Extreme nonlinear optics in a Kerr medium: Exact soliton solutions for a few cycles

Kim, A. V.; Skobelev, S. A.; Anderson, D.; Hansson, Tobias; Lisak, M.

doi:10.1103/physreva.77.043823

Cited by 32 publications

(23 citation statements)

References 17 publications

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“…One may then wish to replace the envelope equation with a nonenvelope one, e.g., with the so-called short-pulse equation for the negative dispersion domain [13,14] (see also the earlier paper [15]). Remarkably, the cusp solutions reappear and still determine the shortest pulse duration [16,17]. We now consider a(t) for σ = 0.…”

Section: B the Case μ > 0 And σ =mentioning

confidence: 98%

Dispersion of nonlinear group velocity determines shortest envelope solitons

2011

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We demonstrate that a generalized nonlinear Schrödinger equation (NSE), which includes dispersion of the intensity-dependent group velocity, allows for exact solitary solutions. In the limit of a long pulse duration, these solutions naturally converge to a fundamental soliton of the standard NSE. In particular, the peak pulse intensity times squared pulse duration is constant. For short durations, this scaling gets violated and a cusp of the envelope may be formed. The limiting singular solution determines then the shortest possible pulse duration and the largest possible peak power. We obtain these parameters explicitly in terms of the parameters of the generalized NSE.

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Section: B the Case μ > 0 And σ =mentioning

confidence: 98%

Dispersion of nonlinear group velocity determines shortest envelope solitons

2011

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“…provided δ 2 ≤ 1/8. As mentioned in [25], in the case of a max ≪ 1 where slowly evolving wave field approximation (SEWA) is valid, the solution to Eq. (33) can be written as…”

Section: Derivation Of the Focusing And Defocusing Complex Short mentioning

confidence: 99%

Defocusing complex short-pulse equation and its multi-dark-soliton solution

2016

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In this paper, we propose a complex short pulse equation of both focusing and defocusing types, which governs the propagation of ultra-short pulses in nonlinear optical fibers. It can be viewed as an analogue of the nonlinear Schrödinger (NLS) equation in the ultra-short pulse regime. Furthermore, we construct the multi-dark soliton solution for the defocusing complex short pulse equation through the Darboux transformation and reciprocal (hodograph) transformation. Oneand two-dark soliton solutions are given explicitly, whose properties and dynamics are analyzed and illustrated.

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“…The second one is to construct a suitable fit to the frequency-dependent dielectric constant ε(ω) in the desired spectral range. Several models have been proposed by this approach including the short-pulse (SP) equation [7,8,9,10].…”

Section: Introductionmentioning

confidence: 99%

Complex short pulse and coupled complex short pulse equations

Feng¹

2015

Physica D: Nonlinear Phenomena

111

109

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In the present paper, we propose a complex short pulse equation and a coupled complex short equation to describe ultra-short pulse propagation in optical fibers. They are shown to be integrable due to the existence of Lax pairs and infinite number of conservation laws. Furthermore, we construct their multi-soliton solutions in terms of pfaffians by virtue of Hirota bilinear method. One- and two-soliton solutions are investigated in details, showing favorable properties in modeling ultra-short pulses with a few optical cycles. Especially, same as the coupled nonlinear Schrodinger equation, interactions between two solitons are basically inelastic, which deserve further study and has potential applications.Comment: A correction version of previous submissio

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Extreme nonlinear optics in a Kerr medium: Exact soliton solutions for a few cycles

Cited by 32 publications

References 17 publications

Dispersion of nonlinear group velocity determines shortest envelope solitons

Dispersion of nonlinear group velocity determines shortest envelope solitons

Defocusing complex short-pulse equation and its multi-dark-soliton solution

Complex short pulse and coupled complex short pulse equations

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