{"product_id":"modern-electromagnetic-scattering-theory-with-applications-isbn-9780470512388","title":"Modern Electromagnetic Scattering Theory with Applications","description":"\u003cp\u003eThis 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\u003c\/p\u003e Preface xi \u003cp\u003eAcknowledgements xiii\u003c\/p\u003e \u003cp\u003eList of Abbreviations xv\u003c\/p\u003e \u003cp\u003e\u003cb\u003e1 Introduction 1\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e1.1 Scattering and Diffraction Theory 1\u003c\/p\u003e \u003cp\u003e1.2 Books on Related Subjects 3\u003c\/p\u003e \u003cp\u003e1.3 Concept and Outline of the Book 5\u003c\/p\u003e \u003cp\u003eReferences 8\u003c\/p\u003e \u003cp\u003e\u003cb\u003e2 Fundamentals of Electromagnetic Scattering 11\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e2.1 Introduction 11\u003c\/p\u003e \u003cp\u003e2.2 Fundamental Equations and Conditions 11\u003c\/p\u003e \u003cp\u003e2.2.1 Maxwell’s Equations 12\u003c\/p\u003e \u003cp\u003e2.2.2 Constitutive Relations 12\u003c\/p\u003e \u003cp\u003e2.2.3 Time-harmonic Scattering Problems 19\u003c\/p\u003e \u003cp\u003e2.3 Approximate Boundary Conditions 26\u003c\/p\u003e \u003cp\u003e2.3.1 Impedance Boundary Conditions 26\u003c\/p\u003e \u003cp\u003e2.3.2 Generalized (Higher-order) Impedance Boundary Conditions 31\u003c\/p\u003e \u003cp\u003e2.3.3 Sheet Transition Conditions 32\u003c\/p\u003e \u003cp\u003e2.4 Fundamental Properties of Time-harmonic Electromagnetic Fields 35\u003c\/p\u003e \u003cp\u003e2.4.1 Energy Conservation and Uniqueness 35\u003c\/p\u003e \u003cp\u003e2.4.2 Reciprocity 39\u003c\/p\u003e \u003cp\u003e2.5 Basic Solutions of Maxwell’s Equations in Homogeneous Isotropic Media 42\u003c\/p\u003e \u003cp\u003e2.5.1 Plane, Spherical, and Cylindrical Waves 43\u003c\/p\u003e \u003cp\u003e2.5.2 Electromagnetic Potentials and Fields of External Currents 46\u003c\/p\u003e \u003cp\u003e2.5.3 Tensor Green’s Function 50\u003c\/p\u003e \u003cp\u003e2.5.4 E and H Modes 54\u003c\/p\u003e \u003cp\u003e2.5.5 Fields with Translational Symmetry 58\u003c\/p\u003e \u003cp\u003e2.6 Electromagnetic Formulation of Huygens’ Principle 61\u003c\/p\u003e \u003cp\u003e2.6.1 Compact Scatterers 62\u003c\/p\u003e \u003cp\u003e2.6.2 Cylindrical Scatterers 67\u003c\/p\u003e \u003cp\u003e2.7 Problems 70\u003c\/p\u003e \u003cp\u003eReferences 84\u003c\/p\u003e \u003cp\u003e\u003cb\u003e3 Far-field Scattering 87\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e3.1 Introduction 87\u003c\/p\u003e \u003cp\u003e3.2 Scattering Cross Section 87\u003c\/p\u003e \u003cp\u003e3.2.1 Monostatic and Bistatic, Backscattering and Forward-scattering Cross Sections, Differential, Total, Absorption, and Extinction Cross Sections 87\u003c\/p\u003e \u003cp\u003e3.2.2 Scattering Width 91\u003c\/p\u003e \u003cp\u003e3.2.3 Backscattering from Impedance-matched Bodies 93\u003c\/p\u003e \u003cp\u003e3.3 Scattering Matrix 95\u003c\/p\u003e \u003cp\u003e3.3.1 Definition 95\u003c\/p\u003e \u003cp\u003e3.3.2 Scattering Matrix in Spherical Coordinates 97\u003c\/p\u003e \u003cp\u003e3.3.3 Scattering Matrix in the Plane of Scattering Coordinates 99\u003c\/p\u003e \u003cp\u003e3.4 Far-field Coefficient 101\u003c\/p\u003e \u003cp\u003e3.4.1 Integral Representations and Far-field