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Mathematical Modeling in Optical ScienceMathematical Modeling in Optical Science

Gang Bao, Lawrence Cowsar, and Wen Masters, Editors

Frontiers in Applied Mathematics 22

This volume addresses 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 mathematical models and the design and analysis of new computational approaches. The book contains cutting-edge discourses on emerging technology in optics that provides significant challenges and opportunities for applied mathematicians, researchers, and engineers.

Each of the three topics is presented through a series of survey papers to provide a broad overview focusing on the mathematical models. Chapters present model problems, physical principles, mathematical and computational approaches, and engineering applications corresponding to each of the three areas. Although some of the subject matter is classical, the topics presented are new and represent the latest developments in their respective fields.


This book is intended to help graduate students and researchers gain broad exposure to model problems in the areas of optical science: diffractive optics, photonic band gap structures, and waveguides. It includes up-to-date results and references for more experienced researchers while providing introductory material for those less familiar with these areas.


Preface; Chapter 1: Overview and Applications of Diffractive Optics Technology, J. Allen Cox; Chapter 2: Variational Methods for Diffractive Optics Modeling, Gang Bao and David C. Dobson; Chapter 3: High-Order Boundary Perturbation Methods, Oscar P. Bruno and Fernando Reitich; Chapter 4: Mathematical Reflections on the Fourier Modal Method in Grating Theory, Lifeng Li; Chapter 5: Electromagnetic Models for Finite Aperiodic Diffractive Optical Elements, Dennis W. Prather, Mark S. Mirotznik, and Shouyuan Shi; Chapter 6: Analysis of the Diffraction from Chiral Gratings, Habib Ammari and Jean Claude Nédélec; Chapter 7: The Mathematics of Photonic Crystals, Peter Kuchment; Chapter 8: Mathematical Analysis and Numerical Approximation of Optical Waveguides, Anne-Sophie Bonnet-Ben Dhia and Patrick Joly; Index.

2001 / xiv + 334 pages / Hardcover / ISBN-13: 978-0-898714-75-3 / ISBN-10: 0-89871-475-3 /
List Price $109.00 / SIAM Member Price $76.30 / Order Code FR22
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