Nonlinear Discrete Optics in the Time Domain

在现代光学中，波的传播动力学和光的非线性驱动自组织被深入地研究。最近，人们的主要兴趣集中在离散光学系统上，因为它们的场动力学遵循一种简单得多的方案，这种方案通常甚至允许解析解。由于具有惊人的相似性，光学离散系统可以用固体物理和量子力学中发展起来的工具来分析，从而使人们能够更深入地理解光-物质相互作用的复杂效应。因此，离散动力学的效应不仅与光学系统有关，而且与一般的非线性动力学问题有关，因为它们对于玻色爱因斯坦凝聚体、等离子体物理或复杂分子结构中的能量传递都是重要的。因此，该项目的潜在结果将远远超出它们所推论的光学的具体背景。本课题致力于研究光脉冲在两个长度略有不同的耦合光纤环路中的非线性演化。这个装置最近也引起了人们对随机量子漫步框架的一些兴趣。该系统中的脉冲演化发生在离散往返行程中，并且还相对于每个往返行程中的脉冲位置进行离散化。到目前为止，这种时间双离散系统的非线性特性还没有得到详细的研究，但将在本项目的框架内进行实验研究。此外，我们的实验装置允许研究各种甚至复值位势的影响，特别是实现所谓的PT对称系统，我们希望在该项目中研究其非线性性质。我们打算第一次实验研究双离散系统中的孤子，特别是PT对称系统中的孤子。我们还想利用我们的装置的多功能性，它允许我们修改群速度色散，分别是传播脉冲的有效质量，并监测由此产生的演化。我们对具有不同符号有效质量的场之间的非线性相互作用特别感兴趣。我们预计会出现自加速、异常减震和自热。我们打算在该项目中获得的结果不仅从基础物理的角度来看是有趣的，而且还可能成为更实际的问题，如光子晶体光纤中超连续谱的优化或光纤激光器中的脉冲演化。

The dynamics of wave propagation together with the nonlinearly driven self organization of light are intensively investigated in modern optics. Recently main interest has focused on discrete optical systems as their field dynamics follows a much simpler scheme, which often allows even for analytical solutions. Because of striking similarities optical discrete systems can be analyzed with tools developed in solid state physics and quantum mechanics thus enabling a deeper understanding of complicated effects of light-matter interaction. Therefore the effects of discrete dynamics, which are the focus of the project, are not only relevant for optical systems, but concern general questions of nonlinear dynamics as they are important for Bose Einstein condensates, in plasma physics or for the energy transfer in complex molecular structures. Potential results of the project will therefore be relevant far beyond the concrete context of optics for which they were deduced. The project is concentrates on the experimental investigation of the nonlinear evolution of optical pulses in two coupled fiber loops of slightly different length in the presence of amplitude and phase modulation. This set up has recently also attracted some interest in the frame work of random quantum walks. Pulse evolution in this system happens in discrete round trips and is also discretized with respect to the position of the pulses in each round trip. Up to now the nonlinear properties of such a temporal double discrete system have not been studied in detail, but shall be experimentally investigated within the framework of this project. In addition our experimental set up allows studying the influence of various and even complex valued potentials and in particular to realize a so-called PT-symmetric system, the nonlinear properties of which we want to investigate within the project. We intend to experimentally study for the first time solitons in a double discrete and in particular in a PT symmetric system. We further want to exploit the versatility of our set-up, which allows us to modify the group velocity dispersion, respectively the effective mass, of propagating pulses and to monitor the resulting evolution. We are particularly interested in the nonlinear interaction between fields with effective masses of different sign. We expect to see self acceleration, anomalous damping and self-heating. The results we intend to obtain within the project are not only interesting from the point of view of fundamental physics, but may also become relevant for more practical issues as the optimization of supercontinuums generation in photonic crystal fibers or of the pulse evolution in fiber lasers.