On the Correct Definition of Polarization for Metamaterials

To compute the electric dipole moment, there are two classical ways: from the charge density or from the current density. Although both ways are equivalent for the case of a local source, they are different when the current density touches the boundary of the integration volume, as may happen for some unit cells of periodic structures. In this paper, we study what is the best choice in order to get the macroscopic polarization of a periodic metamaterial.