Engineering Electrodynamics (Second Edition) : A Collection of Principles, Theorems and Field Representations.

Format:

Book

Author/Creator:

Janaswamy, Ramakrishna.

Series:

IOP Ebooks Series

Language:

English

Physical Description:

1 online resource (779 pages)

Edition:

2nd ed.

Place of Publication:

Bristol : Institute of Physics Publishing, 2025.

Summary:

This book discusses mathematical tools and key concepts of electrodynamics through principles, theorems and practical engineering examples.

Contents:

Outline placeholder

Preface to the second edition

Preface to the first edition

Author biography

Ramakrishna Janaswamy

Symbols

Chapter Maxwell's equations, potentials and boundary conditions

1.1 Time-domain Maxwell's equations

1.1.1 Lorenz gauge, Coulomb gauge, and causality

1.1.2 Existence theorem for fields

1.2 Frequency domain Maxwell's equations

1.2.1 Classification of media

1.2.2 Boundary conditions

1.3 Field determination by radial components

1.3.1 Multipole expansion, Debye potentials and related theorems

1.3.2 Additional theorems related to spherical harmonics

References

Chapter Electrostatics and magnetostatics

2.1 Energy related theorems in electrostatics

2.1.1 Reciprocity theorem in electrostatics

2.2 Principle of virtual displacement for static fields

2.3 Theorems related to harmonic functions

Chapter Gauge invariance for electromagnetic fields

3.1 Gauge invariance for general material media

3.1.1 Stream potentials and Hertzian potentials

3.1.2 Summary for linear media

3.2 Gauge invariance in homogenized media

Chapter Causality and dispersion

4.1 Causal systems

4.1.1 Titchmarsh's theorem and Kramers-Krönig relations

4.2 Dispersive systems

4.2.1 Linear time-invariant causal media

4.3 Causal properties of scattering amplitude

4.3.1 Properties of scattering amplitude

4.3.2 Fundamental limits on antenna gain-bandwidth product

Chapter Uniqueness, energy and momentum

5.1 Uniqueness theorem

5.2 Energy and momentum

5.2.1 Electromagnetic energy and its conservation

5.2.2 Electromagnetic momentum and its conservation

Chapter Duality principle and Babinet's principle

6.1 Duality principle and Babinet's principle

6.1.1 Duality principle.

6.1.2 Babinet's principle

6.1.3 Booker's relation

Chapter Electromagnetic reciprocity

7.1 Reciprocity theorems in frequency and time-domains

7.1.1 Reciprocity theorem for fields

7.1.2 Reciprocity relations involving complex conjugate of fields

7.1.3 Reciprocity theorem for scattering amplitude

7.1.4 Extended reciprocity theorem

7.1.5 Modified reciprocity theorem

7.1.6 Time-domain reciprocity theorems

7.2 Compensation theorem

Chapter Reactance theorems

8.1 Reactance theorems for networks and antennas

8.1.1 Foster's reactance theorem for passive lossless networks

8.1.2 Theorem of Levis and Rhodes for antennas

8.1.3 Susceptance theorem for impulsive voltage source

Chapter Geometrical optics and Fermat's principle

9.1 Geometrical optics and Fermat's principle

9.1.1 Field discontinuities, wavefronts and eikonal equation

9.1.2 Ray equations

9.1.3 Ray tracing

9.1.4 Mechanical interpretation of ray path

9.1.5 Optical path length and Fermat's principle

9.1.6 Sommerfeld-Runge and Snell's laws, Lagrange integral invariant

9.1.7 Transport of the geometrical optics field in lossless medium

9.1.8 Geometrical optics in absorbing media

9.1.9 Other theorems of geometrical optics

9.2 Gradient metasurfaces and generalized Snell's law

Chapter Integral field representations

10.1 Integral representation of fields

10.1.1 Stratton-Chu representation

10.1.2 Franz representation

10.1.3 Surface functions and their fields, equivalence principle: forms-2, 3

10.2 Integral equations, physical optics, Bojarski's identity

10.2.1 Surface integral equations

10.2.2 Scattering by homogeneous object, physical optics

10.2.3 Bojarski's identity

Chapter Characteristic mode theory.

