Fundamentals of the Physical Theory of Diffraction
[BOOK DESCRIPTION]
The book is a complete, comprehensive description of the modern Physical Theory of Diffraction (PTD) based upon the concept of elementary edge waves. The theory is demonstrated with examples of the diffraction of acoustic and electromagnetic waves at perfectly reflecting objects. Readers develop the skills to apply PTD to solve various scattering problems. The derived analytic expressions clearly illustrate the physical structure of the scattered field. They additionally describe all of the reflected and diffracted rays and beams, as well as the fields in the vicinity of caustics and foci. Shadow radiation, a fundamental component of PTD, is introduced and proven to contain half the total scattered power. The equivalence relationships between acoustic and electromagnetic diffracted waves are established and emphasized. Throughout the book, the author enables readers to master both the theory and its practical applications.* Plotted numeric results supplement the theory and facilitate the visualization of individual contributions of distinct parts of the scattering objects to the total diffracted field * Detailed comments help readers understand and implement all the critical steps of the analytic and numeric calculations * Problem sets in each chapter give readers an opportunity to analyse and investigate the diffraction phenomena
[TABLE OF CONTENTS]
Preface xiii
Foreword to the First Edition xv
Preface to the First Edition xix
Acknowledgments xxi
Introduction xxiii
1 Basic Notions in Acoustic and Electromagnetic 1 (48)
Diffraction Problems
1.1 Formulation of the Diffraction Problem 1 (2)
1.2 Scattered Field in the Far Zone 3 (4)
1.3 Physical Optics 7 (16)
1.3.1 Definition of Physical Optics 7 (3)
1.3.2 Total Scattering Cross-Section 10 (1)
1.3.3 Optical Theorem 11 (1)
1.3.4 Introducing Shadow Radiation 12 (5)
1.3.5 Shadow Contour Theorem and the Total 17 (3)
Scattering Cross-Section
1.3.6 Shadow Radiation and Reflected Field 20 (2)
in the Far Zone
1.3.7 Shadow Radiation and Reflection from 22 (1)
Opaque Objects
1.4 Electromagnetic Waves 23 (8)
1.4.1 Basic Field Equations and PO 23 (3)
Backscattering
1.4.2 PO Field Components: Reflected Field 26 (2)
and Shadow Radiation
1.4.3 Electromagnetic Reflection and Shadow 28 (3)
Radiation from Opaque Objects
1.5 Physical Interpretations of Shadow 31 (1)
Radiation
1.5.1 Shadow Field and Transverse Diffusion 31 (1)
1.5.2 Fresnel Diffraction and Forward 32 (1)
Scattering
1.6 Summary of Properties of Physical Optics 32 (1)
Approximation
1.7 Nonuniform Component of an Induced 33 (3)
Surface Field
Problems 36 (13)
2 Wedge Diffraction: Exact Solution and 49 (38)
Asymptotics
2.1 Classical Solutions 49 (6)
2.2 Transition to Plane Wave Excitation 55 (2)
2.3 Conversion of the Series Solution to the 57 (4)
Sommerfeld Integrals
2.4 The Sommerfeld Ray Asymptotics 61 (2)
2.5 The Pauli Asymptotics 63 (5)
2.6 Uniform Asymptotics: Extension of the 68 (4)
Pauli Technique
2.7 Fast Convergent Integrals and Uniform 72 (4)
Asymptotics: The "Magic Zero" Procedure
Problems 76 (11)
3 Wedge Diffraction: The Physical Optics Field 87 (16)
3.1 Original PO Integrals 87 (3)
3.2 Conversion of PO Integrals to the 90 (4)
Canonical Form
3.3 Fast Convergent Integrals and Asymptotics 94 (6)
for the PO Diffracted Field
Problems 100 (3)
4 Wedge Diffraction: Radiation by Fringe 103 (20)
Components of Surface Sources
4.1 Integrals and Asymptotics 104 (8)
4.2 Integral Forms of Functions ?(ｹ) and g(ｹ) 112 (2)
4.3 Oblique Incidence of a Plane Wave at a 114 (6)
Wedge
4.3.1 Acoustic Waves 114 (4)
4.3.2 Electromagnetic Waves 118 (2)
Problems 120 (3)
5 First-Order Diffraction at Strips and 123 (34)
Polygonal Cylinders
5.1 Diffraction at a Strip 124 (16)
5.1.1 Physical Optics Part of the Scattered 124 (4)
Field
5.1.2 Total Scattered Field 128 (4)
5.1.3 Numerical Analysis of the Scattered 132 (3)
Field
5.1.4 First-Order PTD with Truncated 135 (5)
Scattering Sources j(ｹ)h
5.2 Diffraction at a Triangular Cylinder 140 (12)
5.2.1 Symmetric Scattering: PO Approximation 141 (2)
5.2.2 Backscattering: PO Approximation 143 (2)
5.2.3 Symmetric Scattering: First-Order PTD 145 (3)
Approximation
5.2.4 Backscattering: First-Order PTD 148 (2)
Approximation
5.2.5 Numerical Analysis of the Scattered 150 (2)
Field
Problems 152 (5)
6 Axially Symmetric Scattering of Acoustic 157 (54)
Waves at Bodies of Revolution
6.1 Diffraction at a Canonical Conic Surface 158 (11)
6.1.1 Integrals for the Scattered Field 159 (1)
6.1.2 Ray Asymptotics 160 (6)
6.1.3 Focal Fields 166 (1)
6.1.4 Bessel Interpolations for the Field 167 (2)
u(ｹ)s,h
6.2 Scattering at a Disk 169 (7)
6.2.1 Physical Optics Approximation 169 (2)
6.2.2 Relationships Between Acoustic and 171 (1)
Electromagnetic PO Fields
6.2.3 Field Generated by Fringe Scattering 172 (1)
Sources
6.2.4 Total Scattered Field 173 (3)
6.3 Scattering at Cones: Focal Field 176 (7)
6.3.1 Asymptotic Approximations for the 176 (3)
Field
6.3.2 Numerical Analysis of Backscattering 179 (4)
6.4 Bodies of Revolution with Nonzero 183 (13)
Gaussian Curvature: Backscattered Focal Fields
6.4.1 PO Approximation 184 (2)
6.4.2 Total Backscattered Focal Field: 186 (1)
First-Order PTD Asymptotics
6.4.3 Backscattering from Paraboloids 186 (6)
6.4.4 Backscattering from Spherical Segments 192 (4)
6.5 Bodies of Revolution with Nonzero 196 (11)
Gaussian Curvature: Axially Symmetric
Bistatic Scattering
6.5.1 Ray Asymptotics for the PO Field 196 (4)
6.5.2 Bessel Interpolations for the PO 200 (1)
Field in the Region π-ω< or =
to 0 < or = to π
6.5.3 Bessel Interpolations for the PTD 200 (1)
Field in the Region π-ω< or =
to 0 < or = to π
6.5.4 Asymptotics for the PTD Field in the 201 (1)
Region 2ω< 0 < or = to
π-ω Away from the Boundary 0 =
2&omgega;
6.5.5 Uniform Approximations for the PO 202 (3)
Field in the Ray Region 2ω< or -
to 0 < or = to π-ω Including
the GO Boundary 0 = 2ω
6.5.6 Approximation of the PO Field in the 205 (2)
Shadow Region for Reflected Rays
Problems 207 (4)
7 Elementary Acoustic and Electromagnetic Edge 211 (50)
Waves
7.1 Elementary Strips on a Canonical Wedge 212 (1)
7.2 Integrals for j(ｹ)s,h on Elementary Strips 213 (4)
7.3 Triple Integrals for Elementary Edge Waves 217 (3)
7.4 Transformation of Triple Integrals into 220 (5)
One-Dimensional Integrals
7.5 General Asymptotics for Elementary Edge 225 (5)
Waves
7.6 Analytic Properties of Elementary Edge 230 (4)
Waves
7.7 Numerical Calculations of Acoustic 234 (3)
Elementary Fringe Waves
7.8 Electromagnetic Elementary Edge Waves 237 (8)
7.8.1 Electromagnetic EEWs on the 241 (2)
Diffraction Cone Outside the Wedge
7.8.2 Electromagnetic EEWs on the 243 (2)
Diffraction Cone Inside the Wedge
7.8.3 Numerical Calculations of 245 (1)
Electromagnetic Elementary Fringe Waves
7.9 Improved Theory of Elementary Edge Waves: 245 (11)
Removal of the Grazing Singularity
7.9.1 Acoustic EEWs 248 (5)
7.9.2 Electromagnetic EEWs Generated by the 253 (3)
Modified Nonuniform Current
7.10 Some References Related to Elementary 256 (1)
Edge Waves
