毕业设计（论文）
的设计与应用
English Title：Design and Application of vector beam with
fractional orbital angular momentum
学生姓名: 刘晓昌
专业: 物理学
学号: 08027114
指导老师: 周琦
二0一二年六月
摘要
矢量光束中的偏振态在光场时空演化及其与其他物质相互作用中起着非常重要的作用，表现出一些不同于标量光束的新颖特性。因此，矢量光束的研究有重要的科学价值和应用意义。近年来矢量光束独一无二的性质以及潜在的应用价值使得越来越多的科研人员对其产生了浓厚的兴趣，特别是偏振态显现出轴对称性的光束（即轴对称矢量光束）以及椭圆对称性的光束（即椭圆矢量光束）。矢量光束以其独特的发展前景受到广泛的关注。
在本论文中，我们首先介绍了矢量光束的基本概念、产生方法以及应用。通过激光器的谐振腔外干涉或在激光器谐振腔内插入特殊的元件以及利用空间光调制器能够产生各种构型的矢量光束；在第二章中，我们提出了一种利用振幅型空间光调制和偏振分束器件实现矢量光束的方案，数值计算了产生圆对称径向、角向矢量光束以及椭圆矢量光束的调制光栅构型；在第三章中，我们在矢量瑞利——索末菲衍射理论的基础上，介绍了矢量光束经过高数值孔径物镜聚焦的特性，并初步探讨了矢量光束中光子轨道与自
旋角动量，得出椭圆矢量光束光子轨道角动量具有分数值的结论。最后，我们对所研究的内容进行了总结与展望。
关键字：矢量光束；激光器；空间光调制器；衍射理论；角动量
ABSTRACT
The polarization state of the vector beam plays a very important role in the evolution of optical field in temporal and spatial dimensions and the interaction with other matters; dues to some novel features different from the scalar beam are presented. Therefore, the study of vector beam has important scientific value and application significance. In recent years, more and more researchers develop strong interest in the unique nature and potential applications of the vector beams, in particular, the beam with axial symmetry polarization state ( ax symmetric vectoring beam) and elliptical symmetry polarization state (elliptical vector beam). Vector beam has also received widespread attention for its unique development prospects.
In this paper, some basic concepts, generation method and foundational application of vector beamed are first introduced in Chap. 1. Vector beams with various constructs of polarization can be generated by the methods of outer cavity interference, the use of special optical element inserted into resonant c
avity, spatial light modulator and so on. In Chap. 2, we proposed a novel scheme to implement vector beam by synchronously using spatial light modulator working on amplitude mode and polarization beam splitter. The modulation gratings for generating radial, angular vector beam with circle or elliptic symmetry are numerically calculated. Based on vector Rayleigh Sommerfeld diffraction theory，we introduce propagation characteristics of vector beam focused by a objective lens with high numerical aperture in Chap.3. Some preliminary analyzes and discussions of photonic orbital and spin angular momentum of vector beam are also presented. And we find a fractional orbital angular momentum can be obtained in elliptical vector beam. Some conclusions and prospects are draw in final Chapter.
Key words: Vector beam; Laser; Spatial light modulator; Diffraction theory; Angular momentum
目录
绪论 (1)
1.矢量光束及其应用 (2)
1.1 矢量光束的概念 (2)
1.2 矢量光束产生的方法 (4)
1.3 矢量光束的应用 (7)
2. 利用空间光调制器和偏振分束器实现任意构型矢量光束方案.. 9
2.1 空间光调制器与偏振分束器原理 (9)
2.2 矢量光束产生方案 (12)
2.2.1 圆对称径向矢量光束 (14)
2.2.2 圆对称角向矢量光束 (15)
2.2.3 椭圆对称矢量光束 (17)
2.3 本章小结 (20)
3. 矢量光束传播特性 (21)
3.1 光束矢量衍射理论原理 (21)
3.1.1 傍轴标量理论的不自洽性 (21)
3.1.2 角谱分析法 (23)
3.1.3 矢量瑞利一索末菲衍射积分公式法 (24)
3.2 径向、角向矢量光束聚焦特性 (25)
东华理工大学怎么样3.2.1 矢量光束聚焦场的数学描述 (26)
3.2.2 径向偏振光 (27)
3.2.3 角向偏振光 (28)
3.3 椭圆矢量光束角动量 (28)
3.3.1 椭圆矢量光束的光强分布和偏振分布 (29)
3.3.2 椭圆矢量光束的总角动量 (29)
3.3.3 椭圆矢量光束的自旋角动量和轨道角动量 (31)
总结与展望 (33)
致谢 (34)
参考文献 (35)
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