Springer Series on Wave Phenomena – serie

This monograph covers important problems caused by the interaction of different types of surface acoustic waves with surface inhomogeneities. The problem of surface acoustic wave interaction with periodic topographic gratings, widely used in filters and resonators, is given careful consideration. The most important results of surface wave scattering by local defects such as grooves, random roughness and elastic wedges are described. Different theoretical approaches and practical rules for solving the surface wave problems are also presented.

This text, in a sense, continues the treatment of the earlier Volume 6 in the "Springer Series on Wave Phenomena", titled "Geometrical Optics of Inhomogenous Media", by analyzing caustics and their fields on the basis of modern catastrophe theory. This volume covers the key generalizations of geometrical optics related to caustic asymptotic expansions: The Lewis-Kravtsov method of standard functions; Maslov's method of canoncial operators; Orlov's method of interference integrals, as well as their modifications for penumbra, space-time, random and other types of caustics. All the methods are illustrated by worked problems concerning relevant wave-field applications.

The theory of the propagation of plane sound waves in layered structures is presented systematically in this book. The layered structures may be man-made, for example ultrasonic filters, lenses, and surface-wave delay lines, or natural media such as the ocean and the atmosphere with their marked horizontal stratification. A related problem is the propagation of elastic (seismic) waves in the earth's crust. The book retains many features and the general structure of the classic work "Waves in Layered Media" by L.M. Brekhovskikh, but also includes much new material that has not previously been treated in a monograph. Great attention is paid throughout to the physical interpretation of the results obtained. Although the subject of the book is acoustic waves, many of the interesting phenomena can be directly generalized to electromagnetic waves.

Acoustics of Layered Media II presents the theory of sound propagation and reflection of spherical waves and bounded beams in layered media. It is mathematically rigorous but at the same time care is taken that the physical usefulness in applications and the logic of the theory are not hidden. Both moving and stationary media, discretely and continuously layered, including a range-dependent environment, are treated for various types of acoustic wave sources. Detailed appendices provide further background on the mathematical methods.This second edition reflects the notable recent progress in the field of acoustic wave propagation in inhomogeneous media.

Acoustics of Layered Media II presents the theory of sound propagation and reflection of spherical waves and bounded beams in layered media. It is mathematically rigorous but at the same time care is taken that the physical usefulness in applications and the logic of the theory are not hidden. Both moving and stationary media, discretely and continuously layered, including a range-dependent environment, are treated for various types of acoustic wave sources. Detailed appendices provide further background on the mathematical methods.This second edition reflects the notable recent progress in the field of acoustic wave propagation in inhomogeneous media.

Surface Acoustic Waves in Inhomogeneous Media covers almost all important problems of the interaction of different types of surface acoustic waves with surface inhomogeneities. The problems of surface acoustic wave interaction with periodic topographic gratings widely used in filters and resonators are under careful consideration. The most important results of surface wave scattering by local defects such as grooves, random roughness, elastic wedges are given. Different theoretical approaches and practical rules for solving the surface wave problems are presented.

Caustics, Catastrophes and Wave Fields in a sense continues the treatment of the earlier volume 6 "Geometrical Optics of Inhomogeneous Media" in the present book series, by analysing caustics and their fields on the basis of modern catastrophe theory. This volume covers the key generalisations of geometrical optics related to caustic asymptotic expansions: The Lewis-Kravtsov method of standard functions, Maslov's method of caonical operators, Orlov's method of interference integrals, as well as their modifications for penumbra, space-time, random and other types of caustics. All the methods are amply illustrated by worked problems concerning relevant wave-field applications.

Since the fIrst edition of this book was published in the 1994, the theory of wave scattering from rough surfaces has continued to develop intensively. The community of researchers working in this area keeps growing, which provides justifIcation for issuing this second edition. In preparing the second edition, I was challenged by the problem of se­ lecting new material from the many important results obtained recently. Even­ tually, a new section was added to the central Chap. 6 of this book. This sec­ tion describes the operator expansion technique put forward by M. Milder, which conforms well with the general approach adopted in the book and which to my mind is one of the most promising. Remote sensing of the terrain and ocean surface represents one of the most important and interesting challenges to the theory of wave scattering from rough surfaces. Rapid progress in electronics results in sensors with new capabilities. New powerful computers and data communication systems allow more sophisticated data processing techniques. What information about soil or air-sea interaction processes can be obtained from gigaflops of data streaming from air-or space-borne radars? To use this information efficiently, one cannot rely entirely on heuristic approaches and needs adequate theory. I hope that this book will contribute to progress in this important area.

