Diffraction of the creeping waves generated on a perfectly conducting spherical scatterer by a ring source
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To analyze the diffraction of high frequency waves one turns often to the geometrical theory of diffraction (GTD) whose aim is to describe this phenomenon in terms of certain factors. These factors involve, among the others, several diffraction coefficients showing the modifications to be considered when a ray is transformed into another one at a diffraction point. The aim of this paper is to analyze the diffraction of creeping waves generated on a perfectly conducting spherical reflector, and thereby to obtain explicit expressions for certain coefficients related to the diffractions occurring at the edges of spherically curved reflectors. The analysis is performed by using an integral transform technique recently developed by one of the authors. Various ray contributions are isolated, and fairly simple nonuniform expressions for the diffraction coefficients are obtained.Keywords:
Reflector (photography)
Spherical wave
The diffraction of a high-frequency scalar wave by a plane screen can be treated by Keller's geometrical theory of diffraction (GTD). The GTD solution fails however at the edge of the screen and on shadow boundaries where the solution is infinite and discontinuous. These defects are overcome by the "uniform asymptotic theory of edge diffraction" (UAT) which is an extension of GTD. Starting from a new Ansatz that involves Fresnel integrals in an appropriate manner, the uniform theory provides a high-frequency asymptotic solution of the diffraction problem that is uniformly valid near the edge and the shadow boundaries, i.e., the solution satisfies the edge condition and is finite and continuous at shadow boundaries. Away from these regions the UAT solution reduces to that of Keller's theory. So far, the uniform theory has been successfully applied to diffraction through a slit or a circular aperture in a plane screen, and to problems of reflection and diffraction at an open-ended parallel-plane waveguide. Further extensions of UAT to electromagnetic diffraction by a plane screen, and to diffraction (scalar or electromagnetic) by a curved wedge, will be discussed.
Wedge (geometry)
Geometrical optics
Aperture (computer memory)
Physical optics
Reflection
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A systematic theoretical study of approximations to the Kirchhoff diffraction integral is presented, stressing the improved behavior at large angles. This work was motivated by consideration of diffraction in dual tilted dispersive interdigital transducers for surface acoustic wave generation, but the salient features are applicable to diffraction problems in general. Previous treatments of surface acoustic wave (SAW) propagation were limited to nearly forward directions perpendicular to transducer fingers, where the simple Fresnel diffraction theory was adopted. Improvement of the theory for nonforward angles is obtained in which both the Fraunhofer and Fresnel diffractions are correctly included. The conventional diffraction treatment used in optics (as in the textbook by Born and Wolf) is found inaccurate and a new form is presented.
Kirchhoff's diffraction formula
Fresnel zone
Fresnel number
Fresnel integral
Fresnel equations
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The far-field asymptotic solution for the diffraction of an electromagnetic plane wave by a cylinder-tipped half-plane is derived from the exact solution. It is demonstrated that the Fresnel diffraction plays an important role in the transition regions where the solution of the geometrical theory of diffraction fails. The asymptotic solution not only simplifies the numerical calculations but also gives a physical model of the exact solution.
Fresnel number
Fresnel integral
Fresnel equations
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Based on the Huygens-Fresnel principle,the square hole Fraunhofer diffraction is simulated numerically.The theory of diffraction is verified,the diffraction patterns of non-axis space and small square hole are also obtained.This can expand the concepts of diffraction and provide a reference for better undersatnding of diffraction.
