Different ways exist in optics to realize photons carrying nonzero orbital angular momentum. Such photons with rotating wave fronts are called twisted photons. In microwaves, twisted fields can be produced based on small ferrite particles with magnetic-dipolar-mode (MDM) oscillations. Recent studies showed strong localization of the electric and magnetic energies of microwave fields by MDM ferrite disks. For electromagnetic waves irradiating MDM disks, these small ferrite samples appear as singular subwavelength regions with time and space symmetry breakings. The fields scattered by a MDM disk are characterized by topologically distinctive power-flow vortices and helicity structures. In this paper we analyze twisted states of microwave fields scattered by MDM ferrite disks. We show that in a structure of the fields scattered by MDM particles, one can clearly distinguish rotating topological-phase dislocations. Specific long-distance topological properties of the fields are exhibited clearly in the effects of path-dependent interference with two coupled MDM particles. Such double-twisted scattering is characterized by topologically originated split-resonance states. Our studies of topological-phase effects and path-dependent interference in microwave structures with MDM ferrite particles are based on numerical analysis and recently developed analytical models. We present preliminary experimental results aimed to support basic statements of our studies. PACS number(s): 41.20.Jb; 76.50.+g; 81.05.Xj

The dual symmetry between the electric and magnetic fields underlies Maxwell's electrodynamics. Due to this symmetry one can describe topological properties of an electromagnetic field in free space and obtain the conservation law of optical (electromagnetic) helicity. What kind of the field helicity one can expect to see when the electromagnetic-field symmetry is broken? The near fields originated from small ferrite particles with magnetic-dipolar-mode (MDM) oscillations are the fields with the electric and magnetic components, but with broken dual (electric-magnetic) symmetry. These fields -called magnetoelectric (ME) fields -have topological properties different from such properties of electromagnetic fields. The helicity states of ME fields are topologically protected quantum-like states. In this paper, we study the helicity properties of ME fields. We analyze conservation laws of the ME-field helicity and show that the helicity density is related to an imaginary part of the complex power-flow density. We show also that the helicity of ME fields can be a complex value.PACS number(s): 41.20.Jb; 42.50.Tx; 76.50.+g

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)]. 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.

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The near fields in the proximity of a small ferrite particle with magnetic-dipolar-mode (MDM) oscillations have space and time symmetry breakings. Such MDM-originated fields -called magnetoelectric (ME) fields -carry both spin and orbital angular momentums. By virtue of unique topology, ME fields are strongly different from free-space electromagnetic (EM) fields. In this paper, we show that because of chiral topology of ME fields in a near-field region, farfield orbital angular momenta (OAM) can be observed, both numerically and experimentally. In a single-element antenna, we obtain a radiation pattern with an angular squint. We reveal that in far-field microwave radiation a crucial role is played by the ME energy distribution in the near-field region.PACS number(s): 41.20.Jb; 42.50.Tx; 76.50.+g I.