R. Tiberio

A uniform GTD formulation for the diffraction by a wedge with impedance faces

A uniform high-frequency solution is presented for the diffraction by a wedge with impedance faces illuminated by a plane wave perpendicularly incident on its edge. Arbitrary uniform isotropic impedance boundary conditions may be imposed on the faces of the wedge, and both the transverse electric (TE) and transverse magnetic (TM) cases are considered. This solution is formulated in terms of a diffraction coefficient which has the same structure as that of the uniform geometrical theory of diffraction (UTD) for a perfectly conducting wedge. Its extension to the present case is achieved by introducing suitable multiplying factors, which have been derived from an asymptotic evaluation of the exact solution given by Maliuzhinets. When the field point is located on the surface near the edge, a more accurate asymptotic evaluation is employed to obtain a high-frequency expression for the diffracted field, which is suitable for several specific applications. The formulation described in this paper may provide a useful, rigorous basis to search for a more numerically efficient but yet accurate approximation.

High-frequency scattering from a wedge with impedance faces illuminated 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. >

An incremental theory of diffraction: scalar formulation

A formulation is introduced that provides a self-consistent, high-frequency description of a wide class of scattering phenomena within a unified framework. This method is based on the appropriate use of locally tangent canonical problems, with a cylindrical uniform configuration and arbitrary cross section. A generalized localization process is applied to define incremental diffracted field contributions, which are adiabatically distributed along the actual edge discontinuities or shadow boundary lines. Then, the total field is represented as the sum of a generalized geometrical optics field plus incremental diffracted field contributions. This representation of the field is uniformly valid at any incidence and observation aspects, including caustics and shadow boundaries of the corresponding ray field description. This method naturally includes the uniform GTD ray field representation of the scattering phenomenon, when it is applicable. For the sake of convenience in the explanation, the formulation for scalar problems is discussed in this paper. The formulation for vector, electromagnetic problems is given in the subsequent paper on electromagnetic formulation. It is suggested that this method may provide a quite general, self-consistent procedure for predicting the field scattered in the near as well as in the extreme far zone of an arbitrarily shaped, opaque object. >

High-frequency electromagnetic scattering of plane waves from double wedges

The application of a high-frequency solution for the field doubly diffracted in the far zone from a pair of parallel wedges illuminated by a plane wave is described. It is shown how a spectral extension of the uniform geometrical theory of diffraction (GTD) is used to obtain closed-form expressions for the field that are valid at any incidence and observation aspects. These expressions exhibit the proper discontinuities and singularities so that they can be suitably combined with the other singly diffracted fields to provide a uniformly valid ray description of the scattering in the far zone by an obstacle which is illuminated by a plane wave. They smoothly reduce both to those derived by directly applying the uniform GTD solution for single diffraction augmented by slope diffraction and to those recently obtained for grazing illumination of the edges, in their respective regions of validity. The solutions to the scalar problems are then used to construct a dyadic diffraction coefficient for the doubly diffracted field in the ray-fixed coordinate system. Examples of triangular cylinders are considered, and numerical results are presented. >

An incremental theory of diffraction: electromagnetic formulation

A scalar formulation of the incremental theory of diffraction (ITD) has been introduced by Tiberio and Maci (see ibid., vol.42, no.5, 1994), which provides a self-consistent, high-frequency description of a wide class of scattering phenomena, within a unified framework. In this paper, this method is extended to electromagnetic problems. The total field is represented as the sum of a generalized geometrical optics field plus incremental diffracted field contributions. Explicit dyadic expressions of incremental diffraction coefficients are derived for wedge-shaped configurations. The formulation of the field is uniformly valid at any incidence and observation aspects, including caustics and shadow boundaries of the corresponding ray field description. Numerical results are presented and compared with those obtained from different techniques. >

Incremental theory of diffraction: a new-improved formulation

In this paper, a general systematic procedure is presented for defining incremental field contributions. They may provide effective tools to describe a wide class of scattering and diffraction phenomena at any aspect, within a unitary, self-consistent framework. This procedure is based on a generalization of the incremental theory of diffraction (ITD) localization process for uniform cylindrical, local canonical problems with elementary source illumination and arbitrary observation aspects. In particular, it is shown that the spectral integral formulation of the exact solution for the local canonical problem may also be represented as a spatial integral convolution along the longitudinal coordinates of the cylindrical configuration. Its integrand is then directly used to define the relevant incremental field contribution. For the sake of convenience, but without loss of generality, this procedure is illustrated for the case of local wedge configurations. Also, a specific suitable asymptotic analysis is developed to derive new closed form high-frequency expressions from the spectral integral formulation. These expressions for the incremental field contributions explicitly satisfy reciprocity and are applicable at any incidence and observation aspect. This generalization of the ITD localization process together with its more accurate asymptotic analysis provides a definite improvement of the method.

