矢量涡旋光束是一种同时具有偏振态空间变化和螺旋波前结构的新型光束。由于其新颖的光学特性，矢量涡旋光束在超分辨率成像、精密度量、光通信和激光加工等领域有着巨大的应用前景。早期人们对矢量涡旋光束的研究主要集中在柱矢量涡旋光束，随着全庞加莱球、高阶庞加莱球等偏振表征方式的提出，人们已经创建了许多具有奇特结构的矢量涡旋光束。与传统的均匀偏振光束不同，矢量涡旋光束在聚焦场、散射场和倏逝波等高度非均匀场中可以展现出非凡的自旋-轨道相互作用。本文基于衍射角谱理论，分别对高阶庞加莱球矢量涡旋拉盖尔-高斯光束近场的倏逝波和自旋-轨道相互作用，远场的矢量结构和角动量的演化特性进行了理论研究。本文的主要研究内容如下：

（1）介绍了常见的两种偏振态表征方式，即斯托克斯系数和琼斯矢量表示法。进一步介绍了用来表征传统均匀偏振光束偏振态的庞加莱球，以及用来表征矢量涡旋光束任意偏振态的高阶庞加莱球。根据衍射角谱理论，给出了单色电磁波在自由空间中传输的一般描述。基于Parseval定理，提供了倏逝波和传播波光强平面积分在麦克斯韦方程中的一般精确解。推导并分析了傍轴和非傍轴情形中的光学角动量的一般表述形式。

（2）基于衍射角谱理论和Parseval定理分析了高阶庞加莱球矢量涡旋拉盖尔-高斯光束的近场特性。其倏逝波和传播波的光强分布直观地给出了矢量涡旋光束在近场中的传输特性。详细分析了拓扑荷、椭圆率角和束腰宽度等自由度对倏逝波在总光场中的贡献的影响。经过计算发现，较高的拓扑荷数、径向阶数等自由度对倏逝波和传播波的光场分布模式有很大的影响。研究了近场中非傍轴情形由倏逝波引起的自旋-轨道相互作用。结果表明，近场中矢量涡旋光束的轨道角动量同时包含横向电场和纵向电场的贡献，倏逝波中的横向自旋角动量和横向偏振态相关，且由于量子自旋霍尔效应存在自旋方向锁定的现象。这些结果可能为矢量涡旋光束在亚波长结构中的研究和应用提供帮助。

（3）基于衍射角谱理论和稳相法推导并分析了远场高阶庞加莱球矢量涡旋拉盖尔-高斯光束的TE项和TM项电磁场的解析形式模型。通过观察TE项、TM项和总能流密度来分析矢量涡旋光束在远场中矢量结构的演化特性。拓扑荷、椭圆率角等自由度对TE项和TM项能流密度分布有很大的影响，而当束腰宽度减小到接近一个波长时，总能流密度的柱对称性分布被打破。通过改变拓扑荷、椭圆率角等自由度可实现对自旋角动量和轨道角动量的调控，且TE项和TM项电场间的干涉也能产生轨道角动量。这些工作有望为矢量涡旋光束在远场中的传输特性和角动量密度调控相关研究提供有用的信息。

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