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Coupling Coherent Structures and Linear Radiation

相干结构与线性辐射的耦合

基本信息

批准号：
EP/C548612/1
负责人：
Noel Smyth
金额：
$ 14.99万
依托单位：
University of Edinburgh
依托单位国家：
英国
项目类别：
Research Grant
财政年份：
2006
资助国家：
英国
起止时间：
2006 至无数据
项目状态：
已结题

来源：
https://gtr.ukri.org/projects?ref=EP%2FC548612%2F1
关键词：
Coupling Coherent Structures Linear Radiation

项目摘要

A solitary wave is a localised nonlinear wave that propagates at constant velocity without change of form. Such solitary waves have been shown both theoretically and experimentally to exist in optical media, such as optical fibres. Due to their localised nature, they are a natural bit in digital optical systems and are indeed being used as such in the first long distance optical telecommunication systems. The current goal of much research in the science of optical systems, photonics, is to replace electronic signal processing devices with all-optical equivalents, due to the inherent speed and capacity advantages of optical systems. In these all-optical devices, solitary waves from different signal streams can interact, leading to signal switching and other basic signal processing functions. One draw-back of the glass used in optical fibres is that it has a very low nonlinear response and so nonlinear effects are only apparent over long distances. In a groundbreaking series of experiments by the experimental group of Professor Assanto in Rome, it has been shown that due to the high nonlinear response of liquid crystals, solitary waves in liquid crystals, so-called nematicons, display nonlinear features over short length scales. Liquid crystals then are a possible medium in which solitary waves can interact over short length scales, leading to smaller optical devices.Many equations having solitary wave solutions possess exact solutions in terms of inverse scattering, and so all features of the solutions are in principle known. However this is not true of the nonlinear partial differential equations describing optical signal propagation, particularly in more than one space dimension, which is the case for solitary waves in liquid crystals. Hence there is a need for a new theory to analyse solitary waves propagation in higher space dimensions. The development of this theory and the comparison of its results with numerical solutions and experimental results forms the basis of the current research proposal. As solitary waves evolve, they shed dispersive radiation and their evolution is driven and determined by the interaction between the evolving solitary wave and its shed radiation. The main emphasis of the proposed research will be to develop perturbation techniques to determine this interaction so that nematicon evolution in liquid crystals can be accurately predicted. The development of these techniques will be helped by the concurrent numerical solution of the governing equations. The results of the analytical and numerical work will then be compared with experimental results of Professor Assanto to determine their utility and to suggest extensions. In particular, this experimental work is for liquid crystals which have a non-local material response. This non-local response presents significant analytical difficulties as the transverse length scale (transverse to the direction of propagation) of the nematicon is much smaller than the transverse length scale of the variation of the liquid crystal. Preliminary numerical results suggest that the nematicon solution is non-unique, so that multiple solitary wave solutions for given parameter values are possible. This will be further

孤立波是一种以恒定速度传播而不改变形式的局部非线性波。这种孤立波在理论上和实验上都已经被证明存在于光学介质中，比如光纤。由于它们的局部化性质，它们是数字光学系统中的自然比特，并且确实在第一长距离光学电信系统中被这样使用。由于光学系统固有的速度和容量优势，目前光学系统（光子学）科学的许多研究目标是用全光学等效物取代电子信号处理设备。在这些全光器件中，来自不同信号流的孤立波可以相互作用，从而实现信号切换和其他基本的信号处理功能。用于光纤的玻璃的一个缺点是它具有非常低的非线性响应，因此非线性效应仅在长距离上明显。在罗马的Assanto教授实验组的一系列开创性实验中，已经表明，由于液晶的高非线性响应，液晶中的孤立波，即所谓的nematicons，在短长度尺度上显示出非线性特征。因此，液晶是一种可能的介质，在这种介质中，孤立波可以在短的长度尺度上相互作用，从而导致更小的光学器件。许多具有孤立波解的方程在逆散射方面都具有精确解，因此解的所有特征原则上都是已知的。然而，这是不正确的非线性偏微分方程描述光信号的传播，特别是在一个以上的空间维度，这是孤立波在液晶中的情况。因此，需要一种新的理论来分析孤立波在更高空间维度中的传播。该理论的发展及其结果与数值解和实验结果的比较构成了当前研究建议的基础。随着孤立波的演化，它们会释放色散辐射，并且它们的演化由演化孤立波与其释放辐射之间的相互作用驱动和决定。拟议的研究的主要重点将是发展微扰技术，以确定这种相互作用，使液晶中的向列子演变可以准确地预测。控制方程的并行数值解将有助于这些技术的发展。然后将分析和数值计算的结果与Assanto教授的实验结果进行比较，以确定其效用并提出扩展建议。特别是，这项实验工作是为具有非本地材料响应的液晶。这种非局部响应呈现出显著的分析困难，因为向列型子的横向长度尺度（横向于传播方向）远小于液晶的变化的横向长度尺度。初步的数值结果表明，nematicon解决方案是非唯一的，所以多个孤立波解决方案，给定的参数值是可能的。这将进一步