Problems 257 (4)
8 Ray and Caustic Asymptotics for Edge 261 (24)
Diffracted Waves
8.1 Ray Asymptotics 261 (8)
8.1.1 Acoustic Waves 261 (5)
8.1.2 Electromagnetic Waves 266 (1)
8.1.3 Comments on Ray Asymptotics 267 (2)
8.2 Caustic Asymptotics 269 (6)
8.2.1 Acoustic waves 269 (5)
8.2.2 Electromagnetic Waves 274 (1)
8.3 Relationships between PTD and GTD 275 (1)
Problems 276 (9)
9 Multiple Diffraction of Edge Waves: Grazing 285 (20)
Incidence and Slope Diffraction
9.1 Statement of the Problem and Related 285 (1)
References
9.2 Grazing Diffraction 286 (6)
9.2.1 Acoustic Waves 286 (4)
9.2.2 Electromagnetic Waves 290 (2)
9.3 Slope Diffraction in Configuration of 292 (4)
Figure 9.1
9.3.1 Acoustic Waves 292 (3)
9.3.2 Electromagnetic Waves 295 (1)
9.4 Slope Diffraction: General Case 296 (6)
9.4.1 Acoustic Waves 296 (3)
9.4.2 Electromagnetic Waves 299 (3)
Problems 302 (3)
10 Diffraction Interaction of Neighboring Edges 305 (20)
on a Ruled Surface
10.1 Diffraction at an Acoustically Hard 306 (3)
Surface
10.2 Diffraction at an Acoustically Soft 309 (3)
Surface
10.3 Diffraction of Electromagnetic Waves 312 (2)
10.4 Test Problem: Secondary Diffraction at a 314 (4)
Strip
10.4.1 Diffraction at a Hard Strip 314 (3)
10.4.2 Diffraction at a Soft Strip 317 (1)
Problems 318 (7)
11 Focusing of Multiple Acoustic Edge Waves 325 (8)
Diffracted at a Convex Body of Revolution with
a Flat Base
11.1 Statement of the Problem and its 325 (2)
Characteristic Features
11.2 Multiple Hard Diffraction 327 (1)
11.3 Multiple Soft Diffraction 328 (2)
Problems 330 (3)
12 Focusing of Multiple Edge Waves Diffracted 333 (10)
at a Disk
12.1 Multiple Hard Diffraction 334 (2)
12.2 Multiple Soft Diffraction 336 (4)
12.3 Multiple Diffraction of Electromagnetic 340 (1)
Waves
Problems 341 (2)
13 Backscattering at a Finite-Length Cylinder 343 (22)
13.1 Acoustic Waves 343 (11)
13.1.1 PO Approximation 343 (4)
13.1.2 Backscattering Produced by the 347 (5)
Nonuniform Component j(ｹ)
13.1.3 Total Backscattered Field 352 (2)
13.2 Electromagnetic Waves 354 (8)
13.2.1 E-polarization 354 (6)
13.2.2 H-polarization 360 (2)
Problems 362 (3)
14 Bistatic Scattering at a Finite-Length 365 (32)
Cylinder
14.1 Acoustic Waves 365 (21)
14.1.1 PO Approximation 366 (2)
14.1.2 Shadow Radiation as a Part of the 368 (2)
Physical Optics Field
14.1.3 PTD for Bistatic Scattering at a 370 (6)
Hard Cylinder
14.1.4 Beams and Rays of the Scattered Field 376 (5)
14.1.5 PO Shooting-Through Rays and Their 381 (1)
Cancellation by Fringe Rays
14.1.6 Refined Asymptotics for the Specular 382 (4)
Beam Reflected from the Lateral Surface
14.2 Electromagnetic Waves 386
14.2.1 E-Polarization 386 (2)
14.2.2 H-Polarization 388 (2)
14.2.3 Refined Asymptotics for the Specular 390
Beam Reflected from the Lateral Surface
Problems 39 (358)
Conclusion 397 (2)
References 399 (12)
Appendix to Chapter 4: MATLAB Codes for 411 (20)
Two-Dimensional Fringe Waves and Figures
F. Hacivelioglu
L. Sevgi
Appendix to Chapter 6: MATLAB Codes for Axial 431 (8)
Backscattering at Bodies of Revolution
F. Hacivelioglu
L. Sevgi
Appendix to Section 7.7: MATLAB Codes for 439 (4)
Diffraction Coefficients of Acoustic Elementary
Fringe Waves
F. Hacivelioglu
L. Sevgi
Appendix to Section 7.8.3: MATLAB Codes for 443 (4)
Diffraction Coefficients of Electromagnetic
Elementary Fringe Waves
F. Hacivelioglu
L. Sevgi
Appendix to Section 7.9.2: Field dE->(ｰ)mod 447 (4)
Radiated by Modified Uniform Currents J->(ｰ)mod
Induced on Elementary Strips
P. Ya. Ufimtsev
Index 451
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