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This book addresses the most advanced to-date mathematical approach and numerical methods in electromagnetic field theory and wave propagation. It presents the application of developed methods and techniques to the analysis of waves in various guiding structures -shielded and open metal-dielectric waveguides of arbitrary cross-section, planar and circular waveguides filled with inhomogeneous dielectrics, metamaterials, chiral media, anisotropic media and layered media with absorption. It also looks into spectral properties of wave propagation for the waveguide families being considered, and the relevant mathematical techniques such as spectral theory of non-self-adjoint operator-valued functions are described, including rigorous proofs of the existence of various types of waves. Further, numerical methods constructed on the basis of the presented mathematical approach and the results of numerical modeling for various structures are also described in depth.The book is beneficial to a broad spectrum of readers ranging from pure and applied mathematicians in electromagnetic field theory to researchers and engineers who are familiar with mathematics. Further, it is also useful as a supplementary text for upper-level undergraduate students interested in learning more advanced topics of mathematical methods in electromagnetics.

Classical asymptotic expansions, while producing a good approximation for the diffracted fields in general, appear hardly applicable in the case of extremely elongated bodies. Thus, there are problems that are on the one hand too difficult for numerical solvers due to large system size, and on the other hand make the description with classical asymptotic methods hard. The book explains why this happens and suggests the way out. By defining the characteristics of a strongly elongated body it introduces a special class of asymptotic approximations, which are in some sense uniform with respect to the rate of body elongation.Chapter 1 briefly describes the results of V. A. Fock and further developments of his approach towards the problems of diffraction by elongated obstacles. It formulates the cases of moderately and strongly elongated bodies. The rest of the book describes the approach of special parabolic equations, which lead to new asymptotic approximations for the diffracted fields. Chapters 2, 3 and 4 discuss diffraction by bodies of elliptical shape: The elliptic cylinder with a strongly elongated cross section and prolate spheroid with a high aspect ratio. Chapter 5 generalizes the approach to some other shapes such as narrow cones and narrow hyperboloids. Mathematical formulas for the Whittaker functions widely used in the book are collected in the Appendix.The concise derivations are supplied with numerous test examples that compare asymptotic approximations with numerically computed fields and clarify the specifics of high frequency diffraction by strongly elongated bodies. The reference solutions presented in the book enable one to validate the newly developed numerical solvers.

This book provides a comprehensive overview of laser sources and their applications in various fields of science, industry, and technology. After an introduction to the basics of laser physics, different laser types and materials for lasers are summarized in the context of a historical survey, outlining the evolution of the laser over the past five decades. This includes, amongst other aspects, gas lasers, excimer lasers, the wide range of solid-state and semiconductor lasers, and femtosecond and other pulsed lasers where particular attention is paid to high-power sources. Subsequent chapters address related topics such as laser modulation and nonlinear frequency conversion. In closing, the enormous importance of the laser is demonstrated by highlighting its current applications in everyday life and its potential for future developments. Typical applications in advanced material processing, medicine and biophotonics as well as plasma and X-ray generation for nanoscale lithography are discussed. The book provides broad and topical coverage of laser photonics and opto-electronics, focusing on significant findings and recent advances rather than in-depth theoretical studies. Thus, it is intended not only for university students and engineers, but also for scientists and professionals applying lasers in biomedicine, material processing and everyday consumer products. Further, it represents essential reading for engineers using or developing high-power lasers for scientific or industrial applications.