Electromagnetic surface waves on a conducting cylinder

• Two types of surface waves at a cylindrical metal–air boundary are found in a low frequency limit.
• The “outgoing” and “ingoing” surface waves qualitatively differ by the radial profile of the Poynting vector.
• The dispersion relations for the waves of both types are derived.
• Only the wave of “ingoing” type survives in the limit of a planar metal–air boundary.

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.