Elegant Hermite–Airy beams

As () (� ) A ix Ai x can be approximated by (� ) x ex p/ 2 2 , a kind of elegant Hermite-Airy (EHA) beam that is similar to the elegant Hermite-Gaussian (EHG) beam is introduced in this paper. Analytical expression of the EHA beams passing through an ABCD paraxial optical system is derived. By using the method of numerical fitting, the approximate expressions of j 0 2 , j 0 4 , j 2 , j 4 , and j j 0 22 for an EHA beam are presented, respectively. When the transverse mode number is larger than 2, j 0 2 , j 0 4 , j 2 , j 4 , and j j 0 22 of an EHA beam are all larger than those of the EHG beam. Based on the higher-order intensity moments, one can calculate the beam propagation factor, the beam half width, and the kurtosis parameter of the EHA beam passing through an ABCD paraxial optical system. As a numerical example, the propagation characteristics of the EHA beam are demonstrated in free space. Moreover, the propagation properties of the EHA beam are compared with those of the corresponding EHG beam. The evolutionary process of the EHA beam is far slower than that of the corresponding EHG beam. The research denotes that the EHA beams can be used to describe specially distributed optical beams that can not be characterized by the existing EHG beam model. The EHA beam model enriches and replenishes the existing beam model.