Theory of Edge Diffraction in Electromagnetics: Origination and validation of the physical theory of diffraction
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. It contains basic original ideas of the Physical Theory of Diffraction (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. The text's key topics include: Theory of diffraction at black bodies introduces the Shadow Radiation, a fundamental component of the scattered field; RCS of finite bodies of revolutioncones, 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 (socalled nonuniform) currents induced on scattering objects; development of the parabolic equation method for investigation of edgediffraction; and a new exact and asymptotic solutions in the strip diffraction problems, including scattering at an open resonator.
Inspec keywords: blackbody radiation; strips; integral equations; resonators; electromagnetic wave diffraction; conductors (electric); parabolic equations
Other keywords: black bodies; electromagnetic wave diffraction; KirchhoffKottler theory; radiation measurement; strip diffraction; edge waves radiation; openended parallel plate resonator; thin strips; wedge diffraction; reciprocity theorem; integral equations; diffraction/nonuniform currents; parabolic equation; physical theory; concave surfaces; electromagnetics origination; plane wave diffraction; thin conductors; convex perfectly conducting bodies
Subjects: Electromagnetic wave propagation; Electromagnetic waves: theory; Waveguide and microwave transmission line components; General electrical engineering topics; Conductors; Heat radiation; Function theory, analysis; Conference proceedings; Mathematical analysis; Integral equations (numerical analysis)
 Book DOI: 10.1049/SBEW054E
 Chapter DOI: 10.1049/SBEW054E
 ISBN: 9781891121661
 eISBN: 9781613531228
 Format: PDF

Front Matter
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1 Diffraction of Electromagnetic Waves at Black Bodies: Generalization of KirchhoffKottler Theory
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This chapter serves as a historical introduction to the study of edge waves. No less important, this chapter also introduces KirchhoffKottler theory, which is shown to be useful in the analysis of some actual problems. Specifically, it is interesting to determine whether it is possible to use layers of radar absorbing material to eliminate the electromagnetic field scattered by an object. If this is impossible, then to what extent can one decrease the field scattered from an ideal surface that completely absorbs all energy incident upon it? These questions lead us to the well known 'black body' problem.

2 Edge Diffraction at Convex Perfectly Conducting Bodies: Elements of the Physical Theory of Diffraction
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Beginning with this chapter, diffraction problems for perfectly conducting bodies will be investigated. These problems can be rigorously formulated using the Maxwell's equations and boundary conditions. However, their solutions in the analytic form can be found only for geometrically simple bodies, such as infinitely long cylinders, spheres, disks, etc. Besides, these solutions can be effectively used for numerical calculations only then when the dimensions of the scattering objects are smaller than a wavelength. For large objects which are much greater than a wavelength, rigorous solutions usually lose their practical value. Numerical methods of solving boundary value problems for large complex objects are also ineffective. That is why significant attention in diffraction theory is given to approximate methods that can analyze scattering from large complex objects at high frequencies. In this chapter and in Chapters 3, 4, and 7, we present some elements of the Physical Theory of Diffraction (PTD) in its original form. This theory can be considered as a natural extension of the physical optics.

3 Edge Diffraction at Concave Surfaces: Extension of the Physical Theory of Diffraction
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This chapter will study edge waves scattered from an edge of a concave body. To do this, 3.1 will examine the plane wave excitation of a wedgeshaped horn. The main objective here is to determine the field radiated by the nonuniform/fringe current. The results of this section are used in subsequent sections to calculate the radar cross section of a concave bodies of revolution.

4 Measurement of Radiation from Diffraction / Nonuniform Currents
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Chapters 2 and 3 theoretically researched the field radiated by the nonuniform part of the current. This chapter presents a method of measuring this field and examine the depolarization phenomenon of the reflected field. The method of measuring the field radiated by the nonuniform current was first proposed for bodies of revolution in an article by E. N. Maizel's and the author. Subsequently, it is shown that this method is universal in nature and is suitable for any metallic object.

5 Analysis of Wedge Diffraction Using the Parabolic Equation Method
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The results of this chapter show the numerical solutions of parabolic equations allowing one to obtain asymptotic solutions to problems on diffraction from bodies with edges.

6 Current Waves on Thin Conductors and Strips
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This chapter utilizes the parabolic equation method to analyze the diffraction from a thin cylindrical conductor (dipole) and a strip. The possibility of solving this problem was previously mentioned. The theory of dipoles is widely examined in the professional literature. The general physical properties of current waves on dipoles were studied in previous works. This chapter shows that the results obtained in previous works can be derived more simply by using the parabolic equation. In addition, these results include near field calculations, and in the limit as a → ∞ (a is the radius of the dipole), also describe the current waves on a strip.

7 Radiation of Edge Waves: Theory Based on the Reciprocity Theorem
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This chapter constructs an approximate theory of the radiation of higherorder edge waves. This theory is based on the reciprocity theorem and provides a straightforward representation of the scattered field. It was used to calculate the scattering pattern for thin cylindrical conductors (dipoles) and strips. The expressions obtained are valid for arbitrary directions of observation and illumination, satisfy the reciprocity theorem, and permit calculations to be made with satisfactory accuracy, provided kl ≫ 1.

8 Functional and Integral Equations for Strip Diffraction (Neumann Boundary Problem)
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The previous chapters approximated higherorder edge waves. Now, using strips as an example, this chapter will study the properties of these waves in more detail. There are several reasons that prompt us to investigate these problems. Presently, there is significant interest in studying the exact structure of weak signals reflected from various objects. Clearly, their physical nature is related to higherorder edge waves. Besides, diffraction not only from isolated scatterers but also from groups of bodies, is of important practical interest. Referring to duality theory, diffraction from a strip is equivalent to a slot formed by two halfplanes and is a special case of diffraction from two bodies. It is evident that the diffraction interaction of two halfplanes is also caused by edge waves. Understanding strip diffraction is useful for studying these issues.

9 Asymptotic Representation for the Current Density on a Strip
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The preceding chapter showed that the solution to the problem of a strip are multiple integrals of a special type. This chapter studies the asymptotic properties of these integrals as kl → ∞ and develops approximate expressions for the current.

10 Asymptotic Representation for the Scattering Pattern
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The pattern of the scattered field in the far zone, in principle, can be determined by applying a Fourier transform to the asymptotic representations for the current. However, this chapter shows one should not do this since the expressions obtained using this approach do not satisfy the reciprocity theorem. Because of this, an asymptotic relationship was sought for the field in the far zone, proceeding from the exact solutions and functional equations derived from the previous chapter.

11 Plane Wave Diffraction at a Strip Oriented in the Direction of Polarization (Dirichlet Boundary Problem)
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Previously, Chapters 810 examined the asymptotic solution to the Neumann boundary problem. This chapter will present an analogous but abbreviated examination of the Dirichlet boundary problem.

12 Edge Diffraction at OpenEnded Parallel Plate Resonator
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This chapter will examine edge waves excited by a plane wave incident upon a parallel plate waveguide of a finite size. The principal characteristic of this structure is that it exhibits resonant properties, i.e., the ability at some frequencies to store strong electromagnetic fields. The parallel plate waveguide is a simple case of an open resonator, which is utilized in quasioptical generators. The characteristic frequencies of such a resonator were first researched by Fox and Li. These authors used Huygen's principle to formulate an integral equation and numerically determine some of its characteristic functions and characteristic numbers. Subsequently, Vainshtein used physical considerations to conduct an analytical investigation of the characteristic oscillations of a two dimensional planar resonator. Note also that singlemode parallel plate resonators with geometrical parameters kb < 3π/2 and kl >> 1 were considered by Jones and Williams. Here, 2b is the distance between the plates and 2l is their width. The solution of the problem for the case kb << 1, kl ∧<<1 was given by Pimenov.

Appendix 1: Relationships Between the Gaussian System (GS) and the System International (SI) for Electromagnetic Units
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The Gaussian system is widely used in theoretical physics. It is often called the absolute symmetrical system. This system is based on three fundamental units: centimeter (cm), gram (g), and second (s). The units for all electromagnetic quantities are derivatives from these fundamental units and they are established using physical relationships between them. Many Gaussian units are not named. The tables presented below show the relationships between the Gaussian System (GS) of units and the International System (SI) of units, which is based on the units of meter (m), kilogram (kg), second (s), and ampere (A).

Appendix 2: The Key Equivalence Theorem
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Appendix 2 discusses the key equivalence theorem.

Back Matter
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