Stabilization of spatiotemporal solitons in second-harmonic-generating media

Chen, P.Y.P.; Malomed, Boris A.

doi:10.1016/j.optcom.2009.06.027

Cited by 9 publications

(6 citation statements)

References 41 publications

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“…Traveling waves would split into a fundamental and a second harmonic modes. For such a system, the solution principles used in the RTE method remain the same with both u and v involved [19]: As there are two pulse energies E u and E v now involved, we have three choices for assigning energy: The total energy E=E u +E v , or E u and E v by itself.…”

Section: Numerical Example Of Bimodal Wave Propagationmentioning

confidence: 99%

Numerical Solutions of Nonlinear Schrödinger Equation: An Application Example of Nonlinear Analysis

Y.P. Chen

2024

Nonlinear Systems - Recent Advances and Application [Working Title]

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The nonlinear Schrödinger equation is used to show how numerical methods can be used to solve mathematical problems present in nonlinear analysis. The Lanzos-Chevbychev Pseudospectral method is shown to be effective, flexible, and economical to meet various demands in practical applications of mathematical simulations using nonlinear differential equations. The electromagnetic wave propagation through an inhomogeneous, anisotropic, and complex space is used as an example to show how successful mathematical modeling could be used to explain the complex phenomenon of astronomical redshift that is the central issue in the widely debated Hubble tension.

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Section: Numerical Example Of Bimodal Wave Propagationmentioning

confidence: 99%

Numerical Solutions of Nonlinear Schrödinger Equation: An Application Example of Nonlinear Analysis

Y.P. Chen

2024

Nonlinear Systems - Recent Advances and Application [Working Title]

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“…In recent years, an increase in the number of theoretical and experimental works on soliton communications, that aim to overcome the many well-known problems and improve the methods already proposed, was published. Such studies approach themes related to the new soliton generation processes [8,9], soliton propagation processes [10,11] and soliton stabilization processes [12][13][14] in optical fibers.…”

Section: Introductionmentioning

confidence: 99%

“…It should be observed that the perturbed coupled nonlinear Schrödinger differential equations systems, which describe wave propagation in real optical fibers, do not present analytical solution. In the 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 [14,23,24] or the finite element method [25,26]. On the other hand, to solve numerically the resulting system of equations, the authors use various methods like Newton's method [26], Crank-Nicolson method [14], Runge-Kutta Method [27], among others.…”

Section: Introductionmentioning

confidence: 99%

“…In the 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 [14,23,24] or the finite element method [25,26]. On the other hand, to solve numerically the resulting system of equations, the authors use various methods like Newton's method [26], Crank-Nicolson method [14], Runge-Kutta Method [27], among others. A review of the several numerical procedures applied to describe the propagation of solitons in optical fibers is found in [28].…”

Section: Introductionmentioning

confidence: 99%

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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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“…In the literature there are several numerical approaches whose objective is to describe the propagation of solitons in dielectrical environments, most of which use the finite difference method (ISMAIL, 2004;WANG, 2005;CHEN, MALOMED, 2009), the finite element method (DAG, 1999;ISMAIL, 2008) and the split-step method (LIU, 2009 (REICH, 2000), among others. A review of the several numerical procedures applied to describe the propagation of solitons in optical fibers is found in Dehghan and Taleei (2010).…”

Section: Introductionmentioning

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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Stabilization of spatiotemporal solitons in second-harmonic-generating media

Cited by 9 publications

References 41 publications

Numerical Solutions of Nonlinear Schrödinger Equation: An Application Example of Nonlinear Analysis

Numerical Solutions of Nonlinear Schrödinger Equation: An Application Example of Nonlinear Analysis

Numerical stability of solitons waves through splices in quadratic optical media

Sólitons em Fibras Óticas Ideais – Um Desenvolvimento Numérico.

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