Waves In Complex Media

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.

The NATO Advanced Study Institute on Diffuse Waves in Complex Media was held at the "Centre de Physique des Houches" in France from March 17 to 27, 1998. The Schools' scientific content, wave propagation in heterogeneous me dia, has covered many areas of fundamental and applied research. On the one hand, the understanding of wave propagation has considerably improved during the last thirty years. New developments and concepts such as, speckle correlations, weak and strong localization, time reversal, near-field propagation are under active research. On the other hand, wave propagation in random media is now being investigated in many different fields such as applied mathematics, acoustics, optics, atomic physics, geo physics or medical sciences. Each community often uses its own langage to describe the same phenomena. The aim of the School was to gather worldwide specialists to illuminate various aspects of wave propagation in random media. This volume presents fourteen expository articles corresponding to courses and seminars given during the School. They are arranged as follows. The first three articles deal with the phenomena of localization of waves: B. van Tiggelen (p. 1) gives a critical review of the physics of localization, J. Lacroix (p. 61) presents the mathematical theory and A. Klein (p. 73) describes recent results for randomized periodic media.

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.

"Why should we learn about the behavior of waves in optical media with irregular, non-periodic, and even disordered structures? First of all, because they can be found everywhere around us, from complex functional materials to the arrangement of leaves on plant stems and even at the inner core of number theory! Second, because the scattering behavior of waves in complex media surprises us with emergent phenomena driven by interference effects. Third, because waves in complex media unveil profound analogies between the classical and quantum transport regimes beyond standard diffusion theory such as, for example, Anderson light localization. However, while waves in periodic structures have been deeply investigated for more than a century and are discussed by the majority of graduate-level textbooks in optics and photonics, the behavior of waves in more general aperiodic environments is almost exclusively addressed in the specialized literature and consequently has limited impact on graduate curricula. It is my goal to bridge this gap by offering a comprehensive and interdisciplinary textbook that systematically addresses both the conceptual foundation and the scattering properties of optical waves in complex media"--

This book contains review papers presented at the International Workshop on Wave Propagation, Scattering and Emission on Theory, Experiment, Simulation and Inversion (WPSE). The papers are of high quality, covering broad areas: a new mechanism of interaction of electromagnetic waves with complex media, remote sensing information, computational electromagnetics, etc. This book summarizes the most significant progress in wave propagation, encompassing theory, experiment, simulation, and inversion. It will also serve as a good reference for scientists in future research.List of Foreign Invited Speakers: Henry Bertoni (Brooklyn Polytechnic University), Lawrence Carin (Duke U), Al Chang (NASA, Goddard), Margaret Cheney (Rensselaer Polytech Institute), Weng Chew (U of Illinois at Urbana Champaign), Shane Cloude (AEL Consultants, UK), Adrian Fung (U of Texas at Arlington), Al Gasiewski (Environmental Tech Lab, NOAA), Martti Hallikainen (Helsinki U of Technology), Akira Ishimaru (U of Washington), Magdy Iskander (U of Hawaii), J A Kong (MIT), Roger Lang (George Washington U), Alex Maradudin (U of California at Irvine), Eric Michielssen (U of Illinois at Urbana Champaign), Eni Njoku (Caltech, Jet Propulsion Lab), Carey Rappaport (Northeastern U), Marc Saillard (Institut Fresnel), Kamal Sarabandi (U of Michigan), David R Smith (U of California at San Diego), Mitsuo Tateiba (Kyushu University), George Uslenghi (U of Illinois at Chicago), and Werner Wiesbeck (Karlsruhe U).

Deals with the theoretical, analytical and advanced numerical study of the structure and dynamics of one-dimensional as well as two- and three-dimensional solitons and nonlinear waves described by Korteweg-de Vries (KdV), Kadomtsev-Petviashvili (KP), nonlinear Schrodinger (NLS) and derivative NLS (DNLS) classes of equations.

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.