The following two-dimensional problem is considered: An arbitrary antenna is located at the origin which launches surface waves on a reactive half plane

. It is assumed that the other half plane,

, is occupied by a perfect conductor. The antenna is approximated by a distribution of multipoles easily found from the antenna\´s radiation pattern. With this approximation, simple algebraic expressions are obtained for the ratio of the power delivered to the surface wave as compared to the power in the radiated cylindrical field.