Discrete spatio-temporal dynamics in waveguide arrays with cubic nonlinearity

在这个项目中，将研究在不同时空条件下永久一维和二维波导阵列的离散光学特性。这种系统在时间和空间场传播中显示出不同于均匀空间中的常规传播的独特基本性质（例如，特定孤子形成、光子弹、光束的周期性运动、“非衍射”光束）。作为这些调查的基础上，实现高精度多维波导阵列的两个互补的概念。随着密集超短激光脉冲聚焦到块体材料中，可以诱导永久的折射率变化，这允许复杂且柔性形状的嵌入式阵列结构的铭刻。随着光纤技术的发展，具有长传播长度甚至有源（增益）特性的大型阵列变得可行。这种渐逝耦合波导阵列将被用作模型系统，研究线性和非线性条件下的时空传输。我们的工作将分为六个工作包，工作包（a）将研究一维和二维波导阵列中的线性传播。一个广泛的领域的兴趣是在有限阵列中的传播的调查，其中与阵列边界的相互作用，必须考虑到产生各种新的和有趣的效果，如由谐波振荡或离散的塔尔博特效应引起的字段自恢复。另一个结果是存在所谓的准非相干传播，其中相互完全相干的源激发光分布，该光分布等效于由相互非相干的源引起的分布。本软件包的另一个重点是研究不同拓扑结构中的传播。使用飞秒激光脉冲写入的波导阵列打开了分析各种系统的可能性，这些系统只能很难通过其他技术制造。由弯曲波导组成的二维阵列允许引入引起二维场恢复的线性势。此外，倏逝波耦合的形状和距离的波导将进行分析，因为耦合到下一个，但一个波导的调查的目的。在这个工作包中的一个附加点是波导阵列之间的接口的影响。与边界的相互作用给出了一个显着的洞察在阵列中的光的传播行为的演变，因为带结构的变化突然在界面产生交错和unstaggered本地化模式，依赖于transmittance的interfaces.In工作包（B）中的非线性空间传播的一维和二维波导阵列将被调查。传播光与人工缺陷的相互作用将被精确地分析。局部缺陷可以是线性的（例如，省略的波导），但也可以是纯非线性的。这将导致所谓的孤子发射，这将是本工作包的一个重点。另一个重点是调查的影响的维数和阵列的拓扑结构。由于能带结构是阵列几何形状的函数，因此在不同的拓扑结构中激发孤子需要不同的输入峰值功率。因此，从纯平面到二维孤子的过渡将被分析。工作包（c）的重点将放在联网和全光交换的研究上。可以通过在单个波导中的定位来阻挡反射光。因此，传播脉冲可以在波导结处路由到特定方向。这种效应以前从未在实验中观察到过。然而，飞秒激光写入波导提供了一个理想的基础，研究这种现象，因为波导的路径可以选择在任意的方式。在这个工作包中，我们将主要使用光纤波导阵列，因为它们提供了非常长的耦合长度，允许在离散系统中的时间动态的调查。反常色散、克尔非线性和阵列衍射的相互作用产生时空局域化的物体，即所谓的光子弹。对于空间离散系统，理论研究预测了离散-连续光子弹的稳定性，否则它们在连续介质中是动态不稳定的。这种现象以前从未在实验中观察到过。在工作包（e）中，将制作和分析具有耗散效应（增益）的波导阵列。一个主要目标是特别是耗散光子弹和离散时空相似性形式的耗散局域化的实验观察。除了包层泵浦产生的增益外，纤芯泵浦产生的局部集中增益是进一步的研究领域。详细了解这种有源波导阵列中的场的形成和传播，对于新型光纤激光器结构也是非常有意义的，我们的工作将通过专门研究LiNbO 3波导阵列的工作包（f）来完成。这种材料表现出非常强的二次非线性，这是调查的基础上可能只有在离散二次介质的各种效果。此外，铌酸锂波导阵列允许调查的线性，二阶和三阶非线性离散传播的相互作用。

Within this project discrete optical properties in permanent one- and two-dimensional waveguide arrays under different spatio-temporal conditions will be investigated. Such systems show unique fundamental properties in temporal and spatial field propagation differing from conventional propagation in homogeneous spaces (e.g. specific soliton formation, light bullets, periodic motion of beams, "non-diffractive" beams). As a basis for these investigations two complementary concepts for realizing high precision multidimensional waveguide arrays are used. With intensive ultrashort laser pulses focused into bulk material a permanent refractive index change can be induced which allows the inscription of complex and flexibly shaped embedded array structures. With optical fibre technologies large arrays with long propagation lengths and even active (gain) properties become feasible. Such evanescently coupled waveguide arrays will be used as a model system to study spatio-temporal propagation under linear and nonlinear conditions. Our work will be organized in six work packages.Work package (a) will address the study of linear propagation in one- and two-dimensional waveguide arrays. A wide field of interest is the investigation of the propagation in finite arrays, where interactions with the array boundaries have to be taken into account yielding a variety of new and interesting effects such as field self-recovery caused by harmonic oscillation or the discrete Talbot effect. Another consequence is the existence of a so-called quasi-incoherent propagation, where mutually fully coherent sources excite a light distribution which is equivalent to a distribution caused by mutually incoherent sources. Another focus of this package is the investigation of the propagation in different topologies. Using waveguide arrays written by fs laser pulses opens the possibility to analyze a variety of systems which can only be hardly fabricated by other technologies. Two-dimensional arrays consisting of curved waveguides allow the introduction of