基于庞加莱球模型的新型矢量光场的设计、生成及性质研究

Due to the unique polarization feather, novel properties and wide range of applications, the vector optical fields have attracted great attention of many researchers. As is well known, Poincaré sphere is a common representation of polarization state, and can provide new scheme and idea for designing the vector optical fields. Therefore, designing new kind of vector optical fields based on Poincaré sphere has exhibited significant research value and great research potential. In this project, we will propose a new elliptical Poincaré sphere model based on the classical Poincaré sphere model by adding a manipulating dimension. Based on the (elliptical) Poincaré sphere model, a variety of new vector optical fields will be constructed by two-dimensional stretching of spherical surface, projection, spherical curve and section on sphere. We will also describe the geometric phase carried by the new vector optical fields by the (elliptical) Poincaré sphere, and explain the relative new phenomena and properties including optical angular momentum. Furthermore, we will study the spatiotemporal evolution of the new vector optical fields, and explore the new effects, phenomenon and the corresponding physical mechanism. This project will expand the new methods and schemes of constructing vector optical field, and enrich the manipulation method and family of the vector optical field. Hence, this project possesses important research significance and application value.

矢量光场由于其独特的偏振特性、新颖的性质和广泛的应用，吸引了众多国内外学者的关注。众所周知，庞加莱球是偏振态的常用表征方式，可以为矢量光场的设计提供新方案和新思路。因此，利用庞加莱球模型设计新型矢量光场具有重要的研究价值和研究潜力。本项目在经典的庞加莱球模型的基础上增加一个调控维度，提出了新的庞加莱椭球模型；基于庞加莱（椭）球模型，利用球面二维展开、投影、球面曲线和球体截面得到特定的偏振态分布，进而构建多种新型矢量光场；基于庞加莱（椭）球上的几何位相描述矢量光场携带的几何位相，并利用其解释相关光学角动量等方面的现象和性质；研究新型矢量光场时空演化过程中的新效应、新现象并探索其物理机理。本项目为构建矢量光场提供了新原理和新方法，可以丰富矢量光场的调控方式和种类，具有重要的研究意义和应用价值。

庞加莱球是偏振态的一种常用表征方式，具有重要的研究意义和价值。本项目围绕庞加莱球模型，构建新的表征偏振态和矢量光场的模型，设计新型矢量光场，并研究其在时空演化过程中的新颖光学效应和现象。主要的研究进展如下：(1)提出了五维庞加莱球系统模型，可以用于设计、表征和研究矢量光场；(2)利用庞加莱球展开方式，设计了一种新型全庞加莱球矢量光场；(3)基于庞加莱球模型，提出了分区域对称、抛物对称、双极对称、携带旋向非均匀轨道角动量和双曲对称的杂化偏振矢量光场，并研究了其时空演化性质和潜在应用；(4)设计了其他新型矢量光场，研究了其焦场和光学角动量等性质。综合上述结果，本项目提出了多种新模型和新光场，丰富了矢量光场的调控方式，可以为矢量光场的研究提供新的方法和工具，有望在多个领域取得应用。项目执行期间，共发表SCI论文11篇，申请国家发明专利2项。