Nonuniform currents on a wedge illuminated by a TE plane wave

Abstract

Closed-form e%pressions for nonuniform currents on a perfectly conducting, infinite wedge illuminated by transverse electric (TE) plane wave are presented. These expressions are derived by requiiing that they coincide with the corrent 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 wing the expressions developed here are compared with currents computed from the eigenfunction solution of the wedge. Good agreement is obtained throughout. T I. I N T R O D U~O N WO OF THE PRINCIPAL theories of edge diffraction are the geometrical theory of diffraction (GTD) enunciated by Keller [1]-[3] and the physical theory of diffraction (PTD) originated by Ufimtsev [4]. The GTD extends the geometrical optics (GO) by the inclusion of rays diffracted by surface singularities. Keller's theory fails in the vicinities of GO boundaries known as transition regions. To overcome this difficulty, the uniform theory of diffraction (UTD) [5], [6] and the uniform asymptotic theory VAT) [7]-[9] have been devised. A common failing of all ray optic techniques is that they predict infinite fields at caustics. The method of equivalent currents (MEC) alleviates the problem at caustics encountered by GTD and a number of authors have made contributions toward this end [lo]-[14]. This method is based upon prescribing fictitious currents on the true surfaces.In contrast to GTD, PTD is a technique based upon integrating the currents induced on the scatterer. Ufimtsev postulates that the induced current is a sum of the uniform or physical optics (PO) current induced by the GO surface field and the nonuniform current induced by the diffracted field at the surface. The scattered field is obtained as a surface integral of these currents. Thus, PTD is an extension of PO. It must be noted, however, that Ufimtsev does not give explicit expressions for the nonuniform currents, but instead determines the field due to these currents from "indirect considerations." Knott and Senior [15] present an elegant summation of the three techniques, GTD, PTD, and MEC. Lee [16] compared The authors are with the Electromagnetics Group, School of Engineering, IEEE Log Number 8609021. University of Dayton, Dayton, OH 45469.the UAT with PTD and points out that the lack of explicit expressions for nonuniform currents or its dominant contribution is a notable disadvantage of Ufimtsev's theory. Schretter and Bolle [ 171 have attempted to find closed-form appr...

The High-Frequency Magnetic Field at the Edge of a Curved Face Wedge: TE-Polarized Plane Wave or Creeping Wave Illumination

“…5. This is demonstrated in (17) A general conclusion from these plots is that the error decreases as wedge angle or radius increases, consistent with the discussion leading to (16) above. A corollary is that a significant part of the error is due to the contaminating fields launched by edge diffraction from the upper edge of the ogive.…”

“…Substituting for b from (6) and simplifying gives Relative Contamination = e 00:35WA(kr ) : (16) Table I lists relative contamination values (in decibels) from (16) for a set of combinations of wedge angle (in degrees) and radius of curvature (in wavelengths). If the relative contamination is negligible for the direction of incidence shown in Fig.…”

“…The equivalent current is approximated in various ways, such as by comparison of features of the real scatterer with similar features in canonical shapes. The PTD approach has been applied in [16] and [17] for determining the current on the surfaces of a perfectly conducting plane face wedge, for TE and TM polarization, respectively.…”

A hybrid method for scattering by large bodies with cracks and gaps

“…w Figure 1 Original and equivalent problems. (a) Original problem, (b) equivalent problem for exterior region, (c) equivalent problem for interior region and geometry for solving M current density, for example, to obtain the surface currents on a surface between the Q2 and Q, of the object shown in Figure 1, we can divide the surface currents into uniform currents (PO currents), nonuniform currents produced by wedges (whose expressions have been given in [8] and [9]), and currents produced by higher-order diffraction field due to the interaction between wedges [lo].…”