Phase operator method in problem of scattering of electromagnetic waves on ideally conducting surface

Use of an S-matrix is common in a theoretical description of the scattering of electromagnetic waves on irregular surfaces because it relates the amplitudes of the incident and scattered waves. In an earlier article by the author (DAN, Vol 272, No 6, pp 1351-1355) it was proposed that a theory of perturbations be developed not relative to the scattering matrix itself, as is usually done, but relative to its logarithm. It was shown that with such an approach even the first approximation gives results corresponding to the first two approximations in the traditional perturbation theory. The approach proposed in that article is now applied to the problem of scatteing of an electromagnetic wave on an ideally conducting surface: a monochromatic electromagnetic wave of a stipulated frequency is incident on this surface from above, this surface consisting of plane (uniform and nonuniform) waves. A scattering matrix is formed for vertically and horizontally polarized waves for such a surface, as well as a matrix which the author calls a phase operator. With this as a point of departure, a final form of the scattering matrix is proposed for the first approximation (which can be used in subsequent approximations). Not only is a solution of the formulated problem obtained, but the advantageousness of the proposed approach over traditional perturbation theory is demonstrated.