Double diffraction at a pair of coplanar skew edges

This study aims at describing the field propagation in terms of pulsed rays, that are particularly advantageous when dealing with short-pulse excitations. In the framework of the Geometrical Theory of Diffraction we augment Geometrical Optics and uniform singly diffracted field solutions available in the time domain (TD), by TD doubly diffracted (DD) rays, that are expressed in simple closed forms. Impulsive double diffraction at a pair of coplanar edges is here formulated directly in the TD, as a double superposition of impulsive spherical waves. Nonuniform and uniform wavefront approximations for TD-DD fields are determined in closed form, defining two novel TD transition functions. The scalar case with either hard or soft boundary conditions is analyzed first, and then used to build an electromagnetic dyadic DD coefficient for a pair of coplanar edges with perfectly conducting faces. Particular attention is given to the definition of TD transition regions, i.e., the elliptical regions where the TD-DD field does not exhibit a ray optical behavior. The compensation mechanism by which the TD-DD fields repair the discontinuity introduced by singly diffracted fields at their shadow boundaries is also analyzed in detail. Our result for the TD-DD field excited by an impulsive spherical wave is valid only for early times, at and close to (behind) the DD ray wavefront. The TD-DD field response to a more general pulsed excitation is obtained via convolution, and if the exciting signal has no low-frequency components the range of validity of the resulting pulsed response is enlarged to later observation times behind the wavefront.

Calculation of the high-frequency diffraction by two nearby edges illuminated at grazing incidence

The uniform geometrical theory of diffraction (UTD) together with a generalized spectral extension arc applied to calculate the high-frequency scattering by two nearby edges illuminated at grazing incidence. Several examples arc considered which involve the diffraction by a pair of parallel edges where one edge is illuminated by the shadow boundary field of the other. Expressions for the diffracted field have been obtained for plane, cylindrical, and spherical wave illumination with either the electric or magnetic field perpendicular to the edges. Extensive numerical results are given for a pair of staggered parallel half-planes, a thick screen, and a rectangular cylinder. Comparisons with the results calculated by other techniques are also presented to demonstrate the accuracy of the method.

High-frequency scattering from the edges of impedance discontinuities on a flat plane

A high-frequency solution is presented for the scattering of a plane wave at the edges of surface impedance discontinuities on a fiat ground plane. Arbitrary uniform isotropic boundary conditions and a direction of incidence perpendicular to the edges of the discontinuities are considered for both the transverse electric (TE) and transverse magnetic (TM) cases. An asymptotic approximation of the exact solution given by Maliuzhinets and a spectral extension of the geometrical theory of diffraction (GTD) are used. Uniform expressions for the scattered field received at a point on the surface are given, including surface wave contributions. Numerical results are shown and in some examples they are compared with those obtained from a moment method (MM) solution.

Diffraction at a thick screen including corrugations on the top face

A closed-form high-frequency solution is presented for the near-field scattering by a thick screen illuminated by a line source at a finite distance. This solution is applicable to a thick screen with perfectly conducting side walls and either perfectly conducting or artificially soft boundary conditions on the face joining the two wedges. This latter condition is obtained in practice by etching on that face quarter of a wavelength deep corrugations with a small periodicity with respect to the wavelength. It is shown that the artificially soft surface provides a strong shadowing for both polarizations; thus, it is suggested that such configurations may usefully be employed to obtain an effective shielding from undesired interferences. Several numerical calculations have been carried out and compared with those from a method of moments (MoM) solution for testing the accuracy of our formulation, as well as to demonstrate the effectiveness of the corrugations in shielding arbitrarily polarized incident field.