Fundamentals of the Physical Theory of Diffraction

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

Auteur

PYOTR YA. UFIMTSEV, PhD, D.Sc, has been recognized for his outstanding work in the theory of diffraction and propagation of electromagnetic and acoustic waves. Dr. Ufimtsev has been affiliated with the Central Research Radio Engineering Institute of the USSR Defense Ministry, Moscow; the Institute of Radio Engineering and Electronics of the USSR Academy of Sciences, Moscow; the Moscow Aviation Institute; and the University of California at Los Angeles and Irvine. Among Dr. Ufimtsev's many honors and awards are the USSR State Prize and the Leroy Randle Grumman Medal.

Texte du rabat
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 analyze and investigate the diffraction phenomena

Contenu
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 Acoustic Waves 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 ...