The echo area of a perfectly conducting prolate spheroid

An approximate general solution for the electromagnetic backscattering by a perfectly conducting prolate spheroid is derived. The solution is obtained from an estimate of the solution to a transient scattering problem which is deduced, in part, from the known time-dependent backscattered waveform for a perfectly conducting sphere. From the analysis the echo signal as a function of the source frequency for arbitrary orientation of the spheroid and arbitrary linear polarization of the incident plane electromagnetic wave can be predicted in the resonance region. Calculated results for a 2:1 axial ratio spheroid are compared with experimental data for two principal polarizations and major axes ranging from 0.32 to 1.59 wavelengths.     

High-frequency backscatter from a finned cylinder -- Comparison of UTD results with experiment

The far backscattered field from a perfectly conducting, infinitely long, circular cylinder with a fin is calculated for the transverse electric (TE) and transverse magnetic (TM) cases, using the uniform theory of diffraction (UTD). The calculated results are compared to appropriate experimental measurements and good agreement is obtained. A derivation of the effective curvature of the wave diffracted by the edge of the fin and propagating along the fin to the cylinder is presented. A limitation on the method of effective source is discussed.     

Asymptotic analysis of edge-excited currents on a convex face of aperfectly conducting wedge under overlapping penumbra region conditions

The edge-excited surface currents on a convex face of a perfectly conducting curved wedge are investigated in the asymptotic high-frequency limit for the case where the penumbra regions of the edge and surface diffractions overlap. The edge of the wedge is assumed straight, and the incident electromagnetic wave locally plane and normal to the edge. Both polarizations are considered. The surface field induced by the edge diffraction is synthesized in the spirit of the spectral theory of diffraction (STD): the solution for the edge-diffracted field is interpreted as a spectrum of inhomogeneous plane waves, and the surface field excited by each spectral plane wave is obtained by analytical continuation of the Fock (1965) functions into complex space. The main purpose of this work is to prove the reciprocity of a solution deduced previously for the problem of line source radiation from the wedge in question. As a by-product, useful identities for an incomplete Airy function and an Airy-Fresnel integral are developed     

A UTD-PO solution for diffraction of plane waves by an array of perfectly conducting wedges

In this paper, a formulation for plane wave incidence by an array of perfectly conducting wedges is proposed. The solution takes the advantages of the uniform theory of diffraction (UTD) and physical optics (PO), and allows for numerical evaluation of a large number of perfectly conducting wedges. The solution has the major advantage of shortening the computing time over existing formulation when the number of wedges is very large. The source is assumed to be above, below, or level with the edge height. The technique proposed is validated with numerical results from technical literature. Results for cases not previously reported in the technical literature are also presented.     

Electromagnetic diffraction of an obliquely incident plane wave bya right-angled anisotropic impedance wedge with a perfectly conductingface

The diffraction of an arbitrarily polarized electromagnetic plane wave obliquely incident on the edge of a right-angled anisotropic impedance wedge with a perfectly conducting face is analyzed. The impedance tensor on the loaded face has its principal anisotropy axes along directions parallel and perpendicular to the edge, exhibiting arbitrary surface impedance values in these directions. The proposed solution procedure applies both to the exterior and the interior right-angled wedges. The rigorous spectral solution for the field components parallel to the edge is determined through the application of the Sommerfeld-Maliuzhinets technique. A uniform asymptotic solution is provided in the framework of the uniform geometrical theory of diffraction (UTD). The diffracted field is expressed in a simple closed form involving ratios of trigonometric functions and the UTD transition function. Samples of numerical results are presented to demonstrate the effectiveness of the asymptotic expressions proposed and to show that they contain as limit cases all previous three-dimensional (3-D) solutions for the right-angled impedance wedge with a perfectly conducting face     

High-frequency multiple diffraction by a flat strip: Higher order asymptotics

By including correction terms in inverse powers of the wavenumberk, one may hope to extend the range of applicability of multiple edge diffracted geometrical theory of diffraction (GTD) to lower frequencies, and also to extend thereby the range of validity of the corresponding time domain solutions. The correction can be applied to each of the surface rays in the hierarchy that has been proposed by us recently as a model for multiple interaction between parallel edges separated by a plane surface segment on a two-dimensional perfectly conducting scatterer. The surface rays, which were found to explain the structure of the complex resonances in transient scattering, are excited for each interaction by equivalent line sources, dipole line sources, and their derivatives, with strengths determined from the asymptotic expansion of the edge diffracted field. This procedure is applied in detail toE- andH- polarized plane wave scattering by a perfectly conducting flat strip, up to quadruple diffraction, including consistentO(k^{-2})corrections with respect to the dominant term. The procedure is applied also to generate corrected multiple diffracted individual surface ray fields, which lead to an improved equation for the complex resonances in the "layer" synthesized in the complex frequency plane by a surface ray of a particular order. Inclusion of the low frequency corrections reduces further the already small discrepancy between the ray optically calculated low frequency resonances and those computed numerically by the moment method.     

