Diffraction coefficients for higher order edges and vertices,
- L. Kaminetsky, J. B. Keller
- SIAM J. Appl. Math., vol.22,
The Diffraction coefficient for electromagnetic waves incident obliquely incident on a curved edge formed by perfectly conducting plane surfaces. This diffraction coefficient remains valid in the transition region adjacent to shadow and reflection boundaries where the diffraction coefficients of Keller’s original theory fail. Our method is proposed 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. The expressions for the acoustic wedge diffraction coefficients contain Fresnel integral, which ensure that the total field is continuous at shadow and reflection boundaries. Since the diffraction is a local phenomenon, and locally the curved edge structure is wedge shaped, this result is readily extended to the curved wedge. It is interesting that even though the polarizations and the wavefront curvature of the incident, reflected, and diffracted waves are markedly different, the total field calculated from this high frequency solution for the curved wedge is continuous at shadow and reflection boundaries. The Jacoby polynomial series method, which has been demonstrated to provide an efficient means for evaluating the radiation integral of symmetric paraboloid. The analysis leading to the series formula is also useful for deriving an analytic expression for the optimum scan plane for the displacement of the feed. Representative numerical results illustrating the application of the method and the properties of the offset paraboloid are presented.