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.
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