Polarization involves the vectorial nature of light fields. In current applications of optical science, the electromagnetic description of light with its vector features has been shown to be essential: In practice, optical radiation also exhibits randomness and spatial non-uniformity of the polarization state. Moreover, propagation through photonic devices can alter the correlation properties of the light field, resulting in changes in polarization. All these vectorial properties have been gaining importance in recent years, and they are attracting increasing attention in the literature. This is the framework and the scope of the present book, which includes the authors' own contributions to these issues.

The Cargese Summer Institute 1975 on Weak and EZeotromagnetio Interaotions at High Energies was organized by the Universite Pierre et Marie Curie (M. LEVY et J. L. BASDEVANT)~ the KathoZieke Universiteit te Leuven (R. GASTMANS) and the Universite CathoZique de Louvain (D. SPEISER~ J. WEYERS) who made in 1973 the first oon- taots with some Zeoturers~ who~ on the advioe of NATO joined their efforts and worked in oommon. It was the 16th Summer Institute rd heZd at Cargese and the 3 one organized by the two departments of TheoreticaZ Physios at Leuven and Louvain-Za-Neuve. When the two groups decided (independentZy) on the subjeot of the sohooZ~ they oouZd not know how Zuoky their ohoioe eventuaZZy wouZd turn out to be : rareZy has it being possibZe to present an audienoe with suoh a great number of new and deoisive disooveries who are Zikely to stimuZate the imagination of theoreticians and the researoh projeots of experimentaZists aZike. Suoh were the decisive oonfirmation of the neutraZ ourrents~ the di-muon events~ the sZowZy deoaying new partioZes~ eto. The organizers were grate- JUZ indeed that they oouZd find physioists from aZmost alZ great oenters of high energy physios Who had themseZves participated in these disooveries. AZthough the theorists oouZd not matoh during the Zast two years the speotaouZar suooess of their experimentaZ ooZZeagues~ there has been enough important program~ especiaZZy in fieZd theory : renormaZization of gauge theories~ the mechanism disoovered by R. BROUT et aZ. ~ eto.

Speech by Toyosaburo Taniguchi Welcome my friends to the Third International Symposium, Division on the Theory of Condensed Matter, of the Taniguchi Foundation. The need is now greater than ever for Japan to consider how to strengthen and foster international understanding between nations, peoples and societies, and how to contribute towards the establishment of peace and prosperity in the world. For more than twenty years, I have been supporting a symposium on mathe matics in which distinguished scholars from allover the world have engaged in free discussions. In this symposium, all the participants live together in community style. I have heard from members of some of these study groups that this type of setup has helped to strengthen their ties and relationships with their colleagues on a personal basis. What developed in the mathematics group led me to reorganize and strengthen the Taniguchi Foundation only a few years ago through additional funding. In order to effectively translate the objectives of the Foundation into action with the funds available, it becomes necessary to select those fields which are not necessarily in the limelight of popular interest, which means those fields which, I am afraid, are low in funding. I would rather choose from modest unimpressive academic fields than for the Foundation, projects those that stand out in gaudy, gorgeous popular acclaim."

The advances in the theory of diffraction gratings and the applications of these results certainly determine the progress in several areas of applied science and engineering. The polarization converters, phase shifters and filters, quantum and solid-state oscillators, open quasi optical dispersive resonators and power compressors, slow-wave structures and patter forming systems, accelerators and spectrometer; that is still far from being a complete list of devices exploiting the amazing ability of periodic structures to perform controlled frequency, spatial, and polarization selection of signals.

Diffraction gratings used to be and still are one of the most popular objects of analysis in electromagnetic theory. The further development of the theory of diffraction gratings, in spite of considerable achievements, is still very important presently. The requirements of applied optics and microwave engineering present the theory of diffraction gratings with many new problems which force us to search for new methods and tools for their resolution. Just in such way there appeared recently new fields, connected with the analysis, synthesis and definition of equivalent parameters of artificial materials layers and coatings, having periodic structure and possessing features, which can be found in natural materials only in extraordinary or exceptional situations.

In this book the authors present results of the electromagnetic theory of diffraction gratings that may constitute the base of further development of this theory which can meet the challenges provided by the most recent requirements of fundamental and applied science.

