High-frequency diffraction of a line-source field by a half-plane : solutions by ray techniques

The diffraction of an arbitrary cylindrical wave due to a line source and incident on a half-plane is treated by the uniform asymptotic theory of edge diffraction. For large wavenumberk, an asymptotic solution for the total field up to and including terms of orderk^{-3/2}relative to the incident field is derived. This solution is uniformly valid for all observation points, including points near the edge and the shadow boundaries. In particualr, two special cases are considered: A) the line source is located on the half-plane, and radiates anE-polarized wave and B) the line source is located in the aperture complementary to the half-plane and radiates anH-polarized wave. A companion paper will show that our asymptotic solution for Case A) is in complete agreement with the asymptotic expansion of the exact solution. For the same diffraction problem, asymptotic solutions obtained by the method of slope diffraction coefficients and the method of equivalent currents are also discussed. It is found that the latter solutions agree with the exact one only when i) the observation point is away from the edge and the shadow boundaries, and/or ii) the terms of orderk^{-3/2}in the field solution are ignored