Droplet beam generated with the round-tip axicon: Exact solutions for different axicon shapes

TL;DR

This paper provides exact theoretical solutions for droplet quasi-Bessel beams generated by round-tip axicons, revealing how the droplet pattern period varies with axial distance and axicon shape deviations, enabling axicon surface reconstruction.

Contribution

It derives exact Fresnel diffraction integral solutions for different axicon shapes, advancing understanding of droplet beam formation and shape-dependent effects.

Findings

Droplet pattern period varies with axial distance and axicon shape deviations.

Exact solutions enable reconstruction of axicon surface shape.

The analysis improves control over droplet beam generation.

Abstract

We theoretically investigate droplet quasi-Bessel beams for different shapes of the round-tip axicon. Exact solutions for the Fresnel diffraction integrals describing the axial distribution of the electric field amplitude behind the axicon are demonstrated. The analysis of the exact solutions shows that the period of {\guillemotleft}light droplets{\guillemotright} is not a constant value, but depends on the axial distance and on the deviation of the axicon surface from the conical shape far from the rounded region. The predicted effect can be applied for the reconstruction of the exact shape of the axicon surface without 3D scanning.