Pulse Propagation and Capture in Bragg Grating Optical Fibers

NSF Award Abstract - DMS-0204881

Mathematical Sciences: Pulse propagation and capture in Bragg grating optical fibers

Abstract

0204881 Goodman

This 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.