Short optical solitons in fibers

Gromov, E. M.; Talanov, V. I.

doi:10.1063/1.1290744

Cited by 35 publications

(18 citation statements)

References 23 publications

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“…[35][36][37]. If, for some selected parameters, the background amplitude becomes zero, then the quasisolitons are called embedded solitons [37][38][39][40][41]. Mathematical artificiality of the quasisolitons exhibits itself through the fact that they carry infinite energy, but their relevance to the physical reality can be inferred from the results presented above.…”

Section: Discussionmentioning

confidence: 99%

Theory of the soliton self-frequency shift compensation by the resonant radiation in photonic crystal fibers

2004

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We develop a theory of the soliton self-frequency shift compensation by the resonant radiation recently observed in photonic crystal fibers. Our approach is based on the calculation of the soliton plus radiation solution of the generalized nonlinear Schrödinger (GNLS) equation and on subsequent use of the adiabatic theory leading to a system of equations governing evolution of the soliton parameters in the presence of the Raman effect and radiation. Our theoretical results are found to be in good agreement with direct numerical modeling of the GNLS equation.

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Section: Discussionmentioning

confidence: 99%

Theory of the soliton self-frequency shift compensation by the resonant radiation in photonic crystal fibers

2004

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“…Notice that, mathematically speaking, these solutions are simply solitary waves, because the HNLS model is generally non-integrable (it is completely integrable only for specific values of its coefficients [22]). Nevertheless, results from direct numerical simulations reported in References [34,35] show that these bright and dark solitary waves are quite robust during evolution.…”

Section: Conclusion and Discussionmentioning

confidence: 99%

Modeling of ultrashort pulse propagation in lossy nonlinear metamaterials

Tsitsas

Porfyrakis

Frantzeskakis

2016

Math Methods in App Sciences

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Wave propagation in lossy nonlinear metamaterials is analytically investigated by means of perturbation methods. In the left‐handed band of the nonlinear metamaterial, a higher‐order nonlinear Schrödinger equation is obtained, while in the frequency band gap, a dissipative short‐pulse equation is derived. In both cases, dissipation is described by linear terms, which lead to an exponential decay of the solutions. The decay rates, that is, the inverses of the linear loss coefficients in these two models, are found in terms of the dielectric and magnetic properties of the metamaterial. Copyright © 2016 John Wiley & Sons, Ltd.

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“…As a result, the solutions in the form of the stationary shock waves stipulated by the balance of stimulated scattering and the second-order linear dispersion were found. The stationary waves with allowance for nonlinear dispersion and the third-order linear dispersion were studied in [15][16][17] within the framework of an extended nonlinear Schrödinger equation for nonlinear and linear phase modulation in [15] and [16,17], respectively, disregarding the stimulated scattering. In this case, the stationary waves result from the balance of nonlinear dispersion and the third-order linear dispersion.…”

Section: Introductionmentioning

confidence: 99%