Non-radiative coupling between conductive coils is a candidate mechanism forwireless energy transfer applications. In this paper, we propose a power relaysystem based on a near-field metamaterial superlens, and present a thoroughtheoretical analysis of this system. We use time-harmonic circuit formalism todescribe all interactions between two coils attached to external circuits and aslab of anisotropic medium with homogeneous permittivity and permeability. Thefields of the coils are found in the point-dipole approximation usingSommerfeld integrals, which are reduced to standard special functions in thelong-wavelength limit. We show that, even with a realistic magnetic losstangent of order 0.1, the power transfer efficiency with the slab can be anorder of magnitude greater than free-space efficiency when the load resistanceexceeds a certain threshold value. We also find that the volume occupied by themetamaterial between the coils can be greatly compressed by employing magneticpermeability with a large anisotropy ratio.
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