Ray theory of diffraction by a half‐sheet parallel to a flat earth

In this paper, the diffraction by a half‐sheet parallel to a flat earth for H‐ and E‐polarized plane waves are discussed. The half‐sheet is assumed to be perfectly conducting, and the flat earth is an imperfectly conducting dielectric with the complex refractive index n . This problem is solved by using the angular spectrum proposed by Clemmow, which may be also solved by using the Wiener‐Hopf technique. When kd is large, the diffraction fields can be approximated by the geometrical rays even for small r except in the neighborhood of θ = π/2 and 3π/2. Here, r and θ are polar coordinates of the observation point, with the origin as the edge, and d is the distance between the half‐sheet and the flat earth. The far field can be approximated by the simple geometrical rays in all regions (0 < θ < π). The interaction between the edge and the flat earth can be evaluated even for small kd . Exact values by the numerical integration show that these approximate solutions can give very good accuracy even for small r except in the neighborhood of θ = π/2 and 3π/2. These results will give a fundamental concept to the understanding of the diffraction by a finite conducting plane over a flat earth.