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 of k^{-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.

A uniform asymptotic theory of electromagnetic diffraction by a curved wedge

An asymptotic expansion of a multiple integral for knife-edge diffraction is derived. The expansion expresses the field in terms of single-edge diffraction. By considering this expression, a similar expansion for higher order UTD diffracted fields is proposed. By means of a set of transition functions, the result removes some of the shortcomings of the original set out of the UTD when the incident field is not a ray-optical field.

UTD-diffraction coefficients for higher order wedge diffracted fields

High-frequency asymptotic solutions of electromagnetic edge diffraction by two different theories are studied. One is the uniform asymptotic theory which is a refinement of Keller's geometrical theory of diffraction. The other is Ufimtsev's theory of the edge wave, representing an improvedment over the classical physical optics theory. These two theories are summarized, their features compared, and their relations discussed. When the observation point is away from shadow boundaries and caustics, both uniform asymptotic theory and Ufimtsev's theory, up to (and including) order k^{-1/2} , agree with Keller's theory. Near or on shadow boundaries, uniform asymptotic theory gives an explicit field solution, while Ufimtsev's result contains a physical optics integral. The evaluation of that integral is not a trivial task. In a two-dimensional test problem, it is shown that both theories do give, up to order k^{-1/2} , an identical field solution everywhere including the edge, shadow boundaries, and transition regions.

Comparison of uniform asymptotic theory and Ufimtsev's theory of electromagnetic edge diffraction

A spectral domain interpretation of high frequency diffraction phenomena is discussed using the concept of a spectral diffraction coefficient, which resembles Keller's coefficients. The solution of the two-dimensional problems of diffraction of an arbitrary field (with no caustics) by a half-plane is investigated and results are given for any observation angle including, in particular, asymptotic determination of the field at the shadow boundaries. The high frequency scalar diffraction by apertures is formulated in a systematic manner and the formulation, which is valid for any observation angle, is compared with that of other techniques. Results are also given for the diffracted field at the caustics.

A spectral domain interpretation of high frequency diffraction phenomena

The concept of Spectral Theory of Diffraction [STD] was introduced by Mittra and his collaborators [MR] in the 1970s to circumvent some of the problems encountered with the GTD. The basic strategy followed in STD is to represent a complex field, which is not a ray field, in terms of a superposition of plane waves. Such fields are often encountered in diffraction problems.

Spectral Theory of Diffraction

The diffraction of an arbitrary cylindrical wave due to a line source and incident on a half-plane is treated by the uniform asymptotic theory of edge diffraction. For large wavenumber k , an asymptotic solution for the total field up to and including terms of order k^{-3/2} relative to the incident field is derived. This solution is uniformly valid for all observation points, including points near the edge and the shadow boundaries. In particualr, two special cases are considered: A) the line source is located on the half-plane, and radiates an E -polarized wave and B) the line source is located in the aperture complementary to the half-plane and radiates an H -polarized wave. A companion paper will show that our asymptotic solution for Case A) is in complete agreement with the asymptotic expansion of the exact solution. For the same diffraction problem, asymptotic solutions obtained by the method of slope diffraction coefficients and the method of equivalent currents are also discussed. It is found that the latter solutions agree with the exact one only when i) the observation point is away from the edge and the shadow boundaries, and/or ii) the terms of order k^{-3/2} in the field solution are ignored.

Shung-Wu Lee

Papers

High-frequency diffraction of a line-source field by a half-plane: Solutions by ray techniques