Propagation characteristics of circular Airyprime Gaussian beam in gradient refractive index medium

In this paper, the focusing characteristics of a circular Airyprime Gaussian beam (CAPGB) propagating in a gradient refractive index (GRIN) medium is studied for the first time, to the best of our knowledge, and some interesting features are observed. We find that the CAPGB exhibits periodic focus–defocus behavior and completes a period propagation process with two focal points within a half variation period L /2 of the GRIN medium. Meanwhile, the CAPGB has singularity at the positions of z =(2 j +1) L /4 on the optical axis. The focal lengths of bifocal points, the distance between two focal points, the focal intensity, and the focusing ability can be manipulated by beam parameters and the GRIN factor. It is noteworthy that the number (one or two) of focal points in one focusing period, and the focusing period or frequency of the CAPGB in the GRIN medium could be controlled by the beam distribution factor and GRIN factor, respectively. Moreover, the focusing ability of the CAPGB is much higher than that of a circular Airy Gaussian beam in the GRIN medium.