Using the equivalent medium theory, we have investigate the surface retarded modes of a semi-infinite lateral superlattices composed of semiconductor antiferromagnetic layers and insulating nonmagnetic layers in the Voigt geometry. We studied the effect of eddy current on surface retarded modes of a lateral antiferromagnetic/nonmagnetic superlattice when the external field is zero or nonzero. Particularly, we have considered the effect of conduction current and displacement current on the retarded modes, and have obtained for the first time the curves for different cases of the frequency and the spin wave damping versus the wave vector k.