A uniform asymptotic theory of diffraction

The diffraction of a high-frequency scalar wave by a plane screen can be treated by Keller\´s geometrical theory of diffraction (GTD). The GTD solution fails however at the edge of the screen and on shadow boundaries where the solution is infinite and discontinuous. These defects are overcome by the "uniform asymptotic theory of edge diffraction" (UAT) which is an extension of GTD. Starting from a new Ansatz that involves Fresnel integrals in an appropriate manner, the uniform theory provides a high-frequency asymptotic solution of the diffraction problem that is uniformly valid near the edge and the shadow boundaries, i.e., the solution satisfies the edge condition and is finite and continuous at shadow boundaries. Away from these regions the UAT solution reduces to that of Keller\´s theory. So far, the uniform theory has been successfully applied to diffraction through a slit or a circular aperture in a plane screen, and to problems of reflection and diffraction at an open-ended parallel-plane waveguide. Further extensions of UAT to electromagnetic diffraction by a plane screen, and to diffraction (scalar or electromagnetic) by a curved wedge, will be discussed.