Laguerre–Gaussian beams with vortex structure, as a special type of electromagnetic wave, can carry energy, momentum, and angular momentum, which is crucial for understanding of dynamical processes concerning light–matter interaction phenomena. In this paper, we theoretically investigate the local dynamical characteristics of Laguerre–Gaussian vortex beams upon reflection and refraction. Using a hybrid method based on the angular spectrum representation and vector potential in the Lorenz gauge, the explicit analytical expressions for the electric and magnetic field components of reflected and refracted Laguerre–Gaussian beams are derived in the form of a Hermite polynomial. A canonical approach is utilized to examine the energy, momentum, and spin and orbital angular momentum of the Laguerre–Gaussian vortex beams’ reflection and refraction at a plane interface between air and BK7 glass. The effects of the incidence angle, topological charge, and polarization state on these dynamical quantities are simulated and discussed in detail. This study may provide useful insights into the interactions of vortex beams with matter and their further applications.

中文翻译：

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Laguerre-Gaussian涡旋光束反射和折射的动力学特性

具有涡旋结构的Laguerre-Gaussian光束是一种特殊类型的电磁波，可以携带能量，动量和角动量，这对于理解有关光-物质相互作用现象的动力学过程至关重要。在本文中，我们从理论上研究了Laguerre-Gaussian涡旋光束在反射和折射时的局部动力学特性。使用基于Lorenz规范中角谱表示和矢量势的混合方法，以Hermite多项式的形式导出反射和折射Laguerre-Gaussian光束的电场和磁场分量的明确解析表达式。规范方法用于检查能量，动量，以及Laguerre-Gaussian涡旋光束在空气和BK7玻璃之间的平面界面处的反射和折射的自旋和轨道角动量。模拟并详细讨论了入射角，拓扑电荷和极化状态对这些动力学量的影响。这项研究可以为涡流束与物质的相互作用及其进一步应用提供有用的见解。