CONTENTS
Series Editor's Foreword
Preface
Symbol conventions
Chapter 1. Introduction
1.1 Motivation and background
1.2 Overview of waveguides
1.3 Monographic texts on waveguide analysis
Chapter 2 Preliminary
considerations
2.1 Formulation of the wave guidance problem
2.1.1 Statement of the problem
2.1.2 Problem definition in physical terms
2.2 Operator formulation of wave guidance
problems
2.2.1 Modes and mode nomenclature
2.2.2 Examples of mode classification
schemes
2.2.3 Equivalence of operator formulations
Chapter 3 Standard and
generalized eigenvalue problems
3.1 Spectral problem
3.2 Symmetric operators
3.2.1 Generalized eigenproblems
3.3 Nonsymmetric operators
3.4 Pseudo-symmetric and pseudo-transposed
problems
3.5 Pairs of complementary solutions in
generalized eigenproblems
3.5.1 Spectra with inversion symmetry
3.5.2 Complex conjugate pairs of eigenvalues
3.5.3 Orthogonality relations for problems
with spectra possessing inversion symmetry
3.5.4 Higher order symmetry
3.6 Matrix eigenvalue problems
3.7 Completeness of eigenfunctions
3.8 Operator pencils
Chapter 4 Methods for
solving operator equations
4.1 Variational techniques
4.1.1 Symmetric generalized eigenvalue
problems
4.1.2 Nonsymmetric generalized eigenvalue
problems
4.1.3 Significance of variational expressions
4.1.4 The Rayleigh-Ritz procedure
4.2 Method of moments
4.2.1 Galerkin method
4.2.2The least squares method
4.3 Projection methods
4.4 Nonstandard eigenvalue problems
4.5 Iterative techniques for solving eigenvalue
problems
4.5.1 The power method
4.5.2 The inverse iteration method
4.5.3 Perturbation of the operator
4.5.4 The Iterative Eigenfunction Expansion
Method
4.6 Function expansion and discretization
Chapter 5 Preliminary
electromagnetic background
5.1 Energy relations - Poynting theorem
5.1.1 Energy relations in lossless media
5.1.2 Poynting theorem for the waveguides
5.1.3 Energy stored in the field
5.2 Dispersive media
5.2.1 Poynting theorem for weakly anharmonic
fields
5.3 Permittivity and permeability tensors
5.4 Isometries in electromagnetics
5.4.1 Rotations and reflections
5.4.2 Time reversal
5.5 Symmetries in waveguides
5.6 Isotropic guides
5.6.1 Symmetry groups of 2D objects
5.6.2 Symmetry induced properties of modes
5.7 Anisotropic guides
5.7.1 Reversal of the propagation direction
5.7.2 Other transformations
5.8 Consequences of the symmetries
Chapter 6 Waves in a parallel
plate guide
6.1 Isotropic media
6.1.1 Scalar potentials
6.1.2 Layered media - continuity conditions
6.1.3 Operator formulation
6.2 Gyrotropic media
6.2.1 Generalized Hertz potentials
6.2.2 Stratified gyromagnetic medium -
continuity conditions
6.2.3 Operator formulation
6.2.4 Special cases
6.2.5 Eigenfunctions and eigenvalues of
a stratified ferrite medium
Chapter 7 Waves in general
waveguides
7.1 Wave operators for anisotropic medium
7.1.1 Formulations involving six field
components
7.1.2 Formulations involving transverse
field components
7.1.3 Operator pencil
7.2 Properties of operators in lossy anisotropic
guides
7.2.1 Symmetry and pseudo-symmetry of
operators
7.2.2 General anisotropic and gyrotropic
lossy media
7.2.3 Anisotropic lossy media
7.3 Properties of operators in lossless
anisotropic guides
7.3.1 Simplified $\omega $ formulation
7.3.2 Conditions for symmetry of operators
7.3.3 Definiteness of operators
7.4 Power-energy relations for modes in
lossy guides
7.5 Momentum-energy relations for modes
in lossy guides
Chapter 8 Bidirectional
guides and complementary modes
8.1 Relations for complementary modes
8.1.1 Ancillary transformations
8.1.2 Complementary pairs
8.1.3 Physical nature of ancillary transformations
8.1.4Transposed medium guide
8.2 Bidirectional guides
