# Showing papers in "IEEE Transactions on Antennas and Propagation in 1966"

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Abstract: Maxwell's equations are replaced by a set of finite difference equations. It is shown that if one chooses the field points appropriately, the set of finite difference equations is applicable for a boundary condition involving perfectly conducting surfaces. An example is given of the scattering of an electromagnetic pulse by a perfectly conducting cylinder.

14,070 citations

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TL;DR: In this article, the results of measurements at X -band of backscattering from water waves of amplitude less than about 001 wavelength and with wavelengths of the order of the microwave length are presented and compared with theory.

Abstract: The results of measurements at X -band of backscattering from water waves of amplitude less than about 001 wavelength and with wavelengths of the order of the microwave length are presented and compared with theory The measurements have been made for both vertical and horizontal polarizations for grazing angles between 4\deg and 80\deg The results both as to angular dependence and absolute magnitude are in agreement with the theory The ratio of vertical to horizontal backscattering cross section calculated from the theory is compared with that measured on the open sea

275 citations

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TL;DR: In this article, a simplified solution to the problem of multiple diffraction of microwaves over knife-edge obstacles is discussed, where the path loss is obtained directly and quickly by alignment of distances and heights, adequately selected from a path profile.

Abstract: The paper discusses a simplified solution to the problem of multiple diffraction of microwaves over knife-edge obstacles. The path loss is obtained directly and quickly by alignment of distances and heights, adequately selected from a path profile. A theoretical study shows good agreement between the simplified approach and a complete mathematical analysis made by G. Millington in 1962. When the diffraction loss reaches a maximum which might be in excess of 50 dB, the approximate value exceeds the theoretical one by 2 to 5 dB. Predictions are in good agreement, too, with the results of experiments conducted both in France and in the United States. Out of ten examples reported in the paper, nine indicate an error equal or smaller than 3 dB.

264 citations

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TL;DR: In this paper, the theory and equations for the scattering pattern of a dielectric cylinder of infinite length and arbitrary cross-section shape were developed for scattering patterns obtained by this method, and the results for the circular shell agree accurately with the exact classical solution.

Abstract: The theory and equations are developed for the scattering pattern of a dielectric cylinder of infinite length and arbitrary cross-section shape. The harmonic incident wave is assumed to have its electric vector perpendicular to the axis of the cylinder, and the fields are assumed to have no variations along this axis. Although some investigators have approximated the field within the dielectric body by the incident field, a more accurate solution is obtained here by treating the field as an unknown function which is determined by solving a system of linear equations. Scattering patterns obtained by this method are presented for dielectric shells of circular and semicircular cross section, and for a thin plane dielectric slab of finite width. The results for the circular shell agree accurately with the exact classical solution. The effects of surface-wave excitation and mutual interaction among the various portions of the shell are included automatically in this solution.

237 citations

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TL;DR: In this article, an analytical description of vertical polarization cross section at the edge-on aspect derived on the basis of measurement data is presented. But the analysis is based on the geometrical theory of diffraction and does not account for polarization dependence and detailed shape of the cross section vs. angle curve in nonspecular regions.

Abstract: An investigation of the scattering from rectangular flat plates has been carried out to determine analytical formulations suitable for the estimation of radar cross section. Simple physical optics theory provides an accurate means of predicting the near-specular values of plate cross section but fails to account for polarization dependence and detailed shape of the cross section vs. angle curve in nonspecular regions. Calculations based upon the geometrical theory of diffraction show excellent agreement with measured data except at edge-on aspects. This correspondence stems, in part, from the fact that the geometrical theory of diffraction is polarization dependent. The paper is concluded with an analytical description of vertical polarization cross section at the edge-on aspect derived on the basis of measurement data.

186 citations

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TL;DR: In this article, a point-matching solution for scattering by conducting bodies of arbitrary shape is developed for the backscatter echo area of circular and square wire loops, circle and square plates, spheres, and hemispheres.

Abstract: A point-matching solution is developed for scattering by conducting bodies of arbitrary shape. Numerical results are included for the backscatter echo area of circular and square wire loops, circular and square plates, spheres, and hemispheres. The results show good agreement with experimental data. An efficient calculation procedure is achieved by using a wire-grid model instead of a continuous conducting surface. A system of linear equations is generated by enforcing the boundary conditions at the center of each wire segment of the grid, and a digital computer is employed to solve these equations for the currents on the segments. Then it is straightforward to calculate the distant scattered field and the echo area.

