19 Magnetoelectric Near Fields
547
(in an endless cylindrical ferrite rod, in particular) with the homogeneous-precession
mode (Kittel’s mode) [18]. The divergence of both the DC and RF magnetizations
may occur in a ferrite sample in a case of nonhomogeneous-precession modes. These
magnetic-dipole modes—Walker’s modes—in a thin endless cylindrical ferrite rod
were studied in [85]. For these eigenmodes, the RF magnetic field of the incident
EM wave induces a magnetic dipoles, which lies in the r, θ plane of a ferrite rod. In
Fig. 19.10b, the +
(m)
, −
(m) surface magnetic charges correspond to the maximum,
minimum of the charge distributions in the azimuth coordinates. Due to the timereversal symmetry breaking, these surface magnetic charges cannot cause two, clockwise (CW) and counter clockwise (CCW), azimuthal magnetic currents. For the given
direction of bias magnetic field, we may have only CW or CCW induced magnetic
current, which passes over a regular-coordinate angle π at the time phase of π . In
Fig. 19.10b, this is shown as the CW blue-arrow current. We can suppose, however,
that there exists a polaritonic structure with an additional (non-electromagnetic)
phase shift, when the gradient of twisting angle plays the role of the phase gradient.
A global phase texture with coflowing an EM-wave induced magnetic current and
topological magnetic current will provide us with the possibility to have rotational
symmetry by a turn over a regular-coordinate angle 2π at the time phase of π . This
situation is shown in Fig. 19.10b, where the CW magnetic current of a polaritonic
structure is conventionally represented as a circle composed by the blue and red
arrows. It is worth noting, however, that one can view such a phenomenon not in a
ferrite rod, but in the r, θ plane of a ferrite disk with MDM oscillations, where the
non-electromagnetic torque is caused by the topological-phase effects. In the MDM
ferrite-disk resonator, the non-zero circulation of such a magnetic current, observed
at the time phase shift of π , results in appearance of a constant angular momentum
directed along the z axis. This is possible due to an additional phase shift of the
magnetic current along the z axis. The magnetic currents have a helical structure.
When such helical currents (and so helical waves) cannot be observed in a smooth
ferrite rod, they can be seen in a MDM ferrite disk [86].
B. Testing the topological properties of the ME field with small metal rods and
rings in a microwave waveguide
In a structure of a MDM particle embedded in a microwave waveguide, photons
interact strongly and coherently with magnetic excitations. The creation of certain
non-classical states in such a macroscopic system can be observed with help of small
metallic elements placed inside a microwave waveguide near the ferrite disk. Here
we show some of the topological properties of the ME field using small metallic rods
and rings.
A structure of microwave waveguide with a ferrite disk and small metallic rod,
shown in Fig. 19.11a, was studied experimentally in [87] and numerically in [88].
The rod is oriented along an electric field of a rectangular waveguide. Its diameter
is a very small compared to the disk diameter and to the free-space electromagnetic wavelength. On the basis of a comparative analysis of experimental oscillation
spectra, it was argued in [87] that the fact that an additional small capacitive coupling
547
(in an endless cylindrical ferrite rod, in particular) with the homogeneous-precession
mode (Kittel’s mode) [18]. The divergence of both the DC and RF magnetizations
may occur in a ferrite sample in a case of nonhomogeneous-precession modes. These
magnetic-dipole modes—Walker’s modes—in a thin endless cylindrical ferrite rod
were studied in [85]. For these eigenmodes, the RF magnetic field of the incident
EM wave induces a magnetic dipoles, which lies in the r, θ plane of a ferrite rod. In
Fig. 19.10b, the +
(m)
, −
(m) surface magnetic charges correspond to the maximum,
minimum of the charge distributions in the azimuth coordinates. Due to the timereversal symmetry breaking, these surface magnetic charges cannot cause two, clockwise (CW) and counter clockwise (CCW), azimuthal magnetic currents. For the given
direction of bias magnetic field, we may have only CW or CCW induced magnetic
current, which passes over a regular-coordinate angle π at the time phase of π . In
Fig. 19.10b, this is shown as the CW blue-arrow current. We can suppose, however,
that there exists a polaritonic structure with an additional (non-electromagnetic)
phase shift, when the gradient of twisting angle plays the role of the phase gradient.
A global phase texture with coflowing an EM-wave induced magnetic current and
topological magnetic current will provide us with the possibility to have rotational
symmetry by a turn over a regular-coordinate angle 2π at the time phase of π . This
situation is shown in Fig. 19.10b, where the CW magnetic current of a polaritonic
structure is conventionally represented as a circle composed by the blue and red
arrows. It is worth noting, however, that one can view such a phenomenon not in a
ferrite rod, but in the r, θ plane of a ferrite disk with MDM oscillations, where the
non-electromagnetic torque is caused by the topological-phase effects. In the MDM
ferrite-disk resonator, the non-zero circulation of such a magnetic current, observed
at the time phase shift of π , results in appearance of a constant angular momentum
directed along the z axis. This is possible due to an additional phase shift of the
magnetic current along the z axis. The magnetic currents have a helical structure.
When such helical currents (and so helical waves) cannot be observed in a smooth
ferrite rod, they can be seen in a MDM ferrite disk [86].
B. Testing the topological properties of the ME field with small metal rods and
rings in a microwave waveguide
In a structure of a MDM particle embedded in a microwave waveguide, photons
interact strongly and coherently with magnetic excitations. The creation of certain
non-classical states in such a macroscopic system can be observed with help of small
metallic elements placed inside a microwave waveguide near the ferrite disk. Here
we show some of the topological properties of the ME field using small metallic rods
and rings.
A structure of microwave waveguide with a ferrite disk and small metallic rod,
shown in Fig. 19.11a, was studied experimentally in [87] and numerically in [88].
The rod is oriented along an electric field of a rectangular waveguide. Its diameter
is a very small compared to the disk diameter and to the free-space electromagnetic wavelength. On the basis of a comparative analysis of experimental oscillation
spectra, it was argued in [87] that the fact that an additional small capacitive coupling