  Non-radiative coupling between conductive coils is a candidate mechanism for
wireless energy transfer applications. In this paper, we propose a power relay
system based on a near-field metamaterial superlens, and present a thorough
theoretical analysis of this system. We use time-harmonic circuit formalism to
describe all interactions between two coils attached to external circuits and a
slab of anisotropic medium with homogeneous permittivity and permeability. The
fields of the coils are found in the point-dipole approximation using
Sommerfeld integrals, which are reduced to standard special functions in the
long-wavelength limit. We show that, even with a realistic magnetic loss
tangent of order 0.1, the power transfer efficiency with the slab can be an
order of magnitude greater than free-space efficiency when the load resistance
exceeds a certain threshold value. We also find that the volume occupied by the
metamaterial between the coils can be greatly compressed by employing magnetic
permeability with a large anisotropy ratio.