166 citations

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TL;DR: Symmetrical radiation feed patterns which are consequence of specified form of hybrid mode fields as disclosed by focal plane analysis are described in this article, where the authors show that the feed pattern is a consequence of the hybrid mode field.

Abstract: Symmetrical radiation feed patterns which are consequence of specified form of hybrid mode fields as disclosed by focal plane analysis

160 citations

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TL;DR: In the light of rather complete information of these arrays, a comparative study is made on some designs which are proposed by a few authors and shows that none of them are truly optimum.

Abstract: Previous works on nonuniformly spaced arrays are first critically reviewed, then an exhaustive study of a few small arrays is made. The results reveal that among a large number of possible element arrangements, only very few yield reasonably low sidelobe level. Although the majority of these few arrays are characterized by space-tapering, an overwhelming number of space-tapered arrays do not have low sidelobe level. Some statistical studies are made in order to relate the sidelobe level to the element arrangement. Finally, in the light of rather complete information of these arrays, a comparative study is made on some designs which are proposed by a few authors. The results show that none of them are truly optimum.

155 citations

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TL;DR: In this paper, the authors developed integrals from vector field theory for scattering by a perfectly conducting irregular surface at very short wavelengths and showed that the back scattering cross section is proportional to the average number of specular points which are illuminated at a given angle of incidence and the geometric mean of the principal radii of curvature at those points.

Abstract: Integral formulas are developed directly from vector field theory for scattering by a perfectly conducting irregular surface at very short wavelengths It is shown that, in the optical limit, the back-scattered field has no cross polarized component When the integrals are evaluated asymptotically by the method of stationary phase, it turns out that to a first approximation the back scattering cross section is proportional to the average number of specular points which are illuminated at a given angle of incidence and to the geometric mean of the principal radii of curvature at those points The scattering problem is, thus, transformed to a problem in the statistical geometry of irregular surfaces

134 citations

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TL;DR: In this paper, the integral equation for the current is rearranged to permit the introduction of a complex wave number k, and an approximate solution of this equation is then obtained in terms of the three trigonometric functions, \sin k(h-|z|), \cos kz-\cos kh, and \cos \frac{1}{2}k_{0}z - \cos 1 1/2k 0/h, where k 0 is the free-space wave number.

Abstract: The properties of a cylindrical antenna with a continuous ohmic resistance along its length are of interest in the design of certain types of directive broadband antennas and in the determination of the efficiency of dipole antennas. Conventionally, the contribution by ohmic resistance to the distribution of current and the impedance is contained in a particular integral that is either ignored or treated as a higher-order correction to formulas derived for perfectly conducting antennas. An alternative and more useful form has been developed in which the integral equation for the current is rearranged to permit the introduction of a complex wave number k . An approximate solution of this equation is then obtained in terms of the three trigonometric functions, \sin k(h-|z|) , \cos kz-\cos kh , and \cos \frac{1}{2}k_{0}z - \cos \frac{1}{2}k_{0}h , where k_{0} is the free-space wave number. Expressions are derived for the coefficients of these functions and for k . Explicit formulas are given for the distribution of current and the admittance.

93 citations

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TL;DR: In this article, it was shown that the only physically observable part of the volume integrals is twice that produced in the invisible region of the pattern space factor by those field components that vanish in the plane outside of the aperture.

