Characterizing the orbital-angular-momentum (OAM) modes is critically important for OAM-encoded data transfer. However, traditional characterizing approaches rely on either complex and precise experimental configurations or complicated prior information processing. In these scenarios, the correlation features of OAM-dependent speckles from the scattering effect have received little attention. Here, we investigate the cross-correlation characteristics of the OAM speckles resulting from a scattering medium and propose an appealing alternative for spatial mode sorting and demultiplexing based on the OAM-dependent speckles. We demonstrate theoretically and experimentally that the cross-correlation operation between two different OAM-dependent speckles can uniformly derive an annulus pattern, whose dimension is determined by the absolute topological charge difference value between the two corresponding OAM modes. Based on this mechanism, the original coherent OAM modes can be easily sorted by implementing the cross-correlation operation between incoherently measured OAM-dependent speckles. To fully capitalize on the orthogonal feature of the OAM-dependent speckles, we also construct OAM mode demultiplexing experiments using a ground glass diffuser, where both 8-bit grayscale and 24-bit RGB OAM-encoded data demultiplexing are successfully demonstrated with superior error rates. Results show that the OAM-dependent speckles, previously treated as a nuisance for practical applications, can be surprisingly utilized as a competitive candidate for OAM mode sorting and demultiplexing, thus opening new directions in optical communication and information processing.

中文翻译：

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用于空间模式排序和解复用的轨道角动量相关散斑

表征轨道角动量 (OAM) 模式对于 OAM 编码数据传输至关重要。然而，传统的表征方法依赖于复杂而精确的实验配置或复杂的先验信息处理。在这些场景中，散射效应引起的 OAM 相关散斑的相关特征很少受到关注。在这里，我们研究了散射介质产生的 OAM 散斑的互相关特性，并提出了一种基于 OAM 相关散斑的空间模式排序和解复用的有吸引力的替代方案。我们从理论上和实验上证明，两个不同的 OAM 相关散斑之间的互相关运算可以一致地导出环形图案，其尺寸由两个相应的 OAM 模式之间的绝对拓扑电荷差值决定。基于该机制，通过在非相干测量的OAM相关散斑之间进行互相关操作，可以轻松地对原始相干OAM模式进行排序。为了充分利用 OAM 相关散斑的正交特征，我们还使用毛玻璃扩散器构建了 OAM 模式解复用实验，其中 8 位灰度和 24 位 RGB OAM 编码数据解复用均已成功证明具有出色的错误率。结果表明，以前被视为实际应用中的麻烦的依赖于 OAM 的散斑，令人惊讶地可以用作 OAM 模式分类和解复用的竞争候选者，从而为光通信和信息处理开辟新的方向。