Conditions 102\u003c\/p\u003e \u003cp\u003e3.4.2 Reciprocity of Scattered Fields 106\u003c\/p\u003e \u003cp\u003e3.4.3 Forward Scattering 108\u003c\/p\u003e \u003cp\u003e3.4.4 Cylindrical Bodies 113\u003c\/p\u003e \u003cp\u003e3.5 Scattering Regimes 120\u003c\/p\u003e \u003cp\u003e3.5.1 Resonant-size Scatterers 120\u003c\/p\u003e \u003cp\u003e3.5.2 Electrically Large Scatterers 121\u003c\/p\u003e \u003cp\u003e3.6 Electrically Small Scatterers 125\u003c\/p\u003e \u003cp\u003e3.6.1 Physics of Dipole Scattering 126\u003c\/p\u003e \u003cp\u003e3.6.2 Dipole Scattering in Terms of Polarizability Tensors 129\u003c\/p\u003e \u003cp\u003e3.6.3 Magneto-dielectric Ellipsoid 131\u003c\/p\u003e \u003cp\u003e3.6.4 Rotationally Symmetric Particles 137\u003c\/p\u003e \u003cp\u003e3.7 Problems 148\u003c\/p\u003e \u003cp\u003eReferences 162\u003c\/p\u003e \u003cp\u003e\u003cb\u003e4 Planar Interfaces 165\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e4.1 Introduction 165\u003c\/p\u003e \u003cp\u003e4.2 Interface of Two Homogeneous Semi-infinite Media 167\u003c\/p\u003e \u003cp\u003e4.2.1 Reflection and Transmission Coefficients 167\u003c\/p\u003e \u003cp\u003e4.2.2 Brewster’s Angle 173\u003c\/p\u003e \u003cp\u003e4.2.3 Total Internal Reflection 173\u003c\/p\u003e \u003cp\u003e4.2.4 Interfaces with Double-negative Materials 176\u003c\/p\u003e \u003cp\u003e4.2.5 Surface Waves 177\u003c\/p\u003e \u003cp\u003e4.2.6 Vector Solution of Reflection and Transmission Problems 179\u003c\/p\u003e \u003cp\u003e4.3 Arbitrary Number of Planar Layers 182\u003c\/p\u003e \u003cp\u003e4.3.1 Solution by the Method of Characteristic Matrices 182\u003c\/p\u003e \u003cp\u003e4.3.2 Discussion and Limiting Cases 189\u003c\/p\u003e \u003cp\u003e4.4 Reflection and Transmission of Cylindrical and Spherical Waves 195\u003c\/p\u003e \u003cp\u003e4.4.1 Excitation by a Linear Electric Current 195\u003c\/p\u003e \u003cp\u003e4.4.2 Excitation by an Electric Dipole 202\u003c\/p\u003e \u003cp\u003e4.5 A Layer between Homogeneous Half-spaces 207\u003c\/p\u003e \u003cp\u003e4.5.1 Different Half-spaces 207\u003c\/p\u003e \u003cp\u003e4.5.2 A PEC-backed Layer 213\u003c\/p\u003e \u003cp\u003e4.5.3 Layer Immersed in a Homogeneous Space 215\u003c\/p\u003e \u003cp\u003e4.6 Modeling with Approximate Boundary Conditions 224\u003c\/p\u003e \u003cp\u003e4.6.1 Accuracy of Impedance Boundary Conditions 225\u003c\/p\u003e \u003cp\u003e4.6.2 Accuracy of Transition Boundary Conditions 229\u003c\/p\u003e \u003cp\u003e4.6.3 Impedance-matched Surface 232\u003c\/p\u003e \u003cp\u003e4.7 Problems 235\u003c\/p\u003e \u003cp\u003eReferences 249\u003c\/p\u003e \u003cp\u003e\u003cb\u003e5 Wedges 251\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e5.1 Introduction 251\u003c\/p\u003e \u003cp\u003e5.2 The Perfectly Conducting Wedge 253\u003c\/p\u003e \u003cp\u003e5.2.1 Formulation of Boundary Value Problem 254\u003c\/p\u003e \u003cp\u003e5.2.2 Solution by Separation of Variables 256\u003c\/p\u003e \u003cp\u003e5.2.3 Fields and Currents at the Edge 258\u003c\/p\u003e \u003cp\u003e5.2.4 Reduction to an Integral Form 260\u003c\/p\u003e \u003cp\u003e5.2.5 Special Cases 262\u003c\/p\u003e \u003cp\u003e5.2.6 Edge-diffracted and GO Components. Diffraction Coefficient 266\u003c\/p\u003e \u003cp\u003e5.3 