Andrey V. Osipov, Sergei A. Tretyakov

Modern Electromagnetic Scattering Theory with Applications (eBook, PDF)

• Format: PDF

Produktbeschreibung

This self-contained book gives fundamental knowledge about scattering and diffraction of electromagnetic waves and fills the gap between general electromagnetic theory courses and collections of engineering formulas. The book is a tutorial for advanced students learning the mathematics and physics of electromagnetic scattering and curious to know how engineering concepts and techniques relate to the foundations of electromagnetics

Produktdetails

• Verlag: John Wiley & Sons
• Seitenzahl: 824
• Erscheinungstermin: 20. Januar 2017
• Englisch
• ISBN-13: 9781119293286
• Artikelnr.: 47516096

Autorenporträt

Andrey Osipov, Microwaves and Radar Institute, German Aerospace Center (DLR), Germany. Sergei Tretyakov, Department of Radio Science and Engineering, Aalto University, Finland.

Inhaltsangabe

Preface xi Acknowledgements xiii List of Abbreviations xv 1 Introduction 1
1.1 Scattering and Diffraction Theory 1 1.2 Books on Related Subjects 3 1.3
Concept and Outline of the Book 5 References 8 2 Fundamentals of
Electromagnetic Scattering 11 2.1 Introduction 11 2.2 Fundamental Equations
and Conditions 11 2.2.1 Maxwell's Equations 12 2.2.2 Constitutive Relations
12 2.2.3 Time-harmonic Scattering Problems 19 2.3 Approximate Boundary
Conditions 26 2.3.1 Impedance Boundary Conditions 26 2.3.2 Generalized
(Higher-order) Impedance Boundary Conditions 31 2.3.3 Sheet Transition
Conditions 32 2.4 Fundamental Properties of Time-harmonic Electromagnetic
Fields 35 2.4.1 Energy Conservation and Uniqueness 35 2.4.2 Reciprocity 39
2.5 Basic Solutions of Maxwell's Equations in Homogeneous Isotropic Media
42 2.5.1 Plane, Spherical, and Cylindrical Waves 43 2.5.2 Electromagnetic
Potentials and Fields of External Currents 46 2.5.3 Tensor Green's Function
50 2.5.4 E and H Modes 54 2.5.5 Fields with Translational Symmetry 58 2.6
Electromagnetic Formulation of Huygens' Principle 61 2.6.1 Compact
Scatterers 62 2.6.2 Cylindrical Scatterers 67 2.7 Problems 70 References 84
3 Far-field Scattering 87 3.1 Introduction 87 3.2 Scattering Cross Section
87 3.2.1 Monostatic and Bistatic, Backscattering and Forward-scattering
Cross Sections, Differential, Total, Absorption, and Extinction Cross
Sections 87 3.2.2 Scattering Width 91 3.2.3 Backscattering from
Impedance-matched Bodies 93 3.3 Scattering Matrix 95 3.3.1 Definition 95
3.3.2 Scattering Matrix in Spherical Coordinates 97 3.3.3 Scattering Matrix
in the Plane of Scattering Coordinates 99 3.4 Far-field Coefficient 101
3.4.1 Integral Representations and Far-field Conditions 102 3.4.2
Reciprocity of Scattered Fields 106 3.4.3 Forward Scattering 108 3.4.4
Cylindrical Bodies 113 3.5 Scattering Regimes 120 3.5.1 Resonant-size
Scatterers 120 3.5.2 Electrically Large Scatterers 121 3.6 Electrically
Small Scatterers 125 3.6.1 Physics of Dipole Scattering 126 3.6.2 Dipole
Scattering in Terms of Polarizability Tensors 129 3.6.3 Magneto-dielectric
Ellipsoid 131 3.6.4 Rotationally Symmetric Particles 137 3.7 Problems 148
References 162 4 Planar Interfaces 165 4.1 Introduction 165 4.2 Interface
of Two Homogeneous Semi-infinite Media 167 4.2.1 Reflection and
Transmission Coefficients 167 4.2.2 Brewster's Angle 173 4.2.3 Total
Internal Reflection 173 4.2.4 Interfaces with Double-negative Materials 176
4.2.5 Surface Waves 177 4.2.6 Vector Solution of Reflection and
Transmission Problems 179 4.3 Arbitrary Number of Planar Layers 182 4.3.1
Solution by the Method of Characteristic Matrices 182 4.3.2 Discussion and
Limiting Cases 189 4.4 Reflection and Transmission of Cylindrical and
Spherical Waves 195 4.4.1 Excitation by a Linear Electric Current 195 4.4.2
Excitation by an Electric Dipole 202 4.5 A Layer between Homogeneous
Half-spaces 207 4.5.1 Different Half-spaces 207 4.5.2 A PEC-backed Layer
