Diffraction of an obliquely incident high-frequency wave by a cylindrically curved sheet

Abstract

In the application of the geometrical theory of diffraction (GTD) to practical problems, a main role is played by the diffraction coefficients of different kinds. Nevertheless the explicit expressions of the diffraction coefficients associated with edges on certain curved sheets are known only in the case of normal incidence. The canonical problems from which these coefficients are derived can always be reduced to scalar diffraction problems involving two space variables, in which either the electric or the magnetic field is parallel to the edge. Nevertheless, when the incident ray is not normal to the edge at the diffraction point, the related canonical problems inevitably involve three space coordinates and at least two dependent functions. The complexity inherent in such problems caused a lack of knowledge about the diffraction coefficients connected with the edges on curved sheets in the case of oblique incidence. The case of oblique incidence on a perfectly conducting cylindrical sheet is considered and some explicit expressions for the matrix diffraction coefficients are derived. These matrices connect the diffracted far fields of different kinds to the incident electric and magnetic field components parallel to the edge at the diffraction point. The expressions are rather simple and involve the coefficients related to the case of normal incidence in which k is replaced by k sin \theta_{0} ( k and \theta_{0} are the wavenumber and the incidence angle, respectively). The effect of the incidence angle in the attenuation constants associated with the creeping waves are dependent upon \theta_{0} only via the curvature radius of the geodesic lines.