Scattering from a Half-plane (Solution by Factorization Method) 271\u003c\/p\u003e \u003cp\u003e5.3.1 Statement of the Problem 271\u003c\/p\u003e \u003cp\u003e5.3.2 Functional Equation 273\u003c\/p\u003e \u003cp\u003e5.3.3 Factorization and Solution 274\u003c\/p\u003e \u003cp\u003e5.3.4 Scattered Field Far from the Edge 276\u003c\/p\u003e \u003cp\u003e5.4 The Impedance Wedge 279\u003c\/p\u003e \u003cp\u003e5.4.1 Boundary Value Problem, Sommerfeld’s Integrals, and Functional Equations 279\u003c\/p\u003e \u003cp\u003e5.4.2 Normal Incidence (Maliuzhinets’ Solution) 288\u003c\/p\u003e \u003cp\u003e5.4.3 Unit Surface Impedance 297\u003c\/p\u003e \u003cp\u003e5.4.4 Further Exactly Solvable Cases 300\u003c\/p\u003e \u003cp\u003e5.5 High-frequency Scattering from Impenetrable Wedges 306\u003c\/p\u003e \u003cp\u003e5.5.1 GO Components and Surface Waves 307\u003c\/p\u003e \u003cp\u003e5.5.2 Edge-diffracted Field, Diffraction Coefficient, and Scattering Widths 310\u003c\/p\u003e \u003cp\u003e5.5.3 Uniform Asymptotic Approximations 316\u003c\/p\u003e \u003cp\u003e5.5.4 GTD\/UTD Formulation 319\u003c\/p\u003e \u003cp\u003e5.6 Behavior of Electromagnetic Fields at Edges 322\u003c\/p\u003e \u003cp\u003e5.6.1 Determining the Degree of Singularity 322\u003c\/p\u003e \u003cp\u003e5.6.2 Analytical Structure of Meixner’s Series 328\u003c\/p\u003e \u003cp\u003e5.7 Problems 329\u003c\/p\u003e \u003cp\u003eReferences 336\u003c\/p\u003e \u003cp\u003e\u003cb\u003e6 Circular Cylinders and Convex Bodies 339\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e6.1 Introduction 339\u003c\/p\u003e \u003cp\u003e6.2 Perfectly Conducting Cylinders: Separation of Variables and Series Solution 340\u003c\/p\u003e \u003cp\u003e6.2.1 Separation of Variables 342\u003c\/p\u003e \u003cp\u003e6.2.2 Satisfying the Boundary Conditions 342\u003c\/p\u003e \u003cp\u003e6.2.3 Scattered Fields 343\u003c\/p\u003e \u003cp\u003e6.2.4 Numerical Examples 345\u003c\/p\u003e \u003cp\u003e6.3 Homogeneous Cylinders under Normal Illumination 350\u003c\/p\u003e \u003cp\u003e6.3.1 Field Equations and Boundary Conditions 350\u003c\/p\u003e \u003cp\u003e6.3.2 Rayleigh Series Solution 351\u003c\/p\u003e \u003cp\u003e6.3.3 Numerical Examples 352\u003c\/p\u003e \u003cp\u003e6.4 Watson’s Transformation and High-frequency Approximations 354\u003c\/p\u003e \u003cp\u003e6.4.1 Watson’s Transformation 355\u003c\/p\u003e \u003cp\u003e6.4.2 Alternative Solution by Separation of Variables 358\u003c\/p\u003e \u003cp\u003e6.4.3 High-frequency Approximations 360\u003c\/p\u003e \u003cp\u003e6.4.4 Surface Currents in the Penumbra Region. Fock’s Functions 369\u003c\/p\u003e \u003cp\u003e6.5 Coated and Impedance Cylinders under Oblique Illumination 375\u003c\/p\u003e \u003cp\u003e6.5.1 PEC Cylinder with Magneto-dielectric Coating 376\u003c\/p\u003e \u003cp\u003e6.5.2 Impedance Cylinder 383\u003c\/p\u003e \u003cp\u003e6.6 Extension to Generally Shaped Convex Impedance Bodies 392\u003c\/p\u003e \u003cp\u003e6.6.1 Fock’s Principle of the Local Field in the Penumbra Region 393\u003c\/p\u003e \u003cp\u003e6.6.2 Asymptotic Solution for the Field on the Surface of Circular Impedance Cylinders under Oblique Illumination 396\u003c\/p\u003e \u003cp\u003e6.6.3 Fock- and GTD-type Solutions for Electrically