Fig. 1. Structure of phase control in optical phased array. (a) Overall structure; (b) monitoring part

Fig. 2. Flow chart of multi-stage SPGD algorithm

Fig. 3. Grouping example of a two-dimensional 16 beams arrangement using 3-stage SPGD

Fig. 4. Convergence curves of conventional SPGD algorithm and 2-stage SPGD algorithm under conditions of 64/100 beams

Fig. 5. Number of iterations of conventional SPGD algorithm and multi-stage SPGD algorithm under different numbers of beams

Fig. 6. Curve of iteration ratio of conventional SPGD algorithm to multi-stage SPGD algorithm under different numbers of beams

Fig. 7. Number of iterations of multi-stage SPGD with different stage numbers for 64-beam case

Fig. 8. Optimal number of stages for different numbers of beams

Fig. 9. Experimental setup of optical phased array system based on 2-stage SPGD algorithm

Fig. 10. Monitoring signals of two stages. (a)-(d) Light signal of the 1st stage; (e) light signal of the 2nd stage

Fig. 11. Cross section diagrams of beam arrays. (a) 8 beams (4×2 array); (b) 12 beams (3×4 array); (c) 32 beams (8×4 array)

Fig. 12. Number of iterations for different numbers of beams in experiments