  Resonant scattering of electromagnetic (EM) waves by small particles is
considered as one of the basic problem in metamaterial science. At present,
special subwavelength resonators are considered as structural elements in
chiral and bianisotropic metamaterials. There is a general consensus that these
small scatterers behave like "artificial atoms", meta-atoms, with strong
electrical and magnetic responses and an interconnection between these
responses. However, the observed effect of magnetoelectric (ME) coupling in
these meta-atoms is not associated with the near-field manipulation properties
caused by intrinsic magnetoelectricity. This arises the question whether ME
point scatterers of EM radiation really exist. In this paper, we show that
there are mesoscopic structures with electric and magnetic dipole-carrying
excitations that behave like point scatterers with their inherent
magnetoelectricity. In such subwavelength resonators, coherent oscillations of
the electric polarization and magnetization can be considered as quasistatic
oscillations described by electrostatic (ES) and magnetostatic (MS) scalar wave
functions. The ME resonance effect arises from the coupling of two, ES and MS,
oscillations. The near fields of these resonators, called the ME near fields,
are characterized by simultaneous violation of time reversal and inversion
symmetry. In study of ME fields and EM problems associated with these fields,
we put forward the concept of ME-field electrodynamics. Like the axion-field
electrodynamics and the axion-polariton problem, we are talking about modified
Maxwell equations with a presudoscalar source terms and the quantum field
theory for massive particles. While the axion fields are boson scalar fields,
the ME fields are fermionic fields. These fields are characterized by energy
eigenstates with rotational superflows and quantized vortices.
