# Slope diffraction and its application to horns

Abstract: The first order geometrical theory of diffraction (GTD) predicts vanishing fields along the surface of a conducting wedge for the incident electric field polarized parallel to the diffracting edge The slope diffraction coefficient is a valid correction term for incidence angles removed from the shadow boundary A new slope diffraction function for the half plane is presented along with applications This new form of slope diffraction coefficient for the half plane is valid through the shadow region Reciprocity is invoked to find the far-fields for a source on the surface of the conducting wedge In addition to applying the two-dimensional slope diffraction analysis to practical problems, the equivalent current concepts have been extended to include equivalent slope currents for the analysis of either finite or curved edges This new form of the slope diffraction function has been successfully used to provide an H -plane horn pattern analysis that is considerably less tedious than previously possible with GTD Both pure GTD solutions and hybrid solutions using conventional aperture integration for the main beam region and GTD for the far-out side and back lobes are compared with experimental results

Topics:Â DiffractionÂ (58%), Fresnel diffractionÂ (57%), Uniform theory of diffractionÂ (57%)

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Abstract: The uniform geometrical theory of diffraction (GTD) is employed for calculating the edge diffracted fields from the finite ground plane of a microstrip antenna. The source field from the radiating patch is calculated by two different methods: the slot theory and the modal expansion theory. Many numerical and measured results are presented to demonstrate the accuracy of the calculations and the finite ground plane edge effect.

254Â citations

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Abstract: New expressions are derived for the fringe current components of the equivalent edge currents. They are obtained by asymptotic endpoint evaluation of the fringe current radiation integral over the "ray coordinate" measured along the diffracted ray grazing the surface of the local wedge. The resulting expressions, unlike the previous ones, are finite for all aspects of illumination and observation, except for the special case where the direction of observation is the continuation of a glancing incident ray propagating "inwards" with respect to the wedge surface (the Ufimtsev singularity).

178Â citations

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01 Jan 1992

Abstract: A summary of various high-frequency techniques is presented for analyzing the electromagnetic radiation from antennas in the presence of their host environment. These techniques provide physical insight into antenna radiation mechanisms and are found to be highly efficient and accurate for treating a variety of practical antenna configurations. Examples to which these techniques have been applied include open-ended waveguide antennas, horn and reflector antennas, and antennas on aircraft and spacecraft. The accuracy of these techniques is established via numerical results which are compared with those based on other independent methods or with measurements. These high frequency methods can be combined with other techniques, through a hybrid scheme, to solve an even greater class of problems than those which can be solved in an efficient and tractable manner by any one technique alone. >

127Â citations

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Abstract: The equivalent current concept is used to compute the scattering patterns of flat plate structures. It is also used to obtain the broadside scattering lobe for any incidence plane. The essential feature introduced in this paper is that only the components of the equivalent current perpendicular to the incidence plane are used. No special treatment of the singularity in the plane wave diffraction coefficient (which is the basis of the equivalent current concept) is required. Instead, this choice of equivalent current components is such that the singularity at one edge segment is canceled by the singularity at the opposite edge segment. For modern day computers there is sufficient accuracy that the main scattering lobe can be obtained in the limit as one approaches broadside. The same results can be obtained for plate structures made of straight edges by using a new corner diffraction analysis. For certain cases where the observation angle is sufficiently removed from normal incidence to an edge, the corner diffraction analysis appears to yield more accurate results.

107Â citations

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01 Jan 1995Abstract: This dissertation treats the potentials and limitations of wireless LANs intended for the support of services as envisioned for Broadband ISDN. The treatment is based on the assumption that the transmission takes place via millimetre"wave indoor radio channels. A method is discussed for the measurement of the wideband characteristics of millimetre-wave indoor radio channels. Measurements results obtained with this method are presented. These results are used for the development of a statistical model of the millimetre-wave indoor radio channel. In addition, a deterministic channel model is developed based on Geometrical Optics. A discussion concerning the applicability, limitations and accuracy of such a model is included. Results of simulations ba.~ed on the deterministic model developed are presented. These results give an indication of the influence of the environment and antenna radiation patterns on the channel characteristics. Using the measurement results, the maximum feasible bit rate is evaluated for millimetre-wave indoor radio transmission assuming QPSK modulation. In addition, the improvement by channel equalization is examined. The evaluation includes the influence of noise, number of equalizer taps, antenna diversity and antenna directivity pattern. It is shown in which way efficient, reliable and flexible information transfer can be achieved in broadband wireless LANs on the basis of the Asynchronous Transfer Mode. In this context a contention-free multi-access protocol is proposed.

