Feed Ground

Figure 6.17 Extended current paths with a notch and a slot producing multiband operation.

Figure 6.18 Array of thin wires to compose negative permittivity surface [15, 16].

6.2.1.1.3 Material loading on an antenna structure

Loading of materials such as dielectric, magnetic, or metamaterials on an antenna structure is a simple way to produce the SW structure. Since the phase velocity vp in such materials is expressed by using the permittivity ε of the dielectric material and the permeability μ of the magnetic material, as

since ε = εrε0 and μ = μrμ0, and εr and μr are usually greater than unity.

Making use of metamaterials is another useful way to produce SW structure. The metamaterials are known as materials that exhibit uncommon electromagnetic properties not available in nature [15–17]. In reality, metamaterials do not exist; however, equivalent materials have been realized first by using a dense array of thin wires (Figure 6.18), and an array of split ring resonators (SRR) (Figure 6.19) [18–20]. The former exhibits a property of negative permittivity ε and the latter shows negative permeability μ and

Figure 6.19 Array of sprit ring resonators (SRR) to compose negative permeability surface [15, 16].

YP (ω )

Figure 6.20 A T-circuit model representing transmission line (one segment of the periodic connection) [26].

applications of them to antennas have been described in many papers [16–17, 21–23]. Among them, Itoh demonstrated an artificial metamaterial using transmission lines, which achieved equivalent metamaterial performances that exhibit a left-handed (LH) property that resulted from negative permeability and negative permittivity at the same time [24, 25].

Plane-wave propagation in isotropic and homogeneous dielectric can be treated by the concept of TEM propagation in a transmission line, which is comprised of periodic connections of a T-shaped circuit consisting of a series per-unit-length impedance Zs, and a shunt per-unit-length admittance Yp as shown in Figure 6.20 [26]. Here, characteristic impedance Z = Zs /Yp and propagation constant γ = Zs Yp, and Zs and Yp, respectively, are described as

Zs (ω) = jωμ

(6.8)

Yp(ω) = jωε

Figure 6.21 The equivalent transmission line model consisting of circuit parameters L-C; (a) L in series and C in shunt and (b) L-C interchanged circuit [26].

where ε and μ, respectively are the dielectric permittivity and the magnetic permeability of the propagation medium [27]. The transmission line model consisting of circuit parameters C and L, is illustrated in Figure 6.21(a). From Eq. (6.8), the effective constitutive parameters εeff and μeff, respectively, are described as

εeff = C/ l

(6.9)

μeff = L/ l

where l is the unit length.

Interchange of C and L, results in the dual transmission line as shown in Figure 6.21(b). By using (6.8), εeff and μeff can be related with the circuit parameters as

εeff = −1/(ω2 Ll)

(6.10)

μeff = −1/(ω2Cl)

The dispersion characteristics of the equivalent circuit are the same as that shown previously in Figure 6.5(a) and (b). In the SW (Slow Wave) structure, a wave propagates with the phase constant β greater than that in free space k. The transmission line with the constitutive parameters –ε and –μ that are given by (6.10) is considered as the LH (Left Handed) media where the phase velocity vp and the group velocity vg are anti-parallel, and the wave propagates backward [28]. The LH media is characterized by the property of negative propagation constant –k, the attribute of –ε and –μ. The name is originated from the term Right-Hand (RH) Rule that is derived from use of a right hand to indicate the direction of the wave vector k; for example, E × H = S, by the thumb of the right hand as Figure 6.22 shows. In the LH media, the direction of the wave vector k is the opposite to that of the cross product vector S, while in the RH case, directions of both k and S are the same as Figure 6.22(b) illustrates.

In reality, however, this transmission line cannot be implemented perfectly, because there exists unavoidable parasitic series inductance Lp and shunt capacitance Cp. Then a CRLH (Composite Right/Left-Handed) model shown in Figure 6.23 is considered as the most general form of a structure with the LH attributes [26]. The dispersion characteristics of the CRLH transmission line model is depicted in Figure 6.24, which shows a case for ω2 > ω1 [26]. The region between two frequencies ω1 and ω2 denotes a bandgap, where waves do not propagate. This bandgap is generally called the EBG (Electromagnetic Band Gap).

S

H

Figure 6.22 The Right-handed Rule; (a) demonstration for vector cross product and (b) the Right-handed (RH) and Left-handed (LH) cases.

LL CR

Figure 6.23 CRLH model (one segment of equivalent transmission line) [26].

Figure 6.24 Dispersion characteristics of the CRLH transmission line model [26].

The effective constitutive parameters εeff and μeff of this CRLH model are given by

This indicates the nature of CRLH of the artificial transmission line. An SNG transmission line can be realized by loading a host line with series capacitors (corresponding to

–μ lines) or shunt inductors (corresponding to –ε lines).