The following issues will be considered in the book

• Authentic methods of analytical regularization, that perfectly match the requirements of analysis of resonant scattering of electromagnetic waves by gratings;
• Spectral theory of gratings, providing a reliable foundation for the analysis of spatial frequency transformations of electromagnetic fields occurring in open periodic resonators and waveguides;
• Parametric Fourier method and C-method, that are oriented towards the efficient numerical analysis of transformation properties of fields in the case of arbitrary profile periodic boundary between dielectric media and multilayered conformal arrays;
• Rigorous methods for analysis of transient processes and time-spatial transformations of electromagnetic waves in resonant situations, based on development and incorporation in standard numerical routines of FDTD of so called explicit absorbing boundary conditions;
• New approaches to the solution of homogenization problems the key problem arising in construction of metamaterials and meta surfaces;
• New physical results about the resonance scattering of pulse and monochromatic waves by periodic structures, including structures with chiral or left-handed materials;
• Methods and the results of the solutions of several actual applied problems of analysis and synthesis of pattern creating gratings, power compressors, resonance radiators of high capacity short radio pulses, open electromagnetic structures for the systems of resonant quasi optics and absorbing coatings.

This book was originally published in Japanese in honour of Professor S. Chikazumi on the occasion of his retirement from the University of Tokyo in March 1982. Physicists who had been supervised by him or had closely col laborated with him wrote articles on recent developments in magnetism and its engineering applications. In the preface of his excellent textbook Physics of Magnetism (Wiley, 1964), Professor Chikazumi says that recent research in magnetism deals with fundamental physical problems and, at the same time, with more secondary magnetic phenomena, as well as with engineering applications of magnetic materials to electromagnetic machines, permanent magnets and electronic computers, and that the purpose of his textbook is to give a general view of these magnetic phenomena, focusing its main interest at the center of such a broad field. Always keeping such a viewpoint in mind, Professor Chikazumi has contributed a great deal to both fundamental physics and applications of magnetism. This is described in Chap. 1 of this book. Many books have been published on both the physics and applications of magnetism. However, no single book has a viewpoint covering both of them. The recent development of high technology needs such a broad viewpoint for scientists and engineers since it is a product of both fundamental science and technology. Research in magnetism is based on the response which materials show to the application of magnetic fields."

Silicon carbide and other group IV-IV materials in their amorphous, microcrystalline, and crystalline forms have a wide variety of applications.The contributions to this volume report recent developments and trends in the field. The purpose is to make available the current state of understanding of the materials and their potential applications. Eachcontribution focuses on a particular topic, such as preparation methods, characterization, and models explaining experimental findings. The volume also contains the latest results in the exciting field of SiGe/Si heterojunction bipolar transistors. The reader will find this book valuable as a reference source, an up-to-date and in-depth overview of this field, and, most importantly, as a window into the immense range of reading potential applications of silicon carbide. It is essential for scientists, engineers and students interested in electronic materials, high-speed heterojunction devices, and high-temperature optoelectronics.

An international workshop on Elementary Excitations and Fluctuations in Magnetic Systems was held in Turin for five days beginning 25 May, 1987. The workshop followed much the same format as the one with the same title held in San Miniato in 1984 (proceedings: Springer Series in-Solid-State Sciences, Vol. 54), that most participants contributed talks and provided papers for the proceedings. While many of the participants had attended the first workshop, 15 of the 40 invited review papers were presented by scientists who had not. The majority of the talks reported theoretical work concerned with the introduction of new techniques. However, experimental work was also well represented, not least because many of the reported theoretical studies were motivated by experimental findings, and a highlight of the workshop was an extremely stimulating session devoted to recent neutron scattering measure- ments, on various systems, that exploited polarization analysis. The fine venue of the workshop, Villa Gualino, with its excellent facili- ties and spacious accommodation, helped to produce a delightful relaxed and friendly atmosphere. For the use of Villa Gualino and significant financial support we are indebted to our host organization, the Institute for Scien- tific Interchange (lSI). Additional financial support came from the Consiglio Nazionale delle Ricerche (CNR), Centro Interuniversitario di Struttura della Material del Ministero della Pubblica Istruzione (CISM-MPI) and Gruppo Nazionale di Struttura della Materia (GNSM-CNR).

