Propagation of an Airy-Gaussian beam passing through a lens with low effective Fresnel number

Abstract

We derive an analytical propagation expression for the Airy-Gaussian beam propagating through a thin lens, and calculate numerical examples to investigate its focusing properties. It is shown that the pattern formed in the focus plane can be controlled to demonstrate various geometries through tuning the beam parameters associated with the Airy function part. Moreover, we investigate the influence of the Fresnel number on the propagation properties, and find that decreasing values of the Fresnel number not only increase the size of the focusing spot, but also enhance the depth of field effectively. Our results provide a route for generating perfect squared or elliptic spot with extended depth of field through carefully adjusting the beam and optical system parameters, which may find some potential applications in various areas involving in the special beam profile.

Keywords

• Airy-Gaussian beam
• Focusing properties
• Fresnel number
• Light-sheet beam