Engineering Electromagnetics: A collection of theorems, principles and field representations

PRELIMS.pdf
Preface
Author biography
Ramakrishna Janaswamy
CH001.pdf
Chapter 1 Maxwell’s equations, potentials, and boundary conditions
1.1 The time-domain Maxwell’s equations
1.1.1 The 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
CH002.pdf
Chapter 2 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
References
CH003.pdf
Chapter 3 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
References
CH004.pdf
Chapter 4 Causality and dispersion
4.1 Causal systems
4.1.1 Titchmarsh’s theorem and the Kramers–Krönig relations
4.2 Dispersive systems
4.2.1 Linear dielectrics
4.3 Causal properties of scattering amplitude
4.3.1 Properties of scattering amplitude
4.3.2 Fundamental limits on the antenna gain–bandwidth product
References
CH005.pdf
Chapter 5 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
References
CH006.pdf
Chapter 6 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
Reference
CH007.pdf
Chapter 7 Electromagnetic reciprocity
7.1 Reciprocity theorems in the frequency and time domains
7.1.1 Reciprocity theorem for fields
7.1.2 Reciprocity theorem for scattering amplitude
7.1.3 Extended reciprocity theorem
7.1.4 Modified reciprocity theorem
7.1.5 Time domain reciprocity theorem
7.2 Compensation theorem
References
CH008.pdf
Chapter 8 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 an impulsive voltage source
References
CH009.pdf
Chapter 9 Geometrical optics and Fermat’s principle
9.1 Geometrical optics and Fermat’s principle
9.1.1 Field discontinuities, wavefronts, and the eikonal equation
9.1.2 Ray equations
9.1.3 Ray tracing
9.1.4 Mechanical interpretation of the ray path
9.1.5 Optical path length and Fermat’s principle
9.1.6 Sommerfeld–Runge and Snell’s laws, the Lagrange integral invariant
9.1.7 Transport of the geometrical optics field
9.1.8 Other theorems of geometrical optics
9.2 Gradient metasurfaces and the generalized Snell’s law
References
CH010.pdf
Chapter 10 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, and Bojarski’s identity
10.2.1 Surface integral equations
10.2.2 Scattering by a homogeneous object, physical optics
10.2.3 Bojarski’s identity
References
CH011.pdf
Chapter 11 Induction theorem and optical theorem
11.1 Induction and forward scattering theorems
11.1.1 Induction theorem
11.1.2 Forward scattering theorem
References
CH012.pdf
Chapter 12 Eigenfunctions, Green’s functions, and completeness
12.1 Hilbert space
12.1.1 Functionals and operators on Hilbert space
12.1.2 Uniqueness, existence, and Hilbert–Schmidt operators
12.2 Sturm–Liouville problem and Green’s functions
12.2.1 Second order linear differential equations, Green’s functions
12.2.2 Self-adjoint operators
12.2.3 Relation between the Green’s function of the original and adjoint equations
12.2.4 Completeness theorem for self-adjoint differential operators
12.3 Classification of operators and their properties
12.3.1 Spectral representation of operators
12.3.2 Spectral theory of second order differential operators
12.3.3 Completeness theorem in higher dimensions
12.4 Sum of two commutative operators
References
CH013.pdf
Chapter 13 Electromagnetic degrees of freedom
13.1 DoF between communicating volumes in free space
13.1.1 DoF between planar rectangular apertures, prolate spheroidal functions
13.2 Antenna gain limitations due to finite DoF
References
CH014.pdf
Chapter 14 Projection slice theorem and computed tomography
14.1 Radon transform and projection slice theorem
14.2 Computed tomography
References
CH015.pdf
Chapter 15 Free-space Green’s function and its application in various coordinates
