光涡旋星群的集体传播规律与纵向传感
A Collective Propagation Law of Optical Vortex Constellations and Longitudinal Sensing
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中文总结 AI 辅助
本研究揭示并实验验证了标准高斯背景中任意光涡旋星群的近轴纵向传播确定性规律，利用初等对称多项式（ESPs）捕捉其整体演化，为纵向传感提供了新计量工具。
中文摘要 AI 辅助
光涡旋是波动物理中普遍存在的现象，然而高阶拓扑荷在偏离理想状态极小时会分裂为最低阶奇点构成的星群。尽管这些星群在现实场景中十分常见，表征其纵向演化通常依赖详尽的全场描述或对单个奇点的模糊顺序追踪。本文揭示并实验验证了描述标准高斯背景中任意光涡旋星群近轴纵向传播的简单确定性规律，通过将构成奇点的坐标映射到初等对称多项式（ESPs），完整捕捉了星群在传播过程中的整体演化，完全规避了顺序追踪不可区分涡旋的实际需求。我们进一步表明，此类复杂的ESPs为估计纵向位移提供了有用的计量工具。研究结果揭示了此前未被认知的集体涡旋动力学的紧凑描述，为通过奇异测量实现纵向传感开辟了新途径。
英文摘要
Optical vortices are ubiquitous phenomena naturally appearing in wave physics, yet higher-order charges inherently split into constellations of lowest-order singularities at the smallest deviation from an ideal situation. While these constellations are common phenomena in real-world scenarios, characterizing their longitudinal evolution typically relies on exhaustive full-field descriptions or the ambiguous, sequential tracking of individual singularities. Here, we reveal and experimentally demonstrate a simple deterministic law describing the paraxial longitudinal propagation of an arbitrary constellation of optical vortices in standard Gaussian backgrounds. By mapping the constituting singularity coordinates to their elementary symmetric polynomials (ESPs), we capture the holistic evolution of the constellation during propagation, completely bypassing the practical need to sequentially track indistinguishable vortices. We further show that such complex ESPs provide a useful metrological tool for the estimation of longitudinal displacements. Our results reveal a previously unrecognized compact description of collective vortex dynamics, introducing a new route to longitudinal sensing through singularimetry.
