Shaw J.K. Mathematical Principles of Optical Fiber Communications

SIAM, 2004. — 104 p.The synergism between the World Wide Web and fiber optics is a familiar story to researchers in digital communications. Fibers are the enablers of the rates of information flow that make the Internet possible. Currently there are transoceanic optical fiber cables transmitting data at rates in the range of 1 terabit per second (1 Th/s), or 10¹² bits per second. To put this into perspective, ifone imagines that a typical book might occupy 10 megabits, then 1 Tb/s would be equivalent to transmitting 10⁵ books per second, or the contents of a respectable university library in a few minutes. No other medium is capable of this rate of transmission at such distances.
With the maturing of mobile portable telephony and the emerging broadband access market, greater fiber transmission capacity will be essential in the early 21^st century. Since the demand for more capacity drives the development of new optics-based technologies, fiber optics therefore remains a vibrant area for research. The fact that the basic technology is mature means that the open questions are more sharply focused and permit deeper mathematical content.
What are fibers, and why is fiber transmission superior in high bit-rate, long-distance communications? How is it possible to transmit terabit messages in 1 second across an ocean or continent? Or, for that matter, is this figure actually small relative to some theoretical limit? These are the kinds of questions taken up in this book. As it turns out, the answers are usually in equal parts mathematical and physical. Indeed, the development of fiber systems is one of the most fascinating stories in modern science because it involves the interlinked and parallel advances of a number of scientific disciplines such as lasers, optical detectors, novel manufacturing techniques, and mathematical modeling, including wave propagation theory. Mathematics has been especially critical since the key physical parameters in fiber design are determined by intrinsic mathematical constraints. The purpose of this book is to provide an account of this side of the fiber story, from the basics up to current frontiers of research.
To be sure, there is already a great deal of mathematical research underway involving optical fibers. More often than not, mathematical articles on the subject start from an object such as the nonlinear Schrödinger equation and proceed with analysis from that point, leaving out connections between obtained results and actual physical systems. This may be entirely appropriate, since the omission of physical motivation can simply be a matter of taste. However, the new or aspiring researcher misses an opportunity to see the context in which mathematical questions arise. Providing such a context is one goal of this book. It is written not only for both mathematical and engineering researchers who are new to the fiber optics area, but also for experienced investigators who may add richness to their own backgrounds through a better understanding of context and nomenclature, both physical and mathematical.Background and Introduction
Fiber Modes
Fiber Dispersion and Nonlinearity
The Variational Approach
Optical Solitons