Electromagnetic surface waves on a conducting cylinder

We study propagation of electromagnetic surface waves on a metal-air interface in the case when the wave frequency is below the plasma frequency. We derive a reduced wave equation for a metal cylinder with a given radius of curvature. Using the Leontovich boundary condition we find solutions to this equation which we classify as outgoing and incoming surface waves. We derive the dispersion relations of the surface waves of both types and argue that the earlier studies overlooked the waves of the second type although they are the only type which can propagate on a planar metal-air boundary.