The Dyadic Diffraction Coefficient for a Curved Edge
Abstract
A compact dyadic diffraction coefficient for electromagnetic waves obliquely incident on a curved edge formed by perfectly-conducting curved or plane surfaces is obtained. This diffraction coefficient remains valid in the transition regions adjacent to shadow and reflection boundaries, where the diffraction coefficients of Keller's original theory fail. Our method is based on Keller's method of the canonical problem, which in this case is the perfectly-conducting wedge illuminated by plane, cylindrical, conical and spherical waves. When the proper ray-fixed coordinate system is introduced, the dyadic diffraction coefficient for the wedge is found to be the sum of only two dyads, and it is shown that this is also true for the dyadic diffraction coefficients of higher order edges. One dyad contains the acoustic soft diffraction coefficient; the other dyad contains the acoustic hard diffraction coefficient. The expressions for the acoustic wedge diffraction coefficients contain Fresnel integrals, which ensure that the total field is continuous at shadow and reflection boundaries. The diffraction coefficients have the same form for the different types of edge illumination; only the arguments of the Fresnel integrals are different. Since diffraction is a local phenomenon, and locally the curved edge structure is wedge shaped, this result is readily extended to the curved edge. It is interesting that even though the polarizations and the wavefront curvatures of the incident, reflected and diffracted waves are markedly different, the total field calculated from this high-frequency solution for the curved edge is continuous at shadow and reflection boundaries.
Document Details
- Document Type
- Technical Report
- Publication Date
- Jun 01, 1974
- Accession Number
- ADA378401
Entities
People
- P. H. Pathak
- R. G. Kouyoumjian
Organizations
- Ohio State University