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Electromagnetic wave scattering is an active, interdisciplinary area of research with myriad practical applications in fields ranging from atomic physics to medical imaging to geoscience and remote sensing. In particular, the subject of wave scattering by random discrete scatterers and rough surfaces presents great theoretical challenges due to the large degrees of freedom in these systems and the need to include multiple scattering effects accurately. In the past three decades, considerable theoretical progress has been made in elucidating and understanding the scattering processes involved in such problems. Diagrammatic techniques and effective medium theories remain essential for analytical studies; however, rapid advances in computer technology have opened new doors for researchers with the full power of Monte Carlo simulations in the numerical analysis of random media scattering. Numerical simulations allow us to solve the Maxwell equations exactly without the limitations of analytical approximations, whose regimes of validity are often difficult to assess. Thus it is our aim to present in these three volumes a balanced picture of both theoretical and numerical methods that are commonly used for tackling electromagnetic wave scattering problems. While our book places an emphasis on remote sensing applications, the materials covered here should be useful for students and researchers from a variety of backgrounds as in, for example, composite materials, photonic devices, optical thin films, lasers, optical tomography, and X-ray lithography. Introductory chapters and sections are also added so that the materials can be readily understood by graduate students. We hope that our book would help stimulate new ideas and innovative approaches to electromagnetic wave scattering in the years to come. The increasingly important role of numerical simulations in solving electromagnetic wave scattering problems has motivated us to host a companion web site that contains computer codes on topics relevant to the book. These computer codes are written in the MATLAB' programming language and are available for download from our web site at They are provided to serve two main purposes. The first is to supply our readers a hands-on laboratory for performing numerical experiments, through which the concepts in the book can be more dynamically relayed. The second is to give new researchers a set of basic tools with which they could quickly build on projects of their own. The fluid nature of the web site would also allow us to regularly update the contents and keep pace with new research developments.
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The present volume Covers the basic principles and applications of electromagnetic wave scattering and lays the groundwork for the study of more advanced topics in Volumes II and III. We start in 1 with exact and approximate solutions of wave scattering by a single particle of simple shape. Such problems can be solved exactly by expanding the fields in terms of scalar or vector waves in separable coordinates, depending on the geometry of the scatterer. When the size of the scatterer is small, Rayleigh scattering represents a simple and valid approximation. When scattering is weak, the Born approximation can be applied to the volume integral equation for the internal field. Approximate solutions are also useful when the scatterer lacks perfect symmetry as in the case of a finite cylinder. In 2, we discuss basic scattering theory. We introduce the Green's function for the wave equation and its various coordinate representations. From the vector Green's theorem, we derive the Hugyens' Principle and the extinction theorem, which are especially useful for formulating surface integral equations in scattering problems. The reciprocity principle leads to useful symmetry relations in the scattering amplitudes and the Green's function, while energy conservation leads to the optical theorem. The T-matrix formulation with the extended boundary condition technique is a popular method that can be used to calculate scattering from an arbitrarily shaped object. We give explicit results for dielectric spheres and spheroids. In 3, we begin the study of electromagnetic scattering by a random collection of scatterers. The concepts of fluctuating fields and ensemble averaging are of central importance in random media scattering. These and related ideas are explored in this chapter. The specific intensity is often used to describe energy transport through a random medium. The fully polarimetric description of the specific intensity is provided by the Stokes vector. As an application to passive remote sensing, we derive the emissivity of the four Stokes parameters using the fluctuation dissipation theorem. Basic radiative transfer (RT) theory elements including the extinction coefficient and scattering phase matrix are also introduced. In contrast to conventional RT theory, the phase functions are defined in terms of bistatic scattering cross sections. This allows for the development of the dense medium radiative transfer theory (DMRT) to be discussed in Volumes II and III. Many natural media, e.g., snow, vegetation, and ocean surfaces, can be effectively modeled in terms of simple random media. 4 is devoted to the statistical characterizations of such random discrete media and rough surfaces. Useful characterizations include the pair distribution function for volume scatterers and the power spectrum for rough surfaces.
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