Discrete spatio-temporal dynamics in waveguide arrays with quadratic nonlinearity

本计画的目的是研究周期性极化锂酸盐（PPLN）波导阵列中激发的时空动力学。所研究的系统具有很高的自由度，在其线性衍射和色散特性，其类型的非线性，和他们的程度的耗散。这种极端的可变性的基本实验系统的属性将通过结合一个通用的非线性材料（铌酸锂）与先进的微结构technologies. Ti indiffused和fs写入PPLN波导提供了一个可变的非线性由于同时存在的二次和光折变非线性。这两种非线性可以结合起来，以合成所需类型的有效非线性响应。此外，1D和2D波导阵列与诱导的光折射不均匀性和布拉格光栅一起导致角谱的一定间隔的几乎任意的衍射特性和频带结构的成形，从而提供对群速度和群速度色散的控制。与传统的保守和耗散系统之间的严格区分不同，基于光折变布拉格光栅的具有可调反馈的波导谐振器提供了保守/耗散特性的可变性。基于实验配置的这种极端通用性，我们希望观察与某些系统特性相关的非线性动力学现象。将特别强调分类良好的系统类之间的过渡。这项工作将分为三个工作包：PPLN波导阵列的线性和非线性特性的控制：这里将研究PPLN波导阵列中的基本线性和非线性效应。此外，将开发基本的实验技术，通过确定控制线性和非线性系统参数的适当方法，为其他工作包提供先决条件。非线性波导阵列中的时空动力学：本工作包的第一个目的是研究具有不同类型不均匀性的波导阵列中的线性光束衍射，这些不均匀性是由附加光束通过光折变效应引起的。第二个目标是研究均匀和非均匀波导阵列中的时空非线性动力学，其线性和非线性特性再次通过附加的光折变进行修改。波导谐振器阵列中的时空非线性动力学：本工作包将致力于研究由耦合波导谐振器形成的离散耗散系统中的非线性动力学。我们将研究不同类型的有效非线性耗散的引入所产生的具体解决方案。因此，标准将导出特定的离散模式和腔孤子的吸引子和稳定性的形成。

The aim of this project is the investigation of spatial-temporal dynamics of excitations in waveguide arrays of periodically poled lithium niobate (PPLN). The studied systems possess a high degree of freedom in terms of their linear diffraction and dispersion properties, their type of nonlinearity, and their degree of dissipation. This extreme variability of the properties of the underlying experimental system will be achieved by combining a versatile nonlinear material (LiNbO3) with advanced micro-structure-technologies.The Ti-indiffused and fs-written PPLN waveguides offer a variable nonlinearity due to the simultaneous existence of a quadratic and a photorefractive nonlinearity. Both nonlinearities can be combined to synthesize a desired type of the effective nonlinear response. Moreover, l D and 2D waveguide arrays together with induced photorefractive inhomogeneities and Bragg gratings result in almost arbitrary diffraction properties for a certain interval of the angular spectrum and a shaping of the frequency band-structure providing control on group velocity and group velocity dispersion. Unlike the traditional strict distinction between conservative and dissipative systems, waveguide resonators with adjustable feedback based on photorefractive Bragg gratings provide a variability of the conservative/dissipative properties. Based on this extreme versatility of the experimental configuration we want to observe nonlinear dynamical phenomena which are connected to certain system properties. Particular emphasis will be paid to the transitions between the well-categorized system classes. The work will be organized in three work packages:I. Control of linear and nonlinear properties of PPLN waveguide arrays: Here the fundamental linear and nonlinear effects in PPLN waveguide arrays will be investigated. Furthermore the basic experimental techniques will be developed to provide the prerequisites for the other work packages by identifying adequate means of controlling the linear and nonlinear system parameters.II. Spatial-temporal dynamics in nonlinear waveguide arrays: The first aim of this work package is the investigation of linear beam diffraction in waveguide arrays with different types of inhomogeneities which are induced by additional beams via photorefractive effects. The second aim is to study the spatial-temporal nonlinear dynamics in homogeneous and inhomogeneous waveguide arrays, whose linear and nonlinear properties are again modified by additional photorefraction.III. Spatial-temporal nonlinear dynamics in waveguide resonator arrays: This work package will be committed to the study of the nonlinear dynamics in discrete dissipative systems which are formed by coupled waveguide resonators. We will investigate the specific solutions arising from the introduction of dissipation for different types of effective nonlinearities. Hence, criteria will be derived for the shaping of attractors and stability properties of particular discrete pattern and cavity solitons.