Propagation dynamics, Poynting vector and accelerating vortices of a focused Airy vortex beam

• The effects of optical vortex on the main lobe and Poynting vector are stressed.
• The singular behavior of the focused AiVB at focal plane is described.
• Paths of Airy beam and the vortices are different from parabolic trajectories.
• The main lobe rotating about the closest vortex is presented.

Analytical propagation expression of a focused Airy vortex beam (AiVB) is derived, and used to investigate propagation dynamics, Poynting vector and accelerating vortices of a focused AiVB. It is shown that the focused AiVB represents singular behavior at the focal plane, and the ballistic dynamics of the Airy beam is no longer parabolic but polynomial trajectory because its acceleration is a variant value relating to propagation distance. At critical distance the main lobe of Airy beam is overlapped by vortex core, and then it presents rotating about the closest vortex and the Airy-like pattern is self-reconstructed as the propagation distance further increase, which is due to the self-healing property of the Airy beam, on the other hand it is result of the rotation of vortex. The accelerating vortex deflections of the focused AiVB and an individual component are also illustrated by numerical examples. The results show that the vortices exhibit transverse deflection and their accelerating vortex behaviors also follow polynomial rather than parabolic trajectories.