A uniform geometrical theory of diffraction for an edge in a perfectly conducting surface
01 Nov 1974-Vol. 62, Iss: 11, pp 1448-1461
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.
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01 Dec 2005
TL;DR: The principal computational approaches for Maxwell's equations included the high-frequency asymptotic methods of Keller (1962) as well as Kouyoumjian and Pathak (1974) and the integral equation techniques of Harrington (1968) .
Abstract: Prior to abour 1990, the modeling of electromagnetic engineering systems was primarily implemented using solution techniques for the sinusoidal steady-state Maxwell's equations. Before about 1960, the principal approaches in this area involved closed-form and infinite-series analytical solutions, with numerical results from these analyses obtained using mechanical calculators. After 1960, the increasing availability of programmable electronic digital computers permitted such frequency-domain approaches to rise markedly in sophistication. Researchers were able to take advantage of the capabilities afforded by powerful new high-level programming languages such as Fortran, rapid random-access storage of large arrags of numbers, and computational speeds that were orders of magnitude faster than possible with mechanical calculators. In this period, the principal computational approaches for Maxwell's equations included the high-frequency asymptotic methods of Keller (1962) as well as Kouyoumjian and Pathak (1974) and the integral equation techniques of Harrington (1968) .
941 citations
TL;DR: In this paper, the concept of soft and hard surfaces is treated in detail, considering different geometries, and it is shown that both the hard and soft boundaries have the advantage of a polarizationindependent reflection coefficient for geometrical optics ray fields, so that a circularly polarized wave is circularly polarization in the same sense after reflection.
Abstract: A transversely corrugated surface as used in corrugated horn antennas represents a soft boundary. A hard boundary is made by using longitudinal corrugations filled with dielectric material. The concept of soft and hard surfaces is treated in detail, considering different geometries. It is shown that both the hard and soft boundaries have the advantage of a polarization-independent reflection coefficient for geometrical optics ray fields, so that a circularly polarized wave is circularly polarized in the same sense after reflection. The hard boundary can be used to obtain strong radiation fields along a surface for any polarization, whereas the soft boundary makes the fields radiated along the surface zero. >
677 citations
TL;DR: Time delay comparison shows that the amplitudes of many significant multipath components are accurately predicted by this model, and the effective building material properties are derived for two dissimilar buildings based upon comparison of measured and predicted power delay profiles.
Abstract: The paper describes a geometrical optics based model to predict propagation within buildings for personal communication system (PCS) design. A ray tracing model for predicting propagation based on a building blueprint representation is presented for a transmitter and receiver located on the same floor inside a building. Measured and predicted propagation data are presented as power delay profiles that contain the amplitude and arrival time of individual multipath components. Measured and predicted power delay profiles are compared on a location-by-location basis to provide both a qualitative and a quantitative measure of the model accuracy. The concept of effective building material properties is developed, and the effective building material properties are derived for two dissimilar buildings based upon comparison of measured and predicted power delay profiles. Time delay comparison shows that the amplitudes of many significant multipath components are accurately predicted by this model. Path loss between a transmitter and receiver is predicted with a standard deviation of less than 5 dB over 45 locations in two different buildings. >
610 citations
TL;DR: A comprehensive review of the propagation prediction models for terrestrial wireless communication systems is presented and the focus is placed on the application of ray-tracing techniques to the development of deterministic propagation models.
Abstract: A comprehensive review of the propagation prediction models for terrestrial wireless communication systems is presented in this paper. The classic empirical models are briefly described and the focus is placed on the application of ray-tracing techniques to the development of deterministic propagation models. Schemes to increase the computational efficiency and accuracy are discussed. Traditional statistical models are also briefly reviewed for completeness. New challenges to the propagation prediction are described and some new approaches for meeting these challenges are presented.
563 citations
Cites background from "A uniform geometrical theory of dif..."
...Methods for calculation of diffraction coefficients for metal or materials with finite conductivity were developed [88]–[91]....
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References
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TL;DR: The mathematical justification of the theory on the basis of electromagnetic theory is described, and the applicability of this theory, or a modification of it, to other branches of physics is explained.
Abstract: The geometrical theory of diffraction is an extension of geometrical optics which accounts for diffraction. It introduces diffracted rays in addition to the usual rays of geometrical optics. These rays are produced by incident rays which hit edges, corners, or vertices of boundary surfaces, or which graze such surfaces. Various laws of diffraction, analogous to the laws of reflection and refraction, are employed to characterize the diffracted rays. A modified form of Fermat’s principle, equivalent to these laws, can also be used. Diffracted wave fronts are defined, which can be found by a Huygens wavelet construction. There is an associated phase or eikonal function which satisfies the eikonal equation. In addition complex or imaginary rays are introduced. A field is associated with each ray and the total field at a point is the sum of the fields on all rays through the point. The phase of the field on a ray is proportional to the optical length of the ray from some reference point. The amplitude varies in accordance with the principle of conservation of energy in a narrow tube of rays. The initial value of the field on a diffracted ray is determined from the incident field with the aid of an appropriate diffraction coefficient. These diffraction coefficients are determined from certain canonical problems. They all vanish as the wavelength tends to zero. The theory is applied to diffraction by an aperture in a thin screen diffraction by a disk, etc., to illustrate it. Agreement is shown between the predictions of the theory and various other theoretical analyses of some of these problems. Experimental confirmation of the theory is also presented. The mathematical justification of the theory on the basis of electromagnetic theory is described. Finally, the applicability of this theory, or a modification of it, to other branches of physics is explained.
3,032 citations
768 citations
503 citations
01 Sep 1972
TL;DR: In this paper, a systematic use of matrix representation for the wavefront curvature and for its transformations simplify the handling of arbitrary pencils of rays and, consequently, the field computations.
Abstract: The principles of ray optics and, in more detail, some selected applications of ray techniques to electromagnetics are reviewed briefly. It is shown how a systematic use of matrix representation for the wavefront curvature and for its transformations simplify the handling of arbitrary pencils of rays and, consequently, the field computations. The same methods apply to complex rays which give a means of describing the effects of reflections and refractions on Gaussian beams. The relations of ray optics to other disciplines are also briefly discussed.
450 citations
TL;DR: In this paper, the geometrical theory of diffraction was introduced to account for diffraction by introducing new rays called diffracted rays, which are produced when incident rays hit the aperture edge.
Abstract: Diffraction of a wave by an aperture of any shape in a thin screen is treated by a new method—``the geometrical theory of diffraction.'' This is an extension of geometrical optics which accounts for diffraction by introducing new rays called diffracted rays. They are produced when incident rays hit the aperture edge and they satisfy the ``law of diffraction.'' A field is associated with each ray in a quantitative way, by means of the optical principles of phase variation and energy conservation. In addition ``diffraction coefficients'' are introduced to relate the field on a diffracted ray to that on the corresponding incident ray.By this method a simple formula is obtained for the field diffracted by any aperture. It yields the field in the aperture, the diffraction pattern and the transmission cross section. Explicit formulas and numerical results are given for slits and circular apertures. The accuracy of the results increases as the wavelength decreases, but they are useful for wavelengths even as lar...
389 citations