**1. Introduction**

276 Trends in Electromagnetism – From Fundamentals to Applications

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Metamaterial covers exhibit inimitable electromagnetic properties which make them popular in antenna engineering. Two important features of metamaterial covers are: (1) increasing of the transmission rate and (2) control of the direction of the transmission which enable one to design directive antennas. In this chapter, the possibility of increasing both bandwidth and directivity of the printed patch antenna using metamaterial covers is examined. The printed patch antennas are a class of low-profile antennas, which are conformable to planar surfaces, simple and inexpensive to manufacture using printedcircuit technology.

Furthermore, novel polarization-dependent metamaterial (PDMTM) covers, whose transmission phases for two principal polarizations are different, are presented (Veysi et al., 2011). A full-wave Finite Difference Time Domain (FDTD) numerical technique is adopted for the simulations. A schematic of the metamaterial cover with square holes is shown in Fig. 1. It consists of two planar layers with similar square lattices. It was demonstrated in (Pendry et al., 1996; Tsao & Chern, 2006) that in the frequency range, where the wavelength is very large compared to the period of the metamaterial cover, this structure acts as a homogenous medium. The equivalent refractive index of this medium, in the microwave domain, is given by:

$$m\_{\rm eff} = \sqrt{1 - \left(\bigwedge^{p} f\right)^{2}}\tag{1}$$

where *fP* denotes the plasma frequency and *f* denotes the operating frequency. If the operating frequency is selected slightly larger than the natural plasma frequency of the metamaterial cover, the equivalent refractive index will be extremely low. Consequently, the transmission phase at the plasma frequency is extremely low.

The ultra refraction phenomena, in which the transmitted rays are parallel to each other, can be expected where the transmission coefficient reaches its maximum value. In other words, the zero transmission phase occurs at the same frequencies where the magnitude of the transmission coefficient becomes maximum. Hence, it acts similar to an equally phase surface at its plasma frequency. It is evident from Eq.1, that the equivalent refractive index and thus the antenna directivity are very sensitive to the frequency.

As a starting point, we consider a two-layer metallic grid placed on top of the patch antenna backed by a ground plane. The simulations have been carried out to examine the

Theory and Applications of Metamaterial Covers 279

Directive patch antennas are very popular in electromagnetic community. Their attractive features, such as low profile, light weight, low cost and compatibility with Microwave

Two distinctive types of directive antennas are parabolic antennas and large array antennas. Bulk and curved surface of parabolic antennas limits their use in many commercial applications. Also, complex feeding mechanism and loss in the feeding network are two

One solution to these problems is to use metamaterial cover over the patch antenna (Alu et al., 2006; Xu et al., 2008; Zhu et al., 2005; Huang et al., 2009). One of the first works was done by B. Temelkuaran in 2000, (Temelkuaran et al., 2000). In 2002, S. Enoch proposed a kind of metamaterial for directive emission, (Enoch et al., 2002). Another problem associated with microstrip antennas is their narrow bandwidth. The previous works so far (Xu et al., 2008; Zhu et al., 2005; Huang et al., 2009) have dealt only with the enhancement of the antenna directivity using metamaterial cover, but the effect of this cover on the antenna input

Recently, a new metamaterial cover has been proposed to enhance both the antenna bandwidth and directivity, (Ju et al., 2009). But, its directivity is significantly lower compared to the primary metamaterial cover, (Xu et al., 2008; Zhu et al., 2005; Huang et al.,

In this section, it is demonstrated that both the impedance and directivity bandwidths of the proximity-coupled patch antenna can be enhanced using the metamaterial cover. It is known that proximity-coupled patch antennas are sensitive to the transverse feed point location. In the case at hand, a parasitic microstrip line has been used on the opposite side of the feed line to mitigate this drawback (Jafargholi et al., 2011). The dimensions of the

 *P*=0.41λ6GHz, *t* = 0.01 λ6GHz*, L*= 0.31λ6GHz, *h*=0.49λ6GHz (2) Where *λ6GHz* (50mm) denotes the free space wavelength at 6GHz, P is the periodicity, t is the thickness of the metallic grids, *L* is the edge of the square holes and h is the distance between the two sheets which is the same as the distance between the patch antenna and the

In the FDTD simulations, a uniform 0.01*λ6GHz* grid size is used. The resulting transmission curve is plotted in Fig.3. As can be seen, this structure has three microwave plasma frequencies at about 5GHz, 5.81GHz and 8.1GHz which make it suitable for the antenna applications. When the aforementioned metamaterial cover is placed over the conventional proximity-coupled patch antenna, the final metamaterial antenna can be approximated by a

This approximation is similar to that used for the transmission coefficient calculations. It is a simple matter to obtain the surface impedance of this grounded slab as a function of metamaterial parameters. A surface impedance of the grounded slab of thickness *h* is:

**2. Directivity and bandwidth enhancement of proximity-coupled microstrip** 

Monolithic Integrated Circuits (MMICs), do not exist in other antennas.

major disadvantages associated with microstrip array antennas.

impedance has not been investigated.

analyzed metamaterial cover are:

homogenous medium terminated in a ground plane.

**antenna** 

2009).

first sheet.

transmission characteristic of the metamaterial cover, without the ground plane and without the antenna, using FDTD code developed by the authors.

Fig. 2 shows an effective unit cell model of the metamaterial cover which takes into account the image effect of the ground plane. This unit cell is a convenient method of computing of the transmission coefficient of a two layer metamaterial cover placed on top of the patch antenna backed by a ground plane. Here, Perfect Match Layers (PMLs) are applied to realize a medium with no reflection. The normalization in the code consists of choosing the peak magnitude of the transmission coefficient to be unity. Therefore, the magnitude of the transmitted field from the metamaterial cover has been normalized to that without the metamaterial cover. We have used the same methodology applied in the measurements (Enoch et al., 2002). The periodic boundary conditions (PBCs) have been also applied to model an infinite periodic replication. Since an infinite periodic structure has been simulated, the peak magnitude of the transmission coefficient is unity, unlike the results obtained in the measurements (Enoch et al., 2002).

Fig. 1. Schematic view of two layer metamaterial cover together with its unit cell (Veysi et al., 2011).

Fig. 2. FDTD model for metamaterial cover analysis (Veysi et al., 2011).

278 Trends in Electromagnetism – From Fundamentals to Applications

transmission characteristic of the metamaterial cover, without the ground plane and without

Fig. 2 shows an effective unit cell model of the metamaterial cover which takes into account the image effect of the ground plane. This unit cell is a convenient method of computing of the transmission coefficient of a two layer metamaterial cover placed on top of the patch antenna backed by a ground plane. Here, Perfect Match Layers (PMLs) are applied to realize a medium with no reflection. The normalization in the code consists of choosing the peak magnitude of the transmission coefficient to be unity. Therefore, the magnitude of the transmitted field from the metamaterial cover has been normalized to that without the metamaterial cover. We have used the same methodology applied in the measurements (Enoch et al., 2002). The periodic boundary conditions (PBCs) have been also applied to model an infinite periodic replication. Since an infinite periodic structure has been simulated, the peak magnitude of the transmission coefficient is unity, unlike the results

P

W

L P

Fig. 1. Schematic view of two layer metamaterial cover together with its unit cell (Veysi et

Fig. 2. FDTD model for metamaterial cover analysis (Veysi et al., 2011).

the antenna, using FDTD code developed by the authors.

obtained in the measurements (Enoch et al., 2002).

al., 2011).