This research monograph presents a systematic treatment of the theory of the propagation of transient electromagnetic fields (such as optical pulses) through dielectric media which exhibit both dispersion and absorption. The work divides naturally into two parts. Part I presents a summary of the fundamental theory of the radiation and propagation of rather general electromagnetic waves in causal, linear media which are homogeneous and isotropic but which otherwise have rather general dispersive and absorbing properties. In Part II, we specialize on the propagation of a plane, transient electromagnetic field in a homogeneous dielectric. Although we have made some contributions to the fundamental theory given in Part I, most of the results of our own research appear in Part II. The purpose of the theory presented in Part II is to predict and to explain in explicit detail the dynamics of the field after it has propagated far enough through the medium to be in the mature-dispersion regime. It is the subject of a classic theory, based on the research conducted by A. Sommerfeld and L.

There is no respect for mere age in Science or Technology. Yet the cen­ tenary of the discovery, by the third Lord Rayleigh, that elastic waves can be guided by a surface, is memorable for the contradictions which it encompasses: Rayleigh's assessment of his classic 1885 paper as a rather minor mathematical development with a potential value only in seismology on the one hand; on the other the rediscovery of the subject in a totally that of electronic signal processing - which has led to its different fiel- explosive growth over the last twenty years. The new surface acoustic wave (SAW) devices have proved to be per­ electronic components. Today almost all television receivers con­ vasive tain one or more SAW filters, sophisticated radars depend on SAW signal processing, and SAW devices have been incorporated in ultra-high perfor­ mance opto-electronic systems. With the objective of surveying these developments and attempting to predict those that can be foreseen, as well as marking the centenary of Lord Rayleigh's discovery, The Rank Prize Funds' Committee for Opto­ Electronics organised a symposium in London, in July 1985. It was held in the Royal Institution, London, where Rayleigh himself once worked and often lectured. The present volume is the tangible outcome of the symposium, In which international experts survey.ed their various fields, and presented the most exciting recent developments.

This volume is based on lectures and contributed papers presented at the Eighth Course of the International School of Materials Science and Tech­ nology that was held in Erice, Sicily, Italy at the Ettore Majorana Centre for Scientific Culture during the period 1-13 July 1985. The subject of the course was "Electromagnetic Surface Excitations". Forty lectures were given by eleven distinguished scientists and engineers from France, Italy, the United Kingdom, and the United States. In addition to the lectur­ ers, approximately fifty participants representing eleven different countries throughout the world t. ook part in the course. Short contributed papers were presented by seventeen participants on the results of their own re­ search. The subject of the Course is of great importance for both pure science and for practical applications such as telecommunications. A technolog­ ical revolution is occurring in which the transmission of information by means of electrical currents travelling in copper wires is being replaced by transmission by means of light travelling in objects known as optical wave guides. The manipulation and processing of the light signals prior and subsequent to transmission through the wave guide has resulted in a technology often referred to as integrated optics. Important to the opera­ tion of integrated optics devices is the behavior of electromagnetic waves near surfaces and interfaces. One of the goals of the course was to further the dialogue between engineers and physicists in common areas of interest related to the propagation of electromagnetic waves along surfaces.

In the study of short-wave diffraction problems, asymptotic methods - the ray method, the parabolic equation method, and its further development as the "etalon" (model) problem method - play an important role. These are the meth­ ods to be treated in this book. The applications of asymptotic methods in the theory of wave phenomena are still far from being exhausted, and we hope that the techniques set forth here will help in solving a number of problems of interest in acoustics, geophysics, the physics of electromagnetic waves, and perhaps in quantum mechanics. In addition, the book may be of use to the mathematician interested in contemporary problems of mathematical physics. Each chapter has been annotated. These notes give a brief history of the problem and cite references dealing with the content of that particular chapter. The main text mentions only those pUblications that explain a given argument or a specific calculation. In an effort to save work for the reader who is interested in only some of the problems considered in this book, we have included a flow chart indicating the interdependence of chapters and sections.

The topic of surface waves lies at the interface between a number of disci­ plines - physics, theoretical and applied mechanics, electroacoustics, ap­ plied mathematics, surface science and seismology. This volume, based on papers delivered at European Mechanics Colloquium 226, reflects this diversity in approach and background, while showing strong links between phenomena arising from different fields. The emphasis is on recent de­ velopments such as nonlinear and other nonclassical effects,which have great importance for both pure science and for applications such as signal processing, nondestructive evaluation and seismic studies. In recent years there has been considerable progress in the mathe­ matical treatment of nonlinear effects, of viscoelastic and of more novel constitutive effects which modify the predictions of linear elastic and piezo­ electric theory for surface acoustic wave (SAW) propagation. A number of these themes serve to group the contents of this volume. Part I contains recent advances in the rigorous mathematical treatment of nonlinearity, together with a paper giving experimental results showing the need for further theoretical development. Part II deals with anisotropic elasticity, showing that even the linear theory presents many possible behaviours, which are still not fully categorized.