Reply to 'Comment on 'Comparison of excess 1/f noise spectra in trimmed and untrimmed thick film resistors'

An iterative surface current density replacement technique is used to formulate the electromagnetic scattering from any perfectly conducting body defined as the intersection of two bodies for which expressions for the scattering are known. The application of the iterative surface current density replacement technique to the truncated wedge results in a secondary edge diffraction coefficient which is accurate for closely spaced edges, and is identical to the secondary diffraction coefficient of the geometrical theory of diffraction when the edges are separated by a distance which is large compared with the wavelength of the field. Results are presented which show the accuracy of this secondary edge diffraction coefficient when applied to the perfectly conducting truncated wedge and narrow strip.     

Three-dimensional half-plane diffraction: Exact solution and testing of uniform theories

The exact solution of the diffraction problem for a plane electromagnetic wave at oblique incidence on a perfectly conducting half-plane was obtained more than 30 years ago. Recent advances in the high-frequency diffraction theory enable us to present the final solution in much simpler and suggestive forms. This solution is next used to test two uniform theories of edge diffraction. We find that uniform asymptotic theory (UAT) developed by Ahluwalia et al. recovers the exact solution, whereas uniform geometrical theory of diffraction (UTD) developed by Kouyoumjian and Pathak does not. The error of UTD is discussed.     

Current distributions on a perfectly conducting elliptic disk [EMscattering]

Current distributions induced on a perfectly conducting elliptic disk are discussed within the framework of the null-field approach. The elliptic disk is treated as the zero thickness limit of a general ellipsoid. In this limit it is necessary to introduce modified expansion functions for the surface fields. It is shown that these expansion functions inherently satisfy the edge condition and no extra weight factors must be introduced. The first few terms in a low-frequency expansion of the surface currents induced by an incident plane wave are derived, and from this expansion the static limit is analyzed. The theoretical results are illustrated with numerical computations of the surface currents and charge distributions     

High-frequency scattering from a wedge with impedance facesilluminated by a line source. I. Diffraction

The canonical problem of evaluating the scattered field at a finite distance from the edge of an impedance wedge which is illuminated by a line source is considered. The presentation of the results is divided into two parts. In this first part, reciprocity and superposition of plane wave spectra are applied to the left far-field response of the wedge to a plane wave, to obtain exact expression for the diffracted field and the surface wave contributions. In addition, a high-frequency solution is given for the diffracted field contribution. Its expression, derived via a rigorous asymptotic procedure, has the same structure as that of the uniform geometrical theory of diffraction (UTD) solution for the field diffracted by a perfectly conducting wedge. This solution for the diffracted field explicitly exhibits reciprocity with respect to the direction of incidence and scattering     

Construction of heuristic diffraction coefficients in the analytical solutions to the problems in which wave fields of different physical nature are scattered by polygonal flat plates with complex boundary conditions

The heuristic diffraction coefficients of the problem in which the wave field of an arbitrary physical nature is scattered by a polygonal flat plate with complex boundary conditions are determined. Diffraction coefficients are constructed with the help of the geometric optics coefficients of wave field reflection from an infinite plane surface by analogy with the known solution to the electrodynamic problem of diffraction by a perfectly conducting scatterer. It is established that the new approach makes it possible to derive simple formulas for diffraction coefficients. Their accuracy exceeds that of the formulas of the known heuristic analytical methods and tends to the accuracy of rigorous solutions. It is demonstrated that the derived results can be used in both electrodynamics and the other areas of physics, e.g., in calculations of the seismic wave diffraction.     

Nonuniform currents on a wedge illuminated by a TE plane wave

Closed-form expressions for nonuniform currents on a perfectly conducting, infinite wedge illuminated by transverse electric (TE) plane wave are presented. These expressions are derived by requiring that they coincide with the current predicted by the asymptotic diffraction method far from the edge and, further, that they agree with the current predicted by the eigenfunction solution at the edge. The angle of incidence is arbitrary and our expressions remain valid even for glancing angles of incidence when either one or both faces of the wedge are in the vicinity of a geometric optic (GO) boundary. Formulas presented here are simple involving the well-known modified Fresnel functions but are not uniform. Exact expressions for nonuniform currents are available for the two special cases of half-plane and infinite plane. For these special cases, our solution reduces to the exact solution. Currents computed using the expressions developed here are compared with currents computed from the eigenfunction solution of the wedge. Good agreement is obtained throughout.     

Characteristics of near field of the horizontal vibrator located above a square screen

The 3D vector problem concerned with the diffraction of the horizontal half-wave vibrator field by a perfectly conducting and infinitely thin rectangular screen is solved during observations at a finite distance from the vibrator. The technique for calculating the diffracted field, which is based on the laws of geometric diffraction theory and uniform diffraction coefficients obtained from the rigorous solution to the problem of the diffraction of the field of a Hertzian electric dipole at the edge of a perfectly conducting semiplane, is proposed. Fast-acting programs for calculating and analyzing the amplitudes and phases of the components of diffracted and complete vibrator fields in the entire space of observation angles at the set distance of the observation point from a rectangular screen and along the normal to the screen under changes in the distance between the screen and the observation point are developed. The character of the transformation of the spatial amplitude distribution of three field components depending on removal of observation point from an antenna is studied. It is shown that the distance to the far field zone of the investigated radiating system exceeds two wave lengths.     

