# A Novel L-Shaped Metalens for Ultra-Wide Band (UWB) Antenna Gain Improvement
## 3 Design and Results
### AVA with Metalens Design  
In the third design step, the metalens has been integrated into the substrate of the antenna, and placed close to the tapered slot in the end-fire direction, as shown in Figure 1, for the optimization by numerical full-wave simulations in the frequency band \(f=3\div 15\) GHz, in order to refine the results, by improving the realized gain of the antenna without reducing its bandwidth. The optimized values reported in Table 2 have been found via full-wave simulations with a trial-and-error approach. Then, further optimization of the antenna with metalens has been performed by varying, in the full-wave simulation, the number and distribution of the unit cells and the distance along the \(y\)-direction between the metalens and antenna. Several configurations have been simulated and compared. In Figure 8a, the metalens of the optimized AVA L-shaped#1 consists of an array of 41 L-shaped unit cells integrated on the antenna substrate, increasing the antenna length along the \(y\)-axis by \(L_{y}=47\) mm. This antenna exhibited particularly promising performance over the whole band, in particular at high frequencies. The AVA L-shaped#2, shown in Figure 8b, consists of an array of 67 L-shaped unit cells integrated into the antenna substrate; the larger metalens also requires a slight increase in the antenna substrate width along the \(x\)-axis. The AVA L-shaped#2 allows better performance at low frequencies. Figure 7: (**a**) Magnitude and (**b**) phase of the simulated S-parameters and retrieved effective parameters of L-shaped unit cell as a function of frequency. (**c**) Refractive index \(N_{eff}\). In Figure 9a, the modulus of the simulated scattering parameter \(|S_{11}|\) as a function of frequency is illustrated for the AVA without a metalens (black curve) and the AVA L-shaped#1 (magenta curve) and AVA L-shaped#2 (green curve) metalenses. The bandwidth \(f_{auraL\#1}=3\div 15\) GHz of AVA L-shaped#1 is increased with respect to \(f_{AVA}=3\div 13.5\) GHz of the AVA without a metalens. The L-shaped#2 allows an improvement in impedance matching for frequencies of \(f<6.5\) GHz but reduces the \(-10\) dB bandwidth to the range of \(f_{auraL\#2}=3\div 11.8\) GHz. In Figure 9b, the realized gain \(G\) (solid curves) of the three antennas and the gain increase \(\Delta G\) (dashed curves) with respect to the gain without a metalens, simulated as a function of the frequency, are reported, with the same choice for the curve colors. For the AVA L-shaped#1, the gain increase can be observed over the whole frequency range, with an average value of about \(\Delta G_{avg}=2\) dB and a maximum of \(\Delta G_{max}=4.8\) dB at a frequency of \(f=15\) GHz. The maximum gain is \(G_{max}=14.1\) dB at a frequency of \(f=15\) GHz. For the AVA L-shaped#2, a gain increase of about \(\Delta G=2\) dB is obtained for frequencies of  
Figure 8: Schematic of AVA with L-shaped metalenses: (**a**) AVA L-shaped#1—array of 41 L-shaped unit cells, and (**b**) AVA L-shaped#2—triangular array of 67 L-shaped unit cells. Figure 9: Full-wave simulation of the AVA with different L-shaped metalenses: (**a**) modulus of the scattering parameter \(|S_{11}|\) as a function of frequency, and (**b**) realized gain \(G\) and gain increase \(\Delta G\) as a function of frequency. \(f<6\) GHz and \(f>8\) GHz. The simulated maximum gain is \(G_{max}=12.2\) dB at a frequency of \(f=15\) GHz. The L-shaped#1 metalens improves both the antenna bandwidth and the gain in the whole band, especially at higher frequencies. The AVA L-shaped#1 at higher frequencies irradiates a beam more confined than that of AVA L-shaped#2. The L-shaped#2 metalens allows a better gain improvement at the lower frequencies but reduces the bandwidth at higher frequencies.