Large Convex Impedance Bodies 398\u003c\/p\u003e \u003cp\u003e6.7 Problems 403\u003c\/p\u003e \u003cp\u003eReferences 411\u003c\/p\u003e \u003cp\u003e\u003cb\u003e7 Spheres 412\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e7.1 Introduction 412\u003c\/p\u003e \u003cp\u003e7.2 Exact Solution for a Multilayered Sphere 414\u003c\/p\u003e \u003cp\u003e7.2.1 Formulation of the Problem in Terms of Debye’s Potentials 415\u003c\/p\u003e \u003cp\u003e7.2.2 Derivation of the Series Solution 417\u003c\/p\u003e \u003cp\u003e7.2.3 Solution for Impedance Boundary Conditions 427\u003c\/p\u003e \u003cp\u003e7.3 Physics of Scattering from Spheres 429\u003c\/p\u003e \u003cp\u003e7.3.1 Classification of Scattering 430\u003c\/p\u003e \u003cp\u003e7.3.2 Spiral Waves 436\u003c\/p\u003e \u003cp\u003e7.3.3 Debye’s Expansions for Homogeneous Spheres 438\u003c\/p\u003e \u003cp\u003e7.3.4 Waves in Electrically Large Homogeneous Low-absorption Spheres 442\u003c\/p\u003e \u003cp\u003e7.4 Scattered Field in the Far Zone 463\u003c\/p\u003e \u003cp\u003e7.4.1 Far-field Coefficient, Scattering Cross Sections, and Polarization Structure. Approximations for Electrically Large Spheres 463\u003c\/p\u003e \u003cp\u003e7.4.2 Electrically Small Spheres: Dipole, Quasi-static, and Resonance Approximations 471\u003c\/p\u003e \u003cp\u003e7.4.3 PEC Spheres 479\u003c\/p\u003e \u003cp\u003e7.4.4 Core-shell Spheres 483\u003c\/p\u003e \u003cp\u003e7.4.5 Impedance Spheres 488\u003c\/p\u003e \u003cp\u003e7.5 Far-field Scattering from Homogeneous Spheres 493\u003c\/p\u003e \u003cp\u003e7.5.1 Exact Solution and Limiting Cases 494\u003c\/p\u003e \u003cp\u003e7.5.2 Electrically Small Lossy Spheres 495\u003c\/p\u003e \u003cp\u003e7.5.3 Electrically Small Low-absorption Spheres 499\u003c\/p\u003e \u003cp\u003e7.5.4 Electrically Large Lossy Spheres: Relation to the Impedance Sphere and the Role of Absorption 506\u003c\/p\u003e \u003cp\u003e7.5.5 Electrically Large Low-absorption Spheres: Light Scattering from Water Droplets 513\u003c\/p\u003e \u003cp\u003e7.6 Metamaterial Effects in Scattering from Spheres 542\u003c\/p\u003e \u003cp\u003e7.6.1 Small Spheres 542\u003c\/p\u003e \u003cp\u003e7.6.2 Invisibility Cloak 546\u003c\/p\u003e \u003cp\u003e7.7 Problems 552\u003c\/p\u003e \u003cp\u003eReferences 562\u003c\/p\u003e \u003cp\u003e\u003cb\u003e8 Method of Physical Optics 565\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e8.1 Introduction 565\u003c\/p\u003e \u003cp\u003e8.1.1 On Numerical Techniques for Studying Scattering from Arbitrary-shaped Bodies 565\u003c\/p\u003e \u003cp\u003e8.1.2 PO as one of the Approximate Analytical Techniques 566\u003c\/p\u003e \u003cp\u003e8.1.3 Structure of the Chapter 567\u003c\/p\u003e \u003cp\u003e8.2 Principles and General Solution 567\u003c\/p\u003e \u003cp\u003e8.2.1 Principles of PO 567\u003c\/p\u003e \u003cp\u003e8.2.2 Derivation of PO Solutions 569\u003c\/p\u003e \u003cp\u003e8.2.3 PO for Cylindrical Bodies 573\u003c\/p\u003e \u003cp\u003e8.3 Transmission through Apertures 575\u003c\/p\u003e \u003cp\u003e8.3.1 PO Solution 575\u003c\/p\u003e \u003cp\u003e8.3.2 GO Rays and Fresnel Zones 576\u003c\/p\u003e \u003cp\u003e8.3.3 Contribution from the Rim of the Aperture: Edge-diffracted Rays 582\u003c\/p\u003e \u003cp\u003e8.4 Scattering