# Advanced Metamaterial-Integrated Dipole Array Antenna for Enhanced Gain in 5G Millimeter-Wave Bands
## 2 The Design of the Metamaterial-Integrated Dipole Antenna
### Metamaterial Unit Cell Design  
The metamaterial structures have the ability to interact with the electromagnetic waves of any antenna and change the antenna's radiation performance [30]. As the dipole antenna alone offers a very low average gain of 6.7 dBi with a maximum peak gain of 8.1 dBi, a novel metamaterial structure is proposed to enhance the gain of the designed dipole antenna by boosting radiation directivity. Initially, a unit cell is developed for the targeted frequency spectrum. Afterwards, the unit cell is copied and translated to design the proposed metamaterial structure. The simulation setup and results of the designed unit cell, along with its dimensions, are presented in Figure 6. The dimensions of the developed unit cell are shown in Figure 6a, and the parametric values are listed in Table 2. Additionally, the working principle of the metamaterial is illustrated in Figure 6b, where \(n_{i}\) and \(n_{0}\) represent the refractive index in the substrate and air, respectively. [PERSON]'s law states the relation between \(n_{i}\) and \(n_{0}\), as presented in Equation (1):  
\[n_{i}\text{sin}(\theta_{i})=n_{0}\text{sin}(\theta_{0}), \tag{1}\]  
where \(\theta_{i}\) is the angle of incidence and \(\theta_{0}\) is the angle of refraction. This relationship clarifies how the artificial material guides electromagnetic waves, resulting in energy convergence. Whenever \(n_{i}>1\), the energy transmitted through the material will be converged in air, resulting in highly directional radiation that consequently increases the gain of the antenna with end-fire radiation characteristics [31, 32]. On the other hand, to increase the performance of the antenna with broadside radiation, the value of the refractive index should be zero or near zero [33]. Additionally, the characteristic responses and material properties are displayed in Figures 6c and 6d, respectively. The fundamental parameters of a metamaterial unit cell are the effective permittivity (\(\epsilon\)) and permeability (\(\mu\)). These parameters can be expressed by Equation (2) and Equation (3), respectively [34]. \[\epsilon=\frac{n}{z} \tag{2}\] \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Parameter** & **Value (mm)** & **Parameter** & **Value (mm)** & **Parameter** & **Value (mm)** \\ \hline \(u_{1}\) & 1.08 & \(u_{3}\) & 0.495 & \(u_{5}\) & 0.27 \\ \(u_{2}\) & 0.252 & \(u_{4}\) & 0.18 & \(u_{6}\) & 0.09 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: The design parameters and the optimal values of the metamaterial unit cell. Figure 5: Parametric analysis of the dipole array antenna for different parameters: (**a**) for \(P_{1}\) and (**b**) for \(P_{4}\). \[\mu=nz \tag{3}\]  
Here, \(n\) represents the refractive index, and \(z\) is the impedance of the metamaterial. The parameters \(n\) and \(z\) can be easily calculated using Equations (4) and (5) [35; 36] from the characteristic responses shown in Figure 6c, where the electromagnetic wave transmission (S\({}_{21}\)) and reflection (S\({}_{11}\)) characteristics are presented. Furthermore, \(k\) is the free-space wave impedance, \(d\) is the thickness of the virtual homogeneous slab which stands in for the actual geometry, \(m\) = 0, 1, 2, 3, \(\ldots\), and \(R_{01}=(z-1)/(z+1)\). \[z=\pm\sqrt{\frac{(1+S_{11})^{2}-S_{21}^{2}}{(1-S_{11})^{2}-S_{21}^{2}}} \tag{4}\]  
\[n=\frac{1}{k_{0}d}\left\{Im\left[\ln\left(\frac{s_{21}}{1-s_{11}R_{01}}\right) \right]+2m\pi-iRe\left[\ln\left(\frac{s_{21}}{1-s_{11}R_{01}}\right)\right]\right\} \tag{5}\]  
It can be observed from the material properties of the designed metamaterial unit cell, as shown in Figure 6d, that the meta-cell provides a non-resonant mode within the frequency range of 20-44 GHz by exhibiting a stable \(\varepsilon\) value around 8.2, while \(\mu\) remains stable around 4.2. In this scenario, the refractive index of the metamaterial can be estimated from Equation (6), and the refractive index value is more than 1 within the targeted frequency band.