Excitability Mediated by Localized Structures in a Dissipative Nonlinear Optical Cavity

Gomila, Damià; Matías, Manuel A.; Colet, Pere

doi:10.1103/physrevlett.94.063905

Cited by 77 publications

(94 citation statements)

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“…Additionally, the SL line in Fig. 3c) leads to another Type I excitable region (discussed at length in [8]), but at difference with the SNIC bifurcation line, that extends for a wide parameter range, the SL occurs in a very narrow region (Fig. 3c), and therefore it may be more difficult to find experimentally.…”

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confidence: 99%

“…In Ref. [8] it was reported that DS may exhibit excitable behavior. A system is said to be excitable if perturbations below a certain threshold decay exponentially, while perturbations above this threshold induce a large response before going back to the resting state.…”

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confidence: 99%

“…3) the fundamental solution is stable in regions I and V, pinned DS are stable in III and IV and stable trains of DS exist in II and V. The scenario shown in Figs. 3b and 3c, much richer than in [8], is characteristic of systems displaying relaxation oscillations described, for instance, by the Van der Pol equation (see Fig. 2.1.2 in [31]).…”

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confidence: 99%

“…Particularly interesting is the case of dissipative solitons (DS) [2], exponentially localized structures in dissipative systems driven out of equilibrium, as they can behave like discrete objects in continuous systems. DS can display a variety of dynamical regimes such as periodic oscillations [3][4][5], chaos [6,7], or excitability [8]. DS emerge from a balance between nonlinearity and spatial coupling, and driving and dissipation.…”

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confidence: 99%

“…Our results open also the possibility to observe this phenomenon in a wide variety of physical systems. [6,7], or excitability [8]. DS emerge from a balance between nonlinearity and spatial coupling, and driving and dissipation.…”

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confidence: 99%

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Dissipative Soliton Excitability Induced by Spatial Inhomogeneities and Drift

et al. 2013

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We show that excitability is generic in systems displaying dissipative solitons when spatial inhomogeneities and drift are present. Thus, dissipative solitons in systems which do not have oscillatory states, such as the prototypical Swift-Hohenberg equation, display oscillations and Type I and II excitability when adding inhomogeneities and drift to the system. This rich dynamical behavior arises from the interplay between the pinning to the inhomogeneity and the pulling of the drift. The scenario presented here provides a general theoretical understanding of oscillatory regimes of dissipative solitons reported in semiconductor microresonators. Our results open also the possibility to observe this phenomenon in a wide variety of physical systems. [6,7], or excitability [8]. DS emerge from a balance between nonlinearity and spatial coupling, and driving and dissipation. They are unique once the system parameters are fixed, and they are different from the well known conservative solitons that appear as oneparameter families.In optical cavities, DS (also known as cavity solitons) have been proposed as bits for all-optical memories [9-13], due to their spatial localization and bistable coexistence with the fundamental solution. In Ref. [8] it was reported that DS may exhibit excitable behavior. A system is said to be excitable if perturbations below a certain threshold decay exponentially, while perturbations above this threshold induce a large response before going back to the resting state. Excitability is found for parameters close to those where a limit cycle disappears [14]. Excitability mediated by DS is different from the well known dynamics of excitable media, whose behavior stems from the (local) excitability present in the system without spatial degrees of freedom. Excitability of DS is an emergent behavior, arising through the spatial interaction and not present locally. Moreover, the interaction between different excitable DS can be used to build alloptical logical gates [15].In real systems, however, typically solitons are static, so oscillatory or excitable DS are far from being generic. In this work we present a mechanism that generically induces dynamical regimes, such as oscillations and excitable behavior, in which the structure of the DS is preserved. The mechanism relies on the interplay between spatial inhomogeneities and drift, and therefore can be implemented under very general conditions. Inhomogeneities, or defects, are unavoidable in any experimental setup, and drift is also often present in many optical, fluid and chemical systems, due to misalignments of the mirrors [16,17], nonlinear crystal birefringence [18], or parameter gradients [19], in the first case, and due to the flow of a fluid in the others [20,21]. Roughly speaking, the presence of inhomogeneities and drift introduce two competing effects. On the one hand, an inhomogeneity pins a DS at a fixed position and, on the other, the drift tries to pull it out. If the drift overcomes the pinning, DS solitons are released from the in...

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confidence: 99%

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confidence: 99%

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confidence: 99%