光学涡旋轨道角动量及其测量的理论与实验研究
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摘要
光学涡旋是一种具有螺旋型波前结构的特殊光场,是现代奇点光学的一个重要分支,近年来在光学微操纵、光学信息传输、非线性光学、激光光学、微粒波导、生物医学、原子光学和分子光学中得到广泛的研究和应用。光学涡旋一个最重要的特性是具有确定的光子轨道角动量,本论文重点对光学涡旋轨道角动量及其测量方法进行了理论和实验研究。主要内容如下:
1.对光学涡旋进行了简要介绍,总结了光学涡旋的发展历史和研究现状,概述了光学涡旋的应用。
2.系统总结了光学涡旋的角动量理论,对在近轴传播下和非近轴传播下的光学涡旋中光子携带的轨道角动量的大小进行了理论推导,证明了光学涡旋具有确定的轨道角动量,为深入了解光学涡旋奠定了理论基础。
3.对近些年来发展的许多种典型的测量光学涡旋轨道角动量的方法进行了系统归纳。重点介绍了计算全息图法、光学涡旋与平面波干涉法、光学涡旋与它的共轭光干涉法、杨氏双缝干涉实验法、Mach-Zehnder干涉仪法、多孔干涉仪法来测量光学涡旋轨道角动量的原理、实验装置及实验结果。
4.对多孔干涉仪法进行了改进,提出了一种新的测量光学涡旋轨道角动量的方法。它只需记录一幅光束通过多孔屏的远场衍射强度分布图样,然后通过一种简单的算法来提取多孔位置处的相位值,进而定量地确定光学涡旋的轨道角动量,并且在整个过程中无需涉及迭代算法。
5.基于分析光学涡旋通过一个环形通光孔径后的远场衍射强度分布图样的逆傅立叶变换的强度分布,发现强度分布图样中亮环或暗环的数目恰好等于入射光学涡旋拓扑荷的绝对值,这就为测量光学涡旋角动量大小提供了一种新方法。它不需要复杂的相位提取过程,在测量具有大拓扑荷数值的光学涡旋等方面具有许多优势。
Optical vortices have special helical wave fronts, which have attracted great attention to their well-defined orbital angular momentum property. This kind of special optical field has been applied in many fields including optical micromanipulation, atomic optics, biomedicine, nonlinear optics, and quantum information processing. In this thesis, we explored the methods to determine the angular momentum of optical vortices. The major content and result are as follows:
1. The properties of optical vortices are introduced concisely. The history and the main developments of the optical vortices are reviewed, and their main applications are also summarized.
2. The angular momentum of the optical vortices under paraxial condition and non-paraxial condition are analyzed respectively, and it is demonstrated that optical vortices really have a well-defined orbital angular momentum.
3. Different methods for determining the angular momentum of optical vortices are summarized , including the method based on computer-generated hologram , the interferometric method analyzing the interferogram between an optical vortex and a plane wave or its mirror image, the method based on Young's double-slit interference experiment setup or Mach-Zehnder interferometer. Finally, the method based on a multi-pinhole interferometer is introduced, which lays a basis for our newly proposed methods to determine the angular momentum of optical vortices.
4. A method for measuring the orbital angular momentum of optical vortices through extracting the phase values sampled by a multi-pinhole plate is presented. It is demonstrated that the phase of an optical vortex passing through a multipinhole plate can be directly extracted from the Fourier transform of a single diffraction intensity pattern according to a simple algorithm and thus the l state or the OAM of the photons can be measured quantitatively.
5. The spatial frequency properties of the far-field diffraction intensity pattern of an optical vortex after passing through an annular aperture are analyzed. The theoretical analysis reveals that this spatial spectrum (or the Fourier transform) consists of some bright and dark rings and the number of the rings is just equal to the absolute value of the topological charge. Based on this property, a simple method to measure the topological charge of the optical vortex through its diffraction intensity pattern after an annular aperture is demonstrated.
1.对光学涡旋进行了简要介绍,总结了光学涡旋的发展历史和研究现状,概述了光学涡旋的应用。
2.系统总结了光学涡旋的角动量理论,对在近轴传播下和非近轴传播下的光学涡旋中光子携带的轨道角动量的大小进行了理论推导,证明了光学涡旋具有确定的轨道角动量,为深入了解光学涡旋奠定了理论基础。
3.对近些年来发展的许多种典型的测量光学涡旋轨道角动量的方法进行了系统归纳。重点介绍了计算全息图法、光学涡旋与平面波干涉法、光学涡旋与它的共轭光干涉法、杨氏双缝干涉实验法、Mach-Zehnder干涉仪法、多孔干涉仪法来测量光学涡旋轨道角动量的原理、实验装置及实验结果。
4.对多孔干涉仪法进行了改进,提出了一种新的测量光学涡旋轨道角动量的方法。它只需记录一幅光束通过多孔屏的远场衍射强度分布图样,然后通过一种简单的算法来提取多孔位置处的相位值,进而定量地确定光学涡旋的轨道角动量,并且在整个过程中无需涉及迭代算法。
5.基于分析光学涡旋通过一个环形通光孔径后的远场衍射强度分布图样的逆傅立叶变换的强度分布,发现强度分布图样中亮环或暗环的数目恰好等于入射光学涡旋拓扑荷的绝对值,这就为测量光学涡旋角动量大小提供了一种新方法。它不需要复杂的相位提取过程,在测量具有大拓扑荷数值的光学涡旋等方面具有许多优势。
Optical vortices have special helical wave fronts, which have attracted great attention to their well-defined orbital angular momentum property. This kind of special optical field has been applied in many fields including optical micromanipulation, atomic optics, biomedicine, nonlinear optics, and quantum information processing. In this thesis, we explored the methods to determine the angular momentum of optical vortices. The major content and result are as follows:
1. The properties of optical vortices are introduced concisely. The history and the main developments of the optical vortices are reviewed, and their main applications are also summarized.
2. The angular momentum of the optical vortices under paraxial condition and non-paraxial condition are analyzed respectively, and it is demonstrated that optical vortices really have a well-defined orbital angular momentum.
3. Different methods for determining the angular momentum of optical vortices are summarized , including the method based on computer-generated hologram , the interferometric method analyzing the interferogram between an optical vortex and a plane wave or its mirror image, the method based on Young's double-slit interference experiment setup or Mach-Zehnder interferometer. Finally, the method based on a multi-pinhole interferometer is introduced, which lays a basis for our newly proposed methods to determine the angular momentum of optical vortices.
4. A method for measuring the orbital angular momentum of optical vortices through extracting the phase values sampled by a multi-pinhole plate is presented. It is demonstrated that the phase of an optical vortex passing through a multipinhole plate can be directly extracted from the Fourier transform of a single diffraction intensity pattern according to a simple algorithm and thus the l state or the OAM of the photons can be measured quantitatively.
5. The spatial frequency properties of the far-field diffraction intensity pattern of an optical vortex after passing through an annular aperture are analyzed. The theoretical analysis reveals that this spatial spectrum (or the Fourier transform) consists of some bright and dark rings and the number of the rings is just equal to the absolute value of the topological charge. Based on this property, a simple method to measure the topological charge of the optical vortex through its diffraction intensity pattern after an annular aperture is demonstrated.
引文
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