Localized structures in an optical feedback interferometer: properties and interactions

The occurrence of localized structures in a nonlinear optical experiment is a robust phenomenon, persisting in a wide region of the parameter space. We demonstrate how different control parameters determine several properties of localized structures; among these of particular relevance are the contrast and the amplitude and frequency of the oscillations appearing on the tails of the structures. Tuning these oscillations modifies the interactions between pairs of localized structures, thus resulting in a substantial modification of their bound-state spectrum. PACS 42.65.Tg; 05.45.Yv; 42.65.Sf     

Curvature instability in passive diffractive resonators

We study the stability of localized structures in a passive optical bistable system. We show that there is a critical value of the input field intensity above which localized structures are unstable with respect to a curvature instability. Beyond this instability boundary, a transition from the localized branch of solutions to stable hexagons is found.     

Control of localized structures in an optical feedback interferometer

We report a detailed experimental investigation of the dependence of localized structures, observed in a nonlinear optical device, on several control parameters. A first step of the study consists in the determination of the region of existence of localized states as a function of the system variables. Subsequently, we show how different control parameters can be used to the aim of tuning several localized structures properties; among these, of particular relevance are the contrast and the amplitude and frequency of the oscillations appearing on the tails of the structures. A discussion of the relation between the localized states here studied and the one predicted by general model for pattern forming systems is also given.     

Excitability mediated by localized structures in a dissipative nonlinear optical cavity

We find and characterize an excitability regime mediated by localized structures in a dissipative nonlinear optical cavity. The scenario is that stable localized structures exhibit a Hopf bifurcation to self-pulsating behavior, that is followed by the destruction of the oscillation in a saddle-loop bifurcation. Beyond this point there is a regime of excitable localized structures under the application of suitable perturbations. Excitability emerges from the spatial dependence since the system does not exhibit any excitable behavior locally. We show that the whole scenario is organized by a Takens-Bogdanov codimension-2 bifurcation point.     

Rich Localized Coherent Structures of the (2+1)-Dimensional Broer-Kaup-Kupershmidt Equation

Using a Backlund transformation and the variable separation approach, we find there exist abundant localized coherent structures for the (2 + 1)-dimensional Broer-Kaup-Kupershmidt (BKK) system. The abundance of the localized structures for the model is introduced by the entrance of an arbitrary function of the seed solution. For some specialselections of the arbitrary function, it is shown that the localized structures of the BKK equation may be dromions, lumps, ring solitons, peakons, or fractal solitons etc.     

Self-pulsing localized structures in a laser with saturable absorber

We consider a broad area heterostructured semiconductor laser with an integrated saturable absorber in a monolithic configuration. We extend beyond the single-longitudinal mode approximation a model already used to predict transversely localized structures or cavity solitons (CSs) in a shorter device and we numerically demonstrate the existence of self-pulsing transverse localized structures. Like CSs, these structures can simultaneously coexist in different transverse locations.     

Control and managing of localized states in two-dimensional systems with periodic forcing

We study the formation of localized structures in two-dimensional systems with periodic forcing, showing that these types of systems provide an adequate framework for the study and control of localized structures. Theoretically, we introduce a dissipative ϕ ⁴ model as a prototype for a bistable spatially forced system, and we show that with different spatial forcings of small amplitudes, such as square or hexagonal grids, this model exhibits a family of localized structures. By changing the forcing parameters, we control the bistability between the various induced patterns. Experimentally, based on an optical feedback with spatially amplitude-modulated beam, we set-up a two-dimensional forced experiment in a nematic liquid crystal cell. By changing the forcing parameters, the system exhibits a family of localized structures that are confirmed by numerical simulations for the average liquid crystal tilt angle.     

Bistability between different localized structures in nonlinear optics

We report the observation of different localized structures coexisting for the same parameter values in an extended system. The experimental findings are carried out in a nonlinear optical interferometer and are fully confirmed by numerical simulations. The existence of each kind of localized structure is put in relation to a corresponding delocalized pattern observed. A quantitative evaluation of the range of pump parameter allowing bistability between localized structures is given. The phenomenon reported results to be robust in parameter space.     

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

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.     

Forcing and control of localized states in optical single feedback systems

Under feedback extended nonlinear optical systems spontaneously show a variety of periodic patterns and structures. Control gives new insight into these phenomena and it can open the way for potential application of nonlinear optical structures. We briefly review methods to control localized states in single feedback experiments. Application of a Fourier control method allows to modify interaction behavior of the localized states. As a further approach we study a forcing method, using externally created light fields as additional input to the system. Recent experiments show that the forcing method enables to favor addressing positions for localized structures. We demonstrate static addressing and favoring of addressing positions. We extend the forcing method to a dynamic forcing scheme, which allows to move and reposition localized states. Additionally forcing is used to balance experimental imperfections. PACS 05.45.Gg; 42.60.Jf; 42.65.Tg     

Interaction of localized structures in an optical pattern-forming system

We report on the observation and interaction of dissipative localized structures in an optical pattern-forming system. Single localized structures are found to have oscillatory decaying tails originating from diffraction. We observe bound states of two or more constituents. These clusters contain several preferred mutual distances. Numerical simulations show that the corresponding interactions are mediated by the oscillatory tails.     

