# How Perