Conservation laws of femtosecond pulse propagation described by generalized nonlinear Schrödinger equation with cubic nonlinearity

Trofimov, Vyacheslav A.; Stepanenko, S. V.; Razgulin, A. V.

doi:10.1016/j.matcom.2020.11.009

Cited by 4 publications

(6 citation statements)

References 40 publications

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“…To calculate the sample transmission versus intensity for different pulse durations, a numerical model of nonlinear propagation and interaction of radiation with optically transparent Kerr media developed by the Laboratory of Mathematical Modeling in Physics (MSU) was used [11,12]. The model is based on solving the nonlinear Schrödinger equation obtained in the slowly varying wave approximation [13] with the plasma generation equation [14]:…”

Section: Numerical Results and Discussionmentioning

confidence: 99%

Multiphoton and plasma absorption measurements in CaF₂ and UV fused silica at 473 nm

Grudtsyn¹,

Koribut²,

Rogashevskii³

et al. 2021

Laser Phys. Lett.

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Transmission versus intensity in 100 μm CaF2 and UV fused silica samples at a wavelength of 473 nm for different durations of the initial pulse was studied. Fitting the experimental data with a model based on the solution of the nonlinear Schrödinger equation and taking into account multiphoton absorption and absorption by the plasma, as well as the Kerr nonlinearity, diffraction and dispersion of the medium, made it possible to obtain the values of multiphoton (k-number of photons) σk and plasma absorption (inverse bremsstrahlung) σ cross sections. The obtained values are σ 4 = 2.5 × 10−117 cm8 s3, σ = 3.6 × 10−18 cm2 for CaF2 and σ 4 = 4.4 × 10−116 cm8 s3, σ = 3 × 10−18 cm2 for UV fused silica.

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Section: Numerical Results and Discussionmentioning

confidence: 99%

Multiphoton and plasma absorption measurements in CaF₂ and UV fused silica at 473 nm

Grudtsyn¹,

Koribut²,

Rogashevskii³

et al. 2021

Laser Phys. Lett.

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“…When simulating the propagation of optical pulses with a duration of fewer than ten ps in an optical fiber, it is necessary to consider the higher-order chromatic dispersion and Raman scattering. This leads to the inclusion of additional terms in the equations and, as a result, the transition to generalized nonlinear Schrödinger equation GNLSE [11][12][13][35][36][37][38][39]. The use of SSFM for the GNLSE solution becomes significantly more complicated than for the usual NLSE, since the nonlinear operator of GNLSE includes the derivatives of the complex amplitude and its functions in time.…”

Section: Introductionmentioning

confidence: 99%

“…The use of SSFM for the GNLSE solution becomes significantly more complicated than for the usual NLSE, since the nonlinear operator of GNLSE includes the derivatives of the complex amplitude and its functions in time. All of this stimulates interest in the development of algorithms for modeling the propagation of ultrashort optical pulses in optical fibers based on the direct solutions to Maxwell's equations, by the finite difference time domain method (FDTD) [40][41][42][43][44][45][46], GNLSE solutions by finite-difference methods [22,23,38,[47][48][49][50], and, of course, based on GNLSE solutions using improved SSFM algorithms [51][52][53][54][55].…”

Section: Introductionmentioning

confidence: 99%

Algorithm for Solving a System of Coupled Nonlinear Schrödinger Equations by the Split-Step Method to Describe the Evolution of a High-Power Femtosecond Optical Pulse in an Optical Polarization Maintaining Fiber

Bourdine

Burdin

Morozov

2022

Fibers

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This article proposes an advanced algorithm for the numerical solution of a coupled nonlinear Schrödinger equations system describing the evolution of a high-power femtosecond optical pulse in a single-mode polarization-maintaining optical fiber. We use the algorithm based on a variant of the split-step method with the Madelung transform to calculate the complex amplitude when executing a nonlinear operator. In contrast to the known solution, the proposed algorithm eliminates the need to numerically solve differential equations directly, concerning the phase of complex amplitude when executing the nonlinear operator. This made it possible, other things being equal, to reduce the computation time by more than four times.

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“…Due to a complexity of the partial differential equations, such as GLE, and nonlinear Schrödinger equation (NLSE), Gross-Pitaevskii equation, Klein-Gordon equation, and Korteweg-De Vries equation, and others, the exact solutions can be obtained only in particular cases or maybe with strict assumptions. Therefore, solving these problems via computer simulations is an attractive issue and many numerical methods have been proposed and investigated [42][43][44][45][46][47][48][49][50][51][52][53][54][55][56][57][58][59][60][61].…”

Section: Introductionmentioning

confidence: 99%

“…Therefore, many authors have directed their efforts towards developing conservative FDSs for a solution of the nonlinear problem. Among them we emphasize the problem of finding numerical solutions of the NLSE [49][50][51][52][53][54][55][56][57][58][59][60][61]. In [51], a splitting method for the cubic NLSE on a torus that possesses a long-time near-conservation of energy is applied and investigated.…”

Section: Introductionmentioning

confidence: 99%

Conservative Finite-Difference Scheme for 1D Ginzburg–Landau Equation

et al. 2022

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In this study, our attention is focused on deriving integrals of motion (conservation laws; invariants) for the problem of an optical pulse propagation in an optical fiber containing an optical amplifier or attenuator because, to date, such invariants are absent in the literature. The knowledge of a problem’s invariants allows us develop finite-difference schemes possessing the conservativeness property, which is crucial for solving nonlinear problems. Laser pulse propagation is governed by the nonlinear Ginzburg–Landau equation. Firstly, the problem’s conservation laws are developed for the various parameters’ relations: for a linear case, for a nonlinear case without considering the linear absorption, and for a nonlinear case accounting for the linear absorption and homogeneous shift of the pulse’s phase. Hereafter, the Crank–Nicolson-type scheme is constructed for the problem difference approximation. To demonstrate the conservativeness of the constructed implicit finite-difference scheme in the sense of preserving difference analogs of the problem’s invariants, the corresponding theorems are formulated and proved. The problem of the finite-difference scheme’s nonlinearity is solved by means of an iterative process. Finally, several numerical examples are presented to support the theoretical results.

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Conservation laws of femtosecond pulse propagation described by generalized nonlinear Schrödinger equation with cubic nonlinearity

Cited by 4 publications

References 40 publications

Multiphoton and plasma absorption measurements in CaF₂ and UV fused silica at 473 nm

Multiphoton and plasma absorption measurements in CaF₂ and UV fused silica at 473 nm

Algorithm for Solving a System of Coupled Nonlinear Schrödinger Equations by the Split-Step Method to Describe the Evolution of a High-Power Femtosecond Optical Pulse in an Optical Polarization Maintaining Fiber

Conservative Finite-Difference Scheme for 1D Ginzburg–Landau Equation

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Conservation laws of femtosecond pulse propagation described by generalized nonlinear Schrödinger equation with cubic nonlinearity

Cited by 4 publications

References 40 publications

Multiphoton and plasma absorption measurements in CaF2 and UV fused silica at 473 nm

Multiphoton and plasma absorption measurements in CaF2 and UV fused silica at 473 nm

Algorithm for Solving a System of Coupled Nonlinear Schrödinger Equations by the Split-Step Method to Describe the Evolution of a High-Power Femtosecond Optical Pulse in an Optical Polarization Maintaining Fiber

Conservative Finite-Difference Scheme for 1D Ginzburg–Landau Equation

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Multiphoton and plasma absorption measurements in CaF₂ and UV fused silica at 473 nm

Multiphoton and plasma absorption measurements in CaF₂ and UV fused silica at 473 nm