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The plane-wave scattering matrix is used to characterize antennas that are located just above a planar interface that separates two media. The plane-wave transmitting spectrum for the field radiated downward into the lower medium is expressed directly in terms of the current distribution of the transmitting antenna. The transmitting spectrum for a reciprocal antenna determines the plane-wave receiving spectrum for the field that propagates upward in the lower medium. A measurement procedure is discussed for determining the plane-wave transmitting and receiving spectra from measurements with a probe that is located in the lower medium.