Interaction of Localized Structures in an Optical Pattern-Forming System

Schäpers, B.; Feldmann, Michael; Ackemann, T.; Lange, W.

doi:10.1103/physrevlett.85.748

Cited by 201 publications

(110 citation statements)

References 22 publications

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“…Also, this configuration led to the first realization of localized structures in nonlinear optics [215]. The dynamics and interaction of these localized structures have been extensively investigated [216][217][218][219] (Fig. 1.8).…”

Section: Single-feedback-mirror Configurationmentioning

confidence: 99%

Transverse Patterns in Nonlinear Optical Resonators

Staliūnas

Sánchez‐Morcillo

2003

Springer Tracts in Modern Physics

175

156

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This book is devoted to the formation and dynamics of localized structures (vortices, solitons) and of extended patterns (stripes, hexagons, tilted waves) in nonlinear optical resonators such as lasers, optical parametric oscillators, and photorefractive oscillators. Theoretical analysis is performed by deriving order parameter equations, and also through numerical integration of microscopic models of the systems under investigation. Experimental observations, and possible technological implementations of transverse optical patterns are also discussed. A comparison with patterns found in other nonlinear systems, i.e. chemical, biological, and hydrodynamical systems, is given.

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Section: Single-feedback-mirror Configurationmentioning

confidence: 99%

Transverse Patterns in Nonlinear Optical Resonators

Staliūnas

Sánchez‐Morcillo

2003

Springer Tracts in Modern Physics

175

156

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“…This equation allow us to obtain an analytical expression for the front interaction, which is in good agreement with numerical simulations. , and nonlinear optics [8,9]. One can understand these localized patterns as patterns extend only over a small portion of the spatial homogeneous systems.…”

Section: Introductionmentioning

confidence: 99%

“…In the last decade localized patterns or localized structures have been observed in different experiments: liquid crystals [3], gas discharge systems [4], chemical reactions [5], fluids [6], granular media [7], and nonlinear optics [8,9]. One can understand these localized patterns as patterns extend only over a small portion of the spatial homogeneous systems.…”

mentioning

confidence: 99%

Localized patterns and hole solutions in one-dimensional extended systems

Clerc

Falcón

2005

Physica A: Statistical Mechanics and its Applications

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The existence, stability properties, and bifurcation diagrams of localized patterns and hole solutions in one-dimensional extended systems is studied from the point of view of front interactions. An adequate envelope equation is derived from a prototype model that exhibits these particle-type solutions. This equation allow us to obtain an analytical expression for the front interaction, which is in good agreement with numerical simulations. , and nonlinear optics [8,9]. One can understand these localized patterns as patterns extend only over a small portion of the spatial homogeneous systems. From the dynamic point of view, localized patterns in one-dimensional spatial systems are the homoclinic connection for the stationary dynamical system. Recently, from a geometrical point of view, the existence, stability properties, and bifurcation diagrams of localized patterns in one-dimensional extended systems have been studied [10].The aim of this manuscript is to describe how one-dimensional localized patterns and hole solutions arise from front interactions. From a prototype model that exhibits localized patterns and hole solutions, the subcritical Swift-Hohenberg equation, we deduce an adequate equation for the envelope of these particle type solutions. This model has a front solution that connects a stable homogeneous state with an also stable but spatially periodic one. Due to the

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“…1c). This radial modulation is due to the "oscillating tails" of the switching front [10] responsible for such phenomena as stabilization of solitons [10], forming bound states of several solitons ("molecules") [11], or stabilizing large patterns (as shown below), through the forces associated with the gradients of the modulations [12]. We note for clarity that the switching in the lower two rows of Fig.…”

mentioning

confidence: 99%

From coherent to incoherent hexagonal patterns in semiconductor resonators

2001

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We find that hexagonal structures forming in semiconductor resonators can range from coherent patterns to arrangements of loosely bound spatial solitons, which can be individually switched. Such incoherent arrangements are stabilized by gradient forces, as evidenced by the stability of hexagonal structures with single-or multiple-soliton defects. We interpret the experimental observations by numerical simulations based on a model for a large aperture semiconductor microresonator.PACS 42.65.Sf, 42.65.Pc, 47.54.+r Pattern formation in the form of hexagonal structures was predicted years ago for resonators containing a reactive nonlinearity [1]. We have recently given the first proof of the phenomenon using semiconductor microresonators in the dispersive limit [2]. This kind of pattern formation was regarded as an important precursor of optical soliton formation, the latter being of technical importance for all-optical information processing [3]. We showed the existence of these bright and dark spatial solitons recently [4,5].Our finding, that individual bright spots of the hexagonal patterns can for certain parameters be "switched off" without apparent effects for the rest of the hexagonal pattern [2], caused a debate about whether such individually switchable "pixels" in a hexagonal pattern have soliton properties and more in general about the nature of these hexagonal patterns. In this article we clarify these questions by interpreting our experimental observations using numerics on a semiconductor resonator model [6].For completeness we repeat shortly the experimental arrangement: Light of wavelength near the semiconductor band edge (850 nm), generated by a continuous Ti:Al 2 0 3 -laser, irradiates an area of 50-100 µm diameter of the semiconductor resonator sample, with intensity of up to 3 kW/cm 2 . The sample is a quantum-well stack between Bragg mirrors of 99.7 % reflectivity [7]. The optical resonator length is about 3 µm so that a Fresnel number of several 100 is excited, sufficient for complex structure to form. The light is admitted to the sample for durations of a few µs (through a mechanical chopper, to limit thermal phenomena) repeated every ms.As the substrate, on which the resonator sample is grown, is opaque at the wavelength used, all observations are done in reflection. Either by taking ns-snapshots of the illuminated area, or by following the reflected intensity in particular points of the illuminated area as a function of time, using a fast photodiode. Details are given in [2,5].

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Interaction of Localized Structures in an Optical Pattern-Forming System

Cited by 201 publications

References 22 publications

Transverse Patterns in Nonlinear Optical Resonators

Transverse Patterns in Nonlinear Optical Resonators

Localized patterns and hole solutions in one-dimensional extended systems

From coherent to incoherent hexagonal patterns in semiconductor resonators

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