Paraxial equation for the surface wave on a conducting cylinder

We derive a reduced wave equation for the surface waves on an air-metal interface with a given radius of curvature R. Using the Leontovich boundary condition with a small dimensionless surface impedance ξ we find solutions to this equation in terms of the Airy-Fock functions. A relation between the surface waves on a planar and cylindrical metal-air interfaces is elucidated and the dispersion relation of a planar surface wave is recovered as the limit of a sufficiently large curvature radius R.