Transition functions for high-frequency diffraction by a curvedperfectly conducting wedge. II. A partially uniform solution for ageneral wedge angle

For pt.I see ibid., vol.37, no.9, p.1073-9(1989). In pt.I, transition function solutions for the combined surface-edge diffraction were derived from the rigorous, canonical solution for a thin cylindrically curved sheet. Here, similar solutions are derived for the more general case of diffraction by a perfectly conducting curved wedge. In the absence of a canonical solution for this case, the theory developed here is a physical one. It is an extension of the spectral theory of diffraction to the Fock solution for the penumbra region field near a convex surface. For certain domains of illumination aspects and field points, this procedure recovers the results obtained by other authors, starting, however, from more plausible assumptions and providing a ne insight. For other domains, it yields asymptotic solutions for the first time, thus demonstrating greater generality than in the previous approaches. The results are checked in two ways: first, they reduce to the rigorous results of pt.I when specialized to a curved sheet; second, they are shown to agree with a moment-method solution for a structure involving a curved wedge     

Transition functions for high-frequency diffraction by a curvedperfectly conducting wedge. III. Extension to overlapping transitionregions

For pt.II see ibid., vol.37, no.9, p.1080-5(1989). The asymptotic theory of pt.II is extended to the case where the transition region of edge diffraction overlaps the region of surface diffraction. The extension is performed by incorporating Ufimtsev's theory in the spectral domain approach. The dominant part of the scattered field is obtained by asymptotic evaluation of the radiation integral for the Fock current unperturbed by the edge, wherein the surface curvature and the finite distance to the field point are explicitly taken into account. The correction part, due to the fringed currents excited by the edge, is evaluated by the simpler procedure of pt.II. The dominant part involves a pair of new universal functions independent of the wedge angle. The coincide with those deduced in Pt.I from the rigorous canonical solution for a perfectly conducting cylindrically curved sheet. At very high frequencies, the present solution merges smoothly with the partially uniform solution of pt.II and with Keller's solution in the appropriate angular domains of incidence and scattering     

Pulsed beam diffraction by a perfectly conducting wedge: exactsolution

The new canonical problem of scattering of a collimated pulsed beam (PB) by a perfectly conducting wedge is analyzed and solved exactly. The incident PB is modeled by the so called complex-source PB (CSPB). The authors derive an exact closed-form solution for the scattered field and demonstrate, via extensive numerical examples, the local scattering phenomena as a function of the PB parameters (direction, distance from the edge, spatial collimation, and pulse length): if the PB hits near the edge it generates a toroidal diffracted wavepacket that propagates along Keller's cone as well as transitional shadow boundaries effects. These diffraction phenomena diminish as the distance of the impinging wavepacket from the edge grows     

Pulsed beam diffraction by a perfectly conducting wedge: localscattering models

Develops local scattering models for a collimated wavepacket (pulsed beam, PB) impinging on a perfectly conducting wedge. They are derived from an exact solution that has been derived previously. Unlike the exact solution, the local solutions have explicit space-time forms which parameterize the problem in terms of tractable phenomena that may be extended to noncanonical configurations. This is done in the second half of the paper wherein the local models are extended to accommodate astigmatic wavepackets for which there is no exact solution. The local models developed have the format of the geometrical theory diffraction and of the uniform theory of diffraction (UTD), extended to accommodate PB fields: they are governed by transient diffraction functions (time-domain counterparts of the UTD diffraction coefficient) but also include structure functions that describe the space-time distribution of the scattered wavepacket. They explain, uniformly, the physics of the scattering phenomena as a function of the PB parameters: direction, distance from the edge, spatial collimation, and pulse length     

Pulsed field diffraction by a perfectly conducting wedge: aspectral theory of transients analysis

The canonical problem of pulsed field diffraction by a perfectly conducting wedge is analyzed via the spectral theory of transients (STT). In this approach the field is expressed directly in the time domain as a spectral integral of pulsed plane waves. Closed-form expressions are obtained by analytic evaluation of this integral, thereby explaining explicitly in the time domain how spectral contributions add up to construct the field. For impulsive excitation the final results are identical with those obtained previously via time-harmonic spectral integral techniques. Via the STT, the authors also derive new solutions for a finite (i.e., nonimpulsive) incident pulse. Approximate uniform diffraction functions are derived to explain the field structure near the wavefront and in various transition zones. They are the time-domain counterparts of the diffraction coefficients of the geometrical theory of diffraction (GTD) and the uniform theory of diffraction (UTD). An important feature of the STT technique is that it can-be extended to solve the problem of wedge diffraction of pulsed beam fields (i.e., space-time wavepackets)     

Analytical solution for the 2D diffraction of electromagnetic wave by a truncated wedge

Three heuristic approaches are used to derive analytical formulas that represent the solution to the 2D problem of the diffraction of electromagnetic wave by a truncated wedge. The results of numerical calculations are based on the analytical formula. The solutions are analyzed, and advantages and disadvantages are discussed. It is demonstrated that only the solution derived using the method of generalized eikonal makes it possible to describe the scattered field when the dimensional parameter uniformly tends to zero.     