First laboratory observation of freely propagating electrostatic waves produced by intense, localized field structures

Freely propagating electrostatic waves (free modes) are observed to be produced by intense, localized field structures in laboratory measurements performed in an unmagnetized plasma in a state of strong Langmuir turbulence. The freely traveling waves conform to the Langmuir dispersion relation and have an average frequency which is approximately 11% higher than the average frequency of the localized field structures. The observations are consistent with the predictions of strong Langmuir turbulence theory.     

Beam propagation in gain–loss balanced waveguides

Linear and nonlinear localized modes of a slab waveguide with distributed gain and loss are studied. The structure is an optical analog of parity-time symmetric potentials in quantum mechanics. Such waveguide structures support stable localized modes. The explicit equation for the propagation constant of linear modes is obtained. The existence of stable nonlinear modes in such waveguides is demonstrated. Bend losses in such structures are analyzed.     

Domain wall dynamics: Growth laws,localized structures and stable droplets

We discuss the relation between the dynamics of walls separating two equivalent domains and the existence of different kinds of localized structures in systems far from thermodynamic equilibrium. In particular we focus in systems displaying a modulational instability of a flat front where an amplitude equation for the dynamics of the curvature allows to characterize different growth regimes and to predict the existence of stable droplets, localized structures whose stability comes from nonlinear curvature effects.     

Introduction: dissipative localized structures in extended systems

Localized structures belong to the class of dissipative structures found far from equilibrium. Contributions from the most representative groups working on a various fields of natural science such as biology, chemistry, plant ecology, mathematics, optics, and laser physics are presented. The aim of this issue is to gather specialists from these fields towards a cross-fertilization among these active areas of research and thereby to present an overview of the state of art in the formation and the characterization of dissipative localized structures. Nonlinear optics and laser physics have an important part in this issue because of potential applications in information technology. In particular, localized structures could be used as "bits" for parallel information storage and processing.     

New types of spatial structures in multisublattice antiferromagnets

A broad class of three-dimensional space structures in multisublattice antiferromagnets was found in the isotropic approximation (the principal chiral field model on the SU(2) group). According to the Andreev-Marchenko theory, this approximation is applicable to spin glasses and provides qualitative understanding of structures in real multisublattice antiferromagnets. Special substitutions were used to reduce the equations of the model to new equations with simple geometric interpretation. A differential geometry method was applied to obtain various structure types (some of which were determined by arbitrary functions), including localized and nonlocalized textures, structures with the degree of mapping equal to one, antiferromagnetic “targets” and three-dimensional sources, and two-and three-dimensional vortex and spiral structures. Possibilities for experimentally checking the presence of localized, vortex, and spiral structures in antiferromagnets were demonstrated.     

(2+1)维非线性薛定谔方程的环孤子,dromion,呼吸子和瞬子

利用分离变量法,研究了(2+1)维非线性薛定谔(NLS)方程的局域结构.由于在B?cklund变换和变量分离步骤中引入了作为种子解的任意函数,得到了NLS方程丰富的局域结构.合适地选择任意函数,局域解可以是dromion,环孤子,呼吸子和瞬子.dromion解不仅可以存在于直线孤子的交叉点上,也可以存在于曲线孤子的最近邻点上.呼吸子在幅度和形状上都进行了呼吸 关键词： 非线性薛定谔方程 分离变量法 孤子结构     

LSDA+U方法对富勒烯内掺稀土原子的结构和电子结构的理论研究

在密度泛函理论框架下的局域密度近似方法 (LDA)能够准确地给出广延态电子体系的基态电子结构 ,是研究复杂体系的电子结构的一种非常成功的方法。由于这种方法不含参数 ,被广泛地用于微观体系的研究。但是 ,在处理的体系中含有局域电子时 ,由于方法的局限 ,给出的结果与光电子谱等试验结果符合得并不好。LSDA U方法是在局域自旋密度近似的框架下 ,结合模型哈密顿方法 ,对局域电子采用哈伯德模型描述 ,用以改进局域密度近似计算的一种方法。本文利用局域密度近似下的离散变分团簇方法 (DVM )对于内嵌稀土原子的富勒烯Er2 @C82 、Tm @C82 的电子结构进行了第一性原理的计算。对于体系中所含的稀土原子存在强关联的 4f电子 ,在LDA方法计算的基础上 ,考虑 4f电子在位库仑作用 ,用LSDA U方法研究了上述体系 ,得到了可以和XPS和吸收谱相比较的结果。     

Exotic Localized Coherent Structures of New (2+1)-Dimensional Soliton Equation

The variable separation approach is used to obtain localized coherent structures of the new (2 1)-dimensional nonlinear partialdifferential equation. Applying the Backlund transformation and introducing the arbitraryfunctions of the seed solutions, the abundance of the localized structures of this model are derived. Some special types ofsolutions solitoff, dromions, dromion lattice, breathers and instantons are discussed by selecting the arbitrary functionsappropriately. The breathers may breath in their amplititudes, shapes, distances among the peaks and even the numberof the peaks.     

Asymptotics of large bound states of localized structures

We analyze stationary fronts connecting uniform and periodic states emerging from a pattern-forming instability. The size of the resulting periodic domains cannot be predicted with weakly nonlinear methods. We show that what determine this size are exponentially small (but exponentially growing in space) terms. These can only be computed by going beyond all orders of the usual multiple-scale expansion. We apply the method to the Swift-Hohenberg equation and derive analytically a snaking bifurcation curve. At each fold of this bifurcation curve, a new pair of peaks is added to the periodic domain, which can thus be seen as a bound state of localized structures. Such scenarios have been reported with optical localized structures in nonlinear cavities and localized buckling.