Magnetism is one of the basic properties of matter. Mankind has trav elled a long road in discovering and utilizing magnetism, and in this respect the ancient Chinese people have made outstanding contribu tions. In the book 'Lu's Spring and Autumn', written near the end of the Warring States Period, i. e. in the third century B. C. , there is a statement on the "attraction of iron by lodestones". So at that time it was known that magnets can attract ferromagnetic material. At the be ginning ofthe first century A. D. , viz. in the early years ofthe East Hang Dynasty, the famous scholar Wang Chong wrote in his masterpiece 'Len Hen' that the handle of a magnetic dipper pointed to the south. It was thus discovered at the time that magnets can point to the poles of the geomagnetic field. At the beginning of the twelfth century, during the reign of Emperor Hui of the Sung Dynasty, in the two books written by Zhu Yo and Xu Jin, respectively, there are descriptions of the com pass used in navigation. This tells us that the application of compasses was rather widespread at that time. The distinguished scientist Sen Go (1031-1085) discovered the declination of the terrestrial magnetic field. This is four hundred and more years earlier than its discovery by Christopher Columbus in 1492 during his voyage across the Atlantic Ocean. Such facts as these manifest the important contributions of ancient China to global civilization.

The sixth Taniguchi Symposium on the Theory of Condensed Matter was held between 14-18 November 1983 at Kashikojima. Japan. During the Symposium, about twenty participants lived together and discussed the magnetic super conductors and related problems in an active and friendly atmosphere. This volume contains the papers presented at this Symposium. A strong impetus for organizing a Symposium of this subject is afforded by recent intense interest and accumulated information on magnetic and other novel superconductors newly discovered, and indeed the Symposium has pro duced many excellent contributions to this very exciting field of condensed matter theory, as reported in this volume. In order to give the readers a general outline of the subject, a brief sketch of the problem is made in the Introduction. Then the remainder of this volume is divided into four Parts and an Appendix. Part I is devoted to di scuss ions on several aspects of ferromagnetic superconductors includ ing superconductivity in heavy fermion systems. Part II treats problems on anti ferromagnetic superconductors. In Part III three papers on organic supercon ductors are presented. Part IV includes discussions on the exotic supercon ductors. The Appendix is concerned with the new research project towards high Tc superconductors in Japan. The last but not least remark is to mention the activity of the Taniguchi Foundation whose support makes this Symposium possible. For many years Mr."

An international workshop on Elementary Excitations and Fluctuations in Magnetic Systems was held in San Miniato, Italy, for five days beginning 28 May, 1984. The workshop comprised eight working sessions that contai- ned a total of 43 invited talks, and 58 scientists were in attendance from 14 countries. Our aim was to review some topics of current interest in the statistical physics of magnetic materials and models, with an emphasis on theoretical studies and confrontations between these and experimental and computer simulation data. book contains summary papers written by the invited speakers, and This the material will be of immediate interest to graduate students and resear- chers engaged in studies of magnetic properties. There is, perhaps, no ef- fective way to record and convey the benefit of the numerous discussions between the participants that are a significant integral feature of a work- shop. The magnificent .venue of the workshop, I Cappuccini, was made availa- ble to us by the.Cassa di Risparmio San Miniato. Financial support for the workshop was received from Consiglio Nazionale delle Ricerche, Universita degli Studi di Firenze and the Gruppo Nazionale Struttura,della Materia. Our administrative load and the burden of preparing the proceedings for publication was made light by the talents of Carla Pardini (CNR, Florence), and Caroline Monypenny and Jane Warren (Rutherford Appleton Laboratory). Fina 11y, we wish to thank all the participants for their attendance and individual contributions to the success of the workshop.

