Fig. 1. Schematic diagram of 1D self-accelerating Airy beams

Fig. 2. Projection diagram of self-accelerating trajectory of 2D Airy beams

Fig. 3. Schematic diagram of self-healing principle. (a) Main light spot that is not blocked; (b) main light spot is blocked by a baffle, dotted line depicts vanishing trajectory

Fig. 4. Schematic diagram of the experimental device

Fig. 5. Phase distribution of phase mask. (a) One dimension; (b) two dimension

Fig. 6. Results of simulation and experiment. (a) Phase mask;(b) simulated side view of Airy beams; (c)-(f) transverse intensity distribution of the simulated beams, the z coordinates are 25, 35, 45, 55 cm, respectively; (g) experimental results corresponding to (b)-(f)

Fig. 7. Results of self-healing experiment. (a) Light spot that is not blocked; (b) intensity distribution behind block; (c)-(f) intensity distribution at plane with relative distance d=10, 20, 30, 40 mm, respectively

Fig. 8. Abruptly autofocusing beam. (a) Phase mask; (b)-(g) transverse intensity distribution at different location, the propagation distances are d=15, 16, 17, 18, 19, 20 cm, respectively

Fig. 9. Bessel-like beam. (a) Phase mask; (b)-(d) transverse intensity distribution at different location, the propagation distances are d=8, 9, 10 cm, respectively