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Article information
2017 , Volume 22, ¹ 6, p.80-88
Sidelnikov O.S., Redyuk A.A.
Compact finite difference scheme of improved accuracy for Manakov equations
Manakov equations are widely used to numerically simulate the nonlinear propagation of optical pulses through multimode and multicore optical fibers. One of the most important applications of the Manakov equations, taking into account the first derivative with respect to the time variable, refers to the mathematical modelling of extended fiber-optic communication lines based on multimode fibers, when each of several excited spatial modes within one fiber propagates with its own velocity and transfers its information signal. Previously, a compact finite-difference conditionally stable scheme of the increased order of accuracy was proposed for solving the Manakov equations with the first order time derivative. In the paper we propose a new scheme with absolute stability. The scheme has the second order of accuracy in the evolution variable, and the fourth order of accuracy with respect to the time variable. We investigated numerical properties of the proposed scheme and confirm the general order of accuracy using exact solutions of the scalar nonlinear Schrodinger equation and the coupled Schrodinger equations for two polarization components. It was also demonstrated that the proposed scheme allows reduction of the calculation time compared to the split-step Fourier method for modelling the nonlinear propagation of optical signals in multimode fibers within intermediate mode coupling regimes.
[full text]
Keywords: finite-difference scheme, Manakov equations, nonlinear fiber optics, multimode fiber
Author(s):
Sidelnikov Oleg Sergeevich
Position: engineer
Office: Institute of Computational Technologies SB RAS, Novosibirsk State University
Address: 630090, Russia, Novosibirsk, 6, Acad. Lavrentjev avenue
E-mail: o.s.sidelnikov@gmail.com
Redyuk Alexey Alexandrovich
PhD.
Position: Research Scientist
Office: Novosibirsk State University
Address: 630090, Russia, Novosibirsk, Pirogova, 2 str.
E-mail: alexey.redyuk@gmail.com
SPIN-code: 723593 References:
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Bibliography link:
Sidelnikov O.S., Redyuk A.A. Compact finite difference scheme of improved accuracy for Manakov equations // Computational technologies. 2017. V. 22. ¹ 6. P. 80-88
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