It has been known for some time that Bessel–Gaussian beams and their associated families self-heal after encountering obstacles. Recently, it has been shown theoretically and experimentally that radial mode Laguerre–Gaussian (LG) beams would likewise self-heal. In this work, we show that the self-healing occurs after opaque disks but not after circular apertures. We put forward arguments to explain this and perform key experiments, assessing the impact of obstructions on the usual intensity reconstruction, as well as the focal shift effect and the beam propagation factor, $$M^2$$ . In addition, these results are supported by a physical interpretation based on the Abbe experiment of spatial frequency filtering, highlighting that the self-healing process requires a high-spatial frequency component to the field, i.e., LG beams self-heal when modulated by a low spatial frequency filter (opaque disk) but not when modulated by a high-spatial frequency filter (circular aperture). We believe that this work will contribute significantly to the field of laser beam propagation through obstacles.

中文翻译：

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Laguerre-Gaussian 光束在所有障碍之后是否会恢复其空间特性？

一段时间以来，人们都知道贝塞尔-高斯光束及其相关的光束在遇到障碍后会自我修复。最近，理论和实验表明径向模式拉盖尔-高斯 (LG) 光束同样会自我修复。在这项工作中，我们表明自愈发生在不透明磁盘之后，而不是在圆形孔径之后。我们提出了解释这一点的论据并进行了关键实验，评估了障碍物对通常强度重建的影响，以及焦移效应和光束传播因子 $$M^2$$ 。此外，这些结果得到了基于空间频率滤波阿贝实验的物理解释的支持，强调自愈过程需要对场的高空间频率分量，即，LG 光束在由低空间频率滤波器（不透明盘）调制时会自我修复，但在由高空间频率滤波器（圆形孔径）调制时则不会。我们相信这项工作将对激光束通过障碍物传播领域做出重大贡献。