Propagation characteristics of complex variables Airy-Gaussian wave packets within free space

Abstract

The Airy-Gaussian wave packets are the Airy wave packets modulated by the Gaussian wave packets. Basing on the separating variable method, the analytical solution has been accessed according to solving the paraxial beam equation in cylindric coordinates in free space. The Airy-Gaussian wave packets with complex variables are combing the Airy function with the complex variables and the Gaussian beams. The propagation characteristics of the complex variables Airy-Gaussian wave packets are studied. The complex variables Airy-Gaussian wave packets will rotate with the increase of propagating distance. Poynting vector reveals the essence of this phenomenon.