Uniform approximation of paraxial flat-topped beams

TL;DR

This paper develops a uniform asymptotic theory for the propagation of flat-topped Gaussian beams in free space, emphasizing the significance of the error function in describing the wavefield under large Fresnel number conditions.

Contribution

It introduces a novel asymptotic approach to model paraxial flat-topped beams, highlighting the role of the error function in the wavefield description.

Findings

Effective approximation of flat-topped beams in the large Fresnel number regime.

Mathematical description involving the error function provides accurate wavefield modeling.

Abstract

A uniform asymptotic theory of the free-space paraxial propagation of coherent flattened Gaussian beams is proposed in the limit of nonsmall Fresnel numbers. The pivotal role played by the error function in the mathematical description of the related wavefield is stressed.