Optical Skyrmions have many important properties that make them ideal units for high-density data applications, including the ability to carry digital information through a discrete topological number and the independence of spatially varying polarization to other dimensions. More importantly, the topological nature of the optical Skyrmion heuristically suggests a strong degree of robustness to perturbations, which is crucial for reliably carrying information in noisy environments. However, the study of the topological robustness of optical Skyrmions is still in its infancy. Here, we quantify this robustness precisely by proving that the topological nature of the Skyrmion arises from its structure on the boundary and, by duality, is resilient to spatially varying perturbations provided they respect the relevant boundary conditions of the unperturbed Skyrmion. We then present experimental evidence validating this robustness in the context of paraxial Skyrmion beams against complex polarization aberrations. Our work provides a framework for handling various perturbations of Skyrmion fields and offers guarantees of robustness in a general sense. This, in turn, has implications for applications of the Skyrmion where their topological nature is exploited explicitly, and, in particular, provides an underpinning for the use of optical Skyrmions in communications and computing.

光学斯格明子具有许多重要特性，使其成为高密度数据应用的理想单元，包括通过离散拓扑数传输数字信息的能力以及独立于其他维度的空间变化偏振。更重要的是，光学 Skyrmion 的拓扑性质启发式地表明了对扰动的强烈鲁棒性，这对于在嘈杂环境中可靠地传输信息至关重要。然而，对光学斯格明子拓扑鲁棒性的研究仍处于起步阶段。在这里，我们通过证明斯格明子的拓扑性质源于其在边界上的结构，并且通过对偶性，只要它们尊重未受扰动的斯格明子的相关边界条件，就可以对空间变化的扰动产生弹性。然后，我们提供了实验证据，在近轴 Skyrmion 光束对抗复杂偏振像差的背景下验证了这种鲁棒性。我们的工作为处理 Skyrmion 场的各种扰动提供了一个框架，并提供了一般意义上的鲁棒性保证。反过来，这对 Skyrmion 的应用产生了影响，在这些应用中，它们的拓扑特性被明确利用，特别是为光学 Skyrmion 在通信和计算中的使用提供了基础。