Propagation properties and M2 factors of a vortex Airy beam

We investigate the propagation properties and M-2 factor of a vortex Airy beam. The expression of M-2 factor as a function of the modulation parameters a(x) and a(y) is analytically obtained. The results indicate that the M-2 factor can achieve minimum M-2=2.33 when a(x)=a(y)=1.026 for the m= 1st order vortex Airy beam. For m=2, the M-2 factor can achieve minimum M-2=7.53 when a(x)=1.601 and a(y)=0.529 (or a(y)=1.601 and a(x)=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 a(x) and a(y), 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. (c) 2012 Elsevier Ltd. All rights reserved.