Interaction of kink-lattice solitons with small-amplitude waves in finite-size superlattices

Mensah, S. Y.; Dikandé, Alain M.; Allotey, F.K.A.; Mensah, N. G.

doi:10.1006/spmi.1999.0817

Cited by 3 publications

(4 citation statements)

References 15 publications

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“…T . Equation ( 24) and its higher order forms have been extensively discussed in the context of the interaction of kink-lattice solitons with smallamplitude waves in finite-size superlattices [47], and fundamental modes of a trapped probe photon in optical fibers conveying periodic pulse trains [48], amongst many other applications [20,21,29,44]. The three bound state solutions of the first order Lamé equation ( 24) are given by [49]…”

Section: Stability Of Nonlinear Periodic Optical Pulsesmentioning

confidence: 99%

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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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Section: Stability Of Nonlinear Periodic Optical Pulsesmentioning

confidence: 99%

“…and their corresponding eigenvalues respectively read [20] L The constants A i (m) for i = 1, 2, 3 in solution ( 25) can be obtained by considering the fact that the three bound state solutions ϕ 1i (Y) form an orthonormal subset [47][48][49]. Figure 7 clearly depicts the three bound state solutions.…”

Section: Stability Of Nonlinear Periodic Optical Pulsesmentioning

confidence: 99%

On dynamics of elliptic solitons in lossy optical fibers

Nfor¹,

Jaja²

2022

J. Opt.

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“…which is Lamé's equation [39][40][41]. Note that when κ = 1, this equation can be reduced to the Associated Legendre equation as obtained in [8] in the case of a photon trapped by two interacting pulses which retain their individual shapes.…”

Section: The Model and Fundamental Soliton Solutions Of The Probe Equationmentioning

confidence: 99%

“…These modes are more exactly the boundstates of the Lamé equation, and because their formation via the cross-phase effect involves low cost to the pump in terms of momentum transfers they can be looked out like the groundstate modes of the spectrum of trapped states in the probe. The discrete states of Lamé's equation form a complete set of finite orthogonal modes which population depends on the integer quantum number ℓ [40,41]. Quite remarkably, according to formula (8) the value of ℓ is determined by the competition between the self-phase-modulation effect responsible for the fiber nonlinearity and the cross-phase modulation effect on the probe exherted by the pump trap.…”

Section: The Model and Fundamental Soliton Solutions Of The Probe Equ...mentioning

confidence: 99%

Fundamental modes of a trapped probe photon in optical fibers conveying periodic pulse trains

Dikandé

2010

Phys. Rev. A

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Wave modes induced by cross-phase reshaping of a probe photon in the guiding structure of a periodic train of temporal pulses are investigated theoretically with emphasis on exact solutions to the wave equation for the probe. The study has direct connection with recent advances on the issue of light control by light, the focus being on the trapping of a low-power probe by a temporal sequence of periodically matched high-power pulses of a dispersion-managed optical fiber. The problem is formulated in terms of the nonlinear optical fiber equation with averaged dispersion, coupled to a linear equation for the probe including a cross-phase modulation term. Shape-preserving modes which are robust against the dispersion are shown to be induced in the probe, they form a family of mutually orthogonal solitons the characteristic features of which are determined by the competition between the self-phase and cross-phase effects. Considering a specific context of this competition, the theory predicts two degenerate modes representing a train of bright signals and one mode which describes a train of dark signals. When the walk-off between the pump and probe is taken into consideration, these modes have finite-momentum envelopes and none of them is totally transparent vis-à-vis the optical pump soliton.

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Periodic exciton–polariton solitons in semiconductor nanowires

2021

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Exciton–polariton solitons are nonlinear quasiparticles composed of exciton–photon bound states due to the interaction of light with matter. In semiconductor micro-cavity systems, such as semiconductor micro and nanowires, polaritons are characterized by a negative mass which, combined with the repulsive nonlinear exciton–exciton interaction, leads to the generation of bright polariton solitons. In this work, we investigate the dynamics of bright exciton–polariton solitons in a finite-sized microcavity waveguide, assuming radiative losses to be balanced by the external pumping. Bright-soliton solutions to the model equations of motion, which consist of a periodic train of polariton pulses, are obtained in terms of Jacobi elliptic functions. Analytical expressions of the energies of both photonic and excitonic components of the pulse train are found. Results suggest that the size of a nanowire waveguide plays a relevant role in the quantitative estimate of the energy conveyed by polariton solitons propagating in the medium.

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Interaction of kink-lattice solitons with small-amplitude waves in finite-size superlattices

Cited by 3 publications

References 15 publications

On dynamics of elliptic solitons in lossy optical fibers

On dynamics of elliptic solitons in lossy optical fibers

Fundamental modes of a trapped probe photon in optical fibers conveying periodic pulse trains

Periodic exciton–polariton solitons in semiconductor nanowires

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