15.1 Various forms of the free-space Green’s function
15.2 Canonical problems in various coordinate systems
15.2.1 Planar currents radiating in half-space
15.2.2 Dipole radiating in the presence of a conducting wedge
15.2.3 Circumferential magnetic dipole near a conducting circular cylinder
15.2.4 Dipole radiating over a PEC-backed conducting slab
15.2.5 Dipole radiating over a material sphere (ordinary and plasmonic)
References
CH016.pdf
Chapter 16 Asymptotic analysis
16.1 Branch cuts for wave propagation
16.2 Complex waves
16.3 Asymptotic evaluation of integrals
16.3.1 Steepest descent technique
16.3.2 Stationary phase method
16.4 Examples in wave propagation
16.5 Modified saddle point technique
References
CH017.pdf
Chapter 17 Covariant formulation of Maxwell’s equations
17.1 Preliminaries of tensor calculus
17.1.1 Riemannian space
17.1.2 Minkowski space
17.2 The covariant form of Maxwell’s equations in Euclidean pseudo-space
17.3 Maxwell’s equations in an arbitrary spacetime
17.4 Covariant form of Maxwell’s equations in stationary matter
17.5 Transformational electromagnetics
17.5.1 Design of a cylindrical cloak
17.5.2 General transformational equations
References
CH018.pdf
Chapter 18 Maxwell’s equations in the sense of distributions
18.1 Preliminaries of distributions
18.1.1 Derivatives of distributions
18.1.2 Theorem on scalar, vector functions with surface discontinuities
18.2 Derivation of boundary conditions using distributions
18.2.1 Classical boundary conditions
18.2.2 Boundary conditions including GSTCs on interfaces with single-layer, double-layer densities
18.2.3 Boundary conditions for potentials
References
CH019.pdf
Chapter 19 Stochastic representations of wave phenomena
19.1 Preliminaries of stochastic calculus
19.2 Stochastic processes and Brownian motion
19.3 Itô integral and Itô–Doeblin formula
19.4 Solution of PDEs by stochastic technique, Feynman–Kac formulas
References
APP1.pdf
Chapter
A.1 Preliminaries
A.1.1 Analyticity
A.1.2 Singularities
A.2 Theorems from complex analysis
A.3 Integral transforms
References
APP2.pdf
Chapter
B.1 Preliminaries
B.1.1 Surface divergence of tangential vectors
B.2 Theorems from potential theory
References
APP3.pdf
Chapter
C.1 Bessel differential equation
C.2 General properties of Bessel functions
C.2.1 Recurrence relations
C.2.2 Small argument approximations
C.2.3 Analytical continuation and negative orders
C.2.4 Large argument approximations
C.2.5 Large order approximations
C.2.6 Integral relations
C.2.7 Addition theorems
C.2.8 Multiplicative theorem
C.2.9 Upper bounds
C.2.10 Relation to modified Bessel functions
C.2.11 Zeros of Jn(x) and Jn′(x)
C.2.12 Useful integrals involving Bessel functions
C.2.13 Series of Bessel functions
C.3 Spherical Bessel functions
C.3.1 Relation to elementary functions
C.3.2 Small argument approximations
C.3.3 Analytical continuation
C.3.4 Recurrence relations
C.3.5 Addition theorems
C.3.6 Cross products
C.3.7 Some useful series
C.3.8 Spherical Ricatti–Bessel functions
C.4 Plots for Bessel functions
References
APP4.pdf
Chapter
D.1 Legendre differential equation
D.1.1 Independent solutions
D.1.2 Functions with integer orders
D.1.3 Wronskians
D.1.4 Recurrence relations
D.1.5 Integral representations
D.1.6 General properties of associated Legendre functions
D.1.7 Addition theorem
D.1.8 Derivatives with respect to order
D.1.9 Inequalities
D.1.10 Special values of indices
D.1.11 Specific values of argument
D.1.12 Generating function for integer order and degree
D.1.13 Useful integrals involving Legendre functions
D.1.14 Series representation of Legendre polynomials
D.1.15 Plots for associated Legendre functions
References