Square (algebra)
Kirchhoff's diffraction formula
Huygens–Fresnel principle
Fresnel number
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This chapter introduces the principles of diffraction, and describes a number of models used in propagation calculations for spectrum management and planning radio systems. Chapter Contents: 9.1 Introduction 9.2 Classification of diffraction methods 9.3 Knife-edge Fresnel diffraction 9.3.1 Knife-edge geometry 9.3.2 Knife-edge diffraction 9.3.3 Normalised knife-edge diffracted field 9.3.4 Multiple knife-edge diffraction 9.3.5 Evaluation of Fresnel integrals 9.4 Fresnel clearance 9.5 Applications of knife-edge diffraction 9.5.1 Diffraction due to terrain 9.5.2 Diffraction due to a thins creen 9.5.3 Diffraction due to a finite-width obstacle 9.6 Diffraction over curved surfaces 9.6.1 Diffraction over spherical earth 9.6.2 Cascaded cylinders terrain diffraction 9.7 Diffraction over a general terrain path 9.7.1 Issues with irregular terrain models 9.7.2 Hybrid methods for the general path 9.7.3 The 'delta' method 9.8 Ray-based diffraction methods 9.8.1 GTD/UTD in two dimensions 9.8.2 A specific UTD formulation 9.8.3 Sample UTD results 9.8.4 Diffraction in three dimensions 9.8.5 Ray-tracing methods 9.9 Boersma coefficients References Inspec keywords: electromagnetic wave diffraction; telecommunication network planning; radiowave propagation; telecommunication network management Other keywords: radio planning systems; propagation calculations; spectrum management Subjects: Radio links and equipment; Communication network design, planning and routing; Radiowave propagation
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Spherical wave
Geometrical optics
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The diffraction phenomenon of the straight edge was explained by means of the Modified Theory Physics Optics Method (MTPO). And the diffraction intensity of the straight edge versus the diffraction angle was obtained by means of the numerical method. Compared the results of MTPO with the Fresnel Diffraction Method,it shows that both of them agree well with the exact method of the straight edge in a wide diffraction angle. But the MTPO has more precision than the Fresenel Diffraction Method in the geometrical direction.
Fresnel number
Physical optics
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A diffraction coefficient is being proposed for plane-wave scattering by a straight edge in both planar and curved screens which is valid uniformly for all aspect angles. This new form of diffraction coefficient is obtained via Uniform Asymptotic Theory of Diffraction (UAT), where the arguments of the Fresnel integrals of the traditional Uniform Theory of Diffraction (UTD) coefficients are redefined by the Phase Detours (PDs) of the UAT formulations. The proposed coefficient is supported with the monostatic RCS predictions of flat plate and curved plate for soft polarization case. These predictions are compared with existing diffraction coefficients, full-wave simulation and with the available experimental results. This new diffraction coefficient shows superior nature over the existing coefficients when applied to the curved plate problem.
Reflection coefficient
Physical optics
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Abstract This article presents a review of diffraction algorithms based on the uniform theory of diffraction for multiple building transition zone diffractions and proposes an improved uniform theory of diffraction model for fast and more accurate field prediction for multiple diffractions. The proposed method is based on the improved version of the slope uniform theory of diffraction and Fresnel zone concept, called the slope uniform theory of diffraction with convex hull. This article also provides a comparison for uniform theory of diffraction based algorithms and discusses the results for computation time and accuracy. Furthermore, the slope uniform theory of diffraction and the slope uniform theory of diffraction with convex hull methods are compared with a physical optics solution based on numerical computation of the Kirchhoff-Huygens integrals. Results of extensive simulations are presented and discussed for the development of fast and accurate radio network planning tools. Keywords: electromagnetic wave propagationuniform theory of diffractionslope diffractionFresnel zonesconvex hull Acknowledgment This work is partially supported by TUBITAK (The Scientific and Technological Research Council of Turkey) under Grant No. 105E083.
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We investigate the limitations on the use of the uniform theory of diffraction (UTD) slope-diffraction method for propagation past knife edges. The settled field that is diffracted past rows of buildings, as computed by numerical integration, has the characteristics of amplitude and phase variation with a scale length that is large compared to the wavelength and has small amplitude near the edges. Using this field, it is shown that the error in the UTD slope-diffraction method for diffraction past a final screen is connected with the Fresnel width, as compared to the scale length of the settled field.
Fresnel zone
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