Optical rogue waves generation in a nonlinear metamaterial

Essama, Bedel Giscard Onana; Atangana, Jacques; Biya-Motto, Frederick; Mokhtari, Bouchra; Eddeqaqi, N. Cherkaoui; Kofané, Timoléon Crépin

doi:10.1016/j.optcom.2014.06.039

Cited by 25 publications

(17 citation statements)

References 45 publications

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“…(4) and (5) and) from z¼ 0 to ≥ z 1742 m in order to obtain the field representations [17,18,[50][51][52][53], the exact field solution of the nonlinear Schrödinger equation, the field reconstructed by the collective coordinates coming from the bare approximation and the field reconstructed by the dynamics of collective coordinates obtained from the residual field minimization (RFM) are respectively illustrated by the blue, red and black curves [50][51][52][53][54]. In collective coordinates representation, the red curve represents the dynamics of collective coordinates obtained from bare approximation, the black curve represents the dynamics of collective coordinates reconstructed from the residual field minimization and the blue curve represents the fraction of residual field energy (RFE) [50][51][52][53][54]. We consider the solitary wave in an optical environment with the typical following parameters: 3.1.…”

Section: Numerical Resultsmentioning

confidence: 99%

“…are the conventional collective coordinates [18] which have been used so far to represent the pulse amplitude, temporal position, full width at halfmaximum (FWHM) of peak power, the chirp, the frequency and phase, respectively [17][18][19][50][51][52][53]. Note that the parameter X 5 that we called frequency corresponds in fact to the soliton self-frequency shift.…”

Section: Conventional Ansatz (Ca) Functionmentioning

confidence: 99%

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

Atangana

Nnanga

Essama

et al. 2015

Optics Communications

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Section: Numerical Resultsmentioning

confidence: 99%

Section: Conventional Ansatz (Ca) Functionmentioning

confidence: 99%

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

Atangana

Nnanga

Essama

et al. 2015

Optics Communications

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“…[ 34,35 ] The terms

Θ_{2}

ϒ_{0}

, and

ϒ_{a}

are second‐order dispersion and cubic and quintic nonlinearities, respectively. [ 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}

.…”

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%

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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“…For our variational analysis, the desired form of the Gaussian ansatz function f is given by [37] [38]:…”

Section: Conventional Gaussian Ansatz Functionmentioning

confidence: 99%

Peregrine Soliton and Akhmediev Breathers in a Chameleon Electrical Transmission Line

Essama¹,

Essiane²,

Biya-Motto³

et al. 2020

JAMP

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We analyze the particular behavior exhibited by a chaotic waves field containing Peregrine soliton and Akhmediev breathers. This behavior can be assimilated to a tree with "roots of propagation" which propagate randomly. Besides, this strange phenomenon can be called "tree structures". So, we present the collapse of dark and bright solitons in order to build up the above mentioned chaotic waves field. The investigation is done in a particular nonlinear transmission line called chameleon nonlinear transmission line. Thus, we show that this line acts as a bandpass filter at low frequencies and the impact of distance, frequency and dimensionless capacitor are also presented. In addition, the chameleon's behavior is due to the fact that without modifying the appearance structure, it can present alternatively purely right-or left-handed transmission line. This line is different to the composite one.

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Optical rogue waves generation in a nonlinear metamaterial

Cited by 25 publications

References 45 publications

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

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

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

Peregrine Soliton and Akhmediev Breathers in a Chameleon Electrical Transmission Line

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