Abstract: The volume integrals in the complex Poynting theorem are usually assumed to represent stored magnetic and electric energy. But for a planar aperture radiating into a lossless homogeneous medium it is shown that the only physically observable part of the volume integrals is twice that produced in the invisible region of the pattern space factor by those field components that vanish in the plane outside of the aperture. The inductive and capacitive reactive powers corresponding to the observable parts \langle W_{m} \rangle and \langle W_{e} \rangle , respectively, of the volume integrals are found to be given by the following integrals over the invisible region k_{y}^{2} + k_{z}^{2} > k^{2} , 2\omega\langle W_{m} \rangle = \frac{(2\pi)^{2}}{2kZ_{0}} \int \int_{k_{y}^{2}+k_{z}^{2} >k^{2}} \frac{|k_{z}F_{y}-k_{y}F_{z}|^{2}} {\sqrt{k_{y}^{2}+k_{z}^{2}-k^{2}} dk_{y}dk_{z} , 2\omega\langle W_{e} \rangle = \frac{(2\pi)^{2}}{2kZ_{0}} \int \int_{k_{y}^{2}+k_{z}^{2} >k^{2}} \frac{k^{2}}(|F_{y}|^{2}+|F_{z}|^{2})} {\sqrt{k_{y}^{2}+k_{z}^{2}-k^{2}} dk_{y}dk_{z} , for an arbitrary aperture consisting of holes in a conducting plane. They are expressed in terms of the rectangular components F_{y} and F_{z} of the pattern space factor obtained from the tangential components E_{y} and E_{z} of electric field over the holes S , F_{y}(k_{y},k_{z},k) = \frac{1}{(2\pi)^{2}} \int \int\_{s} E_{y}(0,y,z,k)e^{i (k_{y}y+k_{z}z)}dydz F_{z}(k_{y},k_{z},k) = \frac{1}{(2\pi)^{2}} \int \int\_{s} E_{z}(0,y,z,k)e^{i (k_{y}y+k_{z}z)}dydz where Z_{0} = \sqrt{\mu/\epsilon} , and k_{y} and k_{z} are two components of the vector propagation constant of magnitude k=\omega\sqrt{\mu\epsilon} . For the complementary aperture whose space factor is obtained from Z_{0} times the tangential components of magnetic field in the aperture, the formulas for inductive and capacitive reactive power simply interchange. The new formulas are used to make the first known test of the widely held assumption that the reciprocal relationship between Q and bandwidth of nonradiating systems applies also to radiating systems. By direct computation of Q and of bandwidth independently it is shown that the reciprocal relationship does hold for the test case treated (the planar dipole).

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TL;DR: In this article, it was shown that a linearly polarized horn that has the same power pattern in all planes through the axis can be made from a synthetic material for which the boundary conditions on E and H are the same.

Abstract: It is shown that a linearly polarized horn that has the same power pattern in all planes through the axis can be made from a synthetic material for which the boundary conditions on E and H are the same. An arbitrarily close approximation to this requirement can be realized by means of a grooved circular horn.

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TL;DR: In this paper, the effect of shadowing in the case of backscattering of waves from such a surface is studied in the geometric optic limit by analyzing the Gaussian noise signal in a digital computer.

Abstract: A one-dimensional random rough surface is modeled as a Gaussian noise signal. The effect of shadowing in the case of backscattering of waves from such a surface is studied in the geometric optic limit by analyzing the Gaussian noise signal in a digital computer. It is found that presently accepted theories for the shadowing effect are of doubtful validity.

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TL;DR: In this paper, the existence of exponentially increasing plane wave in a permittivity-modulated slab immersed in a medium of arbitrary constant permittivities is investigated by attempting to satisfy the condition of continuity of the fields at the interfaces.

Abstract: Plane waves in a nonconducting charge-free medium with a permittivity given by \epsilon(t) = \epsilon/(1 -2p \cos 2\Omega t) can be written as products of Mathieu functions and exponentials \exp (ikx) . The behavior of the waves, which depends on the choice of the wave number k , is deduced entirely from the properties of the Mathieu functions. In a periodically varying medium of infinite extent, one encounters exponentially increasing waves for certain bands of wave numbers. The existence of such waves in a permittivity-modulated slab immersed in a medium of arbitrary constant permittivity is investigated by attempting to satisfy the condition of continuity of the fields at the interfaces. It is found that the modulation index 2p must exceed a critical value if exponentially increasing waves are to be produced. This critical value is shown to depend on the width of the slab and on the relation of the permittivities of the slab and the surrounding medium. For the case that 2p is less than that critical value, the response of the slab to a normally incident plane wave is described. It is shown that the slab may be designed to act as a parametric oscillator, amplifier, filter, or frequency converter.

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TL;DR: In this paper, a model for the principal Eplane radiation of horn antennas was proposed and a complete pattern, including multiple interactions and images of induced line sources, was obtained in infinite series form.

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.

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TL;DR: In this paper, the problem of finding the illuminations on two planar antennas (directed toward each other) which maximize the efficiency of the power transfer between them was studied.

Abstract: This paper is concerned with the problem of finding the illuminations on two planar antennas (directed toward each other) which maximize the efficiency of the power transfer between them. The two apertures are generally different and their separation, sizes, and shapes are arbitrary (with the exception of some symmetry requirements). It is shown that the optimal phase distributions are such that the two antennas are focused on each other. The optimal amplitude distributions are equal to the field patterns of the mode with minimum diffraction loss in two confocal resonator mirrors, whose separation, sizes, and shapes are equal to those of the apertures in question. For the particular case of rectangular antennas, the optimal amplitude distributions are given by Prolate Spheroidal Wave Functions. The Power Transfer Coefficient between two equal square apertures has been calculated for optimal and uniform (focused and unfocused) illuminations. For moderate to small separations the optimal illuminations yield a very significant increase of the efficiency of the power transfer.

