Diffraction of Plane Waves by a Semicircular Strip

In this paper we use the geometrical theory of diffraction to study the problem of diffraction of a plane wave by a semicircular strip at high frequencies. This is intended to be an introduction to the theory of diffraction by curved strips. In considering curved strips three phenomena become apparent. First, the diffracted waves are reflected and re-reflected many times by the strip. This complicates the asymptotic description of the field enormously. Second, the diffracted wave produces a new type of shadow boundary. Third, a creeping wave is launched from the edge of the strip. We use the method of Lewis and Boersma to compute the first two terms of the diffracted field. The associated uniform expansion is continuous at the edge and at the shadow boundaries of the incident and reflected waves. This lends further support to the validity of that theory. In order to describe the field in the neighbourhood of the shadow boundary of the diffracted wave the creeping wave must be computed. We are not yet able to do this.