Optical metasurfaces, which consist of subwavelength scale meta-atoms, represent a novel platform to manipulate the polarization and phase of light. The optical performance of metasurfaces heavily relies on the quality of nanofabrication. Retrieving the Jones matrix of an imperfect metasurface optical element is highly desirable. We show that this can be realized by decomposing the generalized Jones matrix of a meta-atom into two parallel ones, which correspond to the ideal matrix and a phase retardation. To experimentally verify this concept, we designed and fabricated metasurface polarizers, which consist of geometric phase-controlled dielectric meta-atoms. By scanning the polarization states of the incident and transmitted light, we are able to extract the coefficients of the two parallel matrices of a metasurface polarizer. Based on the results of the Jones matrix decomposition, we also demonstrated polarization image encryption and spin-selective optical holography. The proposed Jones matrix retrieval protocol may have important applications in computational imaging, optical computing, optical communications, and so on.

Polarizers have always been an important optical component for optical engineering and have played an indispensable part of polarization imaging systems. Metasurface polarizers provide an excellent platform to achieve miniaturization, high resolution, and low cost of polarization imaging systems. Here, we proposed freeform metasurface polarizers derived by adjoint-based inverse design of a full-Jones matrix with gradient-descent optimization. We designed multiple freeform polarizers with different filtered states of polarization (SOPs), including circular polarizers, elliptical polarizers, and linear polarizers that could cover the full Poincaré sphere. Note that near-unitary polarization dichroism and the ultrahigh polarization extinction ratio (ER) reaching 50 dB were achieved for optimized circular polarizers. The multiple freeform polarizers with filtered polarization state locating at four vertices of an inscribed regular tetrahedron of the Poincaré sphere are designed to form a full-Stokes parameters micropolarizer array. Our work provides a novel approach, we believe, for the design of meta-polarizers that may have potential applications in polarization imaging, polarization detection, and communication.

本文使用理论与实验相结合的方法研究了斜入射下液晶涂布型C-plate（Liquid crystal coated C-plate，LCC）对逆分散1/4波片（Reverse wavelength dispersion quarter wave plate，RQWP）补偿能力的优化特性。使用扩展琼斯矩阵比较了偏振光以任意角度通过RQWP、RQWP+LCC两种架构后出射光的椭圆率，探究了不同相位延迟RTH的LCC对出射光椭圆率的影响；测试了上述两种架构的圆偏光片在OLED（Organic light emitting-diode display）上的环境光反射率以及反射颜色色坐标。结果表明，LCC能够使45°斜入射时出射光的椭圆率提升10%以上，且在红、绿、蓝三色光条件下，调整LCC的RTH可使膜材架构的总折射率系数NZ趋近于0.5，获得最佳效果。使用RQWP+LCC架构的圆偏光片可使45°极角下OLED的环境光反射率降低3%。在工业生产中直接生产NZ=0.5的膜材拥有较高的技术难度，本文结论对开发NZ=0.5的膜材提供了新的可行方案。

针对光束在级联式液晶偏振光栅传播过程中的斜入射现象会改变其椭圆率进而降低衍射效率的问题，提出了基于偏振补偿的级联式液晶偏振光栅衍射效率优化方法。运用扩展琼斯矩阵分析斜入射角度对液晶偏振光栅相位延迟的影响，结合斯托克斯参数求解不同斜入射角度下液晶偏振光栅出射光束椭圆率的变化，利用矢量衍射理论完成级联式液晶偏振光栅衍射效率模型的建立。基于液晶分子指向矢分布建立斜入射下液晶电控波片的坐标系，分析斜入射角度对液晶电控波片相位延迟的影响，推导出液晶电控波片相位延迟与椭圆率的关系。通过优化液晶电控波片的工作电压补偿斜入射造成的退偏量，实现对椭圆率的偏振补偿。搭建实验平台验证了理论的准确性与方法的有效性。根据测量结果可知，当光束偏转角度从-5°偏转到5°时，本文所提方法提高了级联式液晶偏振光栅3%~4%的衍射效率。

为了表征光束倾斜入射下液晶偏振光栅的衍射特性，提出了液晶偏振光栅斜入射角度-驱动电压-衍射效率的三维模型建模方法。该方法利用吉布斯自由能方程，求解液晶分子指向矢，得到驱动电压与液晶分子倾斜角的表达式，推导出斜入射角度与相位延迟量之间的关系，结合扩展琼斯矩阵表征不同入射角度下液晶偏振光栅的透过率，通过矢量衍射理论，建立了斜入射角度-驱动电压-衍射效率的三维模型。该模型不仅可以定量求解不同斜入射角度下液晶偏振光栅衍射效率，而且能够实现衍射效率最优时驱动电压的标定。通过仿真分析和实验对该模型的有效性进行了验证，结果表明：光束入射角度从0°倾斜到10°时，最优驱动电压由2.2 V降低到2.0 V，液晶偏振光栅衍射效率从85%下降到78%；光束入射角度从0°倾斜到−10°时，最优驱动电压由2.2 V升高到2.4 V，液晶偏振光栅衍射效率从85%下降到74%。

人工微结构超表面近年来在偏振调控与色散调控领域都取得了诸多进展，然而传统方法计算超表面结构对椭圆偏振态的调控效果需要对每一个数据求解方程，因此实现任意偏振的消色差调控依然在复杂度上是一个挑战。一种基于坐标变换的正向计算方法用以快速计算超表面单元对任意偏振态的调控效果被提出，利用纯硅体系下的椭圆柱结构作为调控单元设计了工作在中红外波段的对椭圆偏振态调控的消色差聚焦超表面透镜。结果表明，此种方法与设计在极大简化计算流程的情况下，能够有效实现对椭圆偏振态的操控。相比于之前所报道的基于圆偏振或无偏振依赖的设计，该方法进一步拓展了超表面色散调控的应用范围，具有广阔的应用前景。