涡旋矢量光场的焦场特性

论文总字数：26045字

摘 要

涡旋矢量光束是一种相位分布为螺旋型的新型奇异光束。涡旋光束独特的特性令其在光学微操控、信息编码与传输、量子纠缠、光学散斑场、光控开关等领域有着广阔的应用前景。近年来，为了挖掘涡旋光束更深层次的应用价值，科研人员对涡旋光束产生了强烈的兴趣。因此，有大量关于涡旋光束传输特性与焦场特性研究的论文和文章被发表。

本文首先阐述了涡旋光束的基本概念和主要特性，包括其波前具有螺旋相位结构，中心光强为零(即暗心结构)，并且携带确定的光子轨道角动量。同时详细介绍了四种生成涡旋光束的方法，分别为：(1)计算全息法；(2)螺旋相位板法；(3)自适应螺旋镜法；(4)空间光调制器法。

其次，根据弱旁轴近似下的瑞利—索莫菲矢量积分公式，对方位角偏振最低阶拉盖尔—高斯光束的传播行为进行了深入研究。推导出了被无孔径作用薄透镜聚焦的，拓扑荷为任意整数的方位角变化涡旋矢量光束电场的径向、方位角、纵向分量的解析表达式。

最后，本文通过Matlab对在多种条件下的方位角变化涡旋矢量光场的非旁轴聚焦场与旁轴聚焦场进行了数值仿真，研究其光强图样的特点，分析其焦场特性并探讨了其可能应用。

关键词：涡旋光束，拓扑荷数，拉盖尔—高斯光束，瑞利—索莫菲矢量积分公式，光强图样，Matlab

characteristics of the focal fiELd of Vortex Vector BEAMS

Abstract

Vortex vector beams is a kind of novel singular lights with spiral wave front structure. The unique characteristics of vortex beams make it have a wide application prospect in many fields, such as optical micro manipulation, information coding and transmission, quantum entanglement ,optical speckle fields and optical controlled switching. In recent years, scientific researchers have evinced a keen interest in vortex beams. Therefore, a large number of research and articles about the propagation characteristics and the focal field characteristics have been published.

First of all, outlined the basic concept and the main characteristics of vortex vector beams, including that vortex beams possess spiral wave front structure, the center of light intensity is zero(i.e., dark center structure) and carrying the determined orbital angular momentum. Meanwhile, four methods of generating optical vortex vector beams were introduced, namely, (1) Computer Generated Hologram, (2) Spiral Phase Plate, (3) Adaptive Helical Mirror, (4) Spatial Light Modulator.

Secondly, based on the vectorial Rayleigh-Sommerfeld diffraction formula under the weak nonparaxial approximation, this paper makes deep study on the propagation behavior of a lowest-order Laguerre-Gaussian beam with azimuthal-variant states of polarization. The analytical expressions for the radial, azimuthal, and longitudinal components of the electric field with an arbitrary integer topological chargefocus by a nonaperturing thin lens.

At last, this paper illustrates the nonparaxial and paraxial focal field of azimuthal-variant vortex vector beams in many cases by Matlab simulation. The features of the light intensity patterns are illustrated, the characteristics of the focal field is analyzed and the potential applications are discussed.

KEY WORDS: vortex vector beams, topological charge, Laguerre-Gaussian beam, vectorial Rayleigh-Sommerfeld formulas, light intensity pattern, Matlab

目 录

摘 要 I

Abstract II

第一章 绪 论 1

1.1 引言 1

1.2 涡旋光束的研究背景 1

1.3 涡旋光束的应用 2

1.4 涡旋光束的生成方法 4

1.4.1 计算全息法 4

1.4.2 螺旋相位板法 5

1.4.3 自适应螺旋镜法 6

1.4.4 空间光调制器法 6

1.5本文的研究目的与主要研究内容 7

第二章 涡旋光束三维焦场理论分析 9

2.1非旁轴传输三维电场理论推导 9

2.2旁轴传输三维电场理论推导 12

第三章 涡旋光束焦场光强数值模拟 15

3.1非旁轴聚焦场数值模拟 15

3.2旁轴聚焦场数值模拟 22

3.3不同拓扑荷非旁轴聚焦场数值模拟 25

结论 28

致谢 29

参考文献（References） 30

1. 绪 论

1.1 引言

涡旋是指半径微小的圆柱体在静止的流体中旋转，并带动周围流体作圆周运动的一种流动现象。作为一种物理现象，涡旋广泛存在于自然界中，大气形成的热带气旋与龙卷风，涨潮落潮相互作用产生的潮水涡旋，都属于这种现象。涡旋现象也广泛存在于生活中，不过有些并不能被肉眼所观察到，例如水流中微小的涡旋，甚至由于身体动作而产生的空气中的涡旋气流。

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