Diffraction of a Dipole Field by a Perfectly Conducting Half Plane

The problem of the diffraction of a dipole field by a perfectly conducting half plane or wedge has attracted considerable attention and the literature dates back over half a century. One of the earliest investigations was that of Bromwich (1915) who sought to deduce the solution from a Hertz vector made up of the known solution for the corresponding scalar problem, but it was later realized that the resulting vector solution violates the edge conditions for almost all orientations of the dipole.~ The correct solution for the particular case of an electric dipole with axis normal to the half plane was obtained in 1953. The procedure was to represent the source field as an angular spec· trum of plane waves, and thereby synthesize the solution from the known (Sommerfeld) solution for the diffraction of a plane wave. It was found that the expressions for the field components are compose<! of terms which are derivatives of the scalar solutions for the diffraction of a pointsource field by an acoustically hard or soft half plane, plus terms corresponding to a source-free solution of Maxwell's equations. Many of the later investigations result~d in this same type of representation of the solution, and the additive or source-free contribution essential for the correct edge behavior is now known for all orientations of dipoles, both electric and magnetic (Vandakurov, 1954; Woods, 1957; Williams, 1957; Jones, 1964).