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播和捕获摘要0204881古德曼这个项目通过数学分析、渐近和数值模拟来研究波与局部结构的相互作用。 激发这项研究的是模拟，其中光，通过一个专门的布拉格光栅光纤，在到达一个专门设计的缺陷在一个给定的位置在光纤停止。 一个启发性的假说已经提出来解释这种光的捕获是如何发生的。 该项目旨在了解这种光捕获背后的机制，并利用这种理解来提高这一过程的效率和实用性。 一个主要的工具是推导和分析的常微分方程模型的光脉冲与局部缺陷的相互作用。 为了直观地了解这一物理问题，本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，信息是以光脉冲的形式通过玻璃纤维发送的。 为了处理这些信息，需要对光脉冲进行操纵或重定向。 该项目研究在光纤中的给定点处“捕获”光的可能性，这可能用作光通信设备的组件，例如作为光存储单元中的组件。 该项目还将研究由类似的基本方程描述的物理系统中的波捕获的类似问题。

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.