# Reconstructing Polarization Multiplexing Terahertz Holographic Images with Transmissive Metasurface
## 4 Results and Discussion
The intensity distributions and the corresponding horizontal cross-sections of the intensity distribution at \(y=0\) mm with different \(d_{0}\) are shown in Figure 4a,b, respectively. It can be seen from Figure 4 that when \(d_{0}<d=268\)\(\upmu\)m, the two adjacent foci are indistinguishable resulting from the serious overlap. When the distance \(d\) is equal to 268 \(\upmu\)m, the distribution between two pixels with continuous, non-overlap, and uniform intensity is satisfied. The two focal points are clearly distinguished as the distance \(d\) continues to increase. However, there is obvious cutoff between two focal points, indicating that the intensity is not uniform. Thus, to achieve a better quality of the holographic image, the distance \(d\) between the center of two adjacent foci is chosen to be 268 \(\upmu\)m. Notably, the holographic images can be reconstructed on the focal plane of the metalens with the optimized parameters \(f_{0}=0.85\) THz, \(f=10\) mm, \(N=300\), and \(d=268\)\(\upmu\)m.  
For verification, we design a metalens for generating polarization multiplexing holograms. The phase profiles of the hologram for the incident LCP and RCP lights are accomplished by interleaved meta-atoms with the rotation angles \(\theta_{\text{L}}\) and \(\theta_{\text{R}}\), respectively, as shown in Figure 5a. The merged phase profile can be expressed as Formula (5):  
\[\phi(x,y)=\arg\left\{\sum_{i=1}^{m}\sum_{j=1}^{n}\left[e^{i\varphi_{ij}^{L}(x, y)}+e^{i\varphi_{ij}^{R}(x,y)}\right]\right\}, \tag{5}\]  
where \(\varphi_{ij}^{L}(x,y)\) and \(\varphi_{ij}^{R}(x,y)\) represent the phase profile under LCP and RCP lights incidence, respectively. The patterns of letter and number form the target holograms corresponding to two polarizations (i.e., LCP and RCP input lights, respectively), indicating that these images include polarization information. According to Formula (3), we encoded the phase profiles onto the metalens to achieve the polarization multiplexing holographic images. Figure 5b presents the retrieved phase profile for the holographic image. The reconstructed images with letters \"EL\" and numbers \"17\" on the focal plane under LCP and RCP illumination are clearly shown in Figure 5c,d, respectively. Notably, with the help  
Figure 4: (**a**) Normalized intensity profiles of the two adjacent foci generated on the \(x\)-axis with different distances \(d_{0}\) between the center of two adjacent foci; (**b**) the corresponding horizontal cross-section of the intensity at \(y=0\) mm with different distance \(d_{0}\). of extra spatial freedom (meta-atoms with different rotation angles arranged interleaved), the cross-talk among different polarizations of incident light (i.e., LCP and RCP) can be suppressed. As we know, a linearly polarized (LP) light can be written as a combination of the two orthogonal components (LCP and RCP lights). Hence, in the situation that a LP light illuminates the metasurface, the combination of designed letters \"EL\" and numbers \"17\" are displayed in the reconstructed holographic image in Figure 5e, which forms a new pattern with numbers \"80\". From Figure 5, we can obtain that by utilizing focal points as the pixels of holographic image and switching the incident polarizations, the metalens can reconstruct different holographic images accordingly on its focal plane. To clearly show distributions of the focal points at each location, we demonstrate the holographic images formed by half of the foci, i.e., the distance between two adjacent foci becomes 536 \(\upmu\)m. It means that a fixed interval, rather than the continuous profile, can be observed in the reconstructed holographic images. As shown in Figure 6, the patterns \"EL\" and \"17\" with a fixed focal-point interval can be reconstructed on the focal plane, respectively, by switching the incident polarization from LCP to RCP. A new pattern, numbers \"80\" with a fixed focal-point interval, is also produced under the incidence of LP light. These results verify that the reconstructed images are formed by focal-point pixels.