  Characterizing the orbital angular momentum (OAM) of a vortex beam is
critically important for OAM-encoded data transfer. However, in typical
OAM-based applications where vortex beams transmit through diffusers, the
accompanying scattering effect tends to be either deliberately prevented, or
characterized and then modulated actively based on complex wavefront shaping
and interferometry techniques. Here, we aim to investigate the characteristics
of blurred speckles obtained after a vortex beam transmits through a ground
glass diffuser. It is theoretically and experimentally demonstrated that a
cross-correlation annulus can be identified by implementing the
cross-correlation operation between speckle patterns corresponding to vortex
beams with different OAM values. Besides, it is worth noting that, the size of
the cross-correlation annulus is determined by the absolute value of the
topological charge difference between the two corresponding vortex beams. Based
on this mechanism, the OAM modes can be easily sorted from the incoherently
measured OAM-dependent speckles as well as their cross-correlation.
Furthermore, to make full use of the orthogonal feature of the OAM-dependent
speckles, demultiplexing of OAM-encoded data transfer is verified using a
ground glass diffuser. Both 8-bit grayscale and 24-bit RGB OAM-encoded data
transfers are carried out in experiments with superior error rates. We can
conclude that the OAM-dependent speckles can be not only utilized as a
competitive candidate for the OAM mode sorting function in a simple way but
also provide an efficient method for the demultiplexing of OAM-encoded data
transfer in a practical application.
