Uniform Asymptotic Theory of Diffraction by a Plane Screen
01 Jul 1968-Siam Journal on Applied Mathematics (Society for Industrial and Applied Mathematics)-Vol. 16, Iss: 4, pp 783-807
About: This article is published in Siam Journal on Applied Mathematics.The article was published on 1968-07-01. It has received 181 citations till now. The article focuses on the topics: Asymptotic analysis & Asymptotic curve.
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01 Nov 1974
TL;DR: In this article, a compact dyadic diffraction coefficient for electromagnetic waves obliquely incident on a curved edse formed by perfectly conducting curved plane surfaces is obtained, which is based on Keller's method of the canonical problem, which in this case is the perfectly conducting wedge illuminated by cylindrical, conical, and spherical waves.
Abstract: A compact dyadic diffraction coefficient for electromagnetic waves obliquely incident on a curved edse formed by perfectly conducting curved ot plane surfaces is obtained. This diffraction coefficient remains valid in the transition regions adjacent to shadow and reflection boundaries, where the diffraction coefficients of Keller's original theory fail. Our method is based on Keller's method of the canonical problem, which in this case is the perfectly conducting wedge illuminated by plane, cylindrical, conical, and spherical waves. When the proper ray-fixed coordinate system is introduced, the dyadic diffraction coefficient for the wedge is found to be the sum of only two dyads, and it is shown that this is also true for the dyadic diffraction coefficients of higher order edges. One dyad contains the acoustic soft diffraction coefficient; the other dyad contains the acoustic hard diffraction coefficient. The expressions for the acoustic wedge diffraction coefficients contain Fresenel integrals, which ensure that the total field is continuous at shadow and reflection boundaries. The diffraction coefficients have the same form for the different types of edge illumination; only the arguments of the Fresnel integrals are different. Since diffraction is a local phenomenon, and locally the curved edge structure is wedge shaped, this result is readily extended to the curved wedge. It is interesting that even though the polarizations and the wavefront curvatures of the incident, reflected, and diffracted waves are markedly different, the total field calculated from this high-frequency solution for the curved wedge is continuous at shadow and reflection boundaries.
2,582 citations
TL;DR: In this paper, the authors discuss the morphologies of caustics and their diffraction patterns in catastrophe optics, and discuss the diffraction catastrophes that both clothe and underlie caustic structures.
Abstract: Publisher Summary This chapter discusses the morphologies of caustics and their diffraction patterns. In catastrophe optics, wave motion is viewed in terms of the contrast and interplay among the morphologies of three extreme regimes. Firstly, if the wavelength λ is small in comparison with scales of variation of diffracting objects or refracting media, the wavefield is dominated by the caustics and associated diffraction patterns. Secondly, when waves propagate in environments which can be modeled by a hierarchy of scales extending to the infinitely small, caustics cannot occur and the limit λ → 0 is not geometrical optics. And thirdly, when waves are explored on the scale of λ, the principal features are wavefronts, which are dominated by their singularities in the form of lines in space. The chapter also discusses the diffraction catastrophes that both clothe and underlie caustics. Each structurally stable caustic has its characteristic diffraction pattern, whose wave function has an integral representation in terms of the standard polynomial describing the corresponding catastrophe. The diffraction catastrophes constitute a new hierarchy of functions, different from the special functions of analysis. The newest application of catastrophe optics is to random short waves, whose statistical properties are determined by the random caustic structure.
509 citations
TL;DR: The basic concepts of rays, ray tracing algorithms, and radio propagation modeling using ray tracing methods are reviewed to envision propagation modeling in the near future as an intelligent, accurate, and real-time system in which ray tracing plays an important role.
Abstract: This paper reviews the basic concepts of rays, ray tracing algorithms, and radio propagation modeling using ray tracing methods We focus on the fundamental concepts and the development of practical ray tracing algorithms The most recent progress and a future perspective of ray tracing are also discussed We envision propagation modeling in the near future as an intelligent, accurate, and real-time system in which ray tracing plays an important role This review is especially useful for experts who are developing new ray tracing algorithms to enhance modeling accuracy and improve computational speed
375 citations
TL;DR: In this paper, the diffracted field according to Keller's geometrical theory of diffraction (GTD) can be expressed in a particularly simple form by making use of rotations of the incident and reflected fields about the edge.