82Â citations

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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 Fermatâ€™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.

2,881Â citations

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01 Jan 1961Abstract: Introduction to Antennas.Fundamentals of Antennas.Arrays of Discrete Elements.Dipoles and Monopoles.Loop Antennas.Small Antennas.Microstrip Antennas.Slot Antennas.Slot-Antenna Arrays.Leaky-Wave Antennas.Long-Wire Antennas.Surface-Wave Antennas and Surface-Wave Excited Arrays.Helical Antennas.Frequency-Independent Antennas.Horn Antennas.Lens Antennas.Reflector Antennas.Feeds for Lenses and Reflectors.Electromechanical Scanning Antennas.Frequency-Scan Antennas.Phased Arrays.Conformal and Low-Profile Arrays.Adaptive Antennas.Methods of Polarization Synthesis.Low-Frequency Antennas.Medium-Frequency Broadcast Antennas.High-Frequency Antennas.VHF and UHF Communications Antennas.TV and FM Transmitting Antennas.TV Receiving Antennas.Microwave-Relay Antennas, Radiometer Antennas.Radar Antennas.Microwave Beacon Antennas.Tracking Antennas.Satellite Antennas.Earth Station Antennas.Aircraft Antennas.Seeker Antennas.Direction-Finding Antennas and Systems.ECM and ESM Antennas.Radio-Telescope Antennas.Transmission Lines and Waveguide.Impedance Matching and Broadbanding.Radomes.Microwave Propagation.Antenna Measurements.Materials and Design Data.

1,760Â citations

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Abstract: The fields diffracted by a body made up of finite axially symmetric cone frustums are obtained using the concepts of the geometrical theory of diffraction. The backscattered field for plane-wave incidence on such a target is obtained with particular emphasis on those regions that are usually avoided, namely, the caustic region and its immediate vicinity. The method makes use of equivalent electric and magnetic current sources which are incorporated in the geometrical theory of diffraction. This solution is such that it is readily incorporated in a general computer program, rather than requiring that a new program be written for each shape. Several results, such as the cone, the cylinder and the conically capped cylinder, are given. In addition, the method is readily applied to antenna problems. An example which is reported consists of the radiation by a stub over a circular ground plane. This present theory yields quite good agreement with experimental results reported by Lopez, whereas the original theory given by Lopez is in error by as much as 10 dB.

190Â citations

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01 Aug 1965

Abstract: A review is given of a wide variety of asymptotic methods used in high-frequency scattering. Following brief descriptions of the saddle point method, Watson transformation, and residue series, a survey of the literature is made in which these methods have been employed. The desirability of using high-frequency approximate methods is pointed out. A critical discussion of geometrical optics, physical optics, and the geometrical theory of diffraction is presented. The relationship of these methods to the asymptotic solution of Maxwell's equations is examined. Their applicability and limitations are discussed by referring to numerous examples in the literature.

174Â citations

### "Slope diffraction and its applicati..." refers background in this paper

...This particular field [ 13 ] is readily cast int.0 t,he solution for the E-plane fields of the pyramida.1 horn by multiplying by t.he factor [pE/ ( PE + T) Ill2 to account for the divergence of the rays in the yz plane....

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Abstract: Edge diffraction theory is used in analyzing the radiation characteristics of typical horn antennas. The far-sidelobe and backlobe radiation has been solved without employing field equivalence principles which are impractical in the problem. A corner reflector with a magnetic line source located at the vertex is proposed as a model for the principal E -plane radiation of horn antennas. A complete pattern, including multiple interactions and images of induced line sources, is obtained in infinite series form. Diffraction mechanisms are used for appropriate approximations in the computations. The computed patterns are in excellent agreement with measured patterns of typical horn antennas. Radiation intensity of the backlobe relative to mainlobe intensity is obtained as a back-to-front ratio and plotted as a function of antenna dimensions.

71Â citations