Figure 6.38 Radiation patterns of (a) the loop and (b) the dipole having elements at right-angle [41b].

Figure 6.39 Mapping of terminology expressing metamaterial properties.

6.2.5Applications of metamaterials to make antennas small

There have been increasing trends to employ specific properties of metamaterials to create novel small antennas in the recent decade. Of course, metamaterials do not exist in reality. Artificial metamaterials, for example, transmission lines and waveguides of periodical structure, have been used for creating small antennas. Many papers treating metamaterial applications to small antennas have been published and some practically useful antennas have been reported already.

Terminologies to express metamaterial properties generally used are DNG (Double Negative), SNG (Single Negative), ENG (Epsilon Negative), and MNG (Mu Negative) and they are mapped on a permittivity–permeability chart as Figure 6.39 shows. DNG

Figure 6.40 A transducer representing an antenna system [42].

Figure 6.41 Antenna system model divided into two parts: Space Domain and Immittance Domain [42].

materials are those exhibiting both ε and μ negative, SNG materials are those having the property of either ε or μ negative, and ENG and MNG materials respectively represent negative ε and negative μ materials. There are some other terms, ENZ and MNZ, expressing materials of ε near zero or μ near zero, respectively. The DNG property, as was described in the previous section, corresponds to properties such as LH (LeftHanded), and the NRI (Negative Refraction Index), both the attributes of negative constitutive parameters, −ε and −μ. The term LH is derived from the RH rule (Figure 6.22) as was described in the previous section. It is also well known that in the DNG media, the phase velocity vp and group velocity vg are anti-parallel.

Applications of metamaterials to antennas can be found in various ways: making use of SW structure realized by DNG materials for small sizing, use of composite transmission lines which exhibit both LH (Left-Handed) and RH (Right-Handed) property for small sizing and for radiation pattern control, employing SNG or DNG materials for matching either in space or at the load terminal, and so forth. For matching at the load terminals, a Non-Foster circuit realized by metamaterials is used, and an antenna of small size yet with high efficiency is obtained.

An antenna is a transducer which transforms the field parameters E and H (electric and magnetic field respectively) to the circuit parameters, voltage V and current I as shown in Figure 6.40 [42]. The antenna model represented by a transducer is divided into two parts: Space Domain and Immittance Domain as Figure 6.41 illustrates. The Space Domain defines relationships between the EM fields (E and H) and the current distributions J on the antenna system, which is given by

where Ł denotes the operator and Ł−1 is the inverse operator. The Immittance Domain defines the relationship between the current distributions J and the circuit parameters V