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In materials with an intrinsic magnetoelectric (ME) effect, the energydensity comprises the polarization, magnetization and ME energy densities.These three components of energy define local (subwavelength) characteristicsof electromagnetic (EM) responses in multiferroic materials. In a subwavelengthdomain, coupling between the electric and magnetic dipole oscillations formsthe ME field structures which are characterized by the violation of bothspatial and temporal symmetry. Unlike multiferroics, bi(an)isotropicmetamaterials are associated with an EM response characterized only by spatialsymmetry breaking. This also applies to chiral materials. Since no intrinsicmagnetoelectricity is assumed in such structures, any concepts about the storedME 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 EMfar field characteristics. In this paper, we argue that in the implementationof local (subwavelength) ME meta atoms and systems for near field probing ofchirality, the concept on ME energy is crucial. Real ME energy can occur whenME fields in a singular subwavelength domain are characterized by a violationof both the symmetry of time reversal and spatial reflection.

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