Electromagnetic complex media are artificial materials that affect the propagation of electromagnetic waves in surprising ways not usually seen in nature. Because of their wide range of important applications, these materials have been intensely studied over the past twenty-five years, mainly from the perspectives of physics and engineering. But a body of rigorous mathematical theory has also gradually developed, and this is the first book to present that theory.


Designed for researchers and advanced graduate students in applied mathematics, electrical engineering, and physics, this book introduces the electromagnetics of complex media through a systematic, state-of-the-art account of their mathematical theory. The book combines the study of well posedness, homogenization, and controllability of Maxwell equations complemented with constitutive relations describing complex media. The book treats deterministic and stochastic problems both in the frequency and time domains. It also covers computational aspects and scattering problems, among other important topics. Detailed appendices make the book self-contained in terms of mathematical prerequisites, and accessible to engineers and physicists as well as mathematicians.

"This is an outstanding book that has the potential to become a real classic. It is the first to systematically address the mathematics of electromagnetic wave propagation in complex media. It will be useful not only to mathematicians but also graduate students, physicists, and engineers who want to get a state-of-the-art picture of scattering by complex media."--Gerhard Kristensson, Lund University, Sweden

"This monograph is of a very high standard, allowing the reader to learn many facets of the rapidly growing field of complex media and to get up-to-date information on a number of open research problems."---Vilmos Komornik, Mathematical Reviews