Description
Book SynopsisThis 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.
Table of ContentsChapter 1.Introduction
The purpose of this chapter is to provide a survey of our book by placing what we have to say in a historical context.
Chapter 2. Some concepts and definitions of the set theory, function theory, and operator theory
The purpose of this chapter is to present an overview of the mathematical apparatus used in this book, to give theorems and proofs used in the subsequent book chapters. The presentation focuses in particular on the necessary elements of the spectral theory of nonselfadjoint operator-valued functions.
Chapter 3. Shielded regular waveguides of arbitrary cross-section
This chapter is devoted to the analysis of the wave propagation in shielded waveguides of arbitrary cross-section filled with inhomogeneous dielectrics, metamaterials, chiral media, anisotropic media, and media with absorption. Spectral properties of the problems of wave propagation for the considered waveguide family are investigated. Definitions of various types of waves are formulated, the existence and distribution of the wave spectra are studied.
Chapter 4. Planar waveguides
This chapter addresses waves in plane waveguides filled with inhomogeneous dielectrics, metamaterials, chiral media, anisotropic media, and media with absorption. Spectral properties of the problems of wave propagation for this family of waveguides are investigated in detail.
Chapter 5. Waveguides of circular cross-section
This chapter is devoted to the analysis of wave propagation in circular waveguides filled with inhomogeneous dielectrics, metamaterials, chiral media, anisotropic media, and media with absorption. The notions, results and methods developed in Chapter 3 are applied and concretized for this family of waveguides. The existence of real and complex normal waves and analysis of the distribution of the wave spectra are backed by a variety of numerical results.
Chapter 6. Open regular waveguides of arbitrary cross-section
In this chapter, open waveguides of arbitrary cross-section are considered; the material filling consists of inhomogeneous dielectrics, metamaterials, chiral and anisotropic media, and media with absorption. The problems on normal waves are formulated with the conditions at infinity that enable one to take into account all types of waves, including complex and leaky. Spectral properties of the problems of wave propagation in open waveguides are investigated using the specially developed extensions of the spectral theory and particularly the operator-pencil approach.
Chapter 7. Conclusion
