Propagation trajectory measurement and autofocusing generation of Airy beams using digital propagation

We present a method of measuring the propagation trajectory of Airy beams using digital propagation based on the theory of angular spectrum. The dependence of the transverse displacement of Airy beams on artificial propagation distance in phase masks is investigated with no motion of imaging apparatus. The parabolic propagation trajectory is experimentally verified, which is consistent with theoretical predictions. On this basis, we generate autofocusing beams by combining multiple Airy beams and digital propagation. Results show that this technique can provide accurate and easy measurement of the self-accelerating characteristic in a fixed plane, as well as flexible manipulation without translating the target.