# A Novel L-Shaped Metalens for Ultra-Wide Band (UWB) Antenna Gain Improvement
## 3 Design and Results
### Metalens Design  
In order to improve the radiation characteristics of the AVA, in terms of gain and directivity, without significantly affecting the bandwidth, a novel metalens is designed. For the preliminary design, in the first step, an equivalent homogeneous layer (EHL) has been considered in place of the metalens, with the aim of finding the optimized values of the effective parameters \(\epsilon_{eff}\) and \(\mu_{eff}\) to increase the gain and maintain the bandwidth. As a second step, the design of the metalens unit cell is performed in order to obtain values of the effective parameters \(\epsilon_{eff}\) and \(\mu_{eff}\) as close as possible to the optimized ones. This condition is verified via SPRM [28; 29]. Finally, in the third step, the full simulation of the antenna and metamaterial is performed for the actual design refinement before the antenna fabrication. The EHL is shown in Figure 2 as a green layer. Figure 3 shows the full-wave simulation of the gain \(G\) as a function of the frequency of the AVA (solid curve) and the AVA with EHL having a thickness of \(d_{EHL}=0.832\) mm for the best values of effective permittivity \(\epsilon_{eff}\) and effective permeability \(\mu_{eff}\) (dashed curve). The thickness of \(d_{EHL}=0.832\) mm corresponds to the sum of the substrate and the double metal strips thicknesses, \(d_{EHL}=t+2\times t_{c}\). A metalens having an effective permittivity of \begin{table}
\begin{tabular}{c c c} \hline
**Parameter** & **Description** & **Value (mm)** \\ \hline \(L_{AVA}\) & Antenna length & 73.7 \\ \(W_{AVA}\) & Antenna width & 48 \\ \(L_{m}\) & Feed microstrip length & 8.57 \\ \(w_{m}\) & Feed microstrip width & 1.5 \\ \(x_{1}\) & x-position of point P1 & 15 \\ \(y_{1}\) & y-position of point P1 & 51.7 \\ \(x_{2}\) & x-position of point P2 & 19 \\ \(y_{2}\) & y-position of point P2 & 33.7 \\ \(d_{1}\) & Position of the second point of the first flare edge & 9.7 \\ \(d_{2}\) & Distance between the first and the second flares & 5 \\ \(d_{3}\) & Second flare width & 5 \\ \(d_{4}\) & Distance between the second and the third flares & 10 \\ \(d_{5}\) & Second flare width & 8.7 \\ \(d_{6}\) & Position of the second point of the third flare edge & 6.3 \\ \(t\) & Substrate thickness & 0.762 \\ \(t_{c}\) & Metal strip thickness & 0.035 \\ \hline \end{tabular}
\end{table} 
Table 1: Geometrical parameters of the AVA. Figure 1: Schematic of AVA with geometrical parameters and the region (dashed contour) hosting the metalens. \(\varepsilon_{eff/MG}=5.75\) and an effective permeability of \(\mu_{eff/MG}=1.5\) could allow a maximum gain (MG) improvement of about \(\Delta G=4\) dB. A metalens based on the novel L-shaped unit cell has been optimized. Figure 4a shows the investigated unit cell. The geometry consists of an arrangement of L-shaped metal elements printed on both sides of the antenna substrate. In the proposed unit cell structure, it is possible to recognize an external square ring with four splits and two internal stubs. Different inductive and capacitive effects are induced depending on the electric field orientation of the traveling wave with respect to the metalens plane. Considering the electric field (E-field) polarized along the \(x\)-axis, inductive effects along the metal strips and capacitive effects at the gaps occur, as shown in Figure 4a. The equivalent inductors, namely \(L\), represent the self-inductance produced by the metal L-shaped elements. The equivalent capacitances originate from the electric charges accumulated via the splits, namely \(C_{1}\), and by the coupled charges between the adjacent metal L-shaped elements, namely \(C_{2}\), \(C_{3}\), and \(C_{4}\)[31]. The equivalent circuit of the L-shaped unit cell is depicted in Figure 4b; its effective complex impedance \(Z_{eff}\) can be fine-tuned by varying the geometries of the conductive metal inclusions, the gap width between them, and the dielectric permittivity of the substrate [32; 33].