Scattering of Electromagnetic Waves by Obstacles [electronic resource] / Gerhard Kristensson, gerhard.kristensson@eit.lth.se.
- Author:
- Kristensson, Gerhard, 1949-
- Published:
- : SciTech Publishing Inc., 2016.
- Physical Description:
- 1 online resource (757 pages).
Access Online
- Series:
- Contents:
- Machine generated contents note: 1.1.The Maxwell Equations -- 1.1.1.Boundary Conditions at Interfaces -- 1.1.2.Energy Conservation and Poynting's Theorem -- 1.2.Constitutive Relations -- 1.2.1.Isotropic Media with Dispersion -- 1.2.2.Examples -- 1.2.3.General Linear Media with Dispersion -- 1.2.4.Energy and Passivity -- 1.3.Time-Harmonic Fields and Fourier Transform -- 1.3.1.The Maxwell Equations -- 1.3.2.Constitutive Relations -- 1.3.3.Poynting's Theorem, Active, Passive, and Lossless Media -- 1.3.4.Sum Rules for the Constitutive Relations -- 1.3.5.Reciprocity -- 1.3.6.Special Type of Solutions -- 1.3.7.Ellipse of Polarization -- 1.4.Coherence and Degree of Polarization -- 1.4.1.Unpolarized Field -- 1.4.2.Completely Polarized Field -- 1.4.3.General Degree of Polarization -- 1.4.4.The Stokes Parameters -- 1.4.5.The PoincarĂ© Sphere -- Problems for Chapter 1 -- 2.1.The Green Functions in Isotropic Media -- 2.1.1.Potentials and Gauge Transformations -- 2.1.2.Canonical Problem in Homogeneous Space -- 2.1.3.Non-Radiating Sources -- 2.1.4.Generalizations -- 2.2.The Green Dyadics in Isotropic Media -- 2.2.1.Free-Space Green Dyadic -- 2.2.2.The Green Dyadic for the Electric Field in Free Space -- 2.2.3.Depolarizing Dyadic -- 2.3.The Green Dyadic in Anisotropic Media -- 2.4.The Green Dyadic in Biisotropic Media -- 2.5.Cerenkov Radiation -- 2.5.1.Energy Radiation -- 2.6.Time-Domain Problem -- 2.6.1.Potentials and Gauge Transformations -- 2.6.2.Canonical Problem in Free Space -- 2.6.3.Causality -- Problems for Chapter 2 -- 3.1.Two Scalar Fields -- 3.1.1.Integral Representation of a Scalar Field -- 3.1.2.Integral Representation of a Scalar Field[—]Alternative -- 3.2.Vector and Scalar Fields -- 3.2.1.Integral Representation of a Vector Field -- 3.2.2.Integral Representation of a Vector Field[—]Alternative -- 3.3.Integral Representations of the Maxwell Equations -- 3.3.1.Elimination of Normal Component -- 3.4.Dyadic and Vector Fields -- 3.4.1.Integral Representation of the Electric Field[—]Dyadic Version -- 3.4.2.Alternative Representation of the Electric Field[—]Magnetic Case -- 3.5.Limit Values of the Scalar Integral Representations -- 3.5.1.Corners and Wedges -- 3.6.Limit Values of the Vector Integral Representations[—]Vector Version -- 3.6.1.Maxwell Equations -- 3.6.2.Corners and Wedges -- 3.7.Limit Values of the Vector Integral Representations[—]Dyadic Version -- 3.8.Integral Representation for Biisotropic Materials -- 3.9.Integral Representations in the Time Domain -- 3.9.1.Surface Integral Representations of the Maxwell Equations -- Problems for Chapter 3 -- 4.1.The Far Zone -- 4.1.1.Volume Integral Formulation -- 4.1.2.Surface Integral Formulation -- 4.1.3.Translation of the Origin -- 4.2.Cross Sections -- 4.3.Scattering Dyadic (Matrix) -- 4.3.1.Spherical Coordinate Representation -- 4.3.2.Coherency Matrix -- 4.3.3.Mueller Matrix or Phase Matrix -- 4.3.4.Superposition -- 4.3.5.Translation of the Origin -- 4.3.6.Reciprocity of the Scattering Dyadic -- 4.4.Optical Theorem -- 4.4.1.Extinction -- 4.5.Plane Interface Case and Babinet's Principle -- 4.5.1.Babinet's Principle -- Problems for Chapter 4 -- 5.1.The Scattering Problem -- 5.1.1.The Incident Field -- 5.1.2.Scattering Problem[—]Formulation -- 5.1.3.Scattered Field -- 5.1.4.Far Field Amplitude -- 5.1.5.Scattering Dyadic -- 5.2.Energy Balance in the Time Domain -- 5.3.Connection to the Time-Harmonic Results -- 5.4.Optical Theorem -- 5.5.Some Applications of the Optical Theorem -- 5.5.1.Several Scatterers -- 5.5.2.Layered Scatterers -- Problems for Chapter 5 -- 6.1.Long Wavelength Approximation -- 6.1.1.Near Field Approximation -- 6.1.2.Far Field Amplitude -- 6.1.3.The Scattering Dyadic -- 6.1.4.Cross Sections -- 6.1.5.Internal Field -- 6.1.6.Polarizability Dyadics -- 6.2.Weak-Scatterer Approximation -- 6.2.1.Born Approximation -- 6.3.High-Frequency Approximation -- 6.3.1.Aperture Formulation -- 6.3.2.Reflection at a Metallic Surface -- 6.3.3.Physical Optics Approximation -- 6.3.4.Geometrical Optics Approximation -- 6.4.Sum Rule for the Extinction Cross Section -- 6.4.1.Additional Sum Rules -- 6.5.Scattering by Many Scatterers[—]Multiple Scattering -- 6.5.1.Far Field Approximation -- 6.5.2.Single Scattering -- Problems for Chapter 6 -- 7.1.Preparatory Discussions -- 7.2.Definition of Spherical Vector Waves -- 7.2.1.Expansions of the Fields -- 7.3.Orthogonality and Reciprocity Relations -- 7.3.1.Spherical Scalar Waves -- 7.3.2.Power Transport -- 7.4.Some Properties of the Spherical Vector Waves -- 7.4.1.Linear Independence -- 7.4.2.The Translation Matrices -- 7.5.Expansion of the Green Dyadic -- 7.5.1.The Green Function in Free Space -- 7.5.2.The Green Dyadic for the Electric Field in Free Space -- 7.5.3.Free-Space Green Dyadic -- 7.6.Null-Field Equations -- 7.7.Expansion of Sources -- 7.7.1.Expansion of a Plane Wave -- 7.7.2.Expansion of a Vertical Electric Dipole -- 7.8.Far Field Amplitude and the Transition Matrix -- 7.8.1.Scattering Dyadic -- 7.8.2.Cross Sections -- 7.8.3.Generalized Optical Theorem -- 7.8.4.The Decrease of the Scattered Field -- 7.9.Dipole Moments of a Scatterer -- Problems for Chapter 7 -- 8.1.Scattering by a Perfectly Conducting Sphere -- 8.1.1.Long Wavelength Approximation -- 8.1.2.High-Frequency Asymptotics -- 8.2.Scattering by a Dielectric Sphere -- 8.2.1.Internal Field -- 8.2.2.Long Wavelength Approximation -- 8.2.3.Resonances -- 8.2.4.Interference Structure -- 8.3.Scattering by Layered Spherical Objects -- 8.3.1.Resonance Frequencies in a Spherical Cavity -- 8.4.Scattering by an Anisotropic Sphere -- 8.4.1.Radial Expansion Functions -- 8.4.2.Transition Matrix -- 8.4.3.Non-Uniqueness of the Scattering Problem -- 8.5.Scattering by a Biisotropic Sphere -- 8.5.1.Spherical Vector Waves in a Biisotropic Material -- 8.5.2.The Transition Matrix for a Biisotropic Sphere -- 8.5.3.Long Wavelength Approximation -- Problems for Chapter 8 -- 9.1.The T-Matrix for a Single Homogeneous Scatterer -- 9.1.1.Perfectly Conducting Scatterer -- 9.1.2.Dielectric Scatterer -- 9.2.The T-Matrix for a Collection of Scatterers -- 9.2.1.Iterative Solution -- 9.2.2.Cross Sections -- 9.3.Obstacle above a Ground Plane -- 9.3.1.Formulation of the Problem -- 9.3.2.Integral Representation of the Solution -- 9.3.3.Transformation between Solutions -- 9.3.4.Incident Electric Field -- 9.3.5.Utilizing the Surface Integral Representation -- 9.3.6.Expansion and Elimination of the Surface Fields -- 9.3.7.Decomposition of the Scattered Field -- Problems for Chapter 9 -- 10.1.Basic Equations -- 10.1.1.Decomposition of Dyadics -- 10.2.The Fundamental Equation -- 10.2.1.The Fourier Transform of the Fields -- 10.2.2.Decomposition of the Maxwell Equations -- 10.3.Wave Splitting -- 10.3.1.Power Flux Density -- 10.3.2.Wave Splitting and Projection Dyadics -- 10.4.Propagation of Fields[—]the Propagator Dyadic -- 10.4.1.Reflection and Transmission Dyadics -- 10.4.2.Slab above Ground -- 10.4.3.Composition of Two Slabs -- 10.5.Propagator Dyadics[—]Homogeneous Layers -- 10.5.1.Single Layer -- 10.5.2.Homogeneous Layer[—]Distinct Eigenvalues (Projection Dyadics) -- 10.5.3.Homogeneous Layer[—]Distinct Eigenvalues -- 10.5.4.Several Layers -- 10.6.Examples -- 10.6.1.Isotropic Media -- 10.6.2.Biisotropic Media -- 10.6.3.Anisotropic