from Curved Surfaces 594\u003c\/p\u003e \u003cp\u003e8.4.1 Fock’s Reflection Formula 594\u003c\/p\u003e \u003cp\u003e8.4.2 Application to a Spherical Segment 600\u003c\/p\u003e \u003cp\u003e8.4.3 Reflection Formula in the Far-field Region 605\u003c\/p\u003e \u003cp\u003e8.4.4 Diffraction by an Edge in a Non-metallic Surface 609\u003c\/p\u003e \u003cp\u003e8.5 Advantages and Limitations of Physical Optics 615\u003c\/p\u003e \u003cp\u003e8.6 Problems 616\u003c\/p\u003e \u003cp\u003eReferences 632\u003c\/p\u003e \u003cp\u003e\u003cb\u003e9 Physical Optics Solutions of Canonical Problems 634\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e9.1 Introduction 634\u003c\/p\u003e \u003cp\u003e9.2 Vertices 635\u003c\/p\u003e \u003cp\u003e9.2.1 Vertex on an Edge of a Thin Plate 637\u003c\/p\u003e \u003cp\u003e9.2.2 Apex of a Pyramid 641\u003c\/p\u003e \u003cp\u003e9.2.3 Tip of an Elliptic Cone 643\u003c\/p\u003e \u003cp\u003e9.3 Electrically Large Plates 652\u003c\/p\u003e \u003cp\u003e9.3.1 Arbitrarily Shaped Plates 653\u003c\/p\u003e \u003cp\u003e9.3.2 Circular Disc 658\u003c\/p\u003e \u003cp\u003e9.3.3 Polygonal Plates 663\u003c\/p\u003e \u003cp\u003e9.3.4 Far-field Patterns of Polygonal Plates and Apertures 667\u003c\/p\u003e \u003cp\u003e9.4 Bodies of Revolution 671\u003c\/p\u003e \u003cp\u003e9.4.1 PO Solution for Bodies of Revolution 672\u003c\/p\u003e \u003cp\u003e9.4.2 Imperfectly Reflecting Bodies under Axial Illumination 675\u003c\/p\u003e \u003cp\u003e9.4.3 PEC Bodies under Oblique Illumination 677\u003c\/p\u003e \u003cp\u003e9.4.4 Axial Backscattering 678\u003c\/p\u003e \u003cp\u003e9.4.5 Examples 684\u003c\/p\u003e \u003cp\u003e9.5 Problems 689\u003c\/p\u003e \u003cp\u003eReferences 712\u003c\/p\u003e \u003cp\u003e\u003cb\u003eA Definitions and Useful Relations of Vector Analysis and Differential Geometry 714\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eA.1 Vector Algebra 714\u003c\/p\u003e \u003cp\u003eA.2 Vector Analysis 716\u003c\/p\u003e \u003cp\u003eA.3 Vectors and Vector Differential Operators in Orthogonal Curvilinear Coordinates 717\u003c\/p\u003e \u003cp\u003eA.3.1 General Orthogonal Curvilinear Coordinates 717\u003c\/p\u003e \u003cp\u003eA.3.2 Spherical Coordinates 718\u003c\/p\u003e \u003cp\u003eA.4 Curves and Surfaces in Space 720\u003c\/p\u003e \u003cp\u003eA.4.1 Curves 720\u003c\/p\u003e \u003cp\u003eA.4.2 Surfaces 720\u003c\/p\u003e \u003cp\u003eA.5 Problems 722\u003c\/p\u003e \u003cp\u003eReferences 724\u003c\/p\u003e \u003cp\u003e\u003cb\u003eB Fresnel Integral and Related Functions 725\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eB.1 Fresnel Integral 725\u003c\/p\u003e \u003cp\u003eB.2 Relation to the Error Function 728\u003c\/p\u003e \u003cp\u003eB.3 Transition Functions of Uniform Theories of Diffraction 730\u003c\/p\u003e \u003cp\u003eB.4 Problems 731\u003c\/p\u003e \u003cp\u003eReferences 732\u003c\/p\u003e \u003cp\u003e\u003cb\u003eC Principles of Complex Integration 733\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eC.1 Introduction 733\u003c\/p\u003e \u003cp\u003eC.2 Deforming the Integration Contour 734\u003c\/p\u003e \u003cp\u003eC.2.1 Basic Facts about Functions of a Complex Variable 734\u003c\/p\u003e \u003cp\u003eC.2.2 Integrals over Infinite Contours 