Fundamentals of the physical theory of diffraction

Content: 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 Diffraction Problems 1 1.1 Formulation of the Diffraction Problem / 1 1.2 Scattered Field in the Far Zone / 3 1.3 Physical Optics / 7 1.3.1 Definition of Physical Optics / 7 1.3.2 Total Scattering Cross-Section / 10 1.3.3 Optical Theorem / 11 1.3.4 Introducing Shadow Radiation / 12 1.3.5 Shadow Contour Theorem and the Total Scattering Cross-Section / 17 1.3.6 Shadow Radiation and Reflected Field in the Far Zone / 20 1.3.7 Shadow Radiation and Reflection from Opaque Objects / 22 1.4 Electromagnetic Waves / 23 1.4.1 Basic Field Equations and PO Backscattering / 23 1.4.2 PO Field Components: Reflected Field and Shadow Radiation / 26 1.4.3 Electromagnetic Reflection and Shadow Radiation from Opaque Objects / 28 1.5 Physical Interpretations of Shadow Radiation / 31 1.5.1 Shadow Field and Transverse Diffusion / 31 1.5.2 Fresnel Diffraction and Forward Scattering / 32 1.6 Summary of Properties of Physical Optics Approximation / 32 1.7 Nonuniform Component of an Induced Surface Field / 33 Problems / 36 2 Wedge Diffraction: Exact Solution and Asymptotics 49 2.1 Classical Solutions / 49 2.2 Transition to Plane Wave Excitation / 55 2.3 Conversion of the Series Solution to the Sommerfeld Integrals / 57 2.4 The Sommerfeld Ray Asymptotics / 61 2.5 The Pauli Asymptotics / 63 2.6 Uniform Asymptotics: Extension of the Pauli Technique / 68 2.7 Fast Convergent Integrals and Uniform Asymptotics: The "Magic Zero" Procedure / 72 Problems / 76 3 Wedge Diffraction: The Physical Optics Field 87 3.1 Original PO Integrals / 87 3.2 Conversion of PO Integrals to the Canonical Form / 90 3.3 Fast Convergent Integrals and Asymptotics for the PO Diffracted Field / 94 Problems / 100 4 Wedge Diffraction: Radiation by Fringe Components of Surface Sources 103 4.1 Integrals and Asymptotics / 104 4.2 Integral Forms of Functions f (1) and g(1) / 112 4.3 Oblique Incidence of a Plane Wave at a Wedge / 114 4.3.1 Acoustic Waves / 114 4.3.2 Electromagnetic Waves / 118 Problems / 120 5 First-Order Diffraction at Strips and Polygonal Cylinders 123 5.1 Diffraction at a Strip / 124 5.1.1 Physical Optics Part of the Scattered Field / 124 5.1.2 Total Scattered Field / 128 5.1.3 Numerical Analysis of the Scattered Field / 132 5.1.4 First-Order PTD with Truncated Scattering Sources j(1) h / 135 5.2 Diffraction at a Triangular Cylinder / 140 5.2.1 Symmetric Scattering: PO Approximation / 141 5.2.2 Backscattering: PO Approximation / 143 5.2.3 Symmetric Scattering: First-Order PTD Approximation / 145 5.2.4 Backscattering: First-Order PTD Approximation / 148 5.2.5 Numerical Analysis of the Scattered Field / 150 Problems / 152 6 Axially Symmetric Scattering of AcousticWaves at Bodies of Revolution 157 6.1 Diffraction at a Canonical Conic Surface / 158 6.1.1 Integrals for the Scattered Field / 159 6.1.2 Ray Asymptotics / 160 6.1.3 Focal Fields / 166 6.1.4 Bessel Interpolations for the Field u(1) s,h / 167 6.2 Scattering at a Disk / 169 6.2.1 Physical Optics Approximation / 169 6.2.2 Relationships Between Acoustic and Electromagnetic PO Fields / 171 6.2.3 Field Generated by Fringe Scattering Sources / 172 6.2.4 Total Scattered Field / 173 6.3 Scattering at Cones: Focal Field / 176 6.3.1 Asymptotic Approximations for the Field / 176 6.3.2 Numerical Analysis of Backscattering / 179 6.4 Bodies of Revolution with Nonzero Gaussian Curvature: Backscattered Focal Fields / 183 6.4.1 PO Approximation / 184 6.4.2 Total Backscattered Focal Field: First-Order PTD Asymptotics / 186 6.4.3 Backscattering from Paraboloids / 186 6.4.4 Backscattering from Spherical Segments / 192 6.5 Bodies of Revolution with Nonzero Gaussian Curvature: Axially Symmetric Bistatic Scattering / 196 6.5.1 Ray Asymptotics for the PO Field / 196 6.5.2 Bessel Interpolations for the PO Field in the Region - <
= <
= / 200 6.5.3 Bessel Interpolations for the PTD Field in the Region - <
= <
= / 200 6.5.4 Asymptotics for the PTD Field in the Region 2 <
<
= - Away from the GO Boundary = 2 / 201 6.5.5 Uniform Approximations for the PO Field in the Ray Region 2 <
= <
= - , Including the GO Boundary = 2 / 202 6.5.6 Approximation of the PO Field in the Shadow Region for Reflected Rays / 205 Problems / 207 7 Elementary Acoustic and Electromagnetic Edge Waves 211 7.1 Elementary Strips on a Canonical Wedge / 212 7.2 Integrals for j(1) s,h on Elementary Strips / 213 7.3 Triple Integrals for Elementary Edge Waves / 217 7.4 Transformation of Triple Integrals into One-Dimensional Integrals / 220 7.5 General Asymptotics for Elementary Edge Waves / 225 7.6 Analytic Properties of Elementary Edge Waves / 230 7.7 Numerical Calculations of Acoustic Elementary Fringe Waves / 234 7.8 Electromagnetic Elementary Edge Waves / 237 7.8.1 Electromagnetic EEWs on the Diffraction Cone Outside the Wedge / 241 7.8.2 Electromagnetic EEWs on the Diffraction Cone Inside the Wedge / 243 7.8.3 Numerical Calculations of Electromagnetic Elementary Fringe Waves / 245 7.9 Improved Theory of Elementary Edge Waves: Removal of the Grazing Singularity / 245 7.9.1 Acoustic EEWs / 248 7.9.2 Electromagnetic EEWs Generated by the Modified Nonuniform Current / 253 7.10 Some References Related to Elementary Edge Waves / 256 Problems / 257 8 Ray and Caustic Asymptotics for Edge Diffracted Waves 261 8.1 Ray Asymptotics / 261 8.1.1 Acoustic Waves / 261 8.1.2 Electromagnetic Waves / 266 8.1.3 Comments on Ray Asymptotics / 267 8.2 Caustic Asymptotics / 269 8.2.1 Acoustic waves / 269 8.2.2 Electromagnetic Waves / 274 8.3 Relationships between PTD and GTD / 275 Problems / 276 9 Multiple Diffraction of Edge Waves: Grazing Incidence and Slope Diffraction 285 9.1 Statement of the Problem and Related References / 285 9.2 Grazing Diffraction / 286 9.2.1 Acoustic Waves / 286 9.2.2 Electromagnetic Waves / 290 9.3 Slope Diffraction in Configuration of Figure 9.1 / 292 9.3.1 Acoustic Waves / 292 9.3.2 Electromagnetic Waves / 295 9.4 Slope Diffraction: General Case / 296 9.4.1 Acoustic Waves / 296 9.4.2 Electromagnetic Waves / 299 Problems / 302 10 Diffraction Interaction of Neighboring Edges on a Ruled Surface 305 10.1 Diffraction at an Acoustically Hard Surface / 306 10.2 Diffraction at an Acoustically Soft Surface / 309 10.3 Diffraction of Electromagnetic Waves / 312 10.4 Test Problem: Secondary Diffraction at a Strip / 314 10.4.1 Diffraction at a Hard Strip / 314 10.4.2 Diffraction at a Soft Strip / 317 Problems / 318 11 Focusing of Multiple Acoustic Edge Waves Diffracted at a Convex Body of Revolution with a Flat Base 325 11.1 Statement of the Problem and its Characteristic Features / 325 11.2 Multiple Hard Diffraction / 327 11.3 Multiple Soft Diffraction / 328 Problems / 330 12 Focusing of Multiple Edge Waves Diffracted at a Disk 333 12.1 Multiple Hard Diffraction / 334 12.2 Multiple Soft Diffraction / 336 12.3 Multiple Diffraction of Electromagnetic Waves / 340 Problems / 341 13 Backscattering at a Finite-Length Cylinder 343 13.1 Acoustic Waves / 343 13.1.1 PO Approximation / 343 13.1.2 Backscattering Produced by the Nonuniform Component j(1) / 347 13.1.3 Total Backscattered Field / 352 13.2 Electromagnetic Waves / 354 13.2.1 E-polarization / 354 13.2.2 H-polarization / 360 Problems / 362 14 Bistatic Scattering at a Finite-Length Cylinder 365 14.1 Acoustic Waves / 365 14.1.1 PO Approximation / 366 14.1.2 Shadow Radiation as a Part of the Physical Optics Field / 368 14.1.3 PTD for Bistatic Scattering at a Hard Cylinder / 370 14.1.4 Beams and Rays of the Scattered Field / 376 14.1.5 PO Shooting-Through Rays and Their Cancellation by Fringe Rays / 381 14.1.6 Refined Asymptotics for the Specular Beam Reflected from the Lateral Surface / 382 14.2 Electromagnetic Waves / 386 14.2.1 E-Polarization / 386 14.2.2 H-Polarization / 388 14.2.3 Refined Asymptotics for the Specular Beam Reflected from the Lateral Surface / 390 Problems / 393 Conclusion 397 References 399 Appendix to Chapter 4: MATLAB Codes for Two-Dimensional Fringe Waves and Figures (F. Hacivelioglu and L. Sevgi) 411 Appendix to Chapter 6: MATLAB Codes for Axial Backscattering at Bodies of Revolution (F. Hacivelioglu and L. Sevgi) 431 Appendix to Section 7.7: MATLAB Codes for Diffraction Coefficients of Acoustic Elementary Fringe Waves (F. Hacivelioglu and L. Sevgi) 439 Appendix to Section 7.8.3: MATLAB Codes for Diffraction Coefficients of Electromagnetic Elementary Fringe Waves (F. Hacivelioglu and L. Sevgi) 443 Appendix to Section 7.9.2: Field d E (0) mod Radiated by Modified Uniform Currents J (0) mod Induced on Elementary Strips (P. Ya. Ufimtsev) 447 Index 451