In article number 2000049 by Weijin Chen, Yuntian Chen, and Wei Liu, topological morphologies of electromagnetic multipoles of general complex vectorial forms are explored, and are portrayed through line fields with singularities of half‐integer Hopf indices. With this topological insight, the hidden dimension of radiative circularly polarized Bloch modes is further unveiled, revealing their line singularity origins and establishing equivalences between their topological charges and multipolar Hopf indices.

中文翻译：

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电磁多极：电磁多极的线奇异性和Hopf指数（激光光子，修订版14（7）/ 2020）

在陈维金，陈云天和刘维的文章2000049中，研究了一般复矢量形式的电磁多极的拓扑形态，并通过具有半整数Hopf指数奇异性的线形场进行描绘。有了这种拓扑学见解，辐射圆极化布洛赫模的隐性维度将进一步揭示，揭示它们的线奇点，并建立它们的拓扑电荷与多极霍夫指数之间的等价关系。