Abstract: Diffraction of an arbitrary electromagnetic optical field by a conducting curved wedge is considered. The diffracted field according to Keller's geometrical theory of diffraction (GTD) can be expressed in a particularly simple form by making use of rotations of the incident and reflected fields about the edge. In this manner only a single scalar diffraction coefficient is involved. Near to shadow boundaries where the GTD solution is not valid, a uniform theory based on the Ansatz of Lewis, Boersma, and Ahluwalia is described. The dominant terms, to the order of k^{-1/2} included, are used to compute the field exactly on the shadow boundaries. In contrast with the uniform theory of Kouyoumjian and Pathak, some extra terms occur: one depends on the edge curvature and wedge angle; another on the angular rate of change of the incident or reflected field at the point of observation.
206 citations
TL;DR: In this article, a generalized diffraction synthesis technique for single and dual-reflector antennas fed by either a single feed or an array feed is presented, which combines optimization procedures and diffraction analysis such as physical optics (PO) and physical theory of diffraction (PTD).
Abstract: Stringent requirements on reflector antenna performances in modern applications such as direct broadcast satellite (DBS) communications, radar systems, and radio astronomy have demanded the development of sophisticated synthesis techniques. Presented in the paper is a generalized diffraction synthesis technique for single- and dual-reflector antennas fed by either a single feed or an array feed. High versatility and accuracy are achieved by combining optimization procedures and diffraction analysis such as physical optics (PO) and physical theory of diffraction (PTD). With this technique, one may simultaneously shape the reflector surfaces and adjust the positions, orientations, and excitations of an arbitrarily configured array feed to produce the specified radiation characteristics such as high directivity, contoured patterns, and low sidelobe levels, etc. The shaped reflectors are represented by a set of orthogonal global expansion functions (the Jacobi-Fourier expansion), and are characterized by smooth surfaces, well-defined (superquadric) circumferences, and continuous surface derivatives. The sample applications of contoured beam antenna designs and reflector surface distortion compensation are given to illustrate the effectiveness of this diffraction synthesis technique. >
181 citations
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158 citations
TL;DR: In this paper, a uniform asymptotic theory of diffraction was proposed, which is uniformly valid near edges and shadow boundaries, but not at any caustics other than the edge.
Abstract: Geometrical optics fails to account for the phenomenon of diffraction, i.e., the existence of nonzero fields in the geometrical shadow. Keller's geometrical theory of diffraction accounts for this phenomenon by providing correction terms to the geometrical optics field, in the form of a high‐frequency asymptotic expansion. In problems involving screens with apertures, this asymptotic expansion fails at the edge of the screen and on shadow boundaries where the expansion has singularities. The uniform asymptotic theory presented here provides a new asymptotic solution of the diffraction problem which is uniformly valid near edges and shadow boundaries. Away from these regions the solution reduces to that of Keller's theory. However, singularities at any caustics other than the edge are not corrected.
112 citations
TL;DR: In this paper, a method for obtaining a uniform representation of the diffracted field produced when a scalar wave is incident upon a plane screen with a curved edge is presented, where the first term in this representation is continuous at the edge and on the shadow boundaries.
Abstract: A new result in the geometrical theory of diffraction is presented. It is a method for obtaining a uniform representation of the diffracted field produced when a scalar wave is incident upon a plane screen with a curved edge. The representation is a series expansion associated with the diffracted rays, as in the usual geometrical theory of diffraction. However the first term in this representation is continuous at the edge and on the shadow boundaries. For a normally incident plane wave it is shown that all terms in the ray expansion can be computed and are continuous at the edge and on the shadow boundary. For a nonnormally incident plane wave and for a spherical wave only the first terms of the diffracted field are computed. The results are shown to agree with known results where both are applicable. The applicability of the method to other problems is discussed.
13 citations