In this paper we revisit the nondiffracting properties of the cosine beam (CB). Since the CB is of infinite extension and not physically realizable, we use two apodization pupils to manage its transverse extent: the first one is a Gaussian apodized pupil, giving rise to the cosine-Gauss (CG) beam, and the second one is a window (aperture) apodized pupil, giving rise to the cosine-windowed beam. Based on the second-order intensity moments, we demonstrate analytical expressions for the CG beam width and its nondiffracting range as a function of some key parameters. By considering the CG beam a standing wave resulting from the superposition of two oppositely oblique traveling Gaussian beams, we extend the study to higher-order CG beams. The latter is generated by the superposition of two oppositely oblique Hermite–Gauss (${\textit{HG}_n}$) beams of order $n$, giving birth to a standing nondiffracting Hermite–cosine–Gauss ($\textit{HCG}_n$) beam of order $n$. We also demonstrate the expressions of the higher-order CG beam width and its nondiffracting range ${z_{\max}}$. After demonstrating the nondiffracting nature of the HCG beam family, we test their ability to self-heal and recover against obstacles, and we show the limit distance from which $\textit{HCG}_n$ beams self-heal as a function of obstruction size and CG parameter. The results of this paper are of big interest in fields involving structured light such as particle manipulation, imaging, and light sheet microscopy.

中文翻译：

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余弦光束：无衍射传播和自我修复

在本文中，我们将回顾余弦光束（CB）的非衍射特性。由于CB具有无限的扩展性，而且无法物理实现，因此我们使用两个变迹瞳孔来控制其横向范围：第一个是高斯变迹瞳孔，产生了余弦-高斯（CG）光束，第二个是窗口（孔径）变迹的瞳孔，产生余弦窗光束。基于二阶强度矩，我们证明了CG光束宽度及其非衍射范围作为一些关键参数的函数的解析表达式。通过将CG光束视为由两个相反斜向行进的高斯光束叠加而产生的驻波，我们将研究扩展到了高阶CG光束。后者是由两个相对倾斜的Hermite–Gauss（$ {\ {textit HG} _n} $）梁秩序的$ n $的，生下一个常设无衍射厄米余弦高斯（$ \ {textit HCG} _n $）级光束$ N $。我们还演示了高阶CG光束宽度及其非衍射范围$ {z _ {\ max}} $的表达式。在说明了HCG光束家族的非衍射性质之后，我们测试了它们自我修复并克服障碍的能力，并且我们展示了$ \ textit {HCG} _n $光束根据障碍物大小进行自我修复的极限距离和CG参数。本文的结果在涉及结构化光的领域中引起了极大的兴趣，例如粒子处理，成像和光片显微镜。