# Affordable Thin Lens Using Single Polarized Disparate Filter Arrays for Beyond 5G toward 6G
## 2 Design of Single Polarized Thin Lens
### Single-Polarized Low-Pass and Band-pass Unit Cells  
This section describes the geometry and frequency response of the selected unit cells with three metal layers to design a convex lens based on the capacitive and inductive strips proposed in Section 2.1. Figure 5 shows a side view of the three-metal-layer structure with two substrates and a bondply in the unit cell. Rogers RO3003 having a thickness of 127 \(\upmu\)m is used as a substrate that has a dielectric constant and a loss tangent of 3.0 and 0.001, respectively. Rogers RO2929 is used as the bondply to bond the two substrates. The thickness, permittivity, and loss tangent of the bondply are 38 \(\upmu\)m, 2.9, and 0.003, respectively. Figure 6 shows the low-pass and band-pass unit cells where all the strip elements are connected to the strips in the neighboring unit cells without any gap. If the type of unit cells constituting a lens are homogeneous, such as low-pass or band-pass unit cells, the tunable range of the phase shift is limited to be approximately 180\({}^{\circ}\)[14]. The easiest way to increase the tunable range is to increase the number of layers of the substrate. However, this may lead to an increase in cost, profile, loss, and a deterioration in performance due to increased alignment errors during the process [15]. To solve these problems, a design method to improve the tunable range by using both low-pass and band-pass unit cells is used [16]. In this sense, this paper investigates the proposed single-polarized unit cells under the same conditions as those of the unit cells with three metal layers. A low-pass unit cell consists of single-polarized strip unit cells in all three layers. A band-pass unit cell with an inductive strip placed at layer 2 and two capacitive strips located at layers 1 and 3 is designed.  
Figure 4: Simulated inductance of dual-pol grid and single-pol grid.  
Figure 5: Side view of the three-metal-layer structure with two substrates and a bondply in the unit cell.  
Table 1 summarizes the geometry, insertion loss (IL), and phase of the ten spatially filtering unit cells selected for lens design from the unit cells having the aforementioned capacitive and inductive strips. A total of five low-pass and five band-pass unit cells are used to acquire a wide tunable range of the phase shift. Figure 7 shows the simulated transmittance of both low-pass and band-pass unit cells with different sized patches and different width grids. It can be seen that all unit cells are designed to have an IL of less than 1 dB at the target frequency of 60 GHz to minimize energy loss. Figure 8 shows the plots of the phase shifts of the selected unit cells according to the selected unit cells. It is observed that a tunable range of 274\({}^{\circ}\) at the target frequency of 60 GHz is acquired by combining the phase shifts of the appropriately tuned five low-pass and five band-pass unit cells.  
Figure 8: Simulated phase shift of both low-pass and band-pass unit cells with different patch sizes and grid width.  
Figure 6: Exploded views and dimension parameters of single-pol, (**a**) low-pass, and (**b**) band-pass unit cells.  
Figure 7: Simulated transmittance (s21) of both low-pass and band-pass unit cells with different sized patches and different width grid.