This monograph is concerned with the fundamentals of up-to-date geo­ metrical optics treated as an approximate method of wave theory. Geometrical optics has changed dramatically over the last two decades. Primarily, it has acquired a number of novel disciplines: space-time geo­ metrical optics, the quasi-isotropic approximation, the modern theory of caustics related to catastrophe theory, and perturbation techniques for rays, to name only a few. Another acquisition is the reliable boundaries of appli­ cability for geometrical optics, based upon the concept of the Fresnel volume for a ray. These recent additions to the field are the focus of dis­ cussion in the book. We did not attempt to separate study-oriented and illustrative material from that intended for professionals, but rather we spread it throughout the text to facilitate for the reader the mastering of this attractive, intuitively appealing and efficient ray method. In preparing the manuscript we used a set of lecture notes devised for All-Union Schools on Diffraction and Wave Propagation, published in Rus­ sian. Sections 2.1-4,6 and 10 result from joint efforts of both authors. The other material of the book we wrote separately. I contributed Sects. 2.5,9 and 3.17 and Chap.4; Yu.l. Orlov prepared the rest. Unfortunately, he could not take part in the preparation of the English edition, as he died in 1982 at the age of 41, on the verge of what would have been great achieve­ ments considering his strong and original talent.

In recent years one has witnessed in physics a substantial increase in interest in carrying out fundamental studies in the nonlinear optics of condensed matter. At the Danish universities, this increase has been especially pronounced at the Institute of Physics at the University of Aalborg, where the main activities are centered around fundamental research within the domains of nonlinear quantum optics, nonlinear optics of metals and superconductors, and nonlinear surface optics. In recognition of this it was decided to arrange the first international summer school on nonlinear optics in Denmark at the Institute of Physics at the University of Aalborg. This book is based on the lectures and contributed papers presented at this international summer school, which was held in the period 31 July-4 Au­ gust 1989. About 60 experienced and younger scientists from 12 different countries participated. Twenty-eight lectures were given by 14 distinguished scientists from the United States, Italy, France, Germany, Scotland, England, and Denmark. In addition to the lectures given by the invited speakers, 11 contributed papers were presented. The programme of the summer school em­ phasized a treatment of basic physical properties of the nonlinear interaction of light and condensed matter and both theoretical and experimental aspects were covered. Furthermore, general principles as well as topics of current interest in the research literature were discussed.

This book comprises some of the lecture notes I developed for various one-or two-semester courses I taught at the Colorado School of Mines. The main objective of all the courses was to introduce students to the mathematical aspects of wave theory with a focus on the solution of some specific fundamental problems. These fundamental solutions would then serve as a basis for more complex wave propagation and scattering problems. Although the courses were taught in the mathematics department, the audience was mainly not mathematicians. It consisted of gradu­ ate science and engineering majors with a varied background in both mathematics and wave theory in general. I believed it was necessary to start from fundamental principles of both advanced applied math­ ematics as well as wave theory and to develop them both in some detail. The notes reflect this type of development, and I have kept this detail in the text. I believe it essential in technical careers to see this detailed development at least once. This volume consists of five chapters. The first two on Scalar Wave Theory (Chapter 1) and Green's Functions (Chapter 2) are mainly mathematical although in Chapter 1 the wave equation is derived from fundamental physical principles. More complicated problems involving spatially and even temporally varying media are briefly introduced.

Resonance Acoustic Spectroscopy deals with the analysis ofwaves generated in an elastic body by a plane harmonicacoustic wave. It is the first monograph to treat newanalytical and experimental methods for the investigation ofthe excitation, propagation and re-radiation of elasticwaves in solid, thick-walled and thin-walled elasticscatterers.The material is presented systematically,comprising the formulation of the problem, method ofsolution, algorithm, computation and analysis. A largenumber of computational results are given in the form ofmodal resonances, form functions, dispersion curves andacoustic spectrograms. Particular attention is paid to theinterpretation of the solutions.

For a system consisting of a random medium with roughboundaries, the governing (Bethe-Salpeter) equation forboundary-value transport problems can be written in a formsuch that the medium and the boundaries are treatedon anequal footing. This enables several expressions for thesolution to be obtained by interchanging the roles of themedium and the boundaries, thus allowing the most convenientone to be selected according to the specific situation andthe information required. This book presents a unifiedtheory based on the Bethe-Salpeter equation with particularattention being paid to: boundary-value problems oftransport, layer problems, a fixed scatterer imbedded in abounded random medium, construction of an optical scatteringmatrix for a complete system, and optical wave propagationin a turbulent medium. The last topic is treated in terms offirst moment equations combined with the cluster expansionand, second, the two-scale method based on the Lagrangevariational principle.

Electromagnetic Wave Propagation in Turbulence is devoted to a method for obtaining analytical solutions to problems of electromagnetic wave propagation in turbulence. In a systematic way the monograph presents the Mellin transforms to evaluate analytically integrals that are not in integral tables. Ample examples of application are outlined and solutions for many problems in turbulence theory are given. The method itself relates to asymptotic results that are applicable to a broad class of problems for which many asymptotic methods had to be employed previously.