The Sixth Annual Conference of the Center for Nonlinear Studies at the Los Alamos National Laboratory was held May 5-9, 1986, on the topic "Nonlinearity in Condensed Matter: Lessons from the Past and Prospects for the Future. " As conference organizers, we felt that the study of non linear phenomena in condensed matter had matured to the point where it made sense to take stock of the numerous lessons to be learned from a variety of contexts where nonlinearity plays a fundamental role and to evaluate the prospects for the growth of this general discipline. The successful 1978 Oxford Symposium on nonlinear (soliton) struc ture and dynamics in condensed matter (Springer Ser. Solid-State Sci., Vol. 8) was held at a time when the ubiquity of solitons was just begin ning to be appreciated by the condensed matter community; in subsequent years the soliton paradigm has provided a rather useful framework for in vestigating a large number of phenomena, particularly in low-dimensional systems. Nevertheless, we felt that the importance of nonlinearity in wider arenas than "solitonics" merited a significant expansion in the scope of the conference over that of the 1978 symposium. Indeed, many of the lessons are quite general and their potential for cross-fertilization of otherwise poorly connected disciplines was certainly one of the prime motivations for this conference. Thus, while these proceedings contain many contribu tions pertaining to soliton behavior in different contexts, the reader will find much more as well, particularly in the later chapters."

For several years, the two parallel worlds of Molecular Conductors in one hand and Molecular Magnetism in the other have grown side by side, the former essentially based on radical organic molecules, the latter essentially based on the high spin properties of metal complexes. Over the last few years however, organometallic derivatives have started to play an increasingly important role in both worlds, and have in many ways contributed to open several passages between these two worlds. This volume recognizes this important emerging evolution of both research areas. It is not intended to give a comprehensive view of all possible organometallic materials, and polymers for example were not considered here. Rather we present a selection of the most recent research topics where organometallic derivatives were shown to play a crucial role in the setting of conducting and/or magnetic properties in crystalline materials. First, the role of organometallic anions in tet- thiafulvalenium-based molecular conductors is highlighted by Schlueter, while Kubo and Kato describe very recent ortho-metalated chelating ligands appended to the TTF core and their conducting salts. The combination of conducting and magnetic properties and the search for p-d interactions are analyzed in two comp- mentary contributions by Myazaki and Ouahab, while Valade focuses on the only class of metal bis(dithiolene) complexes to give rise to superconductive molecular materials, in association with organic as well as organometallic cations.

Magnetism in surfaces, heterostructures, small particles, and layered compounds has become an important subject in pure and applied science and a major component of high-technology industrial applications, for example, for magnetic recording and information storage and retrieval. This book presents relevant theoretical techniques and summarizes the optical, electronic, and nuclear experimental techniques used in studying the magnetic properties of such systems. Methods of sample preparation and characterization are also discussed. The book provides an up-to-date account of recent developments in this active interdisciplinary field.

Magnetic resonance has constantly been able to surprise with its ability to exhibit new phenomena. Just when it appears to be entering a quiet middle age it bursts into activity with some new manifestation of its versatility. This happened a few years ago, when observations on anomalous intensities were looked at more closely, and the pursuit of explanations and further evidence laid the foundations of the subjects treated in this volume. In organizing the NATO Advanced Study Institute we attempted to bring together a number, but by no means all, of those who had contributed significantly to the subject, and to obtain from them a comprehensive and detailed exposition of the subject. We were particularly anxious to avoid a set of lectures that dealt solely with the theory of the subject, because much of the interest in chemically induced magnetic polarization is due to its usefulness in applications to chemical problems: it is a real chemical tech nique, not just an amusing diversion for theoreticians. We set about organizing the course with the idea of making it useful to people who wanted to use the technique (for, after all, in the case of nuclear polarization, CIDNP, the technique can be used in any laboratory with minor modification of standard equipment)."

The present volume contains the courses given at a Summer School on "Magne tic Phase Transitions" held at the Ettore Majorana Centre for Scientific Culture, at Erice (Trapani), Italy in July 1983 under the auspices of the Condensed Matter Division of the European Physical Society in their series on Materials Science and Technology. The student participants came from West Germany, Great Britain, Brazil, Greece, Switzerland, Sweden, Italy, USA and The Netherlands. The lecturers came from various European countries, Israel, USA and Canada. The atmosphere at the meeting was excellent and a good spirit of companion ship developed during two weeks of working together. The spread of interests among the lecturers and students was divers;jfied but balanced. The main lec turing contributions are reported in this volume. They represent up-to-date reviews in a pedagogical style. In addition, informal presentations on cur rent research interests were made which have not been included. The school attempted to summarize the current position on the properties of magnetic phase transitions from several points of view. The range and scope of the oretical techniques, and of particular aspects of materials or phenomena as observed experimentally were very well put forward by the lecturers. The grouping of manuscripts in chapters does not represent, however, the sched ule followed during the school. Contributions on mean-field approximations and renormalization-group methods either for static or dynamic phenomena can be found at various places in the following sections."

