三维涡旋光场的偏振特性计算方法的研究

Three-dimensional vortex light field widely exists in many fields, such as super-resolution optical imaging, optical micro-manipulation, near-field optics, and lithography. The traditional 2D polarized light tracing methods are no longer applicable in 3D vortex light field, because the propagation of the beam in 3D vortex light field does not conform to the paraxial transmission conditions. Research the calculation methods of 3D vortex light field polarization characteristics become the key to solve some bottleneck problems in the current vortex optical technology. In the previous work, we completed the polarized ray tracing method for 3D coherent light field. On this basis, the study includes: (1) The mathematical model of coherency matrix in three-dimensional space; (2) The continuous phase space based on discrete Fourier transform; (3) The mathematical model of polarization aberration function, and its influence to PSF and MTF; (4) The intrinsic relationships between the polarization characteristics of the incident vortex beam and the imaging quality of optical systems. This project systematically constructs the theory system of polarized ray tracing for 3D vortex light field from three dimensional promotion of coherency matrix. This work has important significances to us in many aspects, such as accurately analyzing the evolution of polarization properties for 3D vortex light field, optimization design of high performance optical system, and research on the interaction between 3D vortex light field and optical systems.

三维涡旋光场广泛存在于超分辨率光学成像、光学微操控、近场光学以及光刻等领域。由于三维涡旋光场中光束的传播并不符合傍轴传输条件，传统的二维偏振光追迹方法都不再适用，三维涡旋光场偏振特性计算方法的研究成为解决当前涡旋光学技术若干瓶颈问题的关键。前期工作中初步完成了三维相干光场的偏振光追迹方法的研究，在此基础上，本项目的研究内容为：(1)相干矩阵在三维空间中的数学模型；(2)基于离散傅里叶变换的连续位相空间；(3)偏振像差函数的数学模型，及其对点扩束函数和调制传递函数的影响；(4)入射涡旋光场的偏振特性与光学系统成像质量的内在关系。本项目从相干矩阵的三维推广出发，系统地构建三维涡旋光场偏振光追迹的理论体系。对我们精确分析三维涡旋光场的偏振特性演化、优化设计高性能光学系统、研究三维涡旋光场与光学系统的相互作用等方面有着重要的意义。

三维涡旋光场广泛存在于超分辨率光学成像、光学微操控以及光刻等领域。由于三维涡旋光场中光束的传播并不符合傍轴传输条件，传统的二维偏振光追迹方法都不再适用，三维涡旋光场偏振特性计算方法的研究成为解决当前涡旋光学技术若干瓶颈问题的关键。本项目针对三维相干光场的偏振光追迹方法展开研究，推导了相干矩阵在三维空间中的数学模型，从相干矩阵的三维推广出发，系统地搭建了三维涡旋光场偏振光追迹的理论体系，基于离散傅里叶变换的连续位相空间，构建了入射涡旋光场的偏振特性与光学系统成像质量的内在关系，建立了偏振像差函数的数学模型，及对其补偿方法的研究。对精确分析三维涡旋光场的偏振特性演化、优化设计高性能光学系统、研究三维涡旋光场与光学系统的相互作用等方面有着重要意义。