Discrete spatio-temporal dynamics in waveguide arrays with quadratic nonlinearity

本项目的目的是研究周期性极化铌酸锂（PPLN）波导阵列中激发的时空动力学。所研究的系统在线性衍射和色散特性、非线性类型和耗散度方面具有高度的自由度。通过将多功能非线性材料（LiNbO3）与先进的微结构技术相结合，可以实现底层实验系统性能的极端可变性。由于二次非线性和光折变非线性的同时存在，ti扩散和fs写入的PPLN波导提供了可变非线性。这两种非线性可以结合起来合成一种期望类型的有效非线性响应。此外，一维和二维波导阵列与诱导光折变不均匀性和Bragg光栅一起，在角谱的一定间隔内产生几乎任意的衍射特性，并形成可控制群速度和群速度色散的频带结构。与传统的严格区分保守和耗散系统不同，基于光折变布拉格光栅的可调反馈波导谐振器提供了保守/耗散特性的可变性。基于这种实验结构的极端通用性，我们想观察与某些系统特性有关的非线性动力学现象。将特别强调在分类良好的系统类之间的转换。这项工作将分为三个工作包：PPLN波导阵列线性和非线性特性的控制：本文将研究PPLN波导阵列的基本线性和非线性效应。此外，将发展基本的实验技术，通过确定控制线性和非线性系统参数的适当手段，为其他工作包提供先决条件。非线性波导阵列的时空动力学：本工作包的第一个目的是研究由附加光束通过光折变效应引起的具有不同类型非均匀性的波导阵列中的线性光束衍射。第二个目的是研究均匀和非均匀波导阵列的时空非线性动力学，其线性和非线性特性再次被额外的光折射所改变。波导谐振器阵列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的非线性动力学。对于不同类型的有效非线性，我们将研究由于引入耗散而产生的具体解。因此，将推导出吸引子的形成和特定的离散图样和腔孤子的稳定性的准则。

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.