The change of optical vortex on the paraxiality of fully coherent and partially coherent Airy beams

The analytical expressions for the degree of paraxiality for fully coherent and partially coherent Airy vortex beams are obtained, respectively, and used to investigate the change of optical vortex on the degree of paraxiality. The results show that the paraxiality decreases when the optical vortex is nested in the Airy beam, while the noncanonical strength of optical vortex contributes nothing to the change of the paraxiality. A larger truncation factor leads to a higher paraxiality, and the effect of topological charge on the paraxiality gradually emerges with the increasing of the truncation factor. For a partially coherent Airy vortex beam, the paraxiality increases with an increase of transverse scale or truncation factor. While it is also shown that there exists critical value of w0c or ac, where a lower coherence length has an advantage in acquiring a higher paraxiality for w0 < w0c or a < ac. Whereas for w0 > w0c and a > ac, a higher coherence length contributes the partially coherent Airy vortex beam to be more paraxial. In addition, the changes between the paraxiality of the partially coherent Airy beams and partially coherent Airy vortex beams become small as the increasing of transverse scale or truncation factor.