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题名	广义斐波那契光子筛的三维阵列聚焦特性研究
作者	柯杰
学位类别	硕士
答辩日期	2016
授予单位	中国科学院上海光学精密机械研究所
导师	张军勇
关键词	广义斐波那契 光子筛 衍射成像 三维阵列焦点 双涡旋
其他题名	Study on Three-dimensional Array Focusing Properties of generalized Fibonacci Photon Sieves
中文摘要	衍射光学元件在物理学和生命科学领域具有重要的应用前景。体积小、重量轻、设计灵活的光子筛作为一种新型的聚焦成像衍射光学元件受到越来越多研究人员的关注。另一方面，数学上的斐波那契数列被广泛应用在光学元件设计中，比如，多层线性光栅、环形光栅、涡旋波带片、双焦衍射透镜等。广义斐波那契数列的特性也是数学领域研究热点之一。本论文把广义斐波那契数列引入到光子筛等微纳结构设计中，提出了广义斐波那契光子筛结构的设计方法，研究了该器件的三维阵列焦点(m×n)×p特性，其中p代表焦平面个数，m×n代表某个焦平面上阵列焦点的数目，同时对提出的物理模型进行了模拟仿真和实验验证。具体研究内容主要概括为以下六点： 1、调研了广义斐波那契光子筛研究的背景和意义。重点调研对象是具有(1×1)×1特殊阵列焦点的传统光子筛、具有(1×1)×p特殊阵列焦点的多焦点光学器件以及具有(m×n)×p阵列焦点的光学器件。 2、介绍了光子筛衍射理论。重点介绍了筛孔标量衍射和矢量衍射理论，并以振幅型光子筛为例，分析了传统光子筛的聚焦特性。 3、提出了双焦斐波那契光子筛的一般性设计方法。提出通过筛孔位置和孔径大小控制轴上焦点光强分布的方案，同时引入超高斯调制技术对筛孔数目进行调制，进一步提高了广义斐波那契光子筛焦斑的横向分辨率。 4、探讨广义斐波那契光子筛轴上焦点分布内在的数学关系。其焦比(焦距之比)特性完全由广义斐波那契序列的数学特征决定，表现出一定的光学结构拓扑不变性。此外，还发现衍射光学杠杆效应。 5、在振幅型广义斐波那契光子筛的基础上发展出了相位型广义斐波那契光子筛，详细探讨了如何利用相位设计来获得双涡旋焦斑。 6、提出了利用广义斐波那契光子筛实现阵列焦点的方法。利用衍射光学杠杆效应和不同斐波那契序列设计出了混合式广义斐波那契结构，实现了混合阵列焦点功能。 广义斐波那契光子筛独特的聚焦特性，使其在光学开关、纳米光刻、生物仿生眼、多焦成像和测距，甚至在X射线显微技术和太赫兹成像技术都将有新的应用。
英文摘要	Diffractive optical elements (DOEs) have a large number of new significant applications in physical and life sciences. Photon sieve (PS), in consequence of its small size, light weight and flexible design, is a new type of focusing and imaging DOEs, and given more and more attention of scientific researcher. On the other hand, Fibonacci sequence in mathematics has been employed in the development of different photonic devices, for example, multi-layers and linear grating, circular grating, spiral zone plates, and bifocal diffractive lenses. Meanwhile, the mathematical characteristic of generalized Fibonacci sequences is also a hotspot in the field of mathematics. Here, the generalized Fibonacci sequences are firstly introduced into the design of micro-nano structures, such as PS and Fresnel zone plate (FZP). Then, based on the above Fibonacci PS, three dimensional array (m×n)×p focusing properties are mainly discussed, where p is the number of focal planes and m×n represents array foci at focal planes. The simulation and experiments agree well with our proposed physical modeling. The research contents can be summarized as follows: 1. The research background of generalized Fibonacci photon sieves (GFiPS) is investigated in detail. The key researches include traditional photon sieve with (1×1)×1 array foci, axial multi-focal optical devices with (1×1)×p array foci and optical devices with (m×n)×p array foci. 2. The diffraction theory of PS is reviewed. The scalar diffraction and vector diffraction theory are mainly discussed. Taking the amplitude-only PS as an example, the focusing characteristics are analyzed in detail. 3. The design method of a bifocal GFiPS is proposed. The axial intensity distributions are controllable by adjusting the position and size of pinholes. Then Gaussian apodized technology is applied to GFiPS in order to further improve the resolution of the focal spots. 4. The mathematical relationship among the axial multiple foci generated by GFiPS is discussed. We find that the ratio of focal lengths is completely determined by the mathematical characteristics of the corresponding generalized Fibonacci sequences, which is called optical topological invariance. Besides, diffraction optical lever (DOL) is found. 5. The design method of phase-only GFiPSs is proposed. We study their focusing properties in detail, and then successfully get twin axial vortices. 6. Two technologies are presented to extend the number of layers in order to realize three-dimensional array foci. One is the diffractive optical lever; the other is multi-hybrid Fibonacci structures. The focusing properties of GFiPSs make them available for optical switches, nanometer lithography, bionic eyes, multi-focus imaging and ranging, even some new applications in X-ray microscopy and THz imaging.
语种	中文
内容类型	学位论文
源URL	[http://ir.siom.ac.cn/handle/181231/16992]
专题	上海光学精密机械研究所_学位论文
推荐引用方式 GB/T 7714	柯杰. 广义斐波那契光子筛的三维阵列聚焦特性研究[D]. 中国科学院上海光学精密机械研究所. 2016.

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