Fundamentals of the Physical Theory of Diffraction

Transcription

1 Fundamentals of the Physical Theory of Diffraction Pyotr Ya. Ufimtsev BICCNTENNIAL f 1! 1807;! s JWILEY \» ; ai Ir BICENTENNIAL WILEY-INTERSCIENCE A JOHN WILEY & SONS, INC., PUBLICATION

2 Contents Foreword Preface Acknowledgments xi XV xvii Introduction 1. Basic Notions in Acoustic and Electromagnetic Diffraction Problems Formulation of the Diffraction Problem Scattered Field in the Far Zone Physical Optics Definition of the Physical Optics Total Scattering Cross-Section Optical Theorem Introducing the Notion of "Shadow Radiation" Shadow Contour Theorem and thetotal Scattering Cross-Section Summary of Properties of Physical Optics Approximation Nonuniform Component of Induced Surface Field Electromagnetic Waves 27 Problems Wedge Diffraction: Exact Solution and Asymptotics Classical Solutions Transition to the Plane Wave Excitation Conversion of the Series Solution to the Sommerfeld Integrals The Sommerfeld Ray Asymptotics The Pauli Asymptotics Uniform Asymptotics: Extension of the Pauli Technique Comments on Alternative Asymptotics 55 Problems 56 v

3 vi Contents 3. Wedge Diffraction: The Physical Optics Field Original PO Integrals Conversion of the PO Integrals to the Canonical Form Ray Asymptotics for the PO Diffracted Field 67 Problems Wedge Diffraction: Radiation by the Nonuniform Component of Surface Sources Integrals and Asymptotics Integral Form of Functions/ ^ and g^' Oblique Incidence of a Plane Wave at a Wedge 78 Problems First-Order Diffraction at Strips and Polygonal Cylinders Diffraction at a Strip Physical Optics Part of the Scattered Field Total Scattered Field Numerical Analysis of the Scattered Field First-Order PTD with Truncated Scattering Sources /^ Diffraction at a Triangulär Cylinder 99 Problems Symmetrie Scattering: PO Approximation Backscattering: PO Approximation Symmetrie Scattering: First-Order PTD Approximation Backscattering: First-Order PTD Approximation Numerical Analysis of the Scattered Field Axially Symmetrie Scattering of Acoustic Waves at Bodies of Revolution Diffraction at a Canonical Conic Surface Integrals for the Scattered Field Ray Asymptotics FocalFields Bessel Interpolations for the Field u Scattering at a Disk Physical Optics Approximation Field Generated by Nonuniform Scattering Sources Total Scattered Field 132

4 Contents VÜ 6.3 Scattering at Cones: Focal Field Asymptotic Approximations for the Field Numerical Analysis of Backscattering Bodies of Revolution with Nonzero Gaussian Curvature: Backscattered Focal Fields PO Approximation Total Backscattered Focal Field: First-Order PTD Asymptotics Backscattering from Paraboloids Backscattering from Spherical Segments Bodies of Revolution with Nonzero Gaussian Curvature: Axially Symmetrie Bistatic Scattering 155 Problems Ray Asymptotics for the PO Field Bessel Interpolations for the PO Field in the Region n a> < $ < n Bessel Interpolations for the PTD Field in the Region n co < )? TZ Asymptotics for the PTD Field in the Region 2Ü) < # < TZ co away from the GO Boundary & = 2co Uniform Approximations for the PO Field in the Ray Region 2co < tr < TZ co Including the GO Boundary?? = 2a> Approximation for the PO Field in the Shadow Region for Reflected Rays Elementary Acoustic and Electromagnetic Edge Waves Elementary Strips on a Canonical Wedge Integrals for/; h on Elementary Strips Triple Integrals for Elementary Edge Waves Transformation of Triple Integrals into One-Dimensional Integrals General Asymptotics for Elementary Edge Waves Analytic Properties of Elementary Edge Waves Numerical Calculations of Elementary Edge Waves Electromagnetic Elementary Edge Waves Improved Theory of Elementary Edge Waves Acoustic EEWs Electromagnetic EEWs Some References Related to Elementary Edge Waves 209 Problems 210

5 VÜi Contents 8. Ray and Caustics Asymptotics for Edge Diffracted Waves Ray Asymptotics Acoustic Waves Electromagnetic Waves Comments on Ray Asymptotics Caustic Asymptotics 220 Problems Acoustic Waves Electromagnetic Waves Multiple Diffraction of Edge Waves: Grazing Incidence and Slope Diffraction Statement of the Problem and Related References Grazing Diffraction Acoustic Waves Electromagnetic Waves Slope Diffraction in the Configuration of Figure Acoustic Waves Electromagnetic Waves Slope Diffraction: General Case 240 Problems Acoustic Waves Electromagnetic Waves Diffraction Interaction of Neighboring Edges on a Ruled Surface Diffraction at an Acoustically Hard Surface Diffraction at an Acoustically Soft Surface Diffraction of Electromagnetic Waves 252 Problems Focusing of Multiple Acoustic Edge Waves Diffracted at a Convex Body of Revolution with a Fiat Base Statement of the Problem and its Characteristic Features Multiple Hard Diffraction Multiple Soft Diffraction 258 Problems 260

6 Contents ix 12. Focusing of Multiple Edge Waves Diffracted at a Disk Multiple Hard Diffraction Multiple Soft Diffraction Multiple Diffraction of Electromagnetic Waves 267 Problems Backscattering at a Finite-Length Cylinder Acoustic Waves PO Approximation Backscattering Produced by the Nonuniform Componentj* ' Total Backscattered Field Electromagnetic Waves 279 Problems E-Polarization H-Polarization Bistatic Scattering at a Finite-Length Cylinder Acoustic Waves PO Approximation Shadow Radiation as a Part of the Physical Optics Field PTD for Bistatic Scattering at a Hard Cylinder Beams and Rays of the Scattered Field Refined Asymptotics for the Specular Beam Electromagnetic Waves 304 Problems Polarization fl-polarization Refined Asymptotics for the Specular Beam Refiected from the Lateral Surface 308 Conclusion 313 References 315 Index 323