Effects of a localized beam on the dynamics of excitable cavity solitons

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

doi:10.1103/physreva.78.053821

Cited by 18 publications

(24 citation statements)

References 37 publications

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“…A detailed analysis of DS excitability mediated by a SNIC can be found in Ref. [26]. For parameters in region IV a supra-treshold perturbation that brings the system into region II triggers the unpinning of a DS leading to an excitable excursion.…”

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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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“…with height h and half-width σ [26]. This is motivated by the addressing beams used in optical systems to control DS [10,27].…”

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confidence: 99%

Dissipative Soliton Excitability Induced by Spatial Inhomogeneities and Drift

et al. 2013

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“…A detailed analysis of DS excitability mediated by a SNIC can be found in Ref. [26]. For parameters in region IV, a suprathreshold perturbation that brings the system into region II triggers the unpinning of a DS leading to an excitable excursion.…”

Section: H Y S I C a L R E V I E W L E T T E R Smentioning

confidence: 99%

“…Small changes of the parameter values do not substantially modify the results. A single spatial inhomogeneity located at the center is introduced adding a Gaussian profile bðxÞ ¼ h expfÀ½ðx À x 0 Þ= 2 g with height h and half-width [26]. This is motivated by the addressing beams used in optical systems to control DS [10,27].…”

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Dissipative soliton excitability induced by spatial inhomogeneities and drift

Parra‐Rivas

Gomila

Matias

et al. 2013

2013 Conference on Lasers &Amp; Electro-Optics Europe &Amp; International Quantum Electronics Conference CLEO EUROPE/IQEC

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“…As shown recently, pumping the system with a plane wave an a Gaussian beam on top of it, the threshold of excitability can be tuned by changing the amplitude of the Gaussian beam [3]. Here we consider three excitable cavity soliton in a linear arrangement, whose position is fixed by the Gaussian localized beam .…”

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Logical operations using excitable cavity solitons

Jacobo

Gomilla

Colet

et al. 2009

CLEO/Europe - EQEC 2009 - European Conference on Lasers and Electro-Optics and the European Quantum Electronics Conference

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With the goal of designing more compact optical schemes, cavity solitons have emerged as a potentially useful strategy for information storage, where a bit of information is represented by a cavity soliton. Cavity solitons may develop instabilities like start moving, breathing, or oscillating. In the latter case, LS oscillate in time while remaining stationary in space. It has also been demonstrated the existence ofa route in which oscillating Cavity Solitons are destroyed, leading to an excitable regime [1,2].The goal of the present work is to go a step further and discuss the potential of cavity solitons, in particular in a Kerr medium, in carrying out computations, i.e., not just for information storage. The key is the excitability exhibited by these cavity solitons. In particular, we will show how to design logic gates with cavity solitons, namely the AND , OR and NOT gates , as by combination of them one can construct any logical operation. In this work cavity solitons are in the excitable regime, what implies that if suitably perturbed (i.e . with a superthreshold perturbation) elicit a excitable excursion. For our computational porpoises we consider the presence of an excitable excursion as a bit' I ' and the absence of the excursion as a bit '0'.As shown recently, pumping the system with a plane wave an a Gaussian beam on top of it, the threshold of excitability can be tuned by changing the amplitude of the Gaussian beam [3]. Here we consider three excitable cavity soliton in a linear arrangement, whose position is fixed by the Gaussian localized beam . The two outer cavity solitons will represent the input signals , while the central one will be the output signal. By varying the excitability threshold and the distance between the structures the response of the central soliton to perturbations on the outer ones can be controlled and, therefore, different logic gates can be achieved.The logic gates reported in this work are two gates involving two inputs and one output (the AND and OR gates) , and one gate involving one input and one output (the NOT gate) . In Fig.

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Effects of a localized beam on the dynamics of excitable cavity solitons

Cited by 18 publications

References 37 publications

Dissipative Soliton Excitability Induced by Spatial Inhomogeneities and Drift

Dissipative Soliton Excitability Induced by Spatial Inhomogeneities and Drift

Dissipative soliton excitability induced by spatial inhomogeneities and drift

Logical operations using excitable cavity solitons

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