Efficient method of calculation of Raman soliton self-frequency shift in nonlinear optical media

Atangana, Jacques; Nnanga, Bibiane Mireille Ndi; Essama, Bedel Giscard Onana; Mokthari, Bouchra; Eddeqaqi, N. Cherkaoui; Kofané, Timoléon Crépin

doi:10.1016/j.optcom.2014.11.050

Cited by 14 publications

(20 citation statements)

References 49 publications

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“…[ 37,38 ] Moreover, the interaction of light with the metamaterial modifies the nature of the refractive index n . [ 39–43 ] So, the modulation of this refractive index by femtosecond pulses induces the decomposition of the refractive index such that

n = n_{0} + n_{2} I + n_{4} I^{2}

. [ 39,41 ] Femtosecond (shorter) pulses occur when the intensity of the incident light power I increases.…”

Section: Mathematical Description Of the Modelmentioning

confidence: 99%

“…[ 39–43 ] So, the modulation of this refractive index by femtosecond pulses induces the decomposition of the refractive index such that

n = n_{0} + n_{2} I + n_{4} I^{2}

. [ 39,41 ] Femtosecond (shorter) pulses occur when the intensity of the incident light power I increases. The term

n_{0}

stands for the linear refractive index coefficient;

n_{2}

and

n_{4}

correspond to nonlinear refractive index coefficients which are coming from third‐ and fifth‐order susceptibilities.…”

Section: Mathematical Description Of the Modelmentioning

confidence: 99%

“…The term

n_{0}

stands for the linear refractive index coefficient;

n_{2}

and

n_{4}

correspond to nonlinear refractive index coefficients which are coming from third‐ and fifth‐order susceptibilities. [ 39,41 ] Consequently, cubic and quintic nonlinearities are respectively induced by

n_{2}

and

n_{4}

. [ 39–43 ] It clearly appears that the polarizations induced through these susceptibilities generate the cubic and quintic (non‐Kerr) terms in the nonlinear Schrödinger equation, respectively.…”

Section: Mathematical Description Of the Modelmentioning

confidence: 99%

“…[ 39,41 ] Consequently, cubic and quintic nonlinearities are respectively induced by

n_{2}

and

n_{4}

Θ_{3}

and

ϒ_{s}

respectively stand for third‐order dispersion [ 44,45 ] and self‐steepening.…”

Section: Mathematical Description Of the Modelmentioning

confidence: 99%

“…[ 39–43 ] It clearly appears that the polarizations induced through these susceptibilities generate the cubic and quintic (non‐Kerr) terms in the nonlinear Schrödinger equation, respectively. [ 39 ] The parameters

Θ_{3}

and

ϒ_{s}

respectively stand for third‐order dispersion [ 44,45 ] and self‐steepening. [ 34 ] These aforementioned coefficients are defined such that [ 34,35 ]

Θ_{2} = - \frac{1}{n β} (\frac{1}{V_{g}^{2}} - α γ - \frac{1}{4} \frac{β false(ε γ' + μ α' false)}{π})

Θ_{3} = \frac{1}{2 n β} (\frac{Θ_{2}}{V_{g}} + β \frac{1}{24 π^{2}} (ε γ ″ + μ α ″) + \frac{1}{4} \frac{(α γ' + γ α')}{π})

ϒ_{0} = \frac{1}{2} \frac{β μ χ^{(3)}}{n}

ϒ_{a} = - \frac{1}{8} \frac{β μ^{2} {(χ^{false(3 false)})}^{2}}{n^{3}}

ϒ_{s} = \frac{χ^{(3)}}{2 n} (\frac{μ}{n V_{g}} <...>

…”

Section: Mathematical Description Of the Modelmentioning

confidence: 99%

See 4 more Smart Citations

Dynamical Evolution of Sasa–Satsuma Rogue Waves, Breather Solutions, and New Special Wave Phenomena in a Nonlinear Metamaterial

Essama

Essiane

Biya-Motto

et al. 2020

Physica Status Solidi (b)

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Herein, the behavior of the soliton light pulse when quintic –nonlinearity, third‐order dispersion, and self‐steepening come into play in a nonlinear metamaterial for both negative index and absorption regimes is presented. The collective coordinate technique is used with the conventional Gaussian ansatz function to give a good characterization of the pulse profile. In addition to that the ansatz function presents six coordinates describing the internal behavior of the pulse during the propagation. Furthermore, the main goal of this work is to give an exact measure of the internal behavior leading to the generation of rogue events by collective coordinates. Some interesting results are found when the aforementioned linear and nonlinear effects gradually come into play. Among them is the generation of different forms of breather solutions, divergent wave trains, different forms of Sasa–Satsuma rogue waves, parabolic wave trains, Peregrine rogue waves, and “tree structures”. Some special phenomena known as deletion, translation, attenuation, and wall of waves are also shown. However, some new exact rogue solutions of the cubic–quintic nonlinear Schrödinger equation are also found.

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