Diffraction by a half-plane with a special impedance variation

This paper deals with the diffraction of a plane electromagnetic wave incident on a variable impedance half-plane, at right angles to the edge. The problem is dealt with by a method closely related to separation of variables in parabolic coordinates. A class of solutions of the wave equation is obtained in this manner; the boundary conditions which may then be imposed on the half-plane are investigated. These boundary conditions can be chosen in such a way as to permit arbitrary values of reflection and transmission coefficients for the half-plane far away from the edge. The dependence of the diffraction pattern on these coefficients will be discussed.