Topological properties of microwave magnetoelectric fields

Collective excitations of electron spins in a ferromagnetic sample dominated by the magnetic dipole-dipole interaction strongly influence the field structure of microwave radiation. A small quasi-two-dimensional ferrite disk with magnetic-dipolar-mode (MDM) oscillation spectra can behave as a source of specific fields in vacuum, termed magnetoelectric (ME) fields. A coupling between the time-varying electric and magnetic fields in the ME-field structures is different from such a coupling in regular electromagnetic fields. The ME fields are characterized by strong energy confinement at a subwavelength region of microwave radiation, topologically distinctive power-flow vortices, and helicity parameters [E. O. Kamenetskii, R. Joffe, and R. Shavit, Phys. Rev. E 87, 023201 (2013)10.1103/PhysRevE.87.023201]. We study topological properties of microwave ME fields by loading a MDM ferrite particle with different dielectric samples. We establish a close connection between the permittivity parameters of dielectric environment and the topology of ME fields. We show that the topology of ME fields is strongly correlated with the Fano-resonance spectra observed at terminals of a microwave structure. We reveal specific thresholds in the Fano-resonance spectra appearing at certain permittivity parameters of dielectric samples. We show that ME fields originated from MDM ferrite disks can be distinguished by topological portraits of the helicity parameters and can have a torsion degree of freedom. Importantly, the ME-field phenomena can be viewed as implementations of space-time coordinate transformations on waves.