?(2) cascading phenomena and their applications to all-optical signal processing, mode-locking, pulse compression and solitons

Stegeman, George I.; Hagan, David J.; Torner, Lluís

doi:10.1007/bf00698538

Cited by 551 publications

(345 citation statements)

References 168 publications

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“…(3)], E = 12000. We see that, with the increase of the mismatch β, the energy of the FF component of the spinning soliton increases, similar to the case of nonspinning solitons in pure χ (2) media [42,45,46,47].…”

Section: The Model and Spinning Solitonssupporting

confidence: 58%

Stable three-dimensional spinning optical solitons supported by competing quadratic and cubic nonlinearities

et al. 2002

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We show that the quadratic interaction of fundamental and second harmonics in a bulk dispersive medium, combined with self-defocusing cubic nonlinearity, give rise to completely localized spatiotemporal solitons (vortex tori) with vorticity s = 1. There is no threshold necessary for the existence of these solitons. They are found to be stable if their energy exceeds a certain critical value, so that the stability domain occupies about 10 % of the existence region of the solitons. On the contrary to spatial vortex solitons in the same model, the spatiotemporal ones with s = 2 are never stable. These results might open the way for experimental observation of spinning three-dimensional solitons in optical media.

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Section: The Model and Spinning Solitonssupporting

confidence: 58%

Stable three-dimensional spinning optical solitons supported by competing quadratic and cubic nonlinearities

et al. 2002

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“…As it is well known, soliton is a name for a solitary wave, which does not change in the direction of propagation of optical pulse in medium. Modern laser equipments make it possible to realize the so-called colored solitons, when optical waves at several frequencies exist and propagate simultaneously along the nonlinear medium [2,3,4,5,6,9,10,11,12,13,14,15,16,17].…”

Section: Introductionmentioning

confidence: 99%

Numerical Method for 2d Soliton Solution at SHG in Media With Time‐dependent Combined Nonlinearity

Trofimov

Matusevich

2008

Mathematical Modelling and Analysis

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Abstract. The paper describes the iteration method for finding the eigenfunctions and eigenvalues of the system of two nonlinear Schrödinger equations, which describes the process of second harmonic generation by femtosecond pulse in media with the quadratic and cubic nonlinear response. Coefficients, which characterize the nonlinearities, depend on one of the coordinate. The discussed method allows to find soliton solutions of new form corresponding to the first and second eigenvalues for the wide range of the nonlinear coefficients values. For determination of the eigenfunctions of the third and higher order it is necessary to select the initial approximation in a special way.

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“…Interest is driven by the new phenomena that are continuously uncovered, and by their widespread potential applications (reviewed in [1]- [3]). Quadratic solitons are formed by the mutual trapping between the several waves that parametrically interact in the crystal, and they are stable both in waveguides and in higher dimensional configurations, including multiple-pass geometries, in settings for the spatial, temporal, and spatio-temporal trapping of light.…”

Section: Introductionmentioning

confidence: 99%

Quadratic solitons with gain and loss

Torner

Dorring

Torres³

1999

IEEE J. Quantum Electron.

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?(2) cascading phenomena and their applications to all-optical signal processing, mode-locking, pulse compression and solitons

Cited by 551 publications

References 168 publications

Stable three-dimensional spinning optical solitons supported by competing quadratic and cubic nonlinearities

Stable three-dimensional spinning optical solitons supported by competing quadratic and cubic nonlinearities

Numerical Method for 2d Soliton Solution at SHG in Media With Time‐dependent Combined Nonlinearity

Quadratic solitons with gain and loss

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