Discrete solitons in nonlinear optomechanical array

Houwe, Alphonse; Djorwé, Philippe; Abbagari, Souleymanou; Doka, Serge Y.; Engo, S. G. Nana

doi:10.1016/j.chaos.2021.111593

Cited by 15 publications

(14 citation statements)

References 30 publications

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“…MI has been carried out in several structures such as nonlinear optics [5], and fluid dynamics [6]. In our previous work, we have shown that for small perturbations, the variation of the self-Kerr nonlinear term expands the MI growth rates and the MI bands are widely increased [12]. We have also illustrated the exponential growth of the plane wave when the value of the nonlinear term is considered large enough.…”

Section: Introductionmentioning

confidence: 87%

“…Besides that, a self-Kerr nonlinear term has been used in optomechanical systems for instance to generate non-classical mechanical states [10], and for low-power phonon lasing [11]. In [12], self-kerr nonlinearity was used to generate optical solitons in one-dimensional optomechanical array. The authors have shown that solitons are induced by photon-photon interaction and that for strong nonlinear term, choatic solitonic wave start propagating in the structure.…”

Section: Introductionmentioning

confidence: 99%

“…It is obvious that MI can induce unstable/stable modes as well as localized waves for a given wave vector or any other parameter of the system due to its effects. In nonlinear structure, where nonlinear and dispersion terms interact, MI is crucial for the process of generating the localized wave patterns such as dark soliton, bright soliton, rogue wave and breather [2,4,12]. MI has been carried out in several structures such as nonlinear optics [5], and fluid dynamics [6].…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Nonlinear localized wave modes in optomechanical array

Houwe,

Djorwé,

Souleymanou

et al. 2023

Phys. Scr.

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Optomechanical arrays have been used in many areas of research, from nonlinear optics to acoustics. In particular, the optomechanical array has been studied for its interesting properties such as strong optical force and high frequency resonance. In this work, we carry out the modulated wave patterns and nonlinear modes by driving one end of the optomechanical array in the forbidden gap. We use the discrete nonlinear Schr"{o}dinger equation with self-Kerr nonlinear term to determine the threshold amplitude. We then consider the driven amplitude to drive the model above the phonon band. The result is a train of waves with an asymmetric shape in the forbidden gap. For large values of the nonlinear term, we observe unstable modes of the modulation growth rates and the modulated wave patterns also emerge from the driven optomechanical array. At the specific cell index, the pulse train increases in amplitude and brings instability in the bandgap. These results open a new feature of the position modulated self-Kerr nonlinear term as an internal force to drive the nonlinear Schr"{o}dinger equation.

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Section: Introductionmentioning

confidence: 87%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Nonlinear localized wave modes in optomechanical array

Houwe,

Djorwé,

Souleymanou

et al. 2023

Phys. Scr.

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show abstract

“…[19,20] The ability to store and retrieve optical information in a tunable manner often benefits optical engineers and physicists, and coherent localized structure is considered as a key ingredient to managing the flow of information over complex optical networks. Recently, solitons and breathers are introduced into optomechanics, [13,14,[21][22][23] and the realization of micro-solitons driven by light opens up new avenues for optomechanical and related technologies, and may find applications in sensing, information processing, energy storage, and communications. It has been shown that Benjamin-Feir instability closely related to many hydrodynamic phenomena, for example, rogue wave and solitons, [24][25][26][27][28] so our results may introduce an interesting link between cavity optomechanics and hydrodynamics.…”

Section: Introductionmentioning

confidence: 99%

Optomechanically Induced Benjamin–Feir Instability

Xiong

2023

Laser & Photonics Reviews

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Benjamin–Feir instability, which is originally discovered in hydrodynamics and plasma physics, has become a central process of nonlinear physics over the past decades. On‐chip solid‐state devices with controllable Benjamin–Feir instability can exhibit a rich set of spatio‐temporal dynamics that are inherently sensitive to their initial distribution, which are vital for force sensors and information processing. By exploiting the nonlinear photonic evolution and localization in a micro‐fabricated optomechanical chain, the direct signal of optomechanically induced Benjamin–Feir instability is identified within the reach of current experimental techniques. A spatio‐temporal dynamical theory of optomechanically induced Benjamin–Feir instability is represented, which provides a quantitative interpretation of the exponential growth characteristics. Numerical calculations of the spatio‐temporal dynamics in the optomechanical chain are in excellent agreement with this theory. Optomechanically induced Benjamin–Feir instability may entail a wide range of intriguing phenomena and find applications in on‐chip manipulations of light propagation and precision measurements due to their exponential growth characteristics.

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“…In [11], the authors have depicted the chaos-like motion and unstable modes incited by the self-modulated Kerr nonlinearity in optomechanical arrays. The discrete nonlinear Schrödinger equation (DNLSE) is the most well-known discrete model during MI analysis, and localized modes [1][2][3][4][5][6][7][8][9][10][11]. For example, in [25] the authors used the discrete cubic-quintic NLSE to show the effects of the nonlinear terms on the train of waves propagating in the forbidden gap (FG).…”

Section: Introductionmentioning

confidence: 99%

Discrete modulation instability and localized waves of the coupled semi-discrete Hirota equation

Houwe

Abbagari

Akinyemi

et al. 2023

Preprint

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In this paper, we use the numerical simulation of the discrete Hirota equation to point out the localized modes and wave patterns. The discrete modulation instability is used to demonstrate how the nonlinear term generates unstable or stable modes when a little perturbation is introduced. We have also stated that for strong enough nonlinear terms, new bands emerge. Furthermore, by applying an external periodic force, we were able to push one end of the discrete Hirota model into the forbidden frequency gap. We established the threshold amplitude expression and the driven amplitude. According to one finding, the threshold of supratransmission decreases as the nonlinear term of the discrete Hirota equation increases. For specific times of propagation, we showed the propagation of the train of waves as well as the modulated wave patterns. We demonstrated the wave train traveling through the band gap, where energy jumps from the bottom to the top and vice versa, over a significant period of time. These findings will almost certainly pave the way for new nonlinear dynamics applications.

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Discrete solitons in nonlinear optomechanical array

Cited by 15 publications

References 30 publications

Nonlinear localized wave modes in optomechanical array

Nonlinear localized wave modes in optomechanical array

Optomechanically Induced Benjamin–Feir Instability

Discrete modulation instability and localized waves of the coupled semi-discrete Hirota equation

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