Elliptic solitons in optical fiber media

Fandio, Défi Junior Jubgang; Dikandé, Alain M.; Sunda-Meya, Anderson

doi:10.1103/physreva.92.053850

Cited by 39 publications

(20 citation statements)

References 24 publications

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“…and sn (X, ν) ∝ ∑ ∞ ℓ=0 tanh(X − ℓX 0 ). [32] Fig. 2 Periodic optical traps generated by the induction field: (a) the "sn 2 " potential given by formula (10), (b) "cn 2 " potential given by formula (11).…”

Section: The Model and Nonlinear Propagation Equationmentioning

confidence: 99%

Soliton Trains Induced by Adaptive Shaping with Periodic Traps in Four-Level Ultracold Atom Systems

Tchenkoue¹,

Welakuh²,

Dikandé³

2017

Commun. Theor. Phys.

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It is well known that an optical trap can be imprinted by a light field in an ultracold-atom system embedded in an optical cavity, and driven by three different coherent fields. Of the three fields coexisting in the optical cavity there is an intense control field that induces a giant Kerr nonlinearity via electromagnetically-induced transparency, and another field that creates a periodic optical grating of strength proportional to the square of the associated Rabi frequency. In this work elliptic-soliton solutions to the nonlinear equation governing the propagation of the probe field are considered, with emphasis on the possible generation of optical soliton trains forming a discrete spectrum with well defined quantum numbers. The problem is treated assuming two distinct types of periodic optical gratings and taking into account the negative and positive signs of detunings (detuning above or below resonance). Results predict that the competition between the self-phase and cross-phase modulation nonlinearities gives rise to a rich family of temporal soliton train modes characterized by distinct quantum numbers.

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Section: The Model and Nonlinear Propagation Equationmentioning

confidence: 99%

Soliton Trains Induced by Adaptive Shaping with Periodic Traps in Four-Level Ultracold Atom Systems

Tchenkoue¹,

Welakuh²,

Dikandé³

2017

Commun. Theor. Phys.

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“…It should be noted that nonlinear periodic waveforms physically depict a large number of coexisting solitons in optical fibers, which offers a myriad of opportunities in information transmission systems. The use of optical lasers to generate nonlinear periodic waves in optical fibers has received great attention in recent years [16][17][18][19], due to their robust technological applications to boost communication. Furthermore, the most recent applications of soliton combs in optical ring microresonator systems stands tall in a class of its own [20,21].…”

Section: Introductionmentioning

confidence: 99%

“…These nonlinear periodic structures known as soliton crystals are generally described by the Jacobi elliptic mathematical functions, which play the role of carrier waves. In fact, Fandio et al mathematically derived and numerically generated soliton crystals in a monomode fiber in the anomalous dispersion regime [16]. This was achieved by using a purely conservative optical fiber, with the periodic train of pulses generated by time-division multiplexing of an infinitely large number of pulses pumped into the fiber by a pulse mode laser at a given period.…”

Section: Introductionmentioning

confidence: 99%

On dynamics of elliptic solitons in lossy optical fibers

Nfor¹,

Jaja²

2022

J. Opt.

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By exploiting the theory of electromagnetic waves from the Maxwell’s equations, the damped nonlinear Schrödinger equation is shown to govern the evolution of nonlinear periodic optical signals in a lossy optical ﬁber. These optical periodic pulses are mainly generated by the classical process of modulational instability in which nonlinearity is balanced by chromatic dispersion in the anomalous regime, with the linear loss generally suppressing the existence of soliton trains during propagation down the lossy ﬁber. When the periodic optical wave trains are subjected to weak external perturbations, this leads to the exposure of some internal modes of the system which are bound states solutions of the ﬁrst order Lamé equation. These modes generally characterize various fundamental background excitations that co-propagate with the optical periodic signals in the ﬁber. Direct numerical simulations of the damped nonlinear Schrödinger amplitude equation depicts the exponential decrease in the amplitude and corresponding increase in the width of the wave trains during propagation. Power lasers are used in order to compensate for ﬁber losses; this is realized via time-division multiplexing of optical pulses which are periodically pumped into the lossy ﬁber at regular distance within the framework of distributed ampliﬁcation scheme. This leads to the regular energy restoration in the lossy ﬁber as a result of the interactions between the energized multiplexed light signals (generated by the power lasers) and the propagating damped optical pulses, hence ensuring eﬀective transmission over long distances.

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“…Nature provides many examples of coherent nonlinear structures and wave patterns. Among these beautiful nonlinear phenomena are localized large amplitude solitary waves called solitons, which have been observed in neural networks, [1][2][3] optical fiber systems, [4][5][6] and many other physical regimes. Solitons can propagate along one direction over long distances without spreading, and maintaining their form after collision.…”

Section: Introductionmentioning

confidence: 99%

Investigation of bright and dark solitons in α, β-Fermi Pasta Ulam lattice

2021

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We consider the Hamiltonian of α, β-Fermi Pasta Ulam lattice and explore the Hamilton–Jacobi formalism to obtain the discrete equation of motion. By using the continuum limit approximations and incorporating some normalized parameters, the extended Korteweg–de Vries equation is obtained, with solutions that elucidate on the Fermi Pasta Ulam paradox. We further derive the nonlinear Schrödinger amplitude equation from the extended Korteweg–de Vries equation, by exploring the reductive perturbative technique. The dispersion and nonlinear coefficients of this amplitude equation are functions of the α and β parameters, with the β parameter playing a crucial role in the modulational instability analysis of the system. For β greater than or equal to zero, no modulational instability is observed and only dark solitons are identified in the lattice. However for β less than zero, bright solitons are traced in the lattice for some large values of the wavenumber. Results of numerical simulations of both the Korteweg–de Vries and nonlinear Schrödinger amplitude equations with periodic boundary conditions clearly show that the bright solitons conserve their amplitude and shape after collisions.

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Elliptic solitons in optical fiber media

Cited by 39 publications

References 24 publications

Soliton Trains Induced by Adaptive Shaping with Periodic Traps in Four-Level Ultracold Atom Systems

Soliton Trains Induced by Adaptive Shaping with Periodic Traps in Four-Level Ultracold Atom Systems

On dynamics of elliptic solitons in lossy optical fibers

Investigation of bright and dark solitons in α, β-Fermi Pasta Ulam lattice

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