736\u003c\/p\u003e \u003cp\u003eC.3 Steepest Descent Method 737\u003c\/p\u003e \u003cp\u003eC.3.1 Steepest Descent Path 738\u003c\/p\u003e \u003cp\u003eC.3.2 Saddle Point Contribution 739\u003c\/p\u003e \u003cp\u003eC.3.3 Pole Singularity near the Saddle Point 741\u003c\/p\u003e \u003cp\u003eC.3.4 Further Cases 742\u003c\/p\u003e \u003cp\u003eC.4 Problems 743\u003c\/p\u003e \u003cp\u003eReferences 745\u003c\/p\u003e \u003cp\u003e\u003cb\u003eD The Stationary Phase Method 746\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eD.1 Introduction 746\u003c\/p\u003e \u003cp\u003eD.2 One-dimensional Integrals 746\u003c\/p\u003e \u003cp\u003eD.2.1 No Stationary Points on the Integration Interval 747\u003c\/p\u003e \u003cp\u003eD.2.2 Isolated Stationary Points 748\u003c\/p\u003e \u003cp\u003eD.2.3 Two Coalescing Stationary Points 751\u003c\/p\u003e \u003cp\u003eD.3 Two-dimensional Integrals 756\u003c\/p\u003e \u003cp\u003eD.3.1 Stationary Point in the Integration Domain 756\u003c\/p\u003e \u003cp\u003eD.3.2 Stationary Point near the Boundary of the Integration Domain 758\u003c\/p\u003e \u003cp\u003eD.3.3 Contribution from the Boundary of the Integration Domain 760\u003c\/p\u003e \u003cp\u003eD.3.4 Kontorovich’s Formula 763\u003c\/p\u003e \u003cp\u003eD.3.5 Integrand Vanishing on the Boundary 765\u003c\/p\u003e \u003cp\u003eD.3.6 Summary of the Two-dimensional Stationary-phase Method 766\u003c\/p\u003e \u003cp\u003eD.4 Problems 766\u003c\/p\u003e \u003cp\u003eReferences 768\u003c\/p\u003e \u003cp\u003e\u003cb\u003eE Asymptotic Approximations of Bessel Functions of Large Argument and Arbitrary Order 770\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eE.1 Introduction 770\u003c\/p\u003e \u003cp\u003eE.1.1 Basic Definitions and Properties 770\u003c\/p\u003e \u003cp\u003eE.1.2 Large-argument Approximations (|z| â 1) 772\u003c\/p\u003e \u003cp\u003eE.1.3 Content of the Appendix 775\u003c\/p\u003e \u003cp\u003eE.2 Debye’s Asymptotic Approximations 776\u003c\/p\u003e \u003cp\u003eE.2.1 Debye’s Method 776\u003c\/p\u003e \u003cp\u003eE.2.2 WKB Approximation 778\u003c\/p\u003e \u003cp\u003eE.2.3 Bessel Functions on the Complex 𝜈 Plane 791\u003c\/p\u003e \u003cp\u003eE.3 Almost Equal Argument and Order 795\u003c\/p\u003e \u003cp\u003eE.3.1 Approximations in Terms of Airy Functions 796\u003c\/p\u003e \u003cp\u003eE.3.2 Approximations in Terms of Normalized Airy Functions 797\u003c\/p\u003e \u003cp\u003eE.3.3 Zeros in the Neighborhood of the Points 𝜈 = ±z 798\u003c\/p\u003e \u003cp\u003eReferences 799\u003c\/p\u003e \u003cp\u003eIndex 801\u003c\/p\u003e  \u003cstrong\u003eAndrey Osipov\u003c\/strong\u003e, Microwaves and Radar Institute, German Aerospace Center (DLR), Germany. \u003cp\u003e\u003cstrong\u003eSergei Tretyakov\u003c\/strong\u003e, Department of Radio Science and Engineering, Aalto University, Finland.\u003c\/p\u003e","brand":"Wiley","offers":[{"title":"Default Title","offer_id":47989640823013,"sku":"NP9780470512388","price":201.95,"currency_code":"USD","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/1842\/7735\/files\/9780470512388.jpg?v=1761784923","url":"https:\/\/k12savings.com\/es\/products\/modern-electromagnetic-scattering-theory-with-applications-isbn-9780470512388","provider":"K12savings","version":"1.0","type":"link"}