Optical Waveguide Theory: Mathematical Models, Spectral Theory and Numerical Analysis (Springer Series in Optical Sciences, 237)

✍ Scribed by Yury Shestopalov, Yury Smirnov, Eugene Smolkin

• Publisher: Springer
• Year: 2022
• Tongue: English
• Leaves: 269
• Category: Library

✦ Synopsis

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.

✦ Table of Contents

Foreword
Contents
1 Introduction
References
2 Shielded Waveguide
2.1 Method of Operator Pencils
2.1.1 Propagation of Normal Waves in Waveguides
2.1.2 Eigenvalue Problem for Operator Pencil
2.1.3 Property of the Spectrum of Pencil
2.1.4 Theorems of Completeness
2.2 Properties of the System of Eigenwaves and Associated Waves of a Waveguide
2.2.1 Eigenwaves and Associated Waves
2.2.2 Completeness of the System of Transversal Components of Eigenwaves and Associated Waves
2.2.3 Biorthogonal Property for Eigenwaves and Associated Waves
2.2.4 Basis Property of the System of Eigenwaves and Associated Waves
References
3 Planar Waveguide
3.1 TE-Polarized Waves in a Partially Shielded Dielectric Layer
3.1.1 Statement of the Problem
3.1.2 Surface Waves
3.1.3 Leaky Waves
3.2 TE-Polarized Waves in an Inhomogeneous Partially Shielded Dielectric Layer
3.2.1 Statement of the Problem
3.2.2 Sobolev Spaces and Variational Relation
3.2.3 Properties of the Operator Pencil
3.2.4 Completeness of System of Eigenvectors and Associated Vectors of Operator Pencil
3.3 TE-Polarized Waves in an Inhomogeneous Metamaterial Partially Shielded Layer
3.3.1 Statement of the Problem
3.3.2 Sobolev Spaces and Variational Relation
3.3.3 Properties of the Operator Pencil
3.3.4 Completeness of the System of Eigenvectors and Associated Vectors of Operator Pencil
3.4 TE-Polarized Waves in an Inhomogeneous Partially Shielded Lossy Dielectric Layer
3.4.1 Statement of the Problem
3.4.2 Sobolev Spaces and Variational Relation
3.4.3 Properties of the Operator Pencil
3.4.4 Completeness of System of Eigenvectors and Associated Vectors of Operator Pencil
3.5 TM-Polarized Waves in an Inhomogeneous Partially Shielded Dielectric Layer
3.5.1 Statement of the Problem
3.5.2 Sobolev Spaces and Variational Relation
3.5.3 Properties of the Operator Pencil
3.5.4 Completeness of System of Eigenvectors and Associated Vectors of Operator Pencil
3.6 TM-Polarized Waves in an Inhomogeneous Metamaterial Partially Shielded Layer
3.6.1 Statement of the Problem
3.6.2 Sobolev Spaces and Variational Relation
3.6.3 Properties of the Operator Pencil
3.6.4 Completeness of System of Eigenvectors and Associated Vectors of Operator Pencil
3.7 TM-Polarized Waves in an Inhomogeneous Partially Shielded Lossy Dielectric Layer
3.7.1 Statement of the Problem
3.7.2 Sobolev Spaces and Variational Relation
3.7.3 Properties of the Operator Pencil
3.7.4 Completeness of System of Eigenvectors and Associated Vectors of Operator Pencil
3.8 Numerical Simulation
3.8.1 Statement of the Problem
3.8.2 Numerical Method
3.8.3 Numerical Results
References
4 Waveguides of Circular Cross Section
4.1 Surface Waves in Inhomogeneous Waveguides
4.1.1 Statement of the Problem
4.1.2 Sobolev Spaces and Variational Relation
4.1.3 Spectrum of the OVF
4.1.4 Properties of the Spectrum of OVF
4.2 Surface Waves in a Waveguide Filled with Metamaterial Media
4.2.1 Statement of the Problem
4.2.2 Sobolev Spaces and Variational Relation
4.2.3 Spectrum of the OVF
4.2.4 Properties of the Spectrum of OVF
4.3 Surface Waves in a Waveguide Filled with Lossy Medium
4.3.1 Statement of the Problem
4.3.2 Sobolev Spaces and Variational Relation
4.3.3 Spectrum of the OVF of the Problem
4.3.4 Properties of the Spectrum of the OVF
4.4 Surface Waves in a Waveguide Filled with Anisotropic Media
4.4.1 Statement of the Problem
4.4.2 Sobolev Spaces and Variational Relation
4.4.3 Spectrum of the OVF
4.4.4 Properties of the Spectrum of OVF
4.5 Surface Waves in a Waveguide Filled with Inhomogeneous Chiral Media
4.5.1 Statement of the Problem
4.5.2 Sobolev Spaces and Variational Relation
4.5.3 Properties of the OVF
4.5.4 Numerical Results
4.6 Leaky Waves in an Inhomogeneous Waveguide
4.6.1 Statement of the Problem
4.6.2 Sobolev Spaces and Variational Relation
4.6.3 Spectrum of the OVF
4.6.4 Properties of the Spectrum of the OVF
4.7 Leaky Waves in a Waveguide Filled with Metamaterial Media
4.7.1 Statement of the Problem
4.7.2 Sobolev Spaces and Variational Relation
4.7.3 Spectrum of the OVF of the Problem
4.7.4 Properties of the Spectrum of the OVF
4.8 Leaky Waves in a Waveguide Filled with Lossy Medium
4.8.1 Statement of the Problem
4.8.2 Sobolev Spaces and Variational Relation
4.8.3 Spectrum of the OVF
4.8.4 Properties of the Spectrum of the OVF
4.9 Leaky Waves in a Waveguide Filled with Anisotropic Media
4.9.1 Statement of the Problem
4.9.2 Sobolev Spaces and Variational Relation
4.9.3 Spectrum of the OVF
4.9.4 Properties of the Spectrum of the OVF
4.10 Numerical Simulation
4.10.1 Statement of the Problem
4.10.2 Numerical Method
4.10.3 Numerical Results
References
5 Open Waveguides of Arbitrary Cross Section
5.1 Normal Waves in an Open Metal-Dielectric Waveguide
5.1.1 Statement of the Problem
5.1.2 Variational Formulation
5.1.3 Spectrum of the OVF
5.1.4 Properties of OVF N (γ)
5.2 Normal Waves in an Open Inhomogeneous Metal-Dielectric Waveguide
5.2.1 Statement of the Problem
5.2.2 Variational Formulation
5.2.3 Spectrum of the OVF
5.2.4 The Properties of OVF
References
6 Conclusion