19 Magnetoelectric Near Fields
551
microwave structure is a rectangular waveguide cavity with a normally magnetized
ferrite-disk sample. The operating frequency, which is a resonant frequency of the
cavity, is constant. The only external parameter, which varies in the experiment,
is a bias magnetic field. The observed discrete variation of the cavity impedances
is related to discrete states of the cavity fields. Since the effect was obtained at a
given resonant frequency, the shown resonances are not conventional cavity modes
related to the frequency-dependent quantization of the photon wave vector. These
resonances are caused by the quantized variation of energy of a ferrite disk, which
appear due to variation of energy of an external source—the bias magnetic field.
At the regions of a bias magnetic field, designated in Fig. 19.13 as A, a, b, c, d,
…, we do not have MDM resonances. In these regions, a ferrite disk is “seen” by
electromagnetic waves, as a very small obstacle which, practically, does not perturb
a microwave cavity. In this case, the cavity (with an embedded ferrite disk) has good
impedance matching with an external waveguiding structure and a microwave energy
accumulated in a cavity is at a certain maximal level. At the MDM resonances, the
reflection coefficient sharply increases (the states designated in Fig. 19.13 by numbers
1, 2, 3, …). The input impedances are real, but the cavity is strongly mismatched
with an external waveguiding structure. It means that at the MDM-resonance peaks,
the cavity receives less energy from an external microwave source. In these states
of a bias magnetic field, the microwave energy stored in a cavity sharply decreases,
compared to its maximal level in the A, a, b, c, d, … Since the only external parameter,
which varies in this experiment, is a bias magnetic field, such a sharp release of the
microwave energy accumulated in a cavity to an external waveguiding structure
should be related to the emission of discrete portions of energy from a ferrite disk.
This means that at the MDM resonances, a strong and sharp decrease in the magnetic
energy of the ferrite sample should be observed.
When speaking about the eigenstates of the microwave-cavity spectrum observed
at the bias-field variation and constant frequency, we should answer the question
about the eigenfunctions of this spectrum. In general, microwave resonators with
the time-reversal symmetry breakings give an example of a nonintegrable, i.e., path
dependent, system. The time-reversal symmetry breaking effect leads to creation
of the Poynting-vector vortices in a vacuum region the microwave resonators with
enclosed lossless ferrite samples [94–97]. In an analysis of the cavity eigenfunctions,
it makes no sense to consider the reflection of electromagnetic waves from magnetized ferrites from the standpoint of energy flow and ray propagation [98]. One cannot
use an interpretation which allows viewing the modes as pairs of two bouncing electromagnetic plane waves. This interpretation clearly shows that for a structure with
an enclosed magnetized ferrite sample given, for example, in Fig. 19.14, there can
be no identity between the rays 1 → F → 1
and 1
→ F → 1 in the sense that
these rays can acquire different phases when are reflected by the ferrite.
At the same time, it is argued [99] that in quantum mechanics the distinction
between integrable and nonintegrable systems does not work any longer. The initial
conditions are defined only within the limits of the uncertainty relation xp ≥
1
2
.
Since the Schrödinger equation is linear, a quantum mechanical wave packet can be
constructed from the eigenfunctions by the superposition principle. What do we have
551
microwave structure is a rectangular waveguide cavity with a normally magnetized
ferrite-disk sample. The operating frequency, which is a resonant frequency of the
cavity, is constant. The only external parameter, which varies in the experiment,
is a bias magnetic field. The observed discrete variation of the cavity impedances
is related to discrete states of the cavity fields. Since the effect was obtained at a
given resonant frequency, the shown resonances are not conventional cavity modes
related to the frequency-dependent quantization of the photon wave vector. These
resonances are caused by the quantized variation of energy of a ferrite disk, which
appear due to variation of energy of an external source—the bias magnetic field.
At the regions of a bias magnetic field, designated in Fig. 19.13 as A, a, b, c, d,
…, we do not have MDM resonances. In these regions, a ferrite disk is “seen” by
electromagnetic waves, as a very small obstacle which, practically, does not perturb
a microwave cavity. In this case, the cavity (with an embedded ferrite disk) has good
impedance matching with an external waveguiding structure and a microwave energy
accumulated in a cavity is at a certain maximal level. At the MDM resonances, the
reflection coefficient sharply increases (the states designated in Fig. 19.13 by numbers
1, 2, 3, …). The input impedances are real, but the cavity is strongly mismatched
with an external waveguiding structure. It means that at the MDM-resonance peaks,
the cavity receives less energy from an external microwave source. In these states
of a bias magnetic field, the microwave energy stored in a cavity sharply decreases,
compared to its maximal level in the A, a, b, c, d, … Since the only external parameter,
which varies in this experiment, is a bias magnetic field, such a sharp release of the
microwave energy accumulated in a cavity to an external waveguiding structure
should be related to the emission of discrete portions of energy from a ferrite disk.
This means that at the MDM resonances, a strong and sharp decrease in the magnetic
energy of the ferrite sample should be observed.
When speaking about the eigenstates of the microwave-cavity spectrum observed
at the bias-field variation and constant frequency, we should answer the question
about the eigenfunctions of this spectrum. In general, microwave resonators with
the time-reversal symmetry breakings give an example of a nonintegrable, i.e., path
dependent, system. The time-reversal symmetry breaking effect leads to creation
of the Poynting-vector vortices in a vacuum region the microwave resonators with
enclosed lossless ferrite samples [94–97]. In an analysis of the cavity eigenfunctions,
it makes no sense to consider the reflection of electromagnetic waves from magnetized ferrites from the standpoint of energy flow and ray propagation [98]. One cannot
use an interpretation which allows viewing the modes as pairs of two bouncing electromagnetic plane waves. This interpretation clearly shows that for a structure with
an enclosed magnetized ferrite sample given, for example, in Fig. 19.14, there can
be no identity between the rays 1 → F → 1
and 1
→ F → 1 in the sense that
these rays can acquire different phases when are reflected by the ferrite.
At the same time, it is argued [99] that in quantum mechanics the distinction
between integrable and nonintegrable systems does not work any longer. The initial
conditions are defined only within the limits of the uncertainty relation xp ≥
1
2
.
Since the Schrödinger equation is linear, a quantum mechanical wave packet can be
constructed from the eigenfunctions by the superposition principle. What do we have