. https://doi.org/10.3390/fib8060034

Chicago/Turabian Style

Zhavdatovich Sakhabutdinov, Airat; Ivanovich Anfinogentov, Vladimir; Gennadievich Morozov, Oleg; Alexandrovich Burdin, Vladimir; Vladimirovich Bourdine, Anton; Mudarrisovich Gabdulkhakov, Ildaris; Anatolievich Kuznetsov, Artem. 2020. "Original Solution of Coupled Nonlinear Schrödinger Equations for Simulation of Ultrashort Optical Pulse Propagation in a Birefringent Fiber" Fibers 8, no. 6: 34. https://doi.org/10.3390/fib8060034

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