Media -- 10.7.Numerical Computations -- 10.7.1.Reflectivity and Transmissivity -- 10.7.2.Example[—]Dielectric Slab with Uniaxial Layers -- 10.7.3.Example[—]Bianisotropic Media -- 10.8.Asymptotic Analysis -- 10.9.The Green Dyadic -- 10.9.1.Particular Solution or Free-Space Solution -- 10.9.2.Homogeneous Solution in Free Space -- 10.9.3.General Solution -- 10.9.4.The Transmitted Field -- Problems for Chapter 10 -- A.1.Vectors -- A.2.Linear Transformations, Matrices, and Dyadics -- A.2.1.Projections -- A.3.Rotation of Coordinate System -- A.3.1.Euler Angles -- A.3.2.Quaternions -- B.1.Bessel and Hankel Functions -- B.1.1.Useful Integrals -- B.2.Modified Bessel Functions -- B.3.Spherical Bessel and Hankel Functions -- B.3.1.Integral Representations -- B.3.2.Modulus of a Spherical Hankel Function -- B.3.3.Related Functions -- C.1.Legendre Polynomials -- C.1.1.Combinations of Legendre Polynomials -- C.2.Associated Legendre Functions -- C.3.Spherical Harmonics -- C.4.Vector Spherical Harmonics -- C.5.Addition Theorem for the Legendre Polynomials -- C.6.Transformation Formulas -- D.1.The Fourier Transform -- D.1.1.Paley[—]Wiener Theorem -- D.1.2.The Poisson Summation Formula -- D.2.Hilbert Transform and Plemelj's Formulas -- D.2.1.Integral Identities -- D.3.Meiman's Theorem -- D.3.1.Zeros in the Upper Complex Half-Plane -- D.4.Positive-Definite Functions -- D.5.Herglotz Functions -- D.6.The Watson Transformation -- D.7.Zeros and Poles of an Analytic Function -- E.1.Lorentz Transformation -- E.2.Transformation of the Electromagnetic Fields -- E.3.Boundary Conditions at a Moving Interface -- F.1.Cayley[—]Hamilton Theorem -- F.2.Projection Dyadics -- F.2.1.Distinct Eigenvalues -- F.2.2.Diagonalizable Case -- F.2.3.Baker[—]Campbell[—]Hausdorff Formula -- F.3.Hermitian Forms -- F.3.1.Positive-Definite Dyadics and Positive-Definite Matrices -- F.4.Mobius Transform -- F.5.Solid Angle -- F.6.Helmholtz' Theorem -- F.6.1.Uniqueness of the Decomposition -- F.7.The Translation Matrices -- F.7.1.Wigner 3-j Symbol -- F.8.Volterra Equations -- F.9.Vectors and Linear Operators in Hilbert Spaces -- F.9.1.Function Spaces -- G.1.One-Dimensional Case -- G.2.Multi-Dimensional Case -- G.3.Computation of an Integral -- H.1.Cartesian Coordinate System -- H.2.Circular Cylindrical (Polar) Coordinate System -- H.3.Spherical Coordinate System -- I.1.Sets -- I.2.Volumes and Surfaces -- I.3.Vectors and Transformations -- I.4.Symbols and Functions -- I.5.Real and Imaginary Parts of Numbers and Dyadics -- I.6.Curvilinear Coordinates.
- Summary:
- This book is an introduction to some of the most important properties of electromagnetic waves and their interaction with passive materials and scatterers. The main purpose of the book is to give a theoretical treatment of these scattering phenomena, and to illustrate numerical computations of some canonical scattering problems for different geometries and materials. The scattering theory is also important in the theory of passive antennas, and this book gives several examples on this topic. Topics covered include an introduction to the basic equations used in scattering; the Green functions and dyadics; integral representation of fields; introductory scattering theory; scattering in the time domain; approximations and applications; spherical vector waves; scattering by spherical objects; the null-field approach; and propagation in stratified media. The book is organised along two tracks, which can be studied separately or together. Track 1 material is appropriate for a first reading of the textbook, while Track 2 contains more advanced material suited for the second reading and for reference. Exercises are included for each chapter.
- Subject(s):
- Other Subject(s):
- ISBN:
- 9781613532225
View MARC record | catkey: 19170761