Currents induced on a conducting halfplane by a plane wave at arbitrary incidence

Based on Sommerfeld's exact solution for the diffraction of a uniform plane wave by a perfectly conducting halfplane, expressions are given for the current density induced on both sides of the plane for a wave arriving at a general angle of incidence. Polarisation of the incident wave both parallel and transverse to the edge is considered. For both polarisations, computed results are presented of the magnitude and phase of the induced currents on both sides of the plane; angles of incidence over the complete range 0° to 180° are considered.     

High-frequency backscatter from a finned cylinder at grazing incidence--Comparison of two theoretical methods

A closed-form, high-frequency approximation is obtained for the diffracted-reflected-diffracted field contribution to the backscattered field resulting from the grazing illumination of a perfectly conducting, infinitely long, finned cylinder by a normally incident cylindrical transverse magnetic (TM) wave. The result, which is valid for any relative magnitudes of the cylinder radius and the fin width provided both of them are electrically large, is derived by two different methods. One of them is the radiation integral method related to the physical theory of diffraction. The other is the complex ray tracing method related to the spectral theory of diffraction (STD). Relative merits and disadvantages of the two methods are pointed out.     

The physical theory of slope diffraction

The physical theory of diffraction (PTD) has been expanded for the case of slope diffraction, when an incident wave is zero but its derivative is not zero in the direction of a perfectly conducting scattering edge. High frequency asymptotics are found both for elementary edge waves and for the total edge waves scattered by arbitrary curved edges. Great attention is given to fields created by the nonuniform (diffraction) component of edge currents. These fields are usually called ptd corrections to the Physical Optics approach. These corrections are found for diffraction fields in ray regions and in diffraction regions such as the vicinities of shadow boundaries, smooth caustics, and foci.     

Scattering by right angle dielectric wedge

An asymptotic solution of electromagnetic waves scattered by a right-angled dielectric wedge for plane wave incidence is obtained. Scattered far fields are constructed by waves reflected and refracted from dielectric interfaces (geometric-optical fields) and a cylindrical wave diffracted from the edge. The asymptotic edge diffracted field is obtained by adding a correction to the edge diffraction of physical optics approximation, where the correction field in the far-field zone is calculated by solving a dual series equation amenable to simple numerical calculation. The validity of this result is assured by two limits of relative dielectric constantvarepsilonof the wedge. The total asymptotic field calculated agrees with Rawlins' Neumann series solution for smallvarepsilon, and the edge diffraction pattern is shown to approach that of a perfectly conducting wedge for largevarepsilon. Calculated far-field patterns are presented and the accuracy of physical optics approximation is discussed.     

Numerical diffraction coefficients in the shadow transition region

Numerical techniques for the evaluation of diffraction coefficients are extended to shadow transition regions and examined in detail for perfectly conducting and lossy dielectric semi-infinite slabs with a line source in the near-field and polarization along the slab edge. One approach is based on a direct computation of the radiation from a finite two-dimensional slab illuminated from a near-field source, with the current filtered by appropriate windows. For the perfectly conducting half-plane this approach yields diffraction coefficients in the transition region that are in good agreement with uniform theory of diffraction (UTD) analytic values. Alternatively, geometric theory of diffraction (GTD) coefficients are computed once and for all for a far-field source and these are used formally within a UTD or uniform asymptotic theory (UAT) framework. The direct, the UTD, and the UAT approaches are in satisfactory agreement with each other, and predictions for the radiation from finite slabs based on the computed diffraction coefficients are in satisfactory agreement with those of the method of moments (MM)     

Couplage du lancer de rayons et des interactions arêtesurface pour une analyse 3d rapide de cibles complexes

A fast high frequency analysis method of complex 3D perfectly conducting targets is carried out using a Shooting and Bouncing Ray (sbr) approach. A set of rays representating the incident plane wave is shot towards the target and each ray is followed according to reflection and/or diffraction laws. The scattering of intercepted surfaces throughout the multiple bounces, the edge diffraction, the surface- edge and the edge- surface interactions are considered. All these contributions are summed up to compute the target far field. We present Radar Cross Section (rcs) results about an helicopter, a tower and corner reflectors.     

The geometrical theory of diffraction applied to antenna pattern and impedance calculations

The geometrical theory of diffraction is applied to the calculation of the radiation pattern and impedance of a monopole antenna on a perfectly conducting circular ground plane of limited extent. In this calculation, the radiation problem is resolved into two components, one being the monopole contribution and one the edge contribution. The impedance problem is resolved into the components of a reflection from the monopole in an infinite ground plane and a reflection from the circular edge as seen through the antenna. The known solutions of these individual components then permit the calculation of the overall radiation pattern and impedance by superposition. The techniques described are general and are considered applicable to a large class of similar radiating structures.