11.1 Definition and preliminary results

11.2 Characteristic mode theory for PEC bodies

11.2.1 Characteristic fields

11.2.2 Determination of characteristic currents

11.2.3 Modal expansion of currents and fields

11.3 Characteristic mode theory for penetrable objects

11.3.1 Dissipation operator

11.3.2 Near-field operator

11.3.3 Radiation operator and the eigenvalue equation

11.3.4 Orthogonality of modal radiated fields

11.3.5 Interpretation of the eigenvalues

11.3.6 Parameters of interest in terms of characteristic modes

11.3.7 Specialization to 2D

Chapter Induction theorem and optical theorem

12.1 Induction and forward scattering theorems

12.1.1 Induction theorem

12.1.2 Induction theorem examples

12.1.3 Forward scattering theorem

Chapter Eigenfunctions, Green's functions, and completeness

13.1 Hilbert space

13.1.1 Functionals and operators on Hilbert space

13.1.2 Commuting operators and Floquet's theorem

13.1.3 Differential equation with periodic coefficients, Floquet's theorem

13.1.4 Uniqueness, existence, and Hilbert-Schmidt operators

13.2 Sturm-Liouville problem and Green's functions

13.2.1 Second order linear differential equations, Green's functions

13.2.2 Self-adjoint operators

13.2.3 Relation between Green's function of original and adjoint equations

13.2.4 Completeness theorem for self-adjoint differential operators

13.3 Classification of operators and their properties

13.3.1 Spectral representation of operators

13.3.2 Spectral theory of second order differential operators

13.3.3 Completeness theorem in higher dimensions

13.4 Sum of two commutative operators

Chapter Electromagnetic degrees of freedom

14.1 DoF between communicating volumes in free-space.

14.1.1 DoF between planar rectangular apertures, prolate spheroidal functions

14.2 DoF of general radiating systems

14.3 Antenna gain limitations due to finite DoF

Chapter Projection slice theorem and computed tomography

15.1 Radon transform and projection slice theorem

15.2 Computed tomography

Chapter Free-space Green's function and its application in various coordinates

16.1 Various forms of free-space Green's function

16.2 Canonical problems in various coordinate systems

16.2.1 Planar currents radiating in half-space

16.2.2 Dipole radiating in the presence of a conducting wedge

16.2.3 Circumferential magnetic dipole near a conducting circular cylinder

16.2.4 Dipole radiating over a PEC-backed conducting slab

16.2.5 Dipole radiating over a material sphere (ordinary and plasmonic)

Chapter Asymptotic analysis

17.1 Branch cuts for wave propagation

17.2 Complex waves

17.3 Asymptotic evaluation of integrals

17.3.1 Steepest descent technique

17.3.2 Stationary phase method

17.4 Examples in wave propagation

17.5 Modified saddle point technique

Chapter Covariant formulation of Maxwell's equations

18.1 Preliminaries of tensor calculus

18.1.1 Riemannian space

18.1.2 Tensor densities and pseudo-tensors

18.1.3 Geodesics and Christoffel symbols

18.1.4 Absolute and covariant derivatives of tensors

18.1.5 Divergence, curl of tensors

18.1.6 Laplacian and d'Alembertian of invariants

18.2 Minkowski space

18.3 Covariant form of Maxwell's equations in vacuum

18.4 Maxwell's equations in arbitrary spacetime

18.5 Covariant form of Maxwell's equations in stationary matter

18.5.1 3D vector formulation of wave propagation over irregular terrain

18.6 Transformational electromagnetics.

18.6.1 Design of a cylindrical cloak

18.6.2 General transformational equations

Chapter Lagrangian formalism and conservation laws

19.1 Lagrangian formalism and action principle

19.1.1 Examples of discrete and continuous systems

19.1.2 Canonical formulation of Maxwell's equations

19.2 Noether's theorem and conservation laws

19.2.1 Coordinate transformations

Chapter Maxwell's equations in the sense of distributions

20.1 Preliminaries of distributions

20.1.1 Derivatives of distributions

20.1.2 Theorem on scalar, vector functions with surface discontinuities

20.2 Derivation of boundary conditions using distributions

20.2.1 Classical boundary conditions

20.2.2 Boundary conditions including generalized sheet transition conditions on interfaces with single-layer, double-layer densities

20.2.3 Boundary conditions for potentials

20.2.4 Leaky wave antenna designs with impedance boundary and GST conditions

Chapter Stochastic representations of wave phenomenon

21.1 Preliminaries of stochastic calculus

21.2 Stochastic processes and Brownian motion

21.3 Itô integral and Itô-Doeblin formula

21.4 Solution of PDEs by stochastic technique, Feynman-Kac formulas

Chapter

A.1 Preliminaries

A.1.1 Analyticity

A.1.2 Singularities

A.2 Theorems from complex analysis

A.3 Integral transforms

A.3.1 Analytic properties of functions defined by integral transforms

A.3.2 Bilateral Laplace transform

B.1 Preliminaries

B.1.1 Surface divergence of tangential vectors

B.2 Theorems from potential theory

B.3 Separability conditions in orthogonal systems

B.3.1 Rotational coordinate systems

C.1 First and second fundamental forms

C.1.1 Some surface vector identities

Reference.

Chapter.

Notes:

Description based on publisher supplied metadata and other sources.

ISBN:

0-7503-5886-6