  We show that there exists an exact solution for a lossless and reciprocal
periodic surface impedance which ensures full conversion of a single-mode
surface wave propagating along the impedance boundary to a single plane wave
propagating along a desired direction in free space above the boundary. In
contrast to known realizations of leaky-wave antennas, the optimal surface
reactance modulation which is found here ensures the absence of evanescent
higher-order modes of the Floquet wave expansion of fields near the radiating
surface. Thus, all the energy carried by the surface wave is used for launching
the single inhomogeneous plane wave into space, without accumulation of
reactive energy in higher-order modes. The results of the study are expected to
be useful for creation of leaky-wave antennas with the ultimate efficiency,
and, moreover, can potentially lead to novel applications, from microwaves to
nanophotonics.
