2.1 Realization of artificial μ-negative (MNG) medium

Among engineered materials with negative magnetic permeability, artificial magnetic materials (AMMs) have been the subject of interest for many years. This is due to their unique features, including low cost ease of integration with radio frequency/microwave circuits, and the possibility of synthesizing magnetic permeability to certain magnetization and polarization levels at the frequency of interest. This is in contrast to ordinary magnetic materials, like ferrite composites, that are limited in their magnetization levels and as well as suffer from magnetic losses at microwave frequency regime [9].

The idea of creating magnetic materials from conductors was first proposed by Schelkunoff [10]. A wide variety of artificial magnetic inclusions have been proposed and implemented in the literature. One of the popular and widely applied artificial magnetic materials is the split-ring resonator (SRR). Pendry et al. [3] used concentric metallic rings in order to provide further enhancement of the magnetic properties of the rings. The SRR, as shown in Figure 3a, consists of two concentric circular (i.e., edge-coupled) metallic rings printed in a host dielectric medium, with splits at opposite ends of the rings. Another form of "SRR-based" AMM is realized by placing the two split-rings in opposite sides (broadside-coupled) within the host medium [11, 12], which can provide two advantages: firstly, the effects of bianisotropy, or cross polarization, are eliminated due to the broadside nature of the metallic rings (see Figure 3c), and secondly, there is additional capacitive coupling to the composite structure, hence achieving stronger resonance behavior [8, 11, 12], as shown in Figure 3b. Other forms of resonant metallic inclusions, like spiral, omega, Hilbert, can also be adopted to achieve artificial magnetic media, as shown in Figure 3. Significant miniaturization factors can be achieved using either spiralor Hilbert-type resonators [13, 14].

The physical principle of operation behind the artificial magnetic materials, as shown in Figure 3, is almost the same. Let us consider the subwavelength resonant inclusion in Figure 3c and assume that it occupies an infinite space with large number Electromagnetic Field Interaction with Metamaterials DOI: http://dx.doi.org/10.5772/intechopen.84170

Figure 3.

Possible resonant metallic inclusions for synthesizing artificial magnetic materials, (a) edge-coupled circular SRR, (b) edge-coupled square SRR, (c) broadside-coupled SRR, (d) spiral resonator, and (e) Hilbert resonator.

of periodicity in two- or three-dimensional planes (i.e., periodicity implies here repetition factor that is much smaller than λ). Upon an excitation of an external magnetic field, which is orthogonal to the paper plane, to such an infinitely large and homogenized artificial structure, the external magnetic field induces an electromotive force in the inclusions, which in turn results in a circulating effective current flowing around the inclusions. Upon such excitation, a general form for the effective magnetic permeability of any of the AMM structures as shown in Figure 3 can then be expressed as

$$\mu\_{\rm eff} = 1 - \frac{K \, joL\_{\rm eff}}{Z\_{inc} + joL\_{\rm eff}} \tag{11}$$

where K is a normalized fractional surface area that is enclosed by the AMM inclusion and Leff is the effective inductance of the AMM, which is given by

$$L\_{\rm eff} = \frac{\mu\_0 \mathcal{S}}{p} \tag{12}$$

where S isthe surface area ofthe AMM and p isthe periodicity ofthe AMM inclusion that mimics an infinitely large AMM structure. The parameter Zinc in Eq. (11) consists of two parts: Reff, which representsthe encountered ohmic losses due to the finite conductivity of the metallic rings within the AMM inclusions, and Ceff, which isthe mutual capacitive effect due to the close proximity of the AMM metallic rings/strips. Comprehensive analytical modeling approaches can be found in [3, 8, 12–14].
