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