Radiation in the far zone of an elementary emitter located on the boundary of a plane layered structure

A rigorous theory of determining radiation in the far zone of an elementary dipole that is located either on the boundary of a plane-layered structure or inside it is considered. The particular case of radiation from an elementary dipole located on a free boundary of one film is considered in detail, an efficient method for finding the radiation field in the far zone in the surrounding half-spaces is proposed. The directional patterns of point emitters (molecules, nanostructures) located on the free surface of a metal film in the Kretschmann scheme and having an induced dipole moment directed either parallelly or perpendicularly to the film surface are determined.