The Jones matrix is a useful tool to deal with polarization problems, and its number of degrees of freedom (DOFs) that can be manipulated represents its polarization-controlled capabilities. A metasurface is a planar structure that can control light in a desired manner, which, however, has a limited number of controlled DOFs (≤4) in the Jones matrix. Here, we propose a metasurface design strategy to construct a Jones matrix with six DOFs, approaching the upper-limit number of a 2D planar structure. We experimentally demonstrate several polarization functionalities that can only be achieved with high (five or six) DOFs of the Jones matrix, such as polarization elements with independent amplitude and phase tuning along its fast and slow axes, triple-channel complex-amplitude holography, and triple sets of printing-hologram integrations. Our work provides a platform to design arbitrary complex polarization elements, which paves the way to a broader exploitation of polarization optics.

琼斯矩阵是处理极化问题的有用工具，其可操纵的自由度 (DOF) 数代表了其极化控制能力。超表面是一种平面结构，可以以所需的方式控制光，但是在琼斯矩阵中具有有限数量的受控自由度（≤4）。在这里，我们提出了一种超曲面设计策略来构建具有六个自由度的琼斯矩阵，接近二维平面结构的上限数。我们通过实验证明了几种只能通过琼斯矩阵的高（五个或六个）自由度来实现的偏振功能，例如沿其快轴和慢轴具有独立幅度和相位调谐的偏振元件、三通道复幅度全息术和三组印刷全息图集成。