Three-dimensional scalar beam diffraction by a half plane

Abstract

The complex source point technique greatly simplifies the inclusion of source directivity in scattering and diffraction solutions. By replacing its coordinates by appropriate complex coordinates, an omnidirectional source becomes a beam source. Any diffraction solution for the source becomes the corresponding solution for beam diffraction. Geometrical diffraction theory solutions for local beam sources can be most easily obtained in this way. Here the complex source point technique is applied to a canonical solution in geometrical diffraction theory: three-dimensional scalar beam diffraction by a half plane. First, a general three-dimensional solution for a scalar point source and its evolution to a beam source is reviewed. An exact uniform asymptotic solution for point and beam source diffraction by a rigid or soft half plane is then given for arbitrary incidence in three dimensions. A method for numerical evaluation of the diffraction integrals is shown. In this method the Fresnel integrals with complex arguments are converted to complementary error functions with complex arguments, for which efficient computer subroutines are available. The procedure is illustrated by a numerical example and three-dimensional numerical plots are presented. Electromagnetic (vector) field three-dimensional beam diffraction by half planes will yield to the same approach. So also will three-dimensional beam diffraction by wedges using the uniform geometrical theory of diffraction but the resulting expressions are more complicated.