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Characterizing the orbital angular momentum (OAM) of a vortex beam iscritically important for OAM-encoded data transfer. However, in typicalOAM-based applications where vortex beams transmit through diffusers, theaccompanying scattering effect tends to be either deliberately prevented, orcharacterized and then modulated actively based on complex wavefront shapingand interferometry techniques. Here, we aim to investigate the characteristicsof blurred speckles obtained after a vortex beam transmits through a groundglass diffuser. It is theoretically and experimentally demonstrated that across-correlation annulus can be identified by implementing thecross-correlation operation between speckle patterns corresponding to vortexbeams with different OAM values. Besides, it is worth noting that, the size ofthe cross-correlation annulus is determined by the absolute value of thetopological charge difference between the two corresponding vortex beams. Basedon this mechanism, the OAM modes can be easily sorted from the incoherentlymeasured OAM-dependent speckles as well as their cross-correlation.Furthermore, to make full use of the orthogonal feature of the OAM-dependentspeckles, demultiplexing of OAM-encoded data transfer is verified using aground glass diffuser. Both 8-bit grayscale and 24-bit RGB OAM-encoded datatransfers are carried out in experiments with superior error rates. We canconclude that the OAM-dependent speckles can be not only utilized as acompetitive candidate for the OAM mode sorting function in a simple way butalso provide an efficient method for the demultiplexing of OAM-encoded datatransfer in a practical application.

Orbital-angular-momentum dependent speckles for spatial mode sorting and multiplexed data transmission