Design of autofocusing beams based on accelerating beams

Autofocusing Airy-like beams have been designed based on the self-accelerating beams along arbitrary polynomial paths. The evolutions of the autofocusing beam in free space and turbulent atmosphere have been studied. Results show that the energy concentration of the autofocusing beam near the focal plane has a close relationship with its accelerating trajectory. The spot size of the autofocusing beam in the focal plane varies with the acceleration trajectory. The influence of turbulence on different autofocusing beams is different and has a relation with the degree of the curvature of the accelerating beam. The autofocusing beam propagating along a small curvature path has better resistance against turbulence.