linear potentials causing two-dimensional field recovery. Furthermore the evanescent coupling concerning the shape and the distance of the waveguides will be analyzed since the investigation of the coupling to the next but one waveguide is intended. An additional point in this work package is the influence of interfaces between waveguide arrays. The interaction with the boundaries gives a significant insight in the propagation behaviour of the evolving light in the arrays since the band structure changes abruptly at the interface yielding staggered and unstaggered localized modes, dependent of the transmissivity of the interface.In work package (b) the nonlinear spatial propagation in one- and two-dimensional waveguide arrays will be investigated. The interaction of the propagating light with artificial defects will be precisely analyzed. Local defects can be linear (e.g. omitted waveguides) but also purely nonlinear. This causes so-called soliton emission which will be a main point of this work package. Another focus is the investigation of the influence of the dimensionality and the topology of the arrays. Since the band structure is a function of the array geometry the excitation of solitons in different topologies requires different input peak powers. So the transition from pure planar to two-dimensional solitons will be analyzed. The focus in work package (c) will be on the investigation of networking and all-optical switching. Propagating light may be blocked by localization in a single waveguide. Therefore, a propagating pulse may be routed at a waveguide junction into a specific direction. This effect has not been experimentally observed before. However, fs laser written waveguides provide an ideal basis for the investigation of this phenomenon since the paths of the waveguides can be chosen in an arbitrary way.The next consequential step will be the investigation of spatio-temporal nonlinear propagation in work package (d). In this work package we will primarily use waveguide arrays in fibres since they provide extraordinary long coupling lengths which allow the investigation of temporal dynamics in discrete systems. The interplay of the anomalous dispersion, Kerr-nonlinearity and array diffraction yields spatio-temporal localized objects, so-called light bullets. For spatially discrete systems theoretical studies predict the stability of discrete-continuous light bullets, which are otherwise dynamically instable in continuous media. Such phenomena have not been experimentally observed before. Hence, they will be a main focus in our work.In work package (e) waveguide arrays with dissipative effects (gain) will be fabricated and analyzed. A main goal is in particular the experimental observation of dissipative localizations in the form of dissipative light bullets and discrete spatio-temporal similaritons. Besides the gain resulting from cladding pumping, locally concentrated gain by core pumping is a further field of research. A detailed understanding of field formation and propagation in such active waveguide arrays with gain would be also of great interest for new types of fibre laser structures.Our work will be completed by work package (f) that is devoted to waveguide arrays in LiNbO3. This material exhibits an extraordinary strong quadratic nonlinearity which is the base for the investigation of a variety of effects possible only in discrete quadratic media. Furthermore, waveguide arrays in LiNbO3 allow the investigation of the interaction of linear, second- and third-order nonlinear discrete propagation.