Internal vibrations of a vector soliton in the coupled nonlinear Schrödinger equations

Malomed, Boris A.; Tasgal, Richard S.

doi:10.1103/physreve.58.2564

Cited by 45 publications

(29 citation statements)

References 17 publications

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“…In particular, stable solitary wave solutions called vector solitons were found in this system [9,10]. When they are perturbed, they will undergo complicated, long-lasting internal oscillations [15][16][17][18]. These oscillations are caused by the excitation of internal (shape) modes of vector solitons.…”

Section: Introductionmentioning

confidence: 93%

“…More significantly, these equations describe evolution of pulse envelopes along the two orthogonal polarizations in birefringent nonlinear optical fibers [3], which are used in fiber communication systems [4][5][6][7] and all-optical switching devices [8]. The rapid advancement of all-optical communication networks in the past 10 years has generated great interest and progress in mathematical studies of pulse dynamics in the coupled NLS equations [9][10][11][12][13][14][15][16][17][18]. In particular, stable solitary wave solutions called vector solitons were found in this system [9,10].…”

Section: Introductionmentioning

confidence: 99%

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Internal Oscillations and Radiation Damping of Vector Solitons

Pelinovsky

Yang

2000

Stud Appl Math

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Internal modes of vector solitons and their radiation-induced damping are studied analytically and numerically in the framework of coupled nonlinear Schrödinger equations. Bifurcations of internal modes from the integrable systems are analyzed, and the region of their existence in the parameter space of vector solitons is determined. In addition, radiation-induced decay of internal oscillations is investigated. Both exponential and algebraic decay rates are identified.

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Section: Introductionmentioning

confidence: 93%

Section: Introductionmentioning

confidence: 99%

Internal Oscillations and Radiation Damping of Vector Solitons

Pelinovsky

Yang

2000

Stud Appl Math

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“…5 can be estimated the- oretically as well. For this purpose, let us first recall that when a single vector soliton is slightly perturbed, it will undergo positional and width oscillations [20][21][22][23][24]. If this vector soliton supports a discrete internal mode, the eigenvalue of this internal mode will be the frequency of positional oscillations.…”

Section: The Resonance Mechanismmentioning

confidence: 99%

“…If this vector soliton supports a discrete internal mode, the eigenvalue of this internal mode will be the frequency of positional oscillations. Otherwise, positional oscillations are caused by quasi-modes which are located inside but close to the edge of the continuous spectrum, and its frequency is about min{ω 1 , ω 2 }, where ω 1 and ω 2 are positive propagation constants of the vector soliton [24,25]. Width oscillations are caused by radiation modes, and its frequency is about max{ω 1 , ω 2 }.…”

Section: The Resonance Mechanismmentioning

confidence: 99%

Fractal dependence of vector-soliton collisions in birefringent fibers

Yang

Tan

2001

Physics Letters A

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“…[19,20,21], we calculated the respective quantum fluctuations and the photon-number correlators numerically. It should be noted the total intensity of the vectorial solitons, defined in terms of the circular polarizations, remain unchanged during the propagation, but the intensities of the linearlypolarized (x-and y-) components, E x = (U + V )/ √ 2 and E y = (U − V )/i √ 2, evolve periodically, as shown in the insert of Fig.…”

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confidence: 99%

Generation of photon-number-entangled soliton pairs through interactions

2005

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Two new simple schemes for generating macroscopic (many-photon) continuous-variable entangled states by means of continuous interactions (rather than collisions) between solitons in optical fibers are proposed. First, quantum fluctuations around two time-separated single-component temporal solitons are considered. Almost perfect correlation between the photon-number fluctuations can be achieved after propagating a certain distance, with a suitable initial separation between the solitons. The photon-number correlation can also be achieved in a pair of vectorial solitons with two polarization components. In the latter case, the photon-number-entangled pulses can be easily separated by a polarization beam splitter. These results offer novel possibilities to produce entangled sources for quantum communication and computation. Introduction Quantum-noise squeezing and correlations are two key quantum properties that can exhibit completely different characteristics when compared to the predictions of the classical theory. Almost all the proposed applications to quantum measurements and quantum information treatment utilize either one or both of these properties. In particular, solitons in optical fibers have been known to serve as a platform for demonstrating macroscopic quantum properties in optical fields, such as quadrature squeezing, amplitude squeezing, and both intra-pulse and inter-pulse correlations. The development of quantum theories of nonlinear optical pulse propagation in the past years has opened a way to analyze the quantum features of fiber-optic solitons. Experimental progress in demonstrating various quantum properties of these solitons has also been reported, see Refs.[1]-[4] and references therein.

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Internal vibrations of a vector soliton in the coupled nonlinear Schrödinger equations

Cited by 45 publications

References 17 publications

Internal Oscillations and Radiation Damping of Vector Solitons

Internal Oscillations and Radiation Damping of Vector Solitons

Fractal dependence of vector-soliton collisions in birefringent fibers

Generation of photon-number-entangled soliton pairs through interactions

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