# Reconstructing Polarization Multiplexing Terahertz Holographic Images with Transmissive Metasurface
## 4 Results and Discussion  
We fully explore the intensity distributions of the focal point to obtain a high-resolution holographic image since the focal point produced by a metalens is utilized as the pixel of the image. In general, the clear aperture and focal length of the metalens have an effect on the focal point. The clear aperture of the metalens is \(D=PN\), in which \(N\) represents the phase pixel number along the diameter of the metalens [41; 42]. In Figure 3a, the intensity distributions of one focal point with various phase pixel number \(N\) and focal length \(f\) are displayed. For a fixed phase pixel number, the size of the focal point grows as the focal length increases. Conversely, when the focal length remains the same, the size of the focal point decreases with the increase of the phase pixel number, indicating the increase of the clear aperture. The relationship between the phase pixel number (clear aperture) and focal length produces results in agreement with the classical formula for the focal point diameter of a lens \(d=2\lambda_{0}f/D\)[41; 42]. Here, the focal point diameter \(d\) is defined as twice the width at which the intensity drops to \(1/\mathrm{e}^{2}\) (\(13.5\%\)). Figure 3b presents the corresponding horizontal cross-sections of the intensity distribution at \(y=0\) mm with different focal lengths, where the phase pixel number is 100, 200, 300, and 400 (from left to right), respectively. It can be seen that \(d\) decreases with the increase of \(N\). Thus, we can obtain a smaller equivalent pixel size (higher resolution) at a larger phase pixel number because the holographic image is reconstructed by the metalens. Unfortunately, the diffraction becomes more severe at a smaller focal point size due to more concentric ring fringes on its focal plane. It should be considered to obtain a balance between quality  
Figure 2: (**a**) The schematic illustration of the Si meta-atom with rotation angle \(\theta\). \(L\), \(W\), \(H\), and \(P\) are the length, width, height, and period of the meta-atom, respectively; (**b**) the transmission coefficient and phase profile under XLP light illumination; (**c**) the cross-polarized transmittance (red line) and co-polarized transmittance (blue line) with the frequency ranging from 0.6 to 1.1 THz under the LCP light incidence. and resolution of the reconstructed image during the design. Thus, we utilize two crucial parameters, i.e., the focal length \(f=10\) mm and the phase pixel number \(N=300\), to produce the focal point at the subwavelength scale without excessive diffraction. Meanwhile, the focal point diameter \(d\) is 268 \(\upmu\)m, and the dimension of the metalens is 24 mm along both the x- and y-directions. As the metalens width of 24 mm is larger than the focal length of 10 mm, it does not satisfy the Fresnel approximation in diffractive optics [17], namely, \(z\gg\sqrt{\left(x-x_{0}\right)^{2}+\left(y-y_{0}\right)^{2}}\). Therefore, we use the Fresnel-Kirchhoff diffraction integral method. The intensity distribution of two pixels exhibiting continuous, non-overlap, and uniform characteristic is a prerequisite for a better quality of the holographic image. Thus, the distance \(d_{0}\) between the center of two adjacent foci is significant in the formation of holograms with better quality. In general, the continuity of focal points depends on the distance \(d\), which can emerge from the concept of a diffraction limit [41]. The results  
Figure 3: (**a**) Normalized intensity distributions of a single focal point at the focal plane for various combinations of phase pixel numbers \(N\) and focal lengths \(f\); (**b**) the corresponding horizontal cross-section of the intensity at \(y=0\) mm with different focal lengths (colorful solid lines), where the phase pixel number is 100, 200, 300, and 400 (from left to right), respectively. of two focal points produced on the \(x\)-axis with \(x_{1}=134\)\(\upmu\)m and different distances \(d_{0}\) (\(d_{0}<d,d_{0}=d,d_{0}>d,d=268\)\(\upmu\)m) are investigated.