Bao Gang, Cowsar Lawrence, Masters Wen. Mathematical Modeling in Optical Science

Society for Industrial and Applied Mathematics, 2001. — 350 p.This book addresses some recent developments in mathematical modeling in three areas of optical science: diffractive optics, photonic band gap structures, and waveguides. Particular emphasis is on the formulation of the mathematical models and the design and analysis of new computational approaches. Chapters are organized to present model problems, physical principles, mathematical and computational
approaches, and engineering applications corresponding to each of these three areas.
The fundamental importance of optical science is clear. Its various disciplines provide enabling technology applicable to numerous industries, including communication, computing, manufacturing, and data storage. In each of these disciplines, there is an increasing demand for modeling of the relevant physical phenomena.While some members in the applied mathematics community have begun to address a few of the challenging problems in these areas, the barriers to entry are formidable. Much of the existing literature is either highly specialized or lacking focus on the mathematical formulation of the problem.
This book is motivated by a desire to foster communication among the mathematics, physics, and engineering communities on modeling problems in optics. The book's contributors are mathematicians, physicists, and engineers in academia and industry.
While some of the subject matter is classical, the topics in this book are new and represent the latest developments in their respective fields. The model problems discussed in this book are motivated by recent technological developments. For example, in diffractive optics the focus is on micro-optics, i.e., structures of scales comparable to the wavelength of the visible light. Because of the tiny structural scales, wave propagation can no longer be predicted accurately by the classical geometrical optics approximation. Instead, one must solve the Maxwell equations
rigorously.
Each of the three topics is presented through a series of survey papers to provide a broad overview focusing on the mathematical models. It is our sincere hope that this book will help researchers and especially graduate students to gain a broad exposure to these important problems. The book should be readable by both the mathematician and the engineer. For the more experienced researcher in either discipline, the book will provide up-to-date results and references. For graduate students and mathematicians less familiar with these areas, the book will provide
introductory material to the three areas in optics that offer rich and challenging mathematical problems. With an extensive list of references, it should also enhance the accessibility to specialized literature.
In the areas covered by this book, modeling and simulation have become an important part of the engineering process. The applied mathematics community may contribute significantly to the analysis of these models, as well as to the design and analysis of simulation techniques and automated design tools. Because the applied mathematics community has been rapidly addressing many challenging problems of optical science during the last decade, this book is also intended to introduce researchers in appropriate engineering disciplines to recent mathematical advances
in theory, analysis, and computational techniques.