Approximate analytical description of the structured laser beam in the far zone

In the last few years, new ways of structuring light have emerged, with the potential to be used in a wide variety of applications, including materials processing, micro-particle manipulation and charged particle acceleration. One of these techniques is the structured laser beam (SLB). The important advantages of this beam are the simple generation principle using spherical aberration and the potentially infinite propagation range. This makes the SLB a good candidate for use in alignment over long distances or in free space optical communication. However, understanding the distribution of the optical field in such a beam is not trivial and a full analytical description of the SLB is still missing. This paper proposes an approximate analytical scalar description of the SLB complex amplitude, which characterizes the optical field in the far zone with sufficient accuracy for applications such as alignment or optical communication. The proposed approach has been successfully validated through simulations and experimental measurements.