This volume is a new revised printing which includes additional comments and incorporates corrections of misprints found in the first printing. It supplements Fundamentals of the Physical Theory of Diffraction (John Wiley & Sons, Inc., 2007). Together these two books provide a comprehensive description of the high-frequency asymptotic technique-Physical Theory of Diffraction (PTD)-widely used in antenna design and RCS calculations. This book contains basic original ideas of PTD, examples of its practical application, and its validation by the mathematical theory of diffraction. The derived analytic expressions are convenient for numerical calculations and clearly illustrate the physical structure of the scattered field. This book is an essential resource for researchers involved in designing antennas and RCS calculations. It is also useful for students studying high frequency diffraction techniques. Key Topics *Theory of diffraction at black bodies introduces the Shadow Radiation, a fundamental component of the scattered field *RCS of finite bodies of revolution-cones, paraboloids, etc. -models of construction elements for aircraft and missiles *Scheme for measurement of that part of a scattered field which is radiated by the diffraction (so-called nonuniform) currents induced on scattering objects *Development of the parabolic equation method for investigation of edge-diffraction *New exact and asymptotic solutions in the strip diffraction problems, including scattering at an open resonator Table of Contents 1. Diffraction of Electromagnetic Waves at Black Bodies: Generalization of Kirchhoff-Kottler Theory 1.1 Black Bodies 1.2 Vector Analog of Helmholtz Theorems 1.3 Definition of the Black Body and the Shadow Contour Theorem 1.4 Complementary Principle for Thin Black Screens 1.5 Total Scattering Cross Section for Black Bodies 1.6 Black Half-Plane 1.7 Black Strip and Black Disk 1.8 Physical Model of a Black Body 1.9 Observation by M. L. Levin 1.10 Fundamental Properties of Scattering from Black Bodies 2. Edge Diffraction at Convex Perfectly Conducting Bodies: Elements of the Physical Theory of Diffraction 2.1 Uniform and Nonuniform Currents 2.2 Edge Waves Scattered by a Wedge 2.3 Diffraction at a Circumferential Edge 2.4 Cones 2.5 Paraboloids of Revolution 2.6 Spherical Surfaces 2.7 Additional Comments 3. Edge Diffraction at Concave Surfaces: Extension of the Physical Theory of Diffraction 3.1 Field Inside a Wedge-Shaped Horn 3.2 Diffraction at a Circumferential Edge of a Concave Surface of Revolution 3.3 Field of a Reflected Conical Wave 3.4 Radar Cross Section of a Conical Body 3.5 Numerical Calculation of Radar Cross Section 3.6 Additional Comments 4. Measurement of Radiation from Diffraction / Nonuniform Currents 4.1 Backscattering of Waves with Circular Polarization 4.2 Depolarization of Backscattering 4.3 Fundamental Results 5. Analysis of Wedge Diffraction Using the Parabolic Equation Method 5.1 Parabolic Equation 5.2 Formulation of the Problem 5.3 Solution of the Parabolic Equation 5.4 Asymptotic Expansion for w(r, ψ) 5.5 Reflection Method 5.6 Transverse Diffusion and Diffraction of Cylindrical Waves at a Wedge 5.7 Additional Comments 6. Current Waves on Thin Conductors and Strips 6.1 Excitation of an Infinite Conductor by a Point Source 6.2 Transmitting Dipole 6.3 Excitation of a Semi-Infinite Conductor by a Plane Wave 6.4 Passive Dipole 6.5 The Near Field 6.6 Waves of Current on a Strip 6.7 Fundamental Results 6.8 Additional References 7. Radiation of Edge Waves: Theory Based on the Reciprocity Theorem 7.1 Calculation of the Far Field 7.2 Radiation from a Transmitting Dipole 7.3 First and Second-Order Diffraction at a Passive Dipole 7.4 Multiple Diffraction of Edge Waves 7.5 Total Scattered Field 7.6 Short, Passive Dipole 7.7 Results of Numerical Calculations 7.8 Radiation of Edge Waves from a Strip 7.9 Conclusion 8. Functional and Integral Equations for Strip Diffraction (Neumann Boundary Problem) 8.1 Asymptotic Solutions for Strip Diffraction 8.2 Symmetry of Edge Waves 8.3 Formulation and Solution of the Functional Equations 8.4 Scattering Pattern and the Edge Wave Equation 8.5 Infinite Series for the Current and Its Properties 8.6 Convergence of Infinite Series for the Current 8.7 Integral Equation for the Current and Schwarzschild?s Solution 8.7.1 Integral Equation Resulting from the Solution of Functional Equations (8.3.10) 8.7.2 Integral Equation Resulting from Schwarzschild?s Solution 8.7.3 Equivalency of Kernels K(x,z) and Κ(x,z) 8.8 Transformation of Equation (8.5.2) into Equation (8.5.10) 9. Asymptotic Representation for the Current Density on a Strip 9.1 Lemmas on Asymptotic Series for Multiple Integrals 9.2 Asymptotic Series for χn 9.3 Estimates of ?q (m)(q,α), ?(kz,1), and ??m(kz) 9.4 Asymptotic Representation for χn 9.5 First-Order Approximation for the Current 9.6 Nth Order Approximation for the Current 9.6.1 Derivation of an Approximate Formula 9.6.2 Verification of the Edge Conditions 9.6.3 Estimate of the Error 10. Asymptotic Representation for the Scattering Pattern 10.1 Exact Expressions for the Scattering Pattern and Some Properties of ξn(α,α0) 10.2 Asymptotic Representations for ξn(α,α0) 10.2.1 Asymptotic Series for ξn(α,α0) 10.2.2 Estimate of Un,2(α,α0) 10.2.3 Asymptotic Representation for ?m+n(α,α0) 10.3 First-Order Approximation for the Scattering Pattern 10.4 Nth-Order Approximation for the Scattering Pattern 10.4.1 Derivation of an Approximate Formula 10.4.2 Verification of the Boundary Conditions 10.4.3 Estimate of the Error 10.4.4 Total Scattering Cross Section 10.5 Relationship Between Approximations for the Current and the Scattering Pattern 10.6 Additional Comments 11. Plane Wave Diffraction at a Strip Oriented in the Direction of Polarization (Dirichlet Boundary Problem) 11.1 Formulation and Solution of the Functional Equations 11.2 Scattering Pattern and the Edge Wave Equation 11.3 Infinite Series and the Integral Equation for the Current 11.3.1 Series of Functions ξn(z, α0) and Some of Their Properties 11.3.2 Integral Equation for the Current 11.4 Asymptotic Representation for ξn(z,α) 11.5 First-Order Approximation for the Current 11.6 Nth-Order Approximation for the Current 11.7 Scattering Pattern Represented by a Series of Functions ψn(α,α0) 11.8 Asymptotic Representation for ψn(α,α0) 11.9 First-Order Approximation for the Scattering Pattern 11.10 Nth-Order Approximation for the Scattering Pattern 11.11 Relationship Between the Approximations for the Current and the Scattering Pattern 11.12 Fundamental Results of the Mathematical Theory of Edge Diffraction 12. Edge Diffraction at Open-Ended Parallel Plate Resonator 12.1 Derivation of the Fundamental Functional Equations 12.2 Formulation and Solution of the Functional Equations for Edge Waves 12.3 Rigorous Expressions for the Diffracted Field in the Far Zone and Interior to the Resonator 12.4 Physical Interpretation and Asymptotic Expressions for Φn(w,u) 12.5 Approximate Expressions for the Scattering Pattern and Amplitude of Edge Waves 12.6 Resonant Part of the Field Inside the Resonator 12.7 Radiation and Scattering from an Open Resonator 12.8 Results of Numerical Calculations 12.9 Fundamental Results 12.10 Additional Comments Conclusions References Appendix: Relationships Between the Gaussian System (GS) and the System International (SI) for Electromagnetic Units Index