Fig. 1. Concept of high-dimensional multi-ring optical vortices coding/decoding.

Fig. 2. Experimental setup. DFB, distributed feedback laser; SMF, single mode fiber; Col., collimator; PBS, polarized beam splitter; SLM1 and SLM2, liquid-crystal spatial light modulator; L1–L3, lenses; AS, aperture stop; CCD, infrared CCD camera. (a) The coding hologram sequence uploaded on SLM1. (b) The coded multi-ring optical vortices sequence. (c) The decoding hologram. (d) The decoded patterns.

Fig. 3. Experimentally obtained 6 bits high-dimensional multi-ring coding for 64-ary numbers through 16 various OAM states and four various radial indices.

Fig. 4. (a) Dammann vortex grating employed in the experiment to produce 4×4 vortices array in the far field. (b) The captured decoding patterns for some of the symbols (7, 12, 19, 23, 39, 40, 55). The OAM states and radial indices are determined by the locations of the center bright spot and the number of concentric circles, respectively.

Fig. 5. Measured SER and BER versus Fried parameter r0 for the proposed multi-ring vortices-based 6 bits coding/decoding system.

Fig. 6. Experimental results of transmitting a 64×64 gray badge of Beijing Institute of Technology through 6 bits multi-ring vortices coding/decoding with or without atmosphere turbulence. (a) The transmitted image. (b) The recovered image without turbulence. (c) The recovered image with turbulence r0=3mm. (d) The recovered image with turbulence r0=1mm.