213 4.5.3 Layer Immersed in a Homogeneous Space 215 4.6 Modeling with
Approximate Boundary Conditions 224 4.6.1 Accuracy of Impedance Boundary
Conditions 225 4.6.2 Accuracy of Transition Boundary Conditions 229 4.6.3
Impedance-matched Surface 232 4.7 Problems 235 References 249 5 Wedges 251
5.1 Introduction 251 5.2 The Perfectly Conducting Wedge 253 5.2.1
Formulation of Boundary Value Problem 254 5.2.2 Solution by Separation of
Variables 256 5.2.3 Fields and Currents at the Edge 258 5.2.4 Reduction to
an Integral Form 260 5.2.5 Special Cases 262 5.2.6 Edge-diffracted and GO
Components. Diffraction Coefficient 266 5.3 Scattering from a Half-plane
(Solution by Factorization Method) 271 5.3.1 Statement of the Problem 271
5.3.2 Functional Equation 273 5.3.3 Factorization and Solution 274 5.3.4
Scattered Field Far from the Edge 276 5.4 The Impedance Wedge 279 5.4.1
Boundary Value Problem, Sommerfeld's Integrals, and Functional Equations
279 5.4.2 Normal Incidence (Maliuzhinets' Solution) 288 5.4.3 Unit Surface
Impedance 297 5.4.4 Further Exactly Solvable Cases 300 5.5 High-frequency
Scattering from Impenetrable Wedges 306 5.5.1 GO Components and Surface
Waves 307 5.5.2 Edge-diffracted Field, Diffraction Coefficient, and
Scattering Widths 310 5.5.3 Uniform Asymptotic Approximations 316 5.5.4
GTD/UTD Formulation 319 5.6 Behavior of Electromagnetic Fields at Edges 322
5.6.1 Determining the Degree of Singularity 322 5.6.2 Analytical Structure
of Meixner's Series 328 5.7 Problems 329 References 336 6 Circular
Cylinders and Convex Bodies 339 6.1 Introduction 339 6.2 Perfectly
Conducting Cylinders: Separation of Variables and Series Solution 340 6.2.1
Separation of Variables 342 6.2.2 Satisfying the Boundary Conditions 342
6.2.3 Scattered Fields 343 6.2.4 Numerical Examples 345 6.3 Homogeneous
Cylinders under Normal Illumination 350 6.3.1 Field Equations and Boundary
Conditions 350 6.3.2 Rayleigh Series Solution 351 6.3.3 Numerical Examples
352 6.4 Watson's Transformation and High-frequency Approximations 354 6.4.1
Watson's Transformation 355 6.4.2 Alternative Solution by Separation of
Variables 358 6.4.3 High-frequency Approximations 360 6.4.4 Surface
Currents in the Penumbra Region. Fock's Functions 369 6.5 Coated and
Impedance Cylinders under Oblique Illumination 375 6.5.1 PEC Cylinder with
Magneto-dielectric Coating 376 6.5.2 Impedance Cylinder 383 6.6 Extension
to Generally Shaped Convex Impedance Bodies 392 6.6.1 Fock's Principle of
the Local Field in the Penumbra Region 393 6.6.2 Asymptotic Solution for
the Field on the Surface of Circular Impedance Cylinders under Oblique
Illumination 396 6.6.3 Fock- and GTD-type Solutions for Electrically Large
Convex Impedance Bodies 398 6.7 Problems 403 References 411 7 Spheres 412
7.1 Introduction 412 7.2 Exact Solution for a Multilayered Sphere 414 7.2.1
Formulation of the Problem in Terms of Debye's Potentials 415 7.2.2
Derivation of the Series Solution 417 7.2.3 Solution for Impedance Boundary
Conditions 427 7.3 Physics of Scattering from Spheres 429 7.3.1
Classification of Scattering 430 7.3.2 Spiral Waves 436 7.3.3 Debye's
Expansions for Homogeneous Spheres 438 7.3.4 Waves in Electrically Large
Homogeneous Low-absorption Spheres 442 7.4 Scattered Field in the Far Zone
463 7.4.1 Far-field Coefficient, Scattering Cross Sections, and
Polarization Structure. Approximations for Electrically Large Spheres 463
7.4.2 Electrically Small Spheres: Dipole, Quasi-static, and Resonance
Approximations 471 7.4.3 PEC Spheres 479 7.4.4 Core-shell Spheres 483 7.4.5
Impedance Spheres 488 7.5 Far-field Scattering from Homogeneous Spheres 493
7.5.1 Exact Solution and Limiting Cases 494 7.5.2 Electrically Small Lossy
Spheres 495 7.5.3 Electrically Small Low-absorption Spheres 499 7.5.4
Electrically Large Lossy Spheres: Relation to the Impedance Sphere and the
Role of Absorption 506 7.5.5 Electrically Large Low-absorption Spheres:
Light Scattering from Water Droplets 513 7.6 Metamaterial Effects in
