Magnetoelectric energy in electrodynamics: Magnetoelectricity, bi(an)isotropy, and magnetoelectric meta-atoms

Abstract: In materials with an intrinsic magnetoelectric (ME) effect, the energy density comprises the polarization, magnetization and ME energy densities. These three components of energy define local (subwavelength) characteristics of electromagnetic (EM) responses in multiferroic materials. In a subwavelength domain, coupling between the electric and magnetic dipole oscillations forms the ME field structures which are characterized by the violation of both spatial and temporal symmetry. Unlike multiferroics, bi(an)isotropic metamaterials are associated with an EM response characterized only by spatial symmetry breaking. This also applies to chiral materials. Since no intrinsic magnetoelectricity is assumed in such structures, any concepts about the stored ME energy are not applicable. This clearly points to the effect of nonlocality. That is why the basic concepts of bi(an)isotropy can only be analyzed by the EM far field characteristics. In this paper, we argue that in the implementation of local (subwavelength) ME meta atoms and systems for near field probing of chirality, the concept on ME energy is crucial. Real ME energy can occur when ME fields in a singular subwavelength domain are characterized by a violation of both the symmetry of time reversal and spatial reflection.