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TL;DR: In this article, the response of a thin, cylindrical monopole antenna to dc pulse excitation, both in transmission and reception, by use of Fourier transforms and the complex impedance and complex effective height, for pulses of space length ranging from two tenths to twice the monopole length.

Abstract: We have computed the response of a thin, cylindrical monopole antenna to dc pulse excitation, both in transmission and reception, by use of Fourier transforms and the complex impedance and complex effective height, for pulses of space length ranging from two tenths to twice the monopole length. We have also experimentally determined the reponse and have obtained similar results. We conclude from this comparison that present steady-state antenna theory together with Fourier methods will yield reliable results in calculating the response of cylindrical antennas to dc pulses. We have also made certain other measurements of response to pulses and step functions which are reported herein.

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Bell Labs

^{1}TL;DR: In this paper, the radiation impedance of an infinite array of open rectangular waveguides has been calculated by a function-theoretic method for H plane and quasi-E plane beam scanning directions.

Abstract: The radiation impedance of an infinite array of open rectangular waveguides has been calculated by a function-theoretic method for H plane and quasi- E plane beam scanning directions. The mutual coupling between columns has also been obtained. The amplitudes of the coupling coefficients decay asymptotically as r^{-3/2} while the phase difference between successive coupling coefficients approaches that to be expected from free space wave propagation. This asymptotic behavior is independent of waveguide dimensions for both planes of scan. It is similar to the asymptotic behavior of a line-source-excited wave propagating over a lossy surface. This suggests that the interface between an array and free space may in general be treated as such a surface. The coupling coefficients are used to determine the properties of an array, which has a finite number of active elements surrounded by an infinite passive array. Also, the edge effect due to the finiteness of an array is evaluated.

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TL;DR: In this paper, the scattering properties of antennas are discussed in terms of the scattering matrix, and it is shown that one retains some control over the scattering property of the antenna after the radiation pattern is specified.

Abstract: The scattering properties of antennas are discussed in terms of the scattering matrix. It is shown that one retains some control over the scattering properties of the antenna after the radiation pattern is specified and the scattering matrix can be used to optimize these scattering properties. The scattering matrix is used to design a simple antenna which absorbs more power than it scatters under conjugate-matched conditions. A loop-dipole configuration is given which corresponds to the scattering matrix.

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TL;DR: In this article, a set of radiation pattern functions, suitable for synthesis of radiation patterns from circular aperture horn antennas, is obtained by assuming an aperture distribution consisting of the fields of cylindrical waveguide modes.

Abstract: A set of radiation pattern functions, suitable for synthesis of radiation patterns from circular aperture horn antennas, is obtained by assuming an aperture distribution consisting of the fields of cylindrical waveguide modes. A technique is presented for using a linear combination of the radiation pattern functions to approximate a desired radiation pattern. Linear combinations of the radiation pattern functions resulting in maximum secondary gain, when used to illuminate a paraboloidal antenna, are obtained empirically. Using spherical wave theory, maximum performance theoretically obtainable from an antenna is derived as a function of the aperture size of the feed system; the feed efficiency resulting from these theoretical limits on performance is compared to the feed efficiency of patterns obtainable from circular aperture horn antennas, and to experimental results of attempts to realize optimum circular aperture horn patterns.

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TL;DR: In this article, the normalized self-and mutual admittances of two identical bare circular loop antennas have been evaluated when the loops are immersed in either air or an infinite homogeneous conducting medium.

Abstract: The normalized self- and mutual admittances of two identical bare circular loop antennas have been evaluated when the loops are immersed in either air or an infinite homogeneous conducting medium. By decomposing the voltage and current into symmetric and antisymmetric components, the simultaneous integral equations for the distribution of current along the loop have been converted into a single integral equation similar to that for the isolated circular loop antenna which has already been studied. The computed results are presented graphically. The measured results are in good agreement with theory.

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TL;DR: In this article, the complex wave number, the distribution of current, the admittance, and the radiating efficiency of cylindrical antennas made of imperfect conductors are evaluated numerically from a previously derived theory.

