We developed a new alterative technique of the digital sorting of Laguerre–Gaussian beams (LG) by radial numbers resorting to algebra of the high-order intensity moments. The term “digital mode sorting” involves sorting the main mode characteristics (in the form of a mode spectrum) by the computer cells. If necessary, the spatial mode spectrum can be reproduced, for example, by means of a spatial light modulator. In the experiment, we investigated both a single LG mode and a composition of LG modes with the same topological charge but different radial numbers subjected to perturbations via a hard-edged circular aperture. The LG beams sorting was accomplished by monitoring the amplitude spectrum of the triggered secondary LG modes then recovering the sorted modes and the perturbed beam as a whole. We have revealed degenerate states of the perturbed LG beam composition when the one $k$th mode in the amplitude spectrum can be related to a set of LG modes with the same radial numbers. In order to decrypt and to sort beams in such a degenerate state, it is necessary to know several keys, the number of which is equal to the number of LG modes in the initial wave composition. We were also able to analyze and to sort such degenerate mode states. For monitoring the measure of uncertainty arising in the perturbed beam, we measured informational entropy (Shannon entropy).

中文翻译：

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数字分选通过径向数扰乱了拉盖尔-高斯光束。

我们利用高阶强度矩的代数，通过径向数开发了一种新的替代技术，用于对拉盖尔－高斯光束（LG）进行数字排序。术语“数字模式分类”涉及通过计算机单元对主要模式特征（以模式频谱的形式）进行分类。如果需要，可以例如借助空间光调制器来复制空间模式光谱。在实验中，我们研究了单个LG模式和具有相同拓扑电荷但径向数不同的LG模式的组成，这些模式通过硬边圆孔受到扰动。通过监视触发的次级LG模式的振幅谱，然后恢复分类模式和整个扰动光束，可以完成LG光束的分选。振幅谱中的第k个模式可以与一组具有相同径向数的LG模式相关。为了在这种退化状态下对光束进行解密和分类，必须知道几个密钥，其数目等于初始波组成中的LG模式的数目。我们还能够分析和分类这种退化模式状态。为了监视在扰动束中出现的不确定性的度量，我们测量了信息熵（Shannon熵）。