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)]. 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.

Microwave magnetoelectric fields and their role in the matter-field interaction.

We show that in a source-free subwavelength region of microwave fields, there can exist field structures with a 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-two-dimensional ferrite disks with magnetic-dipolar-oscillation spectra. The near fields originating from such particles are characterized by topologically distinctive power-flow vortices, nonzero helicity, and a torsion degree of freedom. The paper consists of two main parts. In the first one, 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 the appearance of microwave ME near fields. In the second main part, we represent numerical and experimental studies of the microwave ME near fields and their interactions with matter. Based on the obtained properties of the ME near fields, we discuss possibilities for effective microwave sensing of natural and artificial chiral structures.

Helical-mode magnetostatic resonances in small ferrite particles and singular metamaterials.

Small ferrite-disk particles with magnetostatic (magneto-dipole) oscillations are characterized by the topological-phase states-the vortex states. In a recently published paper (Kamenetskii et al 2010 Phys. Rev. A 81 053823), it was shown that such magnetic vortices act as traps, providing purely subwavelength confinement of electromagnetic fields. The symmetry properties of magnetostatic-vortex ferrite disks allow one to propose new-type subwavelength microwave structures. In this paper it is demonstrated that the unique topological properties of the fields in a ferrite disk are intimately related to the symmetry breaking effects of magnetostatic oscillations. This analysis is based on postulates about a physical meaning of the magnetostatic-potential function ψ(r, t) as a complex scalar wavefunction, which presumes a long-range phase coherence in magnetic dipole-dipole interactions. The proper solutions are found based on an analysis of magnetostatic-wave propagation in a helical coordinate system. It is shown that while a composition of two helical waves may acquire a geometrical phase over-running of 2π during a period, every separate helical wave has a dynamical phase over-running of π and so behaves as a double-valued function. This results in the appearance of helical-mode magnetostatic resonances in quasi-2D ferrite disks. The solutions give magnetostatic-wave power-flow-density vortices with cores at the disk center and azimuthally running waves of magnetization. The near fields of magnetostatic-vortex ferrite-disk particles are characterized by space-time symmetry violation. For incident electromagnetic waves, such particles, with sizes much less than the free-space electromagnetic wavelength, appear as local singular regions. From the properties of a composition of magnetostatic-vortex ferrite-disk particles, one may propose novel metamaterials-singular metamaterials.

Magnetic-dipolar and electromagnetic vortices in quasi-2D ferrite discs.

Magnetic-dipolar-mode (MDM) oscillations in a quasi-2D ferrite disc show unique dynamical symmetry properties resulting in the appearance of topologically distinct structures. Based on the magnetostatic (MS) spectral problem solutions, in this paper we give evidence for eigen-MS power-flow-density vortices in a ferrite disc. Due to these circular eigen-power flows, the MDMs are characterized by MS energy eigenstates. It becomes evident that the reason for stability of the vortex configurations in saturated ferrite samples is completely different from the nature of stability in magnetically soft cylindrical dots. We found a clear correspondence between analytically derived MDM vortex states and numerically modeled electromagnetic vortices in quasi-2D ferrite discs.

Microwave whirlpools in a rectangular waveguide cavity with a thin ferrite disk.

We study a three-dimensional system of a rectangular waveguide resonator with an inserted thin ferrite disk. The interplay of reflection and transmission at the disk interfaces together with a material gyrotropy effect, gives rise to a rich variety of wave phenomena. We analyze the wave propagation based on full Maxwell-equation numerical solutions of the problem. We show that the power-flow lines of the microwave-cavity field interacting with a ferrite disk, in the proximity of its ferromagnetic resonance, form whirlpool-like electromagnetic vortices. Such vortices are characterized by the dynamical symmetry breaking. The role of ohmic losses in waveguide walls and dielectric and magnetic losses in a disk are the subjects of our investigations.

Self-induced quasistationary magnetic fields.

The interaction of electromagnetic radiation with temporally dispersive magnetic solids of small dimensions may show very special resonant behaviors. The internal fields of such samples are characterized by magnetostatic-potential scalar wave functions. The oscillating modes have the energy orthogonality properties and unusual pseudoelectric (gauge) fields. Because of a phase factor, that makes the states single valued, a persistent magnetic current exists. This leads to appearance of an eigenelectric moment of a small disk sample. One of the intriguing features of the mode fields is dynamical symmetry breaking.

Microwave magnetoelectric particles: an experimental study of oscillating spectrums.

One of the ways to uncover the nature of the microwave magnetoelectric (ME) effect, recently observed in small ferrite resonators with special-form surface metallizations, is a comparative analysis of oscillating spectrums excited by different type rf external fields. Experimental results of the ME coupling in different types of ferrite resonators and different types of surface electrodes are reported and some important conclusions are drawn observing the oscillating spectrums of those particles. A special interest in spectral properties of point ME particles should be found in the field of microwave artificial composite materials-bianisotropic materials.

Energy eigenstates of magnetostatic waves and oscillations.

Effect of excitation of magnetostatic oscillations in a ferrite resonator by the microwave magnetic field was a subject of many publications of more than the last 40 years. The most interesting multiresonance spectrum of absorption peaks one can observe experimentally is a case of disk-form small ferrite resonators. It is shown in this paper that such small ferrite resonators can be considered as "artificial molecular structures" with properties characterized by energy eigenstates of magnetostatic oscillations. A special interest in these properties may be found in the field of microwave artificial composite materials.