随着科学技术的不断进步，光学仪器在各行各业都在迅速的发展。光学透镜广泛应用于望远镜、波前探测、光学成像等领域，一直广受人们的关注。由于依靠光束在传播过程中来积累相位延迟，传统光学透镜一般来讲体积大，在性能方面也有所制约，不符合集成化与智能化的发展。因此急需新的途径和方式来打破原有透镜制作、性能等方面的局限。

超表面是二维超材料的对应物，可以通过亚波长单元灵活地控制光的振幅，相位和偏振。由于超表面的特殊性质，其具有强大的光场操纵能力，可以实现各种新应用，这在过去几年中已得到广泛研究，并在各个领域中迅速发展。与传统的依靠调制光束在传输过程中积累相位延迟的透镜相比，超表面透镜体积小，重量轻，适用于设备小型化和系统的集成。目前，超表面研究的重点已转移到可调功能上。另外，基于Pancharatnam-Berry(P-B)相位原理的超表面透镜，对入射光的螺旋度要求较高，限制了其应用范围。

本文设计了一种基于相变材料的温度可控的多功能超表面透镜。相变材料二氧化钒在相变温度前后具有两种相位状态，分别对应金属态和半导体绝缘态，两种状态在中红外波段透过率具有较大的对比。我们基于P-B相位原理设计超表面实现光波前的调控。首先，通过控制所需工作区域的温度和入射光的偏振，可以实现在任何位置的多焦点，单焦点和无焦点之间切换，并且可以调节输出光的强度和螺旋度。同时，超透镜的焦点可以扩展到一定区域内的任何位置，并具有良好的聚焦效果。另外，设计了一种基于P-B相位原理的偏振敏感强度可调透镜，当入射光分别为线偏振光，左旋圆偏振光和右旋圆偏振光时，其经过超透镜后形成的焦点位置相同，但具有不同的光场强度。因此，可以通过入射光的偏振状态来调节聚焦光场强度。

本论文设计的多功能超表面透镜对线偏振光是不敏感的。对于与水平轴具有不同夹角的线偏振光，经过超透镜后形成的焦斑强度分布基本一致。因此，可以认为我们设计的基于几何相位原理的超表面透镜对线偏振光是不敏感的。最后，我们对多功能超表面进行了色差分析，研究了围绕中心波长变化的入射光经过透镜后焦斑的分布情况，并与理论值进行了对比分析，展现出良好的一致性。

With the continuous advancement of science and technology, optical instruments are developing rapidly in all walks of life. Optical lenses are widely used in telescopes, wavefront detection, optical imaging and other fields, and they have always attracted people's attention. Due to the accumulation of phase delay by the light beam in the propagation process, the traditional optical lens is generally large in size and has some limitations in performance, which does not conform to the development of integration and intelligence. Therefore, new approaches and methods are urgently needed to break the limitations of the original lens production and performance.

Metasurfaces are the counterparts of two-dimensional metamaterials, which can flexibly control the amplitude, phase and polarization of light through sub-wavelength units. Due to the special properties of metasurfaces, it has powerful light field manipulation capabilities and can realize various new applications. This has been extensively studied in the past few years and has been rapidly developed in various fields. Compared with traditional lenses that rely on modulated light beams to accumulate phase delay during transmission, metasurface lenses are small in size and light in weight, and are suitable for device miniaturization and system integration. At present, the focus of metasurface research has shifted to dynamically tunable functions. In addition, the metasurface lens based on the Pancharatnam-Berry (P-B) phase principle has high requirements for the helicity of the incident light, which limits its application range.

In this paper, a temperature-controllable multifunctional metasurface lens based on phase change materials is designed. The phase change material vanadium dioxide has two phase states when it is higher and lower than the phase change temperature, corresponding to the metallic state and the semiconductor insulation state, respectively. In the two states, the transmittance in the mid-infrared band has a greater contrast. We design the metasurface based on the P-B phase principle to realize the control of the light wavefront. First, by controlling the temperature of the required working area and the polarization of the incident light, it is possible to switch between multi-focus, single-focus and no-focus at any position, and the intensity and helicity of the output light can be adjusted. At the same time, the focal point of the metalens can be extended to any position within a certain area, and has a good focusing effect. In addition, a polarization-sensitive intensity adjustable lens based on the PB phase principle is designed. When the incident light is linearly polarized light, left-handed circularly polarized light, and right-handed circularly polarized light, the focal position formed by the metalens is the same. But it has a different light field intensity. Therefore, the focus intensity can be adjusted by the polarization state of the incident light.

The multifunctional metasurface lens designed in this paper is insensitive to linearly polarized light. For linearly polarized light with different angles to the horizontal axis, the intensity distribution of the focal spot formed after passing through the metalens is basically the same. Therefore, it can be considered that the metasurface lens we designed based on the geometric phase principle is insensitive to linearly polarized light. Finally, we conducted a chromatic aberration analysis on the multifunctional metasurface, studied the distribution of the focal spot of the incident light that changes around the center wavelength after passing through the lens, and compared the analysis with the theoretical value, showing good consistency.