8.2.1 Guides without spatial symmetry
8.2.2 Symmetry with respect to the reflection
in a plane perpendicular to the z-axis
8.2.3 Symmetry with respect to the inversion
in a point on the z axis Relations between complementary modal fields
8.2.4 Symmetry with respect to the rotation
by $\pi $ about an axis perpendicular to z
8.2.5 Combined symmetries and reversal
of the biasing magnetic field
8.3 Recapitulation
Chapter 9 Strictly
bidirectional waveguides
9.1 Generalized eigenvalue problems for
strictly bidirectional guides
9.1.1 $\beta $ formulation involving four
field components
9.1.2 $\omega $ formulation involving
four field components
9.1.3 Decoupling of magnetic and electric
fields
9.1.4 Isotropic media
9.2 Quadratic operator pencils
9.3 Properties of operators
9.3.1 Symmetry and pseudo-symmetry of
transverse field formulations
9.3.2 Properties of operators in decoupled
field formulation
9.4 Properties of operators in quadratic
pencils
9.4.1 Definiteness of component operators
9.4.2 Relation between pencils
9.4.3 Critical points
9.4.4 Eigenfunctions at critical points
Chapter 10 Mode orthogonality
10.1 Operator formalism and complementary
solutions
10.2 Orthogonality of modes in general
anisotropic media
10.2.1 Other relations
10.3 Bidirectional guides
10.3.1 Strictly bidirectional structures
10.3.2 Generic relations for bidirectional
guides
10.4 Orthogonality relations for pencils
10.5 Orthogonality at critical points
Chapter
11 Waves in lossless guides
11.1 Classical approach
11.1.1 Energy balance for propagating
waves
11.1.2 Velocity of energy transport
11.2 Operator formalism
11.2.1 Group velocity - revisited
11.2.2 Energy, power and momentum expressions
11.3 Propagating waves
11.3.1 Boundedness of group velocity
11.3.2 Forward and backward waves
11.3.3 Phase and group velocities
11.3.4 Guides loaded with isotropic dielectric
11.3.5 Physical interpretation - energy
and momentum conservation
11.4 Cutoff waves
11.4.1 Power and momentum identities for
cutoff waves
11.4.2 Consequences of the power identities
- capacitive and inductive modes
11.4.3 Variational expression for cutoff
waves
11.4.4 Cutoff modes in strictly bidirectional
guides
11.4.5 Critical points - strictly bidirectional
guides
11.5 Complex waves
11.5.1 Strictly bidirectional guides
11.6 Dispersion characteristics - strictly
bidirectional guides
11.7 Concluding remarks - complex modes
at fixed $\beta $
Chapter 12 Complex modes
12.1 History of the research into complex
modes
12.2 Complex modes in isotropic guides
12.2.1 Complex waves versus propagating
modes in lossy guides
12.2.2 Correspondence between leaky and
complex waves
12.3 Complex modes in gyrotropic guides
12.4 Complex modes in the discontinuity
analysis
12.5 Technical applications of complex
modes
12.6 Theories of complex modes
12.6.1 Weak perturbation of homogeneous
guides
12.6.2 Guide geometries and modes prone
to complex waves
12.6.3 Large inhomogeneity in strictly
bidirectional guides
12.6.4 General physical conditions for
creation of complex modes
12.6.5 Necessary and sufficient conditions
12.7 Validation of the theory of complex
waves
12.7.1 Strong inhomogeneity
12.8 Mode nomenclature
Appendix A Vector and
integral identities
A.1 Multiplication and differentiation
of vectors
A.2 Integral identities
Appendix B Review of linear
spaces
B.1 Linear spaces
B.2 Hilbert spaces and inner products
B.3 Linear operators
B.3.1 Bounded and unbounded operators
B.3.2 Spectral problems
B.4 Sesquilinear forms
Appendix C Sturm-Liouville
problem
C.1 Definition and properties
Appendix D Generalized
eigenfunctions and polynomial operator pencils
D.1 Generalized eigenfunctions
D.2 Polynomial operator pencils
Index