## 3 Results  
The results of the metalens array was simulated by using the finite integration method in the time domain and the open boundary condition was adopted for all directions, while the minimum size of the mesh was set as 40 nm to minimize numerical errors. The incident light was the 4.6 \(\upmu\)m LCP plane wave in the simulation. First, when all of the GST were in an amorphous state, the incident LCP light was converted into the RCP light and focused at the focal plane. Figure 5a shows the light field distribution of the metalens array in the \(xz\) plane. Viewed from this section, the focal length of the metalens array was 62.4 \(\upmu\)m. The result had a slight deviation from the designed 60 \(\upmu\)m because of the discontinuous phase distribution. However, the depth of focus was fairly large, which will have great advantages in many fields such as microscopy, endoscopy, detection cameras, and so on. Figure 6a shows the normalized intensity along the \(z\) direction when \(x=y=0\), exhibiting its great application potential in large focal depth optical systems. Figure 5c shows the light field distribution of the metalens array in the \(xy\) plane at the position of \(z=62.4\)\(\upmu\)m. A \(3\times 3\) focal spot distribution was very clear in the focal plane. Each focal spot was located at the center of each area with the same intensity. The focusing efficiency for the metalens array was 80.2%, which is considerably high for a transmissive metalens array. Here, the focusing efficiency was defined as the ratio of light intensity of the focal plane to the incident plane. Figure 6b shows the normalized intensity of the metalens array in the \(x\) direction while \(y=0\). The full width at half maximum (FWHM) of the spot in the focal plane was 4.60 \(\upmu\)m. The FWHM was less than 1.22\(\lambda/2 NA\), indicating that the resolution of the metalens array has gone beyond the resolution limit of a conventional lens, and has great potential in the high resolution imaging and detection field. In addition, the metalens array can also be employed as a transparent dielectric by applying a voltage to the ITO conductive layer to transfer the phase state of GST into the crystalline state. In this case, the incident LCP will pass through the metalens array where only a very small part of the light is converted into RCP light, thus little light is focused behind the metalens array, as shown in Figure 5b,d. The simulation results prove that the performance of the proposed actively tunable metalens array can be easily controlled and used more flexibly in some occasions. Figure 5: **(a,b)** The light field in the \(xz\) plane for the metalens array when all GST are in an amorphous state and crystalline state. **(c,d)** The light field in the \(xy\) plane for the metalens array when all GST are in amorphous and crystalline states. It is clear that one of the advantages of designing with the P-B phase shift is that it has a broadband response. Figure 7a shows the abrupt phase as a function of wavelength and rotating angle when GST is in the amorphous state. The results prove that the abrupt phase can still linearly cover the 2\(\pi\) range in the whole wavelength range from 4.5 \(\upmu\)m to 5.2 \(\upmu\)m. Figure 7b shows the phase variance with wavelength and angle when GST is in the crystalline state. At the same time, big differences in the conversion efficiency between the amorphous state and crystalline state still exist, as shown in Figure 7c (amorphous state) and Figure 7d (crystalline state), which proves that the tuning ability of the metalens array remains functional. For instance, when the incident lights were 4.5 \(\upmu\)m, 4.85 \(\upmu\)m, and 5.2 \(\upmu\)m, the light fields of the metalens array in the _xz_ plane are shown in Figure 8a,c,e.