Asymptotic solution for line source radiation from a curved perfectly conducting wedge

An asymptotic solution is presented for the radiation of an infinite line source located on a convex face of a perfectly-conducting curved cylindrical wedge. The solution employs a pair of new universal functions. Excellent agreement with a moment method solution is demonstrated for radiation from an original cylinder.<>     

A numerical approach for the diffraction of a Gaussian beam from aperfectly conducting wedge

A finite difference (FD) solution to the problem of high-frequency scattering from a perfectly conducting wedge of arbitrary external angle illuminated by a Gaussian beam is presented. The solution is obtained through the application of the parabolic equation method. The solution is compared with the analytical asymptotic solution available in the literature     

On the diffraction of an electromagnetic skew incident wave by a non perfectly conducting wedge

We study the diffraction by a wedge of an electromagnetic plane wave with skew incidence on the edge, when boundary conditions give us two equations by face with combined electric and magnetic fields. The problem is reduced principally to a non linear scalar functional equation with one unknown. As an example of application, the solution for a wedge with arbitrary angle and relative impedance unity (the most usual model for absorbing material) is given.     

An approximate solution for coupling to a coaxial waveguide whichterminates at a conducting wedge

An integral equation is derived to approximate the aperture electric field for a coaxial waveguide that terminates at a conducting wedge. The integral equation is derived by retaining the standard kernel for the infinite-flange case and adapting the solution for the two-dimensional conducting wedge for use as the excitation term. The solution of this equation gives rise to an approximation to the TEM open-circuit voltage. Because only the excitation term is modified, the equation is useful for connectors that are greater than about one wavelength away from the corner. Theoretical and experimental results for the power transmitted down the coax are presented     

On uniform asymptotic Green's functions for the perfectly conducting cylinder tipped wedge

Uniform asymptotic expressions are derived for the Green's functions describing scattering of electric or magnetic type plane waves by a perfectly conducting cylinder tipped wedge (CTW). These expressions are found to agree analytically with heuristic expressions available using the geometrical theory of diffraction (GTD). Numerical comparison of these expressions with results obtained from eigenfunction expansions show good agreement for cylinder diameters >1.5 lambda.     

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.     

Two-dimensional diffraction by a wedge with impedance boundary conditions

The two dimensional problem of diffraction by a wedge with impedance boundary conditions on its faces is explicitly solved in a form that admits effective numerical simulation by simple perfectly scalable algorithms with unlimited capability for parallel processing. The solution is represented as a superposition of the geometric field that is completely determined by elementary ray analysis and of the waves diffracted by the tip of the wedge. The diffracted field is explicitly represented as a mathematical expectation of a specified functional on trajectories of a random motion determined by the configurations of the problem and by the boundary conditions. The numerical results confirm the efficiency of this approach.     

NONUNIFORM CURRENTS ON A CONDUCTING WEDGE ILLUMINATED BY A TM PLANE WAVE

Closed-form expressions for nonuniform currents induced on a perfectly conductinginfinite wedge illuminated by a TM plane wave are presented.Results computed by using theseexpressions are in good agreement with ones of the eigenfunction solution of the wedge.     

Analytical solution for electromagnetic diffraction on 2-Dperfectly conducting scatterers of arbitrary shape

A method is developed to receive a rigorous analytical solution of the external stationary two-dimensional (2-D) boundary value problem for the Helmholtz equation for perfectly conducting scatterers of an arbitrary shape. The rigorous expression for the scattered field is represented by the sum of integrals along piece-wise contours in a complex plane. In case of necessity a simple analytical asymptotic expression can be obtained     

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.     

An alternative diffraction coefficient for the wedge

A geometrical theory of diffraction (GTD) interpretation of a uniform solution for the wedge given by Mohsen is given. The diffraction coefficients are equal to those given by Kouyoumjian and Pathak except that the Fresnel argument in the two solutions are different. This uniform geometrical theory of diffraction (UTD) result is compared with exact series expansions for a plane wave incident on a90degwedge.     

A uniform asymptotic theory of electromagnetic diffraction by a curved wedge

Diffraction of an arbitrary electromagnetic optical field by a conducting curved wedge is considered. The diffracted field according to Keller's geometrical theory of diffraction (GTD) can be expressed in a particularly simple form by making use of rotations of the incident and reflected fields about the edge. In this manner only a single scalar diffraction coefficient is involved. Near to shadow boundaries where the GTD solution is not valid, a uniform theory based on the Ansatz of Lewis, Boersma, and Ahluwalia is described. The dominant terms, to the order ofk^{-1/2}included, are used to compute the field exactly on the shadow boundaries. In contrast with the uniform theory of Kouyoumjian and Pathak, some extra terms occur: one depends on the edge curvature and wedge angle; another on the angular rate of change of the incident or reflected field at the point of observation.     

Study of scattering by a perfectly conducting wedge with finite sized faces

In this work the scattering of plane waves from a finite sized perfectly conducting wedge as a function of its opening angle and the width of its faces is studied using the combination of physical optics (po) and the physical theory of diffraction (ptd). To find out under which circumstances the ptd contribution is significant compared to the PO, the ratio of the ptd field and the po field is evaluated as a maximum and a mean value over every direction of observation in the Keller cone, as well as in the special direction of backscattering. We employ the incremental length diffraction coefficients for a wedge with finite sized faces based on equivalent edge currents derived recently for truncated wedge strips. The numerical behaviour in the limiting cases of the diffraction coefficients are discussed extensively.