Scattering from Spheres 542 7.6.1 Small Spheres 542 7.6.2 Invisibility
Cloak 546 7.7 Problems 552 References 562 8 Method of Physical Optics 565
8.1 Introduction 565 8.1.1 On Numerical Techniques for Studying Scattering
from Arbitrary-shaped Bodies 565 8.1.2 PO as one of the Approximate
Analytical Techniques 566 8.1.3 Structure of the Chapter 567 8.2 Principles
and General Solution 567 8.2.1 Principles of PO 567 8.2.2 Derivation of PO
Solutions 569 8.2.3 PO for Cylindrical Bodies 573 8.3 Transmission through
Apertures 575 8.3.1 PO Solution 575 8.3.2 GO Rays and Fresnel Zones 576
8.3.3 Contribution from the Rim of the Aperture: Edge-diffracted Rays 582
8.4 Scattering from Curved Surfaces 594 8.4.1 Fock's Reflection Formula 594
8.4.2 Application to a Spherical Segment 600 8.4.3 Reflection Formula in
the Far-field Region 605 8.4.4 Diffraction by an Edge in a Non-metallic
Surface 609 8.5 Advantages and Limitations of Physical Optics 615 8.6
Problems 616 References 632 9 Physical Optics Solutions of Canonical
Problems 634 9.1 Introduction 634 9.2 Vertices 635 9.2.1 Vertex on an Edge
of a Thin Plate 637 9.2.2 Apex of a Pyramid 641 9.2.3 Tip of an Elliptic
Cone 643 9.3 Electrically Large Plates 652 9.3.1 Arbitrarily Shaped Plates
653 9.3.2 Circular Disc 658 9.3.3 Polygonal Plates 663 9.3.4 Far-field
Patterns of Polygonal Plates and Apertures 667 9.4 Bodies of Revolution 671
9.4.1 PO Solution for Bodies of Revolution 672 9.4.2 Imperfectly Reflecting
Bodies under Axial Illumination 675 9.4.3 PEC Bodies under Oblique
Illumination 677 9.4.4 Axial Backscattering 678 9.4.5 Examples 684 9.5
Problems 689 References 712 A Definitions and Useful Relations of Vector
Analysis and Differential Geometry 714 A.1 Vector Algebra 714 A.2 Vector
Analysis 716 A.3 Vectors and Vector Differential Operators in Orthogonal
Curvilinear Coordinates 717 A.3.1 General Orthogonal Curvilinear
Coordinates 717 A.3.2 Spherical Coordinates 718 A.4 Curves and Surfaces in
Space 720 A.4.1 Curves 720 A.4.2 Surfaces 720 A.5 Problems 722 References
724 B Fresnel Integral and Related Functions 725 B.1 Fresnel Integral 725
B.2 Relation to the Error Function 728 B.3 Transition Functions of Uniform
Theories of Diffraction 730 B.4 Problems 731 References 732 C Principles of
Complex Integration 733 C.1 Introduction 733 C.2 Deforming the Integration
Contour 734 C.2.1 Basic Facts about Functions of a Complex Variable 734
C.2.2 Integrals over Infinite Contours 736 C.3 Steepest Descent Method 737
C.3.1 Steepest Descent Path 738 C.3.2 Saddle Point Contribution 739 C.3.3
Pole Singularity near the Saddle Point 741 C.3.4 Further Cases 742 C.4
Problems 743 References 745 D The Stationary Phase Method 746 D.1
Introduction 746 D.2 One-dimensional Integrals 746 D.2.1 No Stationary
Points on the Integration Interval 747 D.2.2 Isolated Stationary Points 748
D.2.3 Two Coalescing Stationary Points 751 D.3 Two-dimensional Integrals
756 D.3.1 Stationary Point in the Integration Domain 756 D.3.2 Stationary
Point near the Boundary of the Integration Domain 758 D.3.3 Contribution
from the Boundary of the Integration Domain 760 D.3.4 Kontorovich's Formula
763 D.3.5 Integrand Vanishing on the Boundary 765 D.3.6 Summary of the
Two-dimensional Stationary-phase Method 766 D.4 Problems 766 References 768
E Asymptotic Approximations of Bessel Functions of Large Argument and
Arbitrary Order 770 E.1 Introduction 770 E.1.1 Basic Definitions and
Properties 770 E.1.2 Large-argument Approximations ( z ?â 1) 772 E.1.3
Content of the Appendix 775 E.2 Debye's Asymptotic Approximations 776 E.2.1
Debye's Method 776 E.2.2 WKB Approximation 778 E.2.3 Bessel Functions on
the Complex ny Plane 791 E.3 Almost Equal Argument and Order 795 E.3.1
Approximations in Terms of Airy Functions 796 E.3.2 Approximations in Terms
of Normalized Airy Functions 797 E.3.3 Zeros in the Neighborhood of the
Points ny = ±z 798 References 799 Index 801