The law of angular momentum conservation is naturally linked to the rotational symmetry of the involved system. Here we demonstrate theoretically how to break the rotational symmetry of a uniaxial crystal via the electro-optic Pockels effect. By numerical method based on asymptotic expansion, we discover the 3D structure of polarization singularities in terms of C lines and L surfaces embedded in the emerging light. We visualize the controllable dynamics evolution of polarization singularities when undergoing the Pockels effect, which behaves just like the binary fission of a prokaryotic cell, i.e., the splitting of C points and fission of L lines are animated in analogy with the cleavage of nucleus and division of cytoplasm. We reveal the connection of polarization singularity dynamics with the accompanying generation of orbital angular momentum sidebands. It is unexpected that although the total angular momentum of light is not conserved, the total topological index of C points is conserved.

中文翻译：

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偏振奇点和轨道角动量边带来自被普克尔斯效应破坏的旋转对称性。

角动量守恒定律与相关系统的旋转对称性自然相关。在这里，我们从理论上演示了如何通过电光普克尔斯效应打破单轴晶体的旋转对称性。通过基于渐近展开的数值方法，我们发现了以嵌入出射光中的 C 线和 L 面表示的偏振奇点的 3D 结构。我们将经历普克尔斯效应时极化奇点的可控动力学演化可视化，其行为就像原核细胞的二元裂变，即 C 点的分裂和 L 线的裂变类似于细胞核的分裂和分裂。的细胞质。我们揭示了极化奇点动力学与轨道角动量边带的伴随产生之间的联系。出乎意料的是，虽然光的总角动量不守恒，但C点的总拓扑指数是守恒的。