Fig. 1. Schematic of OAM mode logical operation based on ODNN.

Fig. 2. Training data set of OAM logic AND gate.

Fig. 3. Training results of ODNN with logic AND operation. (a) Curve of the loss function with the iteration number. (b) Phase and amplitude distributions of diffractive layers.

Fig. 4. Modulation results of ODNN with different logical operations. (a) Logic AND gate. (b) Logic OR gate.

Fig. 5. OAM logic NOT gate based on ODNN. (a) Schematic of the light field modulation by ODNN. (b) Predicted results of ODNNs with different layers.

Fig. 6. (a) Operation truth table and (b) prediction outputs by ODNNs for OAM logic NAND and NOR gates.

Fig. 7. Logic XNOR gate cascaded by the basic logic AND, OR, and NOT units. (a) System diagram of XNOR operation based on cascaded logical gates. (b) Truth table. (c) Predicted results of logic XNOR operation with four input states of “00,” “01,” “10,” and “11.”

Fig. 8. Schematic illustration of logic XOR operation. (a) System diagram of XOR gate cascaded by logic AND, OR, and NOT gates. (b) Truth table. (c) Phase and intensity distribution of results predicted by the logic XOR gate.

Fig. 9. Schematic illustration of the half-adder based on the OAM mode. C: Carry. S: sum. (a) System diagram of the half-adder cascaded by the XOR and AND gates. (b) Truth table. (c) Results of the addition operation performed by the half-adder.

Fig. 10. Test results of four input states with different phase rotation angles.

Fig. 11. Balanced ternary logic AND operation with OAM modes. (a) Truth table. (b) Results predicted by the 5-layer ODNN.