Splitting and accelerating Gaussian beam modulated by Mittag Leffler function

We propose and demonstrate the generation of a Mittag–Leffler Gaussian beam (MLG) throughout the modulation of a Gaussian beam with Mittag–Leffler (ML) complex function. This beam presents splitting and accelerating properties. The key element of our method is the use of a ML function of complex variable. The amplitude distribution of this Mittag–Leffler–Gaussian beam is symmetric and has multiple components with petal shape. Each of these petals has an elliptical Gaussian amplitude distribution and a curved trajectory.