  It is demonstrated theoretically that a thin layer of an anisotropic
antiferromagnetic (AFM) insulator can effectively conduct spin current by
excitation of a pair of evanescent AFM spin wave modes. The spin current
flowing through the AFM is not conserved due to the interaction between the
excited AFM modes and the AFM lattice, and, depending on the excitation
conditions, can be either attenuated or enhanced. When the phase difference
between the excited evanescent modes is close to $\pi/2$, there is an optimum
AFM thickness for which the output spin current reaches a maximum, that can
significantly exceed the magnitude of the input spin current. The spin current
transfer through the AFM depends on the ambient temperature and increases
substantially when temperature approaches the Neel temperature of the AFM
layer.
