Advances in Mathematical Methods for Electromagnetics

Kazuya Kobayashi is a professor in the Department of Electrical, Electronic, and Communication Engineering at Chuo University, Japan. He has received a number of awards including The President's Award (2020) from URSI (International Union of Radio Science) and the M.A. Khizhnyak Award (2016) at the 16th International Conference on Mathematical Methods in Electromagnetic Theory. He is a Fellow of The Electromagnetics Academy and a Fellow of URSI. He has held various positions in the international radio science, electromagnetics, and optics communities including URSI Assistant Secretary-General for AP-RASC (since 2015); Chair of URSI Commission B (since 2017); Chair of the AP-RASC Standing Committee (since 2015); President of the Japan National Committee of URSI (2008-2018); Chair of the PIERS Young Scientists Award Committee, The Electromagnetics Academy (since 2018); Editor of Radio Science (since 2019); and Series Editor of Springer Series in Optical Sciences (since 2020). His research areas include developments of rigorous mathematical techniques as applied to electromagnetic wave problems; radar cross section; and scattering and diffraction.Paul Denis Smith is a professor of mathematics at the Macquarie University, Australia. His awards include the best paper award at the 1987 International Symposium on Electromagnetic Compatibility. He served as associate editor of J. IEEE Antennas and Propagation from 2004 to 2011 and is currently an associate editor of Radio Science and a Board Member for Proceedings of the Royal Society(A). He is president of the Australian URSI Committee and is a member of the Australian Academy of Science National Committee for Space and Radio Science. His research areas include analytical and semi-analytical techniques for wave scattering and diffraction.

• IntroductionChapter 1: New insights in integral representation theory for the solution of complex canonical diffraction problemsChapter 2: Scattering of electromagnetic surface waves on imperfectly conducting canonical bodiesChapter 3: Dielectric-wedge Fourier seriesChapter 4: Green's theorem, Green's functions and Huygens' principle in discrete electromagneticsChapter 5: The concept of generalized functions and universal properties of the Green's functions associated with the wave equation in bounded piece-wise homogeneous domainsChapter 6: Elliptic cylinder with a strongly elongated cross-section: high frequency techniques and function theoretic methodsChapter 7: High-frequency hybrid ray-mode techniquesChapter 8: Scattering and diffraction of scalar and electromagnetic waves using spherical-multipole analysis and uniform complex-source beamsChapter 9: Changes in the far-field pattern induced by rounding the corners of a scatterer: dependence upon curvatureChapter 10: Radiation from a line source at the vertex of a right-angled dielectric wedgeChapter 11: Wiener-Hopf analysis of the diffraction by a thin material stripChapter 12: The Wiener-Hopf Fredholm factorization technique to solve scattering problems in coupled planar and angular regionsChapter 13: On the analytical regularization method in scattering and diffractionChapter 14: Resonance scattering of E-polarized plane waves by two-dimensional arbitrary open cavities: spectrum of complex eigenvaluesChapter 15: Numerical solutions of integral equations for electromagneticsChapter 16: Electromagnetic modelling at arbitrarily low frequency via the quasi-Helmholtz projectorsChapter 17: Resistive and thin dielectric disk antennas with axially symmetric excitation analyzed using the method of analytical regularizationChapter 18: Scattering and guiding problems of electromagnetic waves in inhomogeneous media by improved Fourier series expansion methodChapter 19: Methods and fast algorithms for the solution of volume singular integral equationsChapter 20: Herglotz functions and applications in electromagneticsChapter 21: Scattering and guidance by layered cylindrically periodic arrays of circular cylindersChapter 22: Analytical and numerical solution techniques for forward and inverse scattering problems in waveguidesChapter 23: Beam-based local diffraction tomographyChapter 24: Modal expansions in dispersive material systems with application to quantum optics and topological photonicsChapter 25: Multiple scattering by a collection of randomly located obstacles distributed in a dielectric slabChapter 26: Electromagnetics of complex environments applied to geophysical and biological mediaChapter 27: Innovative tools for SI units in solving various problems of electrodynamics