Abstract: The complex wave number, the distribution of current, the admittance, and the radiating efficiency of cylindrical antennas made of imperfect conductors are evaluated numerically from a previously derived theory[1]. The quantity 2\lambda r^{i}/\zeta_{0} (where r^{i} is the resistance per unit length, \lambda is the free-space wavelength, and \zeta_{0} = 377 ohms) is used as the parameter in a range that extends from zero to 200. Extensive graphs and tables are given.

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TL;DR: In this paper, a variational formulation for the impedance of a finite cylindrical antenna embedded in a dielectric cylinder, which is surrounded by a magnetoionic medium (cold electron plasma) with the static magnetic field impressed in a direction parallel to the antenna axis, was developed.

Abstract: A variational formulation is developed for the impedance of a finite cylindrical antenna embedded in a dielectric cylinder, which is surrounded by a magnetoionic medium (cold electron plasma) with the static magnetic field impressed in a direction parallel to the antenna axis. Closed form expressions are obtained in the limit of low frequencies, and for short antennas in a uniaxial medium. The impedance of a short antenna is nearly the same as for an assumed triangular current distribution, except that further resonances are observed in the vicinity of the gyro frequency, where the antenna becomes electrically long. These resonances may be shifted to frequencies exceeding the gyro frequency in the presence of an insulating layer around the antenna. For very thin insulating layers the wave number of the variationally approximated current distribution is to the first order equal to \sqrt{\epsilon_{1}} k_{0} ( \epsilon_{1} is the leading diagonal element of the permittivity matrix), where the gyro frequency may be both smaller or larger than the plasma frequency. However, this approximation does not apply to current distributions along the insulated antenna. The present calculations are also compared with earlier work on antenna impedances.

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TL;DR: In this paper, the authors present a method for determining the "ideal" feed polarization that should be incident upon a "conic" reflector, which is specified in terms of the polarization characteristics of elemental electric and magnetic dipoles.

Abstract: The family of surfaces of revolution obtained from conic sections are the sphere, ellipsoid, paraboloid, hyperboloid, and plane. These "conic" surfaces find various uses as reflectors in antenna systems because of their focusing or imaging properties. When any of the "conic" reflectors are used, it is of interest to specify an "ideal" polarization of the incident field such that the currents induced in the reflector flow in parallel paths. This specification will permit the reflector to be formed by parallel conducting wires or slats. This paper presents a method for determining the "ideal" feed polarization that should be incident upon a "conic" reflector. It is specified in terms of the polarization characteristics of elemental electric and magnetic dipoles. It will be shown that for any "conic" surface, the "ideal" polarization can always be specified in terms of crossed electric and magnetic dipoles whose relative intensities are related to the eccentricity of the "conic" reflector.

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TL;DR: In this article, the authors investigated the reradiation pattern of a passive Van Atta reflector consisting of half-wave dipoles and determined the influence of scattering and coupling on the length of the transmission lines interconnecting the dipoles.

Abstract: The reradiation pattern of a passive Van Atta reflector consisting of half-wave dipoles is investigated. The character of the reradiation pattern first is deduced by qualitative and physical considerations. Various types of array elements are considered and several geometrical configurations of these elements are outlined. Following this, an analysis is made of the reradiation pattern of a linear Van Atta array consisting of four equispaced half-wave dipoles. The general form of the reradiation pattern is studied analytically. The influence of scattering and coupling is determined and the dependence of the reradiation pattern on the length of the transmission lines interconnecting the dipoles is investigated. The optimum length of the transmission lines is determined. The results, found by the analysis of the reradiation pattern, are verified experimentally. The experimental reflector consists of slot-fed dipoles with open-ended terminations. Line stretchers are inserted into the transmission lines.

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TL;DR: In this paper, a comparison between center fed antennas consisting of a thin-walled circular tube and of a solid conducting cylinder of the same radius and length is made, and the distributions of the surface current in the two cases are obtained by numerical solution of integral equations for the electric field strength in the extensions of the antenna surface.

Abstract: A comparison is made between center fed antennas consisting of a thin-walled circular tube and of a solid conducting cylinder of the same radius and length. The distributions of the surface current in the two cases are obtained by numerical solution of integral equations for the electric field strength in the extensions of the antenna surface. The current distribution and the radiation patterns are calculated for wavelength-to-radius ratios 10, 30, and 100, with the half length of the antenna equal to 0.23, 0.50, and 0.73 wavelengths.