Advanced Theoretical and Numerical Electromagnetics, Volume 2: Field representations and the Method of Moments

Cover
Contents
List of figures
List of tables
List of examples
About the author
Foreword
Preface
Acknowledgements
10 Integral formulas and equivalence principles
10.1 Integral representations with dyadic Green functions
10.2 The integral formulas of Stratton and Chu
10.3 Integral formulas with Kottler’s line charges
10.4 Surface equivalence principles
10.4.1 The Huygens and Love equivalence principles
10.4.2 The Schelkunoff equivalence principle
10.5 Volume equivalence principle
10.6 The equivalent circuit of an antenna
10.6.1 Antenna port connected to a coaxial cable
10.6.2 Antenna port modelled with the delta-gap approximation
References
11 Spectral representations of electromagnetic fields
11.1 Modal expansion in cavities
11.1.1 Vector eigenvalue problems in cavities
11.1.2 Solenoidal modes
11.1.3 Lamellar modes
11.1.4 Orthogonality properties of the cavity eigenfunctions
11.1.5 Stationarity of the Rayleigh quotient
11.1.6 Completeness of the cavity eigenfunctions
11.1.7 Equivalent sources on a cavity boundary
11.2 Modal expansion in uniform cylindrical waveguides
11.2.1 The Marcuvitz-Schwinger equations
11.2.2 Transverse-magnetic modes
11.2.3 Transverse-electric modes
11.2.4 Transverse-electric-magnetic modes
11.2.5 Orthogonality properties of the transverse eigenfunctions
11.2.6 Sources in waveguides
11.3 Wave propagation in periodic structures
11.3.1 Periodic boundary conditions
11.3.2 Bloch modes in a periodic layered medium
11.4 Sources and fields invariant in one spatial dimension
11.4.1 Two-dimensional TM and TE decomposition
11.4.2 The two-dimensional Helmholtz equation
11.4.3 Reflection and transmission at a planar material interface
References
12 Wave propagation in dispersive media
12.1 Constitutive relations in frequency and time domain
12.2 The Kramers-Krönig relations
12.3 Simple models of dispersive media
12.3.1 Conducting medium
12.3.2 Dielectric medium
12.3.3 Polar substances
12.4 Narrow-band signals in the presence of dispersion
12.5 Intra-modal dispersion in waveguides
References
13 Integral equations in electromagnetics
13.1 General considerations
13.2 Surface integral equations for perfect conductors
13.2.1 Electric-field integral equation (EFIE)
13.2.2 EFIE with delta-gap excitation
13.2.3 Magnetic-field integral equation (MFIE)
13.2.4 Interior-resonance problem
13.2.5 Combined-field integral equation (CFIE)
13.2.6 A modified EFIE for good conductors
13.3 Surface integral equations for homogeneous scatterers
13.3.1 The integral equations of Poggio and Miller (PMCHWT)
13.3.2 The Müller integral equations
13.4 Volume integral equations for inhomogeneous scatterers
13.5 Hybrid formulations
13.5.1 Electric-field and volume integral equations
13.5.2 Integral and wave equations
References
14 The Method of Moments I
14.1 General considerations
14.2 Discretization of the EFIE
14.3 Discretization of the MFIE
14.4 Discretization of the CFIE
14.5 Discretization of the PMCHWT equations
14.6 Discretization of the Müller equations
14.7 The basis functions of Rao,Wilton and Glisson
14.8 Area coordinates
14.9 Singular integrals over triangles
14.9.1 Integrals involving
R
14.9.2 Integrals involving
R/
R
14.9.3 Integrals involving
R)
14.10 Discretization of the EFIE with delta-gap excitation
14.11 Scaling of solutions
References
15 The Method of Moments II
15.1 Discretization of volume integral equations
15.2 The basis functions of Schaubert, Wilton and Glisson
15.3 Volume coordinates
15.4 Singular integrals over tetrahedra
15.4.1 Integrals involving
R
15.4.2 Integrals involving
R/
R
15.4.3 Integrals involving
R)
15.4.4 Integrals involving
R), a constant dyadic and
R
15.5 Discretization of EFIE and volume integral equations
15.6 Discretization of integral and wave equations
15.7 Edge elements for the vector wave equation
References
Appendix A: Vector calculus
A.1 Systems of coordinates
A.1.1 Circular cylindrical coordinates
A.1.2 Polar spherical coordinates
A.2 Differential operators
A.3 The Gauss theorem
A.4 The Stokes theorem
A.5 The surface Gauss theorem
A.6 The Helmholtz transport theorem
A.7 Estimates for vector-valued functions
References
Appendix B: Complex analysis
B.1 Derivatives and integrals
B.2 Poles and residues
B.3 Branch points and Riemann surfaces
References
Appendix C: Dirac delta distributions
C.1 Definitions and properties
C.2 Derivatives and weak operators
References
Appendix D: Functional analysis
D.1 Vector and function spaces
D.2 The Bessel inequality
D.3 Linear operators
D.4 The Cauchy-Schwarz inequality
D.5 The Riesz representation theorem
D.6 Adjoint operators
D.7 The spectrum of a linear operator
D.8 The Fredholm alternative
References
Appendix E: Dyads and dyadics
E.1 Scalars, vectors, and beyond
E.2 Dyadic calculus
E.2.1 Sum of dyadics and product with a scalar
E.2.2 Scalar and vector product
E.2.3 Neutral elements
E.2.4 Transpose and Hermitian transpose
E.2.5 Double scalar product and double vector product
E.2.6 Determinant, trace and eigenvalues
E.3 Differential operators
References
Appendix F: Properties of smooth surfaces
F.1 An estimate for ˆn(r
r
r)
F.2 Solid angle subtended at a point
F.3 Points in an open neighbourhood
F.4 Criterion for the Hölder continuity of scalar fields
References
Appendix G: A surface integral involving the time-harmonic scalar Green function
G.1 Two estimates for
G(
r, r
G.2 Finiteness and Hölder continuity
References
Appendix H: Formulas
H.1 Vector identities and inequalities
H.2 Dyadic identities
H.3 Differential identities
H.4 Integral identities
H.5 Legendre polynomials and functions
H.5.1 Nomenclature
H.5.2 Differential equation
H.5.3 Explicit expressions for the lowest orders
H.5.4 Orthogonality relationships
H.5.5 Functional relationships
H.6 Bessel functions
H.6.1 Nomenclature
H.6.2 Differential equation
H.6.3 Functional relationships
H.6.4 Asymptotic behavior for small argument (|z|
H.6.5 Asymptotic behavior for large argument (|z|
H.6.6 Recursion relationships
H.6.7 Wronskians and cross products
H.6.8 Integral relationships
H.6.9 Series
References
Index