Optical Waveguide Theory: Mathematical Models, Spectral Theory and Numerical Analysis

ISBN-13: 9789811905834 / Angielski / Twarda / 2022 / 272 str.

Yury Shestopalov; Yury Smirnov; Eugene Smolkin

Spis treści

Chapter 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

O autorze

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 and Supercomputer 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.

Blurb

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.