Influence of Boundaries on Localized Patterns

Kozyreff, Gregory; Assemat, Pauline; Chapman, S. Jonathan

doi:10.1103/physrevlett.103.164501

Cited by 33 publications

(44 citation statements)

References 31 publications

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“…Thus, in presence of gradients of different origins, the stable positions of CSs will be those where the forces applied on them compensate. This view may however, be mitigated by the recent theoretical demonstration in [111] that CS may also feel the boundaries, even if they are far from them, so that only a finite set of positions are allowed. This point lacks; however, a clear experimental demonstration.…”

Section: Soliton-forcementioning

confidence: 85%

Cavity Solitons in VCSEL Devices

Barbay

Kuszelewicz

Tredicce

2011

Advances in Optical Technologies

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We review advances on the experimental study of cavity solitons in VCSELs in the past decade. We emphasize on the design and fabrication of electrically or optically pumped broad-area VCSELs used for CSs formation and review different experimental configurations. Potential applications of CSs in the field of photonics are discussed, in particular the use of CSs for all-optical processing of information and for VCSELs characterization. Prospects on self-localization studies based on vertical cavity devices involving new physical mechanisms are also given.

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Section: Soliton-forcementioning

confidence: 85%

Cavity Solitons in VCSEL Devices

Barbay

Kuszelewicz

Tredicce

2011

Advances in Optical Technologies

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“…In each case we applied multiplicative spatial forcing by allowing the parameter a to depend on space. Forcing of this type preserves the homogeneous state u = 0 while selecting preferred locations for the spatial structures, somewhat in the manner of finite domain boundary conditions [25,26]. We first examined the effects of periodic forcing with wavelength equal to the natural wavelength generated by the Swift-Hohenberg equation.…”

Section: Discussionmentioning

confidence: 99%

“…As it does so, a defect is created that flattens the central region creating a state reminiscent of a two-pulse state [5,24]. The resulting behavior resembles that of localized structures in SH23 on nonperiodic domains with mixed boundary conditions [25,26].…”

Section: A Periodic Heterogeneity F Pmentioning

confidence: 99%

Spatial localization in heterogeneous systems

2014

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We study spatial localization in the generalized Swift-Hohenberg equation with either quadratic-cubic or cubic-quintic nonlinearity subject to spatially heterogeneous forcing. Different types of forcing (sinusoidal or Gaussian) with different spatial scales are considered and the corresponding localized snaking structures are computed. The results indicate that spatial heterogeneity exerts a significant influence on the location of spatially localized structures in both parameter space and physical space, and on their stability properties. The results are expected to assist in the interpretation of experiments on localized structures where departures from spatial homogeneity are generally unavoidable.

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“…It is one of the most studied partial differential equation in various areas of nonlinear science [68][69][70]. It constitutes a paradigmatic evolution equation that exhibits periodic spatio-temporal patterns as well as localized structures [6,7,11,71,72]. , and Ωτ = −η sin(Ω).…”

Section: Derivation Of the Swift-hohenberg Equation With Delaymentioning

confidence: 99%

“…In the absence of delayed feedback, these localized structures exist in the sub-critical domain where a uniform solution and a branch of spatially periodic solution are both linearly stable [6,7,71,72]. However, in the presence of delay term X(x, y, t − τ ) the DSHE equation (14) loses the gradient structure.…”

Section: Pinning and Feedback Delaymentioning

confidence: 99%

Spontaneous motion of localized structures and localized patterns induced by delayed feedback

et al. 2010

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Abstract.We study the properties of 2D dissipative structures in a coherently driven optical resonator subjected to a delayed feedback. It has been predicted that delayed feedback can lead to the spontaneous motion of bright localized structures [M. Tlidi et al., Phys. Rev. Lett. 103, 103904 (2009)]. We study here the phenomenon in detail. In particular, we show that the delayed feedback induces a spontaneous motion of periodic patterns and dark localized structures. We focus our analysis on nascent optical bistability regime where the space time dynamics is described by a variational Swift-Hohenberg equation. In the absence of delayed feedback, dark localized structures and patterns do not move. This behavior occurs when the product of the delay time and the feedback strength exceeds some critical value.

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Influence of Boundaries on Localized Patterns

Abstract: OATAO is an open access repository that collects the work of Toulouse researchers and makes it freely available over the web where possible.

Cited by 33 publications

References 31 publications

Cavity Solitons in VCSEL Devices

Cavity Solitons in VCSEL Devices

Spatial localization in heterogeneous systems

Spontaneous motion of localized structures and localized patterns induced by delayed feedback

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