## 1 Introduction  
For conventional convex lens, its surface needs to be shaped to satisfy the following hyperbolodial phase profile:  
\[\varphi(x,y,f)=-\frac{2\pi}{\lambda}(\sqrt{x^{2}+y^{2}+f^{2}}-f) \tag{1}\]  
where \((x,y)\) is the coordinate of exit surface in lens; \(\lambda\) is the incident wavelength; and \(f\) is the focal length. The phase distribution is accomplished by optical path accumulation in the conventional lens, so it cannot have a thin and small size due to the limited refractive index of materials and processing technology. These limitations result in the fact that conventional lens no longer meet the requirement of modern nano-devices. Metasurfaces, a kind of novel 2-D metamaterial with the ability to flexibly manipulate the amplitude, phase, and polarization of light by adjusting the size or orientation of resonators [1; 2; 3; 4], has been applied in many fields such as optical computing, beam steering, imaging, cloaking, hologram, and so on [5; 6; 7; 8; 9; 10; 11; 12; 13; 14]. As one of the most practicable appliancesof metasurfaces, the metalens has been designed to solve the problems of integration with modern nano-devices. Compared with conventional lens, metalens possess a smaller size due to a meta-unit induced abrupt phase shift for its phase distribution. Recently, many researchers have been dedicated to improving the optical performance of metalens, for example, focusing several discrete wavelengths at the same position [15; 16]; achromatic focusing at a continuous broadband [17; 18]; multi-focus for different wavelengths or polarized light [19; 20]; and tunable ability utilizing stretchable materials, liquid metal, or phase change materials [20; 21; 22; 23]. All of these contributions have explored an exciting field to replace conventional lens with metalens to obtain better optical performance and higher integration. Nevertheless, for some special appliances such as wavefront detection and display in adaptive optics, a single metalens is not enough anymore. The idea of a metalens array provides a new way to combine novel metalens with conventional optical technology. For instance, a microlens array is used as the wavefront splitting element to focus the incident light of every sub-aperture in adaptive optics, therefore the wavefront is detected by the offset of the focused position [24]. The metalens array is constructed by a large number of well-arranged functional metalenses that can also focus the incident light separately. Compared with a conventional microlens array, the metalens array is much smaller, which fits the trend of miniature devices. In addition, the metalens exhibits higher imaging resolution, corresponding to a higher detection accuracy. The great potential of a metalens array has gradually attracted the attention of researchers. Lately, [PERSON] et al. experimentally examined and explored a flat-lens array at a terahertz range based on C-shape split-ring resonators (CSRRs) [25]; and [PERSON] et al. proposed a Hartmann-Shack metalens array based on transmissive dielectric silicon [26]. However, once these metalens arrays have been fabricated, their functions cannot be engineered, which has limited their practical application. The development of using phase change materials might be an ideal approach to solve the above-mentioned problems. As a typical phase change material, Ge\({}_{2}\)Sb\({}_{2}\)Te\({}_{5}\) (GST) is used for optical disk media at the beginning [27; 28; 29]. It has two different phase states including an amorphous state and a crystalline state. With appropriate thermal, electrical, or optical stimulus, the phase state of GST can be easily tuned [27; 28; 29]. When the GST is tuned between two states, the corresponding permittivity will be changed simultaneously, which can be used to realize active control.