Closed-form expressions for uniform currents on a wedge illuminated by TM plane wave

Closed-form expressions for nonuniform currents on a perfectly conducting, infinite wedge illuminated by a transverse magnetic plane wave are presented. The expressions are derived by requiring that they agree with the current predicted by the eigenfunction solution close to the edge and J.B. Keller´s geometrical theory of diffraction (1962) far from the edge. The angle of incidence is arbitrary and the expressions remain uniformly valid even for glancing angles of incidence when the geometrical optics boundaries are in the vicinity of the wedge faces. The formulas presented are simple, involving Fresnel functions with complex arguments. These functions can be expressed in terms of complimentary error functions which may be computed using standard subroutine packages. Exact expressions for nonuniform currents are available for the two special cases of half-planes and infinite planes. Closed-form expressions for the axial electric field, and hence all the field components in the vicinity of the wedge axes, are also obtained. Currents computed using expressions obtained are compared with currents computed from the eigenfunction solution of the wedge, with good agreement throughout