Shedding and interaction of solitons in imperfect medium

Chertkov, Michael; Gabitov, Ildar R.; Kolokolov, I. V.; Лебедев, В. В.

doi:10.1134/1.1427121

Cited by 10 publications

(9 citation statements)

References 17 publications

(30 reference statements)

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“…Therefore, we come to a set of deterministic (like in classical mechanics) equations for the soliton positions and the phase velocities (the latter play the role of classical momenta). The general setting is familiar from [5]. However, the dependence of the intersoliton forces on the separation between the solitons in the polarization problems is different: the force does not depend on the separation.…”

Section: Solitons In a Disorderedmentioning

confidence: 99%

“…The intersoliton separation changes on the order of the soliton width at z int ~ 1/ Ӷ z degr . We use and generalize here an approach developed previously to describe solitons interacting in an isotropic medium with fluctuating dispersion [5]. The soliton interaction, in the case of [5], decays algebraically.…”

mentioning

confidence: 99%

“…We use and generalize here an approach developed previously to describe solitons interacting in an isotropic medium with fluctuating dispersion [5]. The soliton interaction, in the case of [5], decays algebraically. By contrast, in the anisotropic case discussed in this letter, the interaction is separation-independent.…”

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confidence: 99%

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Solitons in a disordered anisotropic optical medium

et al. 2001

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1 The propagation of a pulse through an optical fiber with randomly varying anisotropy is usually addressed in the context of the Polarization Mode Dispersion (PMD). PMD is signal broadening caused by inhomogeneity of the medium birefringence. In the linear case, the study of PMD was pioneered by Poole [1], who showed that the pulse broadens as the two principal states of polarization split under the action of the random birefringence (see also [2]). Mollenauer et al. have numerically studied a nonlinear model of birefringent disorder in [3], where it was shown that a soliton, launched into the birefringent fiber, does not split, but it does undergo spreading [3] (see also [4]). In this letter, we develop an analytical approach and confirm that a single soliton does degrade due to disorder in the birefringence. The degradation is observable once the soliton traverses the distance z degr ~ D -1 , where D stands for the strength of the noise in the birefringence, measured in units of the soliton width and period ( D Ӷ 1 is assumed, the typical case for telecommunication fibers).The major finding of this letter is a new phenomenon which occurs on scales much shorter than z degr . We report that the interaction between solitons induced by their combined radiation (generated by disorder) is an important factor affecting the soliton dynamics. Initially stationary solitons experience a relative acceleration, ~ D . The intersoliton separation changes on the order of the soliton width at z int ~ 1/ Ӷ z degr . We use and generalize here an approach developed previously to describe solitons interacting in an isotropic medium with fluctuating dispersion [5]. The soliton interaction, in the case of [5], decays algebraically. By contrast, in the anisotropic case discussed in this letter, the interaction is separation-independent. The reason is that, in 1 This work was submitted by the authors in English. D this case, a different type of wave scatters from the solitons. In the isotropic case, the scattering of the radiated waves, emitted by a soliton, by another soliton is not refracted. In the anisotropic case, radiation from one soliton pushes (literally) the other soliton, because the scattering potential is not transparent.Let us briefly formulate the problem. The electric field E , corresponding to a wave packet carrying frequency ω , can be decomposed into complex components E = 2Re[ E ω exp( ik 0 z -i ω t )], where z is the coordinate along the fiber. Concomitant averaging over fast oscillations and over the structure of fundamental mode (a monomode regime is assumed) constitutes the coarse-grained description for the signal envelope described by the two-component complex field Ψ α , = Ψ 1 ( z ) e 1 + Ψ 2 ( z ) e 2 , where e 1, 2 are unit vectors orthogonal to each other and to the waveguide direction. The averaging results in the envelope equation [6,7] (1) Here, the wave packet is subjected to dispersion in retarded time t and to the Kerr nonlinearity, which is described by the last two terms on the left-hand side of ...

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Section: Solitons In a Disorderedmentioning

confidence: 99%

mentioning

confidence: 99%

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Solitons in a disordered anisotropic optical medium

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“…The probability density function (PDF) is essentially Gaussian for timing jitter [8][9][10][11] in systems without control and may have substantially non-Gaussian tails in systems with in-line filtering and amplitude modulation. Here, we consider a single-soliton propagation, the effects related to soliton interaction are described in [2,3,[12][13][14].…”

Section: Introductionmentioning

confidence: 99%

Non-Gaussian error probability in optical soliton transmission

Falkovich

Kolokolov

Лебедев

et al. 2004

Physica D: Nonlinear Phenomena

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We find the probability distribution of the fluctuating parameters of a soliton propagating through a medium with additive noise. Our method is a modification of the instanton formalism (method of optimal fluctuation) based on a saddle-point approximation in the path integral. We first solve consistently a fundamental problem of soliton propagation within the framework of noisy nonlinear Schrödinger equation. We then consider model modifications due to in-line (filtering, amplitude and phase modulation) control. It is examined how control elements change the error probability in optical soliton transmission. Even though a weak noise is considered, we are interested here in probabilities of error-causing large fluctuations which are beyond perturbation theory. We describe in detail a new phenomenon of soliton collapse that occurs under the combined action of noise, filtering and amplitude modulation.

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“…38. Here the solution description by the adiabatic approximation is actually deterministic: in the leading order the PDFs are ␦ functions, with the width of the pulse being the inverse of its amplitude.…”

Section: A Statistical Approach: Probability Distribution Functions mentioning

confidence: 99%

Pinning method of pulse confinement in optical fiber with random dispersion

et al. 2002

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Pulse propagation in optical fiber links with randomness in the dispersion is investigated theoretically and numerically for systems with and without dispersion management. The main effects of locally correlated noise are inevitable pulse destruction and statistical broadening. However, periodic/quasi-periodic management of fiber randomness, achieved by setting the accumulated dispersion to its nominal value (pinning), essentially decreases pulse broadening. If the pinning period is short enough, we observe a statistical state that is numerically indistinguishable from the steady state in the dispersion-managed case.

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Shedding and interaction of solitons in imperfect medium

Cited by 10 publications

References 17 publications

Solitons in a disordered anisotropic optical medium

Solitons in a disordered anisotropic optical medium

Non-Gaussian error probability in optical soliton transmission

Pinning method of pulse confinement in optical fiber with random dispersion

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