旋转对称等离子体涡旋透镜中对称相容的angular momentum守恒关系
Symmetry-compatible angular momentum conservation relation in plasmonic vortex lenses with rotational symmetries
摘要：
等离子体涡旋透镜（PVL）在等离子体自旋轨道耦合过程中产生涡旋模式，称为等离子体涡旋（PVs），为实现许多基于光学涡旋的应用提供了一个有前途的平台。最近，据报道，单个PVL可以生成多个PV。本文利用有限群的表示理论，揭示了生成的PV的对称性起源，并基于对称性原理导出了一个新的守恒关系。具体地，对称性原理将PVL的近场划分为区域，将整数（其为拓扑电荷）指定给区域，并且特别地，给出PVL中心处的PV的拓扑电荷的上限。将对称性原理进一步应用于自旋-轨道耦合过程，得到了一个新的守恒关系。基于这种关系，一个两步的过程中，建议通过PVL的对称性链接的入射场的角动量与所产生的PV之一。这一理论得到了数值计算的证实。这项工作提供了一个替代的，但必不可少的对称性的角度来看，在PVL的自旋轨道耦合的动力学，形成了一个强有力的补充之前进行的物理研究，因此奠定了坚实的基础，灵活地操纵PVs新兴的基于涡旋的纳米光子应用。
英文摘要：
Plasmonic vortex lenses (PVLs), producing vortex modes, known as plasmonic vortices (PVs), in the process of plasmonic spin-orbit coupling, provide a promising platform for the realization of many optical vortex-based applications. Very recently, it has been reported that a single PVL can generate multiple PVs. This work exploits the representation theory of finite groups, reveals the symmetry origin of the generated PVs, and derives a new conservation relation based on symmetry principles. Specifically, the symmetry principles divide the near field of the PVL into regions, designate integers, which are the topological charges, to the regions, and, particularly, give an upper bound to the topological charge of the PV at the center of the PVL. Further application of the symmetry principles to the spin-orbit coupling process leads to a new conservation relation. Based on this relation, a two-step procedure is suggested to link the angular momentum of the incident field with the one of the generated PVs through the symmetries of the PVL. This theory is well demonstrated by numerical calculations. This work provides an alternative but essential symmetry perspective on the dynamics of spin-orbit coupling in PVLs, forms a strong complement for the physical investigations performed before, and therefore lays down a solid foundation for flexibly manipulating the PVs for emerging vortex-based nanophotonic applications.
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