What is thermodynamics? What does statistical physics teach us? In the pages of this slim book, we confront the answers. The reader will discover that where thermodynami cs provi des a 1 arge scal e, macroscopi c theory of the ef fects of temperature on physical systems, statistical mechanics provides the microscopic analysis of these effects which, invariably, are the results of thermal disorder. A number of systems in nature undergo dramatic changes in aspect and in their properties when subjected to changes in ambient temperature or pres sure, or when electric or magnetic fields are applied. The ancients already knew that a liquid, a solid, or a gas can represent different states of the same matter. But what is meant by "state"? It is here that the systematic study of magnetic materials has provided one of the best ways of examining this question, which is one of the principal concerns of statistical physics (alias "statistical mechanics") and of modern thermodynamics."

Many novel cooperative phenomena found in a variety of systems studied by scientists can be treated using the uniting principles of synergetics. Examples are frustrated and random systems, polymers, spin glasses, neural networks, chemical and biological systems, and fluids. In this book attention is focused on two main problems. First, how local, topological constraints (frustrations) can cause macroscopic cooperative behavior: related ideas initially developed for spin glasses are shown to play key roles also for optimization and the modeling of neural networks. Second, the dynamical constraints that arise from the nonlinear dynamics of the systems: the discussion covers turbulence in fluids, pattern formation, and conventional 1/f noise. The volume will be of interest to anyone wishing to understand the current development of work on complex systems, which is presently one of the most challenging subjects in statistical and condensed matter physics.

WAVE TURBULENCE is a state of a system of many simultaneously excited and interacting waves characterized by an energy distribution which is not in any sense close to thermodynamic equilibrium. Such situations in a choppy sea, in a hot plasma, in dielectrics under arise, for example, a powerful laser beam, in magnets placed in a strong microwave field, etc. Among the great variety of physical situations in which wave turbulence arises, it is possible to select two large limiting groups which allow a detailed analysis. The first is fully developed wave turbulence arising when energy pumping and dissipation have essentially different space scales. In this case there is a wide power spectrum of turbulence. This type of turbulence is described in detail e. g. in Zakharov et al. 1 In the second limiting case the scales in which energy pumping and dissipation occur are the same. As a rule, in this case a narrow, almost singular spectrum of turbulence appears which is concentrated near surfaces, curves or even points in k-space. One of the most important, widely investigated and instructive examples of this kind of turbulence is parametric wave turbulence appearing as a result of the evolution of a parametric instability of waves in media under strong external periodic modulation (laser beam, microwave electromagnetic field, etc. ). The present book deals with parametric wave turbulence.

Starting in 1995 numerical modeling of the Earth's dynamo has ourished with remarkable success. Direct numerical simulation of convection-driven MHD- ow in a rotating spherical shell show magnetic elds that resemble the geomagnetic eld in many respects: they are dominated by the axial dipole of approximately the right strength, they show spatial power spectra similar to that of Earth, and the magnetic eld morphology and the temporal var- tion of the eld resembles that of the geomagnetic eld (Christensen and Wicht 2007). Some models show stochastic dipole reversals whose details agree with what has been inferred from paleomagnetic data (Glatzmaier and Roberts 1995; Kutzner and Christensen 2002; Wicht 2005). While these models represent direct numerical simulations of the fundamental MHD equations without parameterized induction effects, they do not match actual pla- tary conditions in a number of respects. Speci cally, they rotate too slowly, are much less turbulent, and use a viscosity and thermal diffusivity that is far too large in comparison to magnetic diffusivity. Because of these discrepancies, the success of geodynamo models may seem surprising. In order to better understand the extent to which the models are applicable to planetary dynamos, scaling laws that relate basic properties of the dynamo to the fundamental control parameters play an important role. In recent years rst attempts have been made to derive such scaling laws from a set of numerical simulations that span the accessible parameter space (Christensen and Tilgner 2004; Christensen and Aubert 2006).

Palaeomagnetism and archaeomagnetism are fascinating specialized studies because they are applicable to such a wide range of problems in geology, archaeology and geophysics. They can also be undertaken cheaply, when compared with most other geophysical techniques, and, at first sight, simply. In fact, real comprehension of the magnetic processes that have occurred in rocks and other types of material over several thousands or many millions of years is still extremely difficult to assess and measure. On this basis, this book cannot explain all such features, nor can it attempt to cover all the actual and potential applications of the method. All that can be attempted is to give an impression of the ways in which such techniques can be used in a wide variety of fields, and how these techniques are usually applied. The magnetization of rocks is, in fact, one of the earliest of the true sciences, but we are still not in a position to answer many of the problems posed. Consequently some of the examples given of applications are, essentially, state-of-the-art comments, rather than being a review as such. The changing position of the geomagnetic poles with time is still not adequately defined, for example, and some of the more recent conventional views are given, although the emphasis is placed on more subjective, probably more controversial, evaluations.

On the 6th, 7th' and 8th April 1983, a conference entitled "Magnetism, planetary rotation and convection in the Solar System" was held in the School of Physics at the University of Newcastle upon Tyne. The purpose of the meeting was to celebrate the 60th birthday of Prof. Stanley Keith Runcorn and his, and his students' and associates', several decades of scientific achievement. The social programme, which consisted of excursions in Northumberland and Durham with visits to ancient castles and churches, to Hexham Abbey and Durham Cathedral, and dinners in Newcastle and Durham, was greatly enjoyed by those attending the meeting and by their guests. The success ofthe scientific programme can be judged by this special edition of Geophysical Surveys which is derived mainly from the papers given at the meeting. The story starts in the late 1940s when the question of the origin of the magnetic field of the Earth and such other heavenly bodies as had at that time been discovered as having a magnetic field, was exercising the minds of several scientists; notably P. M. S. Blackett at Manchester, W. M. Elsasser at the University of Pennsylvania and E. C. Bullard at Cambridge. Two alternative mechanisms were proposed. In one the magnetic field was in some way connected with the distributed angular momentum of a rotating body; in the other, electric currents in conducting parts within the body were proposed as the source of magnetic field.

Multiobjective Shape Design in Electricity and Magnetism is entirely focused on electric and magnetic field synthesis, with special emphasis on the optimal shape design of devices when conflicting objectives are to be fulfilled. Direct problems are solved by means of finite-element analysis, while evolutionary computing is used to solve multiobjective inverse problems. This approach, which is original, is coherently developed throughout the whole manuscript. The use of game theory, dynamic optimisation, and Bayesian imaging strengthens the originality of the book. Covering the development of multiobjective optimisation in the past ten years, Multiobjective Shape Design in Electricity and Magnetism is a concise, comprehensive and up-to-date introduction to this research field, which is growing in the community of electricity and magnetism. Theoretical issues are illustrated by practical examples. In particular, a test problem is solved by different methods so that, by comparison of results, advantages and limitations of the various methods are made clear.

Physics and Chemistry of Transition-Metal Oxides includes both theoretical and experimental approaches to the variety of phenomena found in the transition-metal oxides, including high-temperature superconductivity, colossal magnetoresistance, and metal-insulator transition. These are the central issues in materials science and condensed matter physics/chemistry, and readers can obtain up-to-date information on what is happening in this field of research.

"Micromagnetics and Recording Materials" is a book trying to give a systematic theory of computational applied magnetism, based on Maxwell equations of fields and Landau-Lifshitz equations of magnetic moments. The focused magnetic materials are magnetic recording materials utilized in computer hard disk drives. Traditionally, Micromagnetics includes the areas of magnetization curve theory," domain theory" and read and write process analyses in recording systems . As Springer Briefs, this book includes the first two areas of micromagnetics. M-H loops of hard magnetic thin film media, soft magnetic layers and Tunneling MagnetoResistive spin valves are solved based on the microstructures of thin films. Static domain structures and dynamic switching processes are analyzed in the arbitrary-shaped magnetic devices such as write head pole tips and magnetic force microscope tips. The book is intended for researchers who are interested in applied magnetism and magnetic recording in all disciples of physical science.

Prof. Dan Weiworks at Tsinghua University, China."