Transverse dynamics in cavity nonlinear optics (2000–2003)

Mandel, P.; Tlidi, Mustapha

doi:10.1088/1464-4266/6/9/r02

Cited by 131 publications

(55 citation statements)

References 331 publications

(256 reference statements)

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“…To be specific, we focus on the Swift-Hohenberg equation, which has been proposed as a prototypical example for pattern forming systems, in areas as diverse as nonlinear optics [15], Rayleigh-Bénard convection [2], granular media [1], chemical reactions [14], liquid crystals and solidification; see [4] and references there. Most of those systems exhibit stationary stripe (or roll) patterns, that is, planar patterns which are independent of x and periodic in y, where x and y are coordinates in the plane of observation.…”

Section: Introductionmentioning

confidence: 99%

Interfaces between rolls in the Swift-Hohenberg equation

Hărăguş

Scheel²

2007

IJDSDE

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We study the existence of interfaces between stripe or roll solutions in the Swift-Hohenberg equation. We prove the existence of two different types of interfaces: corner-like interfaces, also referred to as knee solutions, and step-like interfaces. The analysis relies upon a spatial dynamics formulation of the existence problem and an equivariant center manifold reduction. In this setting, the interfaces are found as heteroclinic and homoclinic orbits of a reduced system of ODEs.

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Section: Introductionmentioning

confidence: 99%

Interfaces between rolls in the Swift-Hohenberg equation

Hărăguş

Scheel²

2007

IJDSDE

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“…In particular, LSs could be used as bits for information storage and processing. Several overviews have been published on this active area of research [31,9,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48].…”

Section: Introductionmentioning

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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“…These structures consist of bright or dark pulses in the transverse plane orthogonal to the propagation axis. The spatial confinement of light was investigated more than two decades ago (for reviews, see [5][6][7][8][9][10]). When they are sufficiently far away from each other, localized peaks are independent and randomly distributed in space.…”

Section: Introductionmentioning

confidence: 99%

Cavity solitons in vertical-cavity surface-emitting lasers

Vladimirov

Pimenov

Gurevich

et al. 2014

Phil. Trans. R. Soc. A.

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We investigate a control of the motion of localized structures (LSs) of light by means of delay feedback in the transverse section of a broad area nonlinear optical system. The delayed feedback is found to induce a spontaneous motion of a solitary LS that is stationary and stable in the absence of feedback. We focus our analysis on an experimentally relevant system, namely the vertical-cavity surface-emitting laser (VCSEL). We first present an experimental demonstration of the appearance of LSs in a 80 µm aperture VCSEL. Then, we theoretically investigate the self-mobility properties of the LSs in the presence of a time-delayed optical feedback and analyse the effect of the feedback phase and the carrier lifetime on the delay-induced spontaneous drift instability of these structures. We show that these two parameters affect strongly the space-time dynamics of twodimensional LSs. We derive an analytical formula for the threshold associated with drift instability of LSs and a normal form equation describing the slow time evolution of the speed of the moving structure.

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Transverse dynamics in cavity nonlinear optics (2000–2003)

Cited by 131 publications

References 331 publications

Interfaces between rolls in the Swift-Hohenberg equation

Interfaces between rolls in the Swift-Hohenberg equation

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

Cavity solitons in vertical-cavity surface-emitting lasers

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