Magnetoelectric Energy in Electrodynamics: Magnetoelectricity,Bi(an)isotropy,and Magnetoelectric Meta-Atoms

Magnetoelectricity denotes the relationship between electric polarization and magnetization. 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 that 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, it is argued 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.