Spatio-temporal localization in dissipative and discrete systems

与前一阶段一样，该理论项目旨在为耗散和/或离散光学系统的非线性局部化理论提供真正的贡献，并弥合与研究单位进行的实验之间的差距。这项工作将分为四个工作包：a)时间耗散孤子；b)超材料中的空腔孤子；c)波导阵列中的时空定位；d)实验组的理论支持。在工作包(a)中，将研究耗散光学系统中的时间孤子。我们将重点关注两个系统，即首先是由半导体光放大器（SOA），可饱和吸收器（SA）和滤波器组成的周期性半导体器件，其次是具有适当被动锁模机制的短脉冲光纤激光系统。我们之前的研究表明，前一种系统可能表现出耗散孤子解，目前还没有真正分类和理解，但可能作为超快脉冲再生器。后一种系统对于产生具有确定性质的短脉冲非常重要，但也被认为是耗散孤子动力学最有前途的试验台之一。这两个主题都涉及一个仍有待解决的基本问题，即真正识别所有性质并利用耗散孤子在未来具有巨大应用潜力的系统中的吸引人的特性。工作包(b)将处理空腔孤子超材料的研究，作为我们离散空腔孤子工作的自然延续。目的是研究微纳米结构超材料的可定制线性特性与平面腔中各种非线性之间的相互作用。预计通过工程色散和衍射，将会产生新类型的腔孤子。研究的超材料范围从二维波导阵列、光子晶体到负折射率材料。利用耗散系统固有的增益，其特点是与环境进行稳定的能量交换，损耗，这被认为是所谓的负折射率超材料的关键问题，可以在这里被潜在地克服。离散系统中的时空效应和光定位将是工作包(c)的重点。利用二维波导阵列的多用途色散关系和使用具有增益和损耗（耗散系统）的波导阵列有望产生新的效果。一般情况下，我们将研究光弹的保守构型和耗散构型。这些子弹将是离散连续的对象。一个主要目标将是研究相干耦合有源光纤中的脉冲产生。理论模型将包括紧密结合方程和更一般的晶格方法。我们的工作将由工作包(d)完成，该工作包致力于提供我们在耗散和离散系统方面的理论专业知识，并为实验伙伴设计实验和评估实验结果提供先进的建模工具。在这次合作中，还将提供必要的先进建模能力。

As in the previous period this theoretical project aims at both providing genuine contributions to the theory of nonlinear localization in dissipative and/or discrete optical systems and bridging the gap to the experiments performed in the research unit. The work will be organized in four work packages a) temporal dissipative solitons, b) cavity solitons in metamaterials, c) spatio-temporal localization in waveguide arrays and d) theoretical support for experimental groups. In work package (a) temporal solitons in dissipative optical systems will be investigated. We shall focus on two systems, namely first a periodic semiconductor device that consists of a semiconductor optical amplifier (SOA), a saturable absorber (SA) and a filter and secondly a short-pulse fibre laser system with an appropriate passive mode-locking mechanism. Our previous studies imply that the former system may exhibit dissipative soliton solutions, not really categorized and understood to date, but may potentially serve as ultrafast pulse regenerator. The latter system is of paramount interest for the generation of short pulses with definite properties, but is also considered as one of the most promising test beds for dissipative soliton dynamics. Both subjects are related to a fundamental issue still to be addressed, namely to really identify all properties and to take advantage of the attractive peculiarities of dissipative solitons in systems with a future large application potential.Work package (b) will address the study of cavity solitons metamaterials as a natural continuation of our work on discrete cavity solitons. The aim is to investigate the interplay between tailorable linear properties of micro- and nanostructured metamaterials and various nonlinearities in planar cavities. It is expected that by engineering dispersion and diffraction new classes of cavity solitons will exist. Metamaterials looked at will range from 2D waveguide arrays, via photonic crystals to negative refractive index materials. Using the gain inherent to dissipative systems, which are characterized by a steady energy exchange with the environment, the losses, which are considered a critical issue for so-called negative index metamaterials, can potentially be overcome here.Spatio-temporal effects and light localization in discrete systems will be the focus in work package (c). Novel effects are expected from exploiting the versatile dispersion relation of two-dimensional (2D) waveguide arrays and by using waveguide arrays with gain and loss (dissipative system). Optical bullets in conservative as well as dissipative configurations will be studied in general. These bullets will be discrete-continuous objects. One major goal will be to study pulse generation in coherently coupled active fibres. Theoretical models will include tight-binding equations and the more general lattice approach.Our work will be completed by work package (d) that is devoted to providing our theoretical expertise in dissipative and discrete systems and the access to advanced modelling tools to the experimental partners in designing experiments and in evaluating their results. Within this collaboration also the necessary advanced modelling capacity will be provided.