I. Introduction
Metamaterial is an artificially engineered material that obtains its unusual electromagnetic properties from structure rather than its composition. Metamaterial is generally constructed by embedding specific inclusions such as periodic structures in a host medium. Previous studies have applied metamaterial in waveguides and antenna designs [1], [2]. A metamaterial with a near-zero effective refractive index can reshape the far-field pattern of an embedded antenna. A matched zero-index slab can also transform curved wave fronts into planar ones [3]. Metamaterial made of wire medium has been studied intensively and particularly on its effective refractive index, permittivity, and permeability. A structure composed of metallic mesh wires, which has very small electrical length in the period and wire thickness, can be treated as a homogeneous medium with a low plasma frequency [4]. Regarding the optical domain, a dielectric medium embedded with metallic nano-particles and nano-wires has zero effective permittivity, creating band gaps [5]. Moreover, split ring resonators can produce an effective negative permeability over a microwave frequency band [6]. The first left-handed metamaterial in microwave frequency was developed while the extraordinary refraction phenomenon was also demonstrated [7]. Metamaterials with both negative permittivity and permeability over an overlapping near-infrared wavelength range have a low loss negative-refractive-index [8], [9]. A three-dimensional optical metamaterial made of cascaded “fishnet” structures has a negative index within wide-band range [10]. Some researchers also used the effective medium method to consider the metamaterial slab as a uniform medium. Single-mode approximation can mathematically extract the effective parameters using the reflection- and transmission-coefficients of the metamaterial slab [11]. Antenna design benefits from the specific properties of metamaterial. For instance, a metamaterial consisting of six identical metallic grids with a square lattice embedded in a foam [12]. They placed a monopole source in the middle of the structure, and a metal plate on the bottom of structure to control the emission. Experimental and numerical analysis proves that this metamaterial can modify the emission of an embedded source. Researchers have proposed and analyzed an epsilon-near-zero metamaterial for tailoring the phase of radiation pattern of arbitrary sources for some canonical geometries [13]. Other researchers studied a strongly modulated photonic crystal with an effective refractive index controllable by the band structure [14]. Experimental results prove that such a metamaterial can modify the emission of an embedded source and enhance its gain and directivity [15].
Structure configuration: (a) photo of the 3 D fishnet metamaterial, and (b) front view of the fishnet structure.