Gaussian laser beam transformation into an optical vortex beam by helical lens

TL;DR

This paper analyzes how a hybrid optical element called a helical lens transforms a Gaussian laser beam into an optical vortex, detailing the diffraction, phase singularity, and vortex properties at various distances.

Contribution

It introduces the concept of a helical lens combining a spiral phase plate and a lens, and investigates its diffraction and vortex formation effects on Gaussian beams.

Findings

The helical lens creates a phase singularity of order p.

The output beam's parameters and vortex profiles are characterized.

The study details the beam's behavior in near and far fields.

Abstract

In this article we investigate the Fresnel diffraction characteristics of the hybrid optical element which is a combination of a spiral phase plate (SPP) with topological charge p and a thin lens with focal length f, named the helical lens (HL). As incident a Gaussian laser beam is treated, having its waist a distance from the HL plane and its axis passing through the centre of the HL. It is shown that the SPP introduces a phase singularity of p-th order to the incident beam, while the lens transforms the beam characteristic parameters. The output light beam is analyzed in detail: its characteristic parameters and focusing properties, amplitude and intensity distributions and the vortex rings profiles and radii, at any z distance behind the HL plane, as well as in the near and far field.