Propagation properties and M2 factors of a vortex Airy beam

We investigate the propagation properties and M2 factor of a vortex Airy beam. The expression of M2 factor as a function of the modulation parameters ax and ay is analytically obtained. The results indicate that the M2 factor can achieve minimum M2=2.33 when ax=ay=1.026 for the m=1st order vortex Airy beam. For m=2, the M2 factor can achieve minimum M2=7.53 when ax=1.601 and ay=0.529 (or ay=1.601 and ax=0.529). These results indicate that the far field divergence of the beam width in the sense of root-mean-square beam is related to modulation parameters ax and ay, and increases with increasing vortex order. Numerical calculations provide an intuitive physical picture for the effect of the modulation parameters on the propagation of the vortex Airy beam.

► Analytical expressions for the M2 factors of a vortex Airy beam are derived.
► Numerical calculations provide an intuitive physical picture to confirm the analytical results.
► Numerical calculations indicate that the beams rotate with large ax and ay.
► Physical sense is investigated when M2 factors achieve the minimum.