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.
Yury Shestopalov is a professor of mathematics at the University of Gävle, Sweden. His work mainly contributes to the spectral theory of operators and its application to electromagnetics, along with numerical and data analysis, including development of computational codes, software and program packages. He received his Ph.D. and Doctor of Science degrees in mathematics and physics from Moscow State University (MSU) in 1978 and 1988, respectively, and has accomplished a full university career from teaching assistant to professor and a department head at MSU, Karlstad University and the University of Gävle (since 2013). He has also continuously devoted himself to higher education, including establishment the MSU Kolmogorov Advanced Education and Science Center (AESC) and initiation of the Faculty of Higher Pedagogical Education at MSU, as well as participation in academic conferences and symposia.
Yury Smirnov is the head of the Department of Mathematics andSupercomputer Modelling at Penza State University, Russia. His work is concerned with mathematical theory and methods for electromagnetic problems, and developing numerical methods. He received his Doctor of Science in physics and mathematics from MSU in 1995 and has served in his current position as professor since 1998. He founded a scientific school in the field of mathematical methods for solving problems of electromagnetics, and he has been honored with more than 35 grants in Russia, France and Germany.
Eugene Smolkin is a docent at the Department of Mathematics and Supercomputing, Penza State University. His work primarily focuses on analysis of wave propagation in dielectric waveguides and nonlinear media. He received his Ph.D. degree in applied mathematics from the Marchuk Institute of Numerical Mathematics of the Russian Academy of Sciences (INM RAS) in 2015.
