Influence of the Raman-effect on solitons in optical fibers

Akhmediev, Nail; Krolikowski, W.; Lowery, Arthur J.

doi:10.1016/0030-4018(96)00283-0

Cited by 49 publications

(58 citation statements)

References 16 publications

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“…Nevertheless, twohumped solutions that propagate without change of form were already associated with the model NLS plus IRS [6]. They accelerate along the fiber distance and their mean frequency linearly downshifts, in accordance to what is also observed in single hump propagation, which is known as soliton self-frequency shift [7].…”

Section: Introductionsupporting

confidence: 51%

“…The equation (5) is a non-autonomous ODE which reduces to Th.A4.5 3 humps since this would violate the theorem that says that there is a unique orbit through any point of the phase space [6]. However, the non-autonomous character of (5) allows this possibility.…”

Section: The Generalized Nonlinear Schrödinger Equation and The Accelmentioning

confidence: 98%

“…However, the non-autonomous character of (5) allows this possibility. Hence for small γ, our multihumped solution may be compared to a mixture of the homoclinic orbit and some periodic orbits inside it of equation (6). Moreover, we expect they have no counterpart for γ = 0.…”

Section: The Generalized Nonlinear Schrödinger Equation and The Accelmentioning

confidence: 99%

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Existence and stability of multihumped femtosecond solitons

Facão

Carvalho

Parker

2009

2009 11th International Conference on Transparent Optical Networks

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The propagation of bound soliton pairs in nonlinear photonic crystal fibers has recently been experimentally observed. The system may be modeled by a generalized nonlinear Schrödinger equation (GNLSE) which includes higher intrapulse Raman Scattering, self-steepening and higher order dispersion. Here, we find multihumped pulses as result of an accelerating similarity reduction of a GNLSE containing the intrapulse Raman scattering. Numerical simulations of the suitable GNLSE using these solutions as input showed that they are not stable, however, they may be related with the experimentally observed bound pairs since they propagate steadily for distances compared to the ones observed. Keywords: intrapulse Raman scattering; bound solitons; photonic crystal fibers. INTRODUCTIONIn recent experiments, the propagation of bound pairs of short pulses was observed in highly nonlinear photonic crystal fibers (PCF) [1,2]. The propagation of such short pulses in nonlinear fibers is affected by the standard group velocity dispersion and the Kerr effect, which are well described by the nonlinear Schrödinger equation (NLS), and by higher order effects like third order dispersion, self-steepening and intrapulse Raman scattering (IRS) [3]. The occurrence of bound solitons in the NLS is possible and predicted by the inverse scattering method as N-soliton solutions for which the velocities are all equal [4].The NLS bound solitons propagate with periodic oscillations, with a period related to its beating frequencies, and are known to decay when they are in presence of higher order effects like the IRS [5]. Nevertheless, twohumped solutions that propagate without change of form were already associated with the model NLS plus IRS [6]. They accelerate along the fiber distance and their mean frequency linearly downshifts, in accordance to what is also observed in single hump propagation, which is known as soliton self-frequency shift [7].Here, we obtain multihumped solutions of the NLS plus IRS equation as solutions of the ordinary differential equation (ODE) that results from an accelerating similarity reduction. Their profiles have characteristics that suffer small changes with the IRS strength. The stability of these solutions is studied by numerical simulation of the full evolution equation and their relation with the observed bound soliton pairs in PCFs is studied.

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Section: Introductionsupporting

confidence: 51%

Section: The Generalized Nonlinear Schrödinger Equation and The Accelmentioning

confidence: 98%

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Existence and stability of multihumped femtosecond solitons

Facão

Carvalho

Parker

2009

2009 11th International Conference on Transparent Optical Networks

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“…The qualitative explanation will be done on the base of the powerful concept of gravity-like potential introduced in Refs. (Allen & Everly 1978, Akhmediev et.al. 1996.…”

Section: Mechanical Analogy Methodsmentioning

confidence: 99%

Raman Solitons and Mechanical Analog Method

Agüero¹,

Karasik²

2011

APR

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“…3.3b. Raman shifted solitons are themselves constantly shaking off some radiation even without presence of the higher order dispersions [76]. This radiation is not reflected by the solitons (because its GVD is anomalous) and it fills the space between them, see Fig.…”

Section: Mixing Of Solitons With Dispersive Radiation Radiation Trapmentioning

confidence: 98%