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.

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.

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.

The previous chapters approximated higher-order 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 higher-order 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 half-planes and is a special case of diffraction from two bodies. It is evident that the diffraction interaction of two half-planes is also caused by edge waves. Understanding strip diffraction is useful for studying these issues.

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.

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 single-mode 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 2 discusses the key equivalence theorem.