Electromagnetic reflection from a conducting surface: Geometrical optics solution

The reflection of electromagnetic waves from a smooth conducting surface at high frequencies is studied in this paper. Both the incident and reflected fields are expanded in asymptotic series of the form , where is the phase function, and { } are amplitude vectors. Explicit formulas based on a ray technique are given for calculating the first two orders of the electric field, magnetic field, and surface current. When the conducting surface is a paraboloid (or a sphere) and the incident field is a plane wave in its axial direction, our solution recovers the exact solution (or the first two orders of the exact asymptotic solution), As a special case, our result is compared with the work of Schensted. It appears that the latter is only partially correct.