Um Desenvolvimento Numérico nas Equações Dinâmicas de Sólitons em Fibras Óticas

Queiroz, Diogo Albino de; Natti, Paulo Laerte; Romeiro, Neyva Maria Lopes; Natti, Érica Regina Takano

doi:10.5433/1679-0375.2006v27n2p121

Cited by 3 publications

(3 citation statements)

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“…It should be observed that the perturbed coupled nonlinear Schrödinger differential equations systems, which describe wave propagation in real optical media, do not present analytical solution (Korpinar, 2019). In literature there are several numerical approaches, whose objective is to describe the propagation of perturbed solitons in dielectric environments, most of them using the finite difference method (Cirilo, Natti, Romeiro, Natti, & Oliveira, 2010;Mahboub & Bekhti, 2014;Li, Li, Cao, & Li, 2017) or the finite element method (Queiroz, Natti, Romeiro, & Natti, 2006;Saka, 2012;Karczewska, Rozmej, Szczecinski, & Boguniewicz, 2016). On the other hand, to solve numerically the system of generated equations, authors use various methods like Newton's method (Syafwan, Susanto, Coix, & Malomed, 2012), Crank-Nicolson method (Liang, Khaliq, & Sheng, 2014), Runge-Kutta Method (Shirazi, Solaimani, Farnam, Ghalandari, & Aleomraninejad, 2017), among others (Dehghan & Taleei, 2010;Gupta, Dalal, & Mishra, 2014;Gupta, Dalal, & Mishra, 2015;Choudlhary, Jha, Mishra, & Vandana, 2018).…”

Section: Introductionmentioning

confidence: 99%

Numerical stability of solitons waves through splices in quadratic optical media

et al. 2020

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The propagation of soliton waves is simulated through splices in quadratic optical media, in which fluctuations of dielectric parameters occur. A new numerical scheme was developed to solve the complex system of partial differential equations (PDE) that describes the problem. Our numerical approach to solve the complex problem was based on the mathematical theory of Taylor series of complex functions. In this context, we adapted the Finite Difference Method (FDM) to approximate derivatives of complex functions and resolve the algebraic system, which results from the discretization, implicitly, by means of the relaxation Gauss-Seidel method. The mathematical modeling of local fluctuations of dielectric properties of optical media was performed by Gaussian functions. By simulating soliton wave propagation in optical fibers with Gaussian fluctuations in their dielectric properties, it was observed that the perturbed soliton numerical solution presented higher sensitivity to fluctuations in the dielectric parameter β, a measure of the nonlinearity intensity in the fiber. In order to verify whether the fluctuations of β parameter in the splices of the optical media generate unstable solitons, the propagation of a soliton wave, subject to this perturbation, was simulated for large time intervals. Considering various geometric configurations and intensities of the fluctuations of parameter β, it was found that the perturbed soliton wave stabilizes, i.e., the amplitude of the wave oscillations decreases as the values of propagation distance increases. Therefore, the propagation of perturbed soliton wave presents numerical stability when subjected to local Gaussian fluctuations (perturbations) of the dielectric parameters of the optical media.

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Section: Introductionmentioning

confidence: 99%

Numerical stability of solitons waves through splices in quadratic optical media

et al. 2020

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“…In (QUEIROZ et al, 2006), a adapted numerical procedure provided the numerical solution of (1), when 0 = δ . In the specific case of the propagation of solitons in special optical fibers, and in optimal situations, the walk-off wave phenomenon can be disregarded (ARTIGAS; TORNER; AKHMEDIEV, 1999), which justifies taking 0 = δ in such situations.…”

Section: Solitons In Dielectric Fibersmentioning

confidence: 99%

Sólitons em Fibras Óticas Ideais – Um Desenvolvimento Numérico.

et al. 2010

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ResumoThis work developed a numerical procedure for a system of partial differential equations (PDEs) describing the propagation of solitons in ideal optical fibers. The validation of the procedure was implemented from the numerical comparison between the known analytical solutions of the PDEs system and those obtained by using the numerical procedure developed. It was discovered that the procedure, based on the finite difference method and relaxation Gauss-Seidel method, was adequate in describing the propagation of soliton waves in ideals optical fibers. Key-words: Optical communication. Solitons. Finite differences. Relaxation Gauss-Seidel method. AbstractEste trabalho desenvolveu um procedimento numérico para um sistema de equações diferenciais parciais (EDP's) que descreve a propagação de sólitons em fibras óticas ideais. A validação do procedimento foi implementada a partir da comparação numérica entre as soluções analíticas conhecidas do sistema de EDP's e aquelas obtidas por meio do procedimento numérico desenvolvido. Verificou-se que o procedimento, baseado no método das diferenças finitas e no método de Gauss-Seidel com relaxação, mostrou-se adequado na descrição da propagação das ondas sólitons em fibras óticas ideais. Palavras-chave: Comunicação ótica. Sólitons. Diferenças finitas. Método de Gauss-Seidel com relaxação.

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“…São exemplos de aplicações: escoamentos compressíveis (BONHAUS, 1998), (LE BEAU;, TEZDUYAR, 2006), dinâmica costeira (CARBONEL; GALEÃO), escoamentos bifásicos (SILVA; COUTINHO; PARSONS), dispersão de poluentes e contaminantes (VÁSQUEZ; MEYER, 2005), (MURCIA;LACAZ, 2002), (OLIVEIRA;MEYER, 2006), escoamento confinado com separação (TEZDUYAR; KALRO, 1995), estudo de estabilidade de escoamentos viscoplásticos (BAAIJENS; HULSEN; ANDERSON, 2004), eletromagnetismo (DELIÉGE, 2003) e telecomunicações (QUEIROZ et al, 2006).…”

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Simulação numérica de escoamentos: uma implementação com o método Petrov-Galerkin.

Hwang¹

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O método SUPG ("Streamline Upwind Petrov-Galerkin") é analisado quanto a sua capacidade de estabilizar oscilações numéricas decorrentes de escoamentos convectivo-difusivos, e de manter a consistência nos resultados. Para esta finalidade, é elaborado um programa computacional como uma implementação algorítmica do método, e simulado o escoamento sobre um cilindro fixo a diferentes números de Reynolds. Ao final, é feita uma revelação sobre a solidez do método. Palavras-chave: escoamento, simulação numérica, método Petrov-Galerkin.

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Um Desenvolvimento Numérico nas Equações Dinâmicas de Sólitons em Fibras Óticas

Cited by 3 publications

References 12 publications

Numerical stability of solitons waves through splices in quadratic optical media

Numerical stability of solitons waves through splices in quadratic optical media

Sólitons em Fibras Óticas Ideais – Um Desenvolvimento Numérico.

Simulação numérica de escoamentos: uma implementação com o método Petrov-Galerkin.

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