Collaborative Research on High Bit-Rate Communication: From Mathematical Development to Fiber Design

Brown University, Providence RI

Investigators

Abstract

NSF Award Abstract - DMS-0073923 Mathematical Sciences: Collaborative Research on High Bit-Rate Communication - From Mathematical Development to Fiber Design Abstract 0073923 Jones This project will focus on the development of mathematical and computational techniques for addressing the critical issues of optical fiber communication technology. The modeling and methods will be aimed at the more efficient use of fiber bandwidth. It will include both single channel and Wavelength Division Multiplexing techniques. The group will develop methods for the investigation of theoretical models of the main fiber optics technologies. This includes the emerging techniques of dispersion compensation, distributed amplification, wavelength division multiplexing, and uses of the newly developed dispersion-profiled fiber. Also to be investigated will be the influence of dispersion management on four-wave interactions and therefore on the stability of bit-patterns in multi-channel systems. Each of these methods involves, in some way, the spatial management of dispersion and other physical effects. In general, this leads to an inhomogeneous evolutionary partial differential equation with rapidly varying coefficients. Much of the mathematical and computational theory will be aimed at a deeper understanding of these equations and their properties within the specific context of optical transmission. An emphasis will be placed on the averaging theory, stabilization of pulses and pulse interactions. Increasing the bit-rate in optical fiber communications is a challenge that is both scientifically exciting and technologically imperative. An objective of this project will be to take the involvement of mathematical investigations in improving the efficacy of optical communications to a new level. We shall intertwine the development of the underlying mathematics, numerical techniques and the practical, experimental implementation of new scenarios through a group effort that involves representatives from academia, government laboratories and industry. The development of new mathematical and computational techniques is crucial for the both the formulation of new strategies and their initial evaluation. This effort will take the methods of modern applied mathematics into the fiber optics engineering community. It will pave the road for further interactions between applied mathematicians and electrical engineers and promises to make the field of optical communications even more vigorous. At the same time, the work will stimulate new areas of applied mathematics, such as the study of averaging methods for strongly inhomogeneous partial differential equations, stability and interaction of pulses, and development of effective computational methods for rapidly varying systems.