Pulse Propagation and Capture in Bragg Grating Optical Fibers

NSF奖摘要-DMS-0204881数学科学：布拉格光栅光纤中的脉冲传输和捕获古德曼这个项目通过数学分析、渐近性和数值模拟来研究波与局域结构的相互作用。推动这项研究的是模拟，在模拟中，通过专门的布拉格光栅光纤的光在到达光纤中给定位置的特殊工程缺陷时被阻止。已经提出了一个启发式假设来解释这种光捕获是如何发生的以及为什么发生的。该项目旨在了解这种光捕捉背后的机制，并利用这种理解来提高这一过程的效率和有用性。一个主要的工具是常微分方程式的推导和分析，常微分方程式模拟光脉冲与局域缺陷的相互作用。为了直观地了解这个物理问题，该项目将研究其他非线性波动方程中的相关问题。在现代光通信中，信息以光脉冲的形式通过玻璃纤维发送。为了处理信息，需要在光脉冲传播的过程中对其进行操纵或重新定向。该项目研究在光纤中的给定点处“捕获”光的可能性，该光纤可用作光通信设备的组件，例如作为光存储单元中的组件。该项目还将研究类似的物理系统中的波捕获问题，这些问题由类似的基本方程描述。

NSF Award Abstract - DMS-0204881Mathematical Sciences: Pulse propagation and capture in Bragg grating optical fibersAbstract0204881 GoodmanThis project studies the interaction of waves with localized structures, through mathematical analysis, asymptotics, and numerical simulation. Motivating this study are simulations in which light, travelling through a specialized Bragg grating optical fiber, is stopped upon reaching a specially engineered defect at a given location in the fiber. A heuristic hypothesis has been put forward to explain how and why this trapping of light occurs. The project aims to understand the mechanism behind this light capture, and to use this understanding to improve the efficiency and usefulness of this process. A main tool is the derivation and analysis of ordinary differential equations that model the interaction of the light pulse with the localized defect. In order to gain intuition about this physical problem, the project will look at related problems in other nonlinear wave equations.In modern optical communications, information is sent as pulses of light through glass fibers. To process the information requires light pulses to be manipulated or redirected as they travel. This project investigates the possibility of "trapping" light at a given point in an optical fiber, which could be useful as a component of optical communication devices, for example as a component in an optical memory unit. The project will also look at similar problems of wave trapping in physical systems that are described by similar underlying equations.