Orbital-angular-momentum-dependent speckles for spatial mode sorting and demultiplexing

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.