A compact dyadic diffraction coefficient for electromagnetic waves obliquely incident on a curved edse formed by perfectly conducting curved ot 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 Fresenel 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 wedge. 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 wedge is continuous at shadow and reflection boundaries.

A uniform geometrical theory of diffraction for an edge in a perfectly conducting surface

Asymptotic solutions of oscillatory initial value problems

On etudie la decroissance des solutions de l'equation des ondes dans l'exterieur de plusieurs objets strictement convexes. On exprime une condition suffisante pout decroissance exponentielle d'energie locale en terme de periode et d'application de Poincare des rayons periodiques dans le domaine exterieur

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Decay of solutions of the wave equation in the exterior of several convex bodies

The short wavelength or high frequency asymptotic theory of the reduced wave equation and of Maxwell’s equations is presented. The theory is applied to representative problems involving reflection, transmission, and diffraction in both homogeneous and inhomogeneous media. It is a slightly revised version of a report1 written in 1964 by the authors. Despite its age, it still provides a convenient introduction to the formal asymptotic theory and to the geometrical theory of diffraction.

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R. M. Lewis

Papers

Asymptotic Solution of Some Diffraction Problems