Page 114 - Maxwell House

94 Chapter 2

zero or close to zero conductivity. We have used a similar approach in section 2.2.7 to get the
artificial dielectric material. Evidently, the average or macroscopic conductivity of mixed
medium rises as the volume density of high conductive inclusion increases. Therefore, such
“solid plasma” should behave as ideal plasma. If so, low density of metal inclusions means low
frequency and vice versa while the resonance frequency could be moved up and down by

simple variation of inclusion number per volume unit.
Now, let us consider the idea of the permeability control by developing ferrimagnetic-dielectric
composite. To proceed, we look back at Drude-Lorentz’s model again, but now for pure
ferrimagnetics and will try to build "magnetic meta-atoms" imitating the low-frequency domain
wall oscillations. First of all, let us rewrite (2.89) in the form

2

′
′′
() = () − () = 1 − (2.100)

2
2
− 0 −(/)
Assuming that the synthesized material must be low loss (/ → 0) we have
2

′
() ≈ 1 − (2.101)

2
− 0 2
Therefore, the real part of permeability is negative as soon as
2
2 > − (2.102)
2
0
To imitate the domain structure, we could artificially form the 3-D lattice of multiple and
isolated from each other electrically small high
conductive metal ring immersed in host medium
with zero or close to zero conductivity, as
shown in Figure 2.8.7. Evidently, each ring
carries the magnetic moment . Then the

magnetic moment of unit domain is equal to
≈ | | where N is the number of rings

Figure 2.8.8 Gap-ring and its equivalent within the sell/domain d x d x d (see Figure
circuit 2.8.7). The next step is to get resonance in ring
structure at the defined frequencies. Firstly,
such structure can carry some self-resonances but they are located at very high frequencies if
the inequality (2.99) is satisfied. Meanwhile, we can transfer each closed ring into ordinary ℒ
resonance circuit by creating the narrow gap in the ring, as shown in Figure 2.8.8, thereby
adding some gap capacitor and shifting down the
resonance frequency. Therefore, any boost in magnetic
energy concentration or inductance and in electric
energy level or capacitance could shift the resonance
frequency down. For example, creating the narrow gap Figure 2.8.9 Split-ring
in the ring, as shown in Figure 2.8.8, we can add some resonators
gap capacitor that reduces the resonance frequency.
Theoretical analysis and experiment show that we need more because the loop diameter occurs
two big at the desired frequency to satisfy (2.99). Therefore, our goal to enlarge the
concentration of electric or magnetic energy while keeping the resonance circuit as small as
possible. Figure 2.8.9 demonstrates set of so-called split-ring resonators meeting this
23
requirement. Figure 2.8.10 illustrates the metamaterial lattice. The array of rectangular split-
23 Public Domain Image, source: https://en.wikipedia.org/wiki/Photonic_metamaterial