液晶指向场幂函数分布的拓扑相位光学元件及特性研究

Through the manipulation of the spatial phase profile of light, the direction of propagation of light can be controlled by the liquid crystal (LC) topological phase optical elements (TPOEs) in a desirable manner. Due to the outstanding optical performance of the LC TPOEs, they have caught more and more attentions of the researchers in academia as well as industry. Some questions were inspired during our investigation on the LC polarization grating (power=1) and PB phase lens (power=2), which are the LC TPOEs based on directors spatially varying with one-dimensional power function. Q1: Will there be some new optical properties when the power is greater than 3? Q2: How will the optical performance evolve when the power goes up from 0 to 1? Q3: What if the power is less than 0? This project is aimed at answering all above questions. In the project, we mainly concentrate on the fundamental research on the LC TPOEs with the directors spatially varying with power functions or power series. Through the investigation on the optical properties of the LC TPOEs, we will put forward the frontier of our knowledge on such kind of optical elements, and figure out how their diffraction patterns evolve with various values of the power. We will physically analyze and explain the new optical phenomena brought about from the experiment and exploit the potential applications for the LC TPOEs, specifically, some new applications of the LC TPOEs with several optical-functional properties that are integrated in a single LC cell will be developed. Therefore, this project possesses both fundamental research of great significance and value of application. Through this project, we will accumulate experience in the fundamental research on the LC TPOEs with spatially varying directors, and it will definitely provide a solid base for our further research on the LC TPOEs with the spatially varying directors based on logarithmic, exponential, or even inverse trigonometric function, etc.

液晶拓朴相位光学元件通过对光束的空间相位调制来控制光的传播方向，因其光学性能出色，目前已得到学术界乃至工业界越来越多的关注。对液晶指向场分布为一维空间幂函数的偏振光栅（幂指数为1）和PB相位透镜（幂指数为2）的研究，给我们以启发性思考：当幂指数为3以上时，光学上有何新特性？当幂指数为0到1之间的非整数时，光学性能如何演变？当幂指数为负数时，又有何光学现象发生？这些问题都将属于本项目的研究范畴，我们将以指向场分布为幂函数或者幂级数的液晶拓朴相位光学元件的基础研究为主导，通过研究其光学特性，掌握相关规律，开拓人们对其新的认知，对其所带来的新光学现象进行物理分析和应用探索，开发具有复合光学特性的液晶拓朴相位光学元件的应用，因此本项目兼具重要的基础研究意义及应用价值。通过本项目的开展，更可以为我们之后对指向场分布为对数、指数、乃至反三角等函数的液晶拓朴相位光学元件的研究提供经验积累，打下坚实基础。

本项目研究的内容是拓扑相位液晶光学器件，也称作几何相位液晶光学器件。光在通过一个由液晶材料构成的满足半波条件的光学平面，且该平面内液晶指向场分布为α (x, y) = f (x, y)时，可以额外地产生一个相应的几何相位，其中α (x, y)是在(x, y)处的液晶指向矢与实验室坐标x轴的夹角，f(x,y)是关于空间x和y的函数。几何相位本质上取决于液晶指向矢的空间分布α (x, y)。通过本项目的研究，我们在理论上找到了一种方法来快速高效地实现对于任意指向矢分布地液晶几何相位光学元件；我们在对于液晶几何相位光学元件的实验研究中也有一些进展，我们成功研制了多个光学元件，包括：具有复合光学特性的液晶轴棱镜-透镜、集成了光栅和透镜的液晶几何光学元件、光控反射式液晶几何相位器件、光控透射式液晶圆形达曼光栅、铁电液晶圆形达曼光栅以及在模糊态和透明态之间用低电压切换的液晶智能玻璃，项目期间共发表了5篇SCI期刊论文。