Propagation of a vortex elliptical Airy beam

Because elliptical beams have many special properties and applications, an elliptical Airy beam with and without a vortex phase has been proposed. Based on the definition of the elliptical Airy beam, an experimental setup for the generation is given, and the formula for the evolution of the intensity is derived. Meanwhile, from the propagation of the Airy beam in vacuum, the abruptly autofocusing length is derived. Based on the formula of the abruptly autofocusing length, the intensity distributions at some special locations are analyzed and discussed, especially in the autofocusing point. Study shows that some interesting intensity profiles are reformed due to the asymmetry intensity distribution of the elliptical Airy beam and abrupt autofocusing of the circular Airy beam during propagation. The different eccentricity of the elliptical Airy beam has similar properties, such as the beam split with the propagation distance and the reformed beam shaped like a ”light knife” (very narrow beam) at some positions due to the convergence process out of synchronization along the x- and y-axis. When we impart a vortex on the elliptical Airy beam, the intensity distribution will rotate and split with the propagation distance.