A collection of lectures on a variety of modern subjects in wave scattering, including fundamental issues in mesoscopic physics and radiative transfer, recent hot topics such as random lasers, liquid crystals, lefthanded materials and time-reversal, as well as modern applications in imaging and communication. There is a strong emphasis on the interdisciplinary aspects of wave propagation, including light and microwaves, acoustic and elastic waves, propagating in a variety of "complex" materials (liquid crystals, media with gain, natural media, magneto-optical media, photonic and phononic materials, etc.). It addresses many different items in contemporary research: mesoscopic fluctuations, localization, radiative transfer, symmetry aspects, and time-reversal. It also discusses new (potential) applications in telecommunication, soft matter and imaging.

An interdisciplinary introduction to the structural and scattering properties of complex photonic media, focusing on deterministic aperiodic structures and their conceptual roots in geometry and number theory. An essential tool for students at the graduate or advanced undergraduate level.

Recent advances in wave propagation in random media are certainly consequences of new approaches to fundamental issues, as well as of a strong interest in potential applications. A collective effort has been made to present in this book the state of the art in fundamental concepts, as well as in biomedical imaging techniques. As an example, the recent introduction of wave chaos, and more specifically random matrix theory - an old tool from nuclear physics - to the study of multiple scattering, has pointed the way to a deeper understanding of wave coherence in complex media. At the same time, efficient new approaches for retrieving information from random media promise to allow wave imaging of small tumors in opaque tissues. Review chapters are written by experts in the field, with the aim of making the book accessible to the widest possible scientific audience: graduate students and research scientists in theoretical and applied physics, optics, acoustics, and biomedical physics.

This IMA Volume in Mathematics and its Applications WAVE PROPAGATION IN COMPLEX MEDIA is based on the proceedings of two workshops: • Wavelets, multigrid and other fast algorithms (multipole, FFT) and their use in wave propagation and • Waves in random and other complex media. Both workshops were integral parts of the 1994-1995 IMA program on "Waves and Scattering." We would like to thank Gregory Beylkin, Robert Burridge, Ingrid Daubechies, Leonid Pastur, and George Papanicolaou for their excellent work as organizers of these meetings. We also take this opportunity to thank the National Science Foun dation (NSF), the Army Research Office (ARO, and the Office of Naval Research (ONR), whose financial support made these workshops possible. A vner Friedman Robert Gulliver v PREFACE During the last few years the numerical techniques for the solution of elliptic problems, in potential theory for example, have been drastically improved. Several so-called fast methods have been developed which re duce the required computing time many orders of magnitude over that of classical algorithms. The new methods include multigrid, fast Fourier transforms, multi pole methods and wavelet techniques. Wavelets have re cently been developed into a very useful tool in signal processing, the solu tion of integral equation, etc. Wavelet techniques should be quite useful in many wave propagation problems, especially in inhomogeneous and nonlin ear media where special features of the solution such as singularities might be tracked efficiently.

One of the most methodical treatments of electromagnetic wave propagation, radiation, and scattering—including new applications and ideas Presented in two parts, this book takes an analytical approach on the subject and emphasizes new ideas and applications used today. Part one covers fundamentals of electromagnetic wave propagation, radiation, and scattering. It provides ample end-of-chapter problems and offers a 90-page solution manual to help readers check and comprehend their work. The second part of the book explores up-to-date applications of electromagnetic waves—including radiometry, geophysical remote sensing and imaging, and biomedical and signal processing applications. Written by a world renowned authority in the field of electromagnetic research, this new edition of Electromagnetic Wave Propagation, Radiation, and Scattering: From Fundamentals to Applications presents detailed applications with useful appendices, including mathematical formulas, Airy function, Abel’s equation, Hilbert transform, and Riemann surfaces. The book also features newly revised material that focuses on the following topics: Statistical wave theories—which have been extensively applied to topics such as geophysical remote sensing, bio-electromagnetics, bio-optics, and bio-ultrasound imaging Integration of several distinct yet related disciplines, such as statistical wave theories, communications, signal processing, and time reversal imaging New phenomena of multiple scattering, such as coherent scattering and memory effects Multiphysics applications that combine theories for different physical phenomena, such as seismic coda waves, stochastic wave theory, heat diffusion, and temperature rise in biological and other media Metamaterials and solitons in optical fibers, nonlinear phenomena, and porous media Primarily a textbook for graduate courses in electrical engineering, Electromagnetic Wave Propagation, Radiation, and Scattering is also ideal for graduate students in bioengineering, geophysics, ocean engineering, and geophysical remote sensing. The book is also a useful reference for engineers and scientists working in fields such as geophysical remote sensing, bio–medical engineering in optics and ultrasound, and new materials and integration with signal processing.

The past decade has witnessed breakthroughs in the understanding of the wave localization phenomena and its implications for wave multiple scattering in inhomogeneous media. This book brings together review articles written by noted researchers in this field in a tutorial manner so as to give the readers a coherent picture of its status. It would be valuable both as an up-to-date reference for active researchers as well as a readable source for students looking to gain an understanding of the latest results.

This book offers a clear and interdisciplinary introduction to the structural and scattering properties of complex photonic media, focusing on deterministic aperiodic structures and their conceptual roots in geometry and number theory. It integrates important results and recent developments into a coherent and physically consistent story, balanced between mathematical designs, scattering and optical theories, and engineering device applications. The book includes discussions of emerging device applications in metamaterials and nano-optics technology. Both academia and industry will find the book of interest as it develops the underlying physical and mathematical background in partnership with engineering applications, providing a perspective on both fundamental optical sciences and photonic device technology. Emphasizing the comprehension of physical concepts and their engineering implications over the more formal developments, this is an essential introduction to the stimulating and fast-growing field of aperiodic optics and complex photonics.

Publisher description

A timely and authoritative guide to the state of the art of wave scattering Scattering of Electromagnetic Waves offers in three volumes a complete and up-to-date treatment of wave scattering by random discrete scatterers and rough surfaces. Written by leading scientists who have made important contributions to wave scattering over three decades, this new work explains the principles, methods, and applications of this rapidly expanding, interdisciplinary field. It covers both introductory and advanced material and provides students and researchers in remote sensing as well as imaging, optics, and electromagnetic theory with a one-stop reference to a wealth of current research results. Plus, Scattering of Electromagnetic Waves contains detailed discussions of both analytical and numerical methods, including cutting-edge techniques for the recovery of earth/land parametric information. The three volumes are entitled respectively Theories and Applications, Numerical Simulation, and Advanced Topics. In the third volume, Advanced Topics, Leung Tsang (University of Washington) and Jin Au Kong (MIT), cover: * Two-dimensional random rough surface scattering * Kirchhoff and related methods for rough surface scattering * Analytic theory of volume scattering based on cascading of layers * Analytic wave theory for medium with permittivity fluctuations * Multiple scattering theory for discrete scatterers * Quasicrystalline approximation in dense media scattering * Dense media scattering * Backscattering enhancement

This self-contained book gives fundamental knowledge about scattering and diffraction of electromagnetic waves and fills the gap between general electromagnetic theory courses and collections of engineering formulas. The book is a tutorial for advanced students learning the mathematics and physics of electromagnetic scattering and curious to know how engineering concepts and techniques relate to the foundations of electromagnetics