  We show that in a source-free subwavelength region of microwave fields there
can exist the field structures with local coupling between the time-varying
electric and magnetic fields differing from the electric-magnetic coupling in
regular-propagating free-space electromagnetic waves. To distinguish such field
structures from regular electromagnetic (EM) field structures, we term them as
magnetoelectric (ME) fields. We study a structure and conservation laws of
microwave ME near fields. We show that there exist sources of microwave ME near
fields - the ME particles. These particles are represented by small quasi-2D
ferrite disks with the magnetic-dipolar-oscillation spectra. The near fields
originated from such particles are characterized by topologically distinctive
power-flow vortices, non-zero helicity, and a torsion degree of freedom. Our
studies of the microwave ME near fields are combined in two successive papers.
In this paper we give a theoretical background of properties of the electric
and magnetic fields inside and outside of a ferrite particle with
magnetic-dipolar-oscillation spectra resulting in appearance of the microwave
ME near fields. Based on the obtained structures of the ME near fields, we
discuss effects of so-called ME interactions observed in artificial
electromagnetic materials. In the next paper, we represent numerical and
experimental studies of the microwave ME near fields and their interactions
with matter.
