Temporal localized structures in photonic crystal fibre resonators and their spontaneous symmetry-breaking instability

Bahloul, L.; Cherbi, L.; Hariz, A.; Tlidi, Mustapha

doi:10.1098/rsta.2014.0020

Cited by 16 publications

(8 citation statements)

References 41 publications

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“…We have described spatially localized structures, recent investigations have shown that temporal localized structures have been found in fibre resonators [104,90,105,106,107,108] and in VCSELS with a saturable absorber [109]. On the other hand, it has been shown that the combinated influence of diffraction and chromatic dispersion leads to the formation of three dimensional localized structures often called light bullet [110,111,112,113].…”

Section: Discussionmentioning

confidence: 99%

Localized Structures in Broad Area VCSELs: Experiments and Delay-Induced Motion

Tlidi

Averlant

Vladimirov

et al. 2015

Springer Proceedings in Physics

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We investigate the space-time dynamics of a Vertical-Cavity SurfaceEmitting Laser (VCSEL) subject to optical injection and to delay feedback control. Apart from their technological advantages, broad area VCSELs allow creating localized light structures (LSs). Such LSs, often called Cavity Solitons, have been proposed to be used in information processing, device characterization, and others. After a brief description of the experimental setup, we present experimental evidence of stationary LSs. We then theoretically describe this system using a mean field model. We perform a real order parameter description close to the nascent bistability and close to large wavelength pattern forming regime. We theoretically characterize the LS snaking bifurcation diagram in this framework. The main body of this chapter is devoted to theoretical investigations on the time-delayed feedback control of LSs in VCSELs. The feedback induces a spontaneous motion of the LSs, which we characterize by computing the velocity and the threshold associated with such motion. In the nascent bistability regime, the motion threshold and the velocity

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Section: Discussionmentioning

confidence: 99%

Localized Structures in Broad Area VCSELs: Experiments and Delay-Induced Motion

Tlidi

Averlant

Vladimirov

et al. 2015

Springer Proceedings in Physics

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“…to have a finite domain of existence delimited by two pump power values [10], as well as to stabilize dark temporal LSs [11][12][13]. In the absence of fourth order dispersion, with only second or/and third orders of dispersion, fronts interaction leads to the formation of moving LS in a regime far from any modulational instability [14].…”

Section: Driving Fieldmentioning

confidence: 99%

“…The nonlinear Schrödinger equation supplemented by the cavity boundary condition leads to a generalized Lugiato-Lefever equation [10]. The inclusion of the fourth order dispersion allows the modulational instability (MI) to have a finite domain of existence delimited by two pump power values [10], as well as to stabilize dark temporal LSs [11][12][13]. In the absence of fourth order dispersion, with only second or/and third orders of dispersion, fronts interaction leads to the formation of moving LS in a regime far from any modulational instability [14].…”

Section: Introductionmentioning

confidence: 99%

Swift-Hohenberg equation with third-order dispersion for optical fiber resonators

et al. 2019

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We investigate the dynamics of a ring cavity made of photonic crystal fiber and driven by a coherent beam working near to the resonant frequency of the cavity. By means of a multiple-scale reduction of the Lugiato-Lefever equation with high order dispersion, we show that the dynamics of this optical device, when operating close to the critical point associated with bistability, is captured by a real order parameter equation in the form of a generalized Swift-Hohenberg equation. A Swift-Hohenberg equation has been derived for several areas of nonlinear science such as chemistry, biology, ecology, optics, and laser physics. However, the peculiarity of the obtained generalized Swift-Hohenberg equation for photonic crystal fiber resonators is that it possesses a third-order dispersion. Based on a weakly nonlinear analysis in the vicinity of the modulational instability threshold, we characterize the motion of dissipative structures by estimating their propagation speed. Finally, we numerically investigate the formation of moving temporal localized structures often called cavity solitons.

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“…Experimental investigation of this radiation induced by the high order dispersion was carried out in [13,14]. Numerical studies on CSs bound states in the presence of high order dispersions have been reported in [15,[17][18][19][20][21][22].In this letter, we provide an analytical description of how two CSs can interact under the action of the Cherenkov radiation induced by high order dispersion. For this purpose, we use the paradigmatic Lugiato-Lefever model with the third order dispersion term.…”

mentioning

confidence: 99%

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confidence: 99%

Effect of Cherenkov radiation on localized-state interaction

2018

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We study theoretically the interaction of temporal localized states in all fiber cavities and microresonator-based optical frequency comb generators. We show that Cherenkov radiation emitted in the presence of third order dispersion breaks the symmetry of their interaction and greatly enlarges the interaction range thus facilitating the experimental observation of the soliton bound states. Analytical derivation of the reduced equations governing slow time evolution of the positions of two interacting localized states in the Lugiato-Lefever model with third order dispersion term is performed. Numerical solutions of the model equation are in close agreement with analytical predictions.PACS numbers: 42.60. Da, 42.60.Fc, 42.65.Sf, 42.65.Tg, 05.45.Yv Frequency comb generation in microresonators has revolutionized such research disciplines as metrology and spectroscopy [1,2]. This due to the development of laser-based precision spectroscopy, including the optical frequency comb technique [3]. Driven optical microcavities widely used for the generation of optical frequency combs can be modeled by Lugiato-Lefever equation [4] that possesses solutions in the form of localized structures also called cavity solitons (CSs) [5,6]. Localized structures of the Lugiato-Lefever model have been theoretically predicted in [7] and experimentally observed in [8]. In particular, temporal CSs manifest themselves in the form of short optical pulses propagating in the cavity. The experimental evidence of temporal CSs interaction performed in [8] indicated that due to a very fast decay of the their tails, stable CS bound states are hardly observable. It has been also theoretically shown that when periodic perturbations are present [9, 10], radiation of weakly decaying dispersive waves, i.e., so-called Cherenkov radiation emitted by CSs leads to a strong increase of their interaction range [11,12]. Experimental investigation of this radiation induced by the high order dispersion was carried out in [13,14]. Numerical studies on CSs bound states in the presence of high order dispersions have been reported in [15,[17][18][19][20][21][22].In this letter, we provide an analytical description of how two CSs can interact under the action of the Cherenkov radiation induced by high order dispersion. For this purpose, we use the paradigmatic Lugiato-Lefever model with the third order dispersion term. We derive the equations governing the time evolution of the position of two well-separated CSs interacting weakly via their exponentially decaying tails. We demonstrate that the presence of the third order dispersion term breaking the parity symmetry of the model equation leads to a great increase of the CS interaction range and affects strongly the nature of the CSs interaction. We show that the interference between the dispersive waves emitted by two interacting CSs produces an oscillating pattern responsible for the stabilization of the CS bound states. In particular, we show that when two CSs interact, one of them remains almost unaffected by the...

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Temporal localized structures in photonic crystal fibre resonators and their spontaneous symmetry-breaking instability

Cited by 16 publications

References 41 publications

Localized Structures in Broad Area VCSELs: Experiments and Delay-Induced Motion

Localized Structures in Broad Area VCSELs: Experiments and Delay-Induced Motion

Swift-Hohenberg equation with third-order dispersion for optical fiber resonators

Effect of Cherenkov radiation on localized-state interaction

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