Source: http://jme.ojs.galoa.net.br/index.php/jme/article/view/20
Timestamp: 2019-04-22 22:12:48+00:00

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Simulating the propagation of optical pulses in a single mode optical fiber is of fundamental importance for studying the several effects that may occur within such medium when it is under some linear and nonlinear effects. In this work, we simulate it by implementing the nonlinear Schrödinger equation using the Split-Step Fourier method in some of its approaches. Then, we compare their running time, algorithm complexity and accuracy regarding energy conservation of the optical pulse. We note that the method is simple to implement and presents good results of energy conservation, besides low temporal cost. We observe a greater precision for the symmetrized approach, although its running time can be up to 126% higher than the other approaches, depending on the parameters set. We conclude that the time window must be adjusted for each length of propagation in the fiber, so that the error regarding energy conservation during propagation can be reduced.
AGRAWAL, G. P. Nonlinear Fiber Optics. 3rd. ed. San Diego, USA: Academic Press, 2001.
BALAC, S.; FERNANDEZ, A. Mathematical analysis of adaptive step-size techniques when solving the nonlinear schrödinger equation for simulating light-wave propagation in optical fibers. Optics Communications, Elsevier, v. 329, n. 1, p. 1–9, 2014.
in optics. Journal of Computational Physics, Elsevier, v. 280, n. 1, p. 295–305, 2015.
Turkic World Mathematical Society, v. 5, n. 2, p. 298–307, 2015.
DUO, S.; ZHANG, Y. Mass-conservative fourier spectral methods for solving the fractional nonlinear schrödinger equation. Computers & Mathematics with Applications, Elsevier, v. 71, n. 11, p. 2257–2271, 2016.
GROSZ, D. Efeitos não lineares em sistemas de comunicação óptica de longas distâncias e altas taxas. Tese (Doutorado em Física) — Instituto de Física da Unicamp, Campinas, 1998.
KEISER, G. Optical Fibers Communications. 3rd. ed. USA: McGraw-Hill, 2000.
Presbiteriana Mackenzie, São Paulo, 2010.
LIN, C.-Y.; ASIF, R.; HOLTMANNSPOETTER, M.; SCHMAUSS, B. Step-size selection for split-step based nonlinear compensation with coherent detection in 112-gb/s 16-qam transmission. Chinese Optics Letters, Chinese Optical Society, v. 10, n. 2, p. 020605, 2012.
LIU, X. Adaptive higher-order split-step fourier algorithm for simulating lightwave propagation in optical fiber. Optics Communications, Elsevier, v. 282, n. 7, p. 1435–1439, 2009.
MUSLU, G. M.; ERBAY, H. Higher-order split-step fourier schemes for the generalized nonlinear schrödinger equation. Mathematics and Computers in Simulation, Elsevier, v. 67, n. 6, p. 581–595, 2005.
RIBEIRO, J. A. J. Comunicações Ópticas. 4. ed. São Paulo: Saraiva, 2003.
SHAO, J.; LIANG, X.; KUMAR, S. Comparison of split-step fourier schemes for simulating fiber optic communication systems. IEEE Photonics Journal, IEEE, v. 6, n. 4, p. 7200515, 2014.
SHAO, J.; LIANG, X.; KUMAR, S. An efficient scheme of split-step fourier method for fiber optic communication systems. In: INTERNATIONAL SOCIETY FOR OPTICS AND PHOTONICS. Photonics North 2014. Montréal, Canada, 2014. v. 9288, p. 928806.
WASHBURN, B. Numerical Solutions to the nonlinear Schrödinger Equation. (Thesis). Atlanta, GA, 2002. 134–157 p.
ZHANG, J.; LI, X.; DONG, Z. Digital nonlinear compensation based on the modified logarithmic step size. Journal of Lightwave Technology, IEEE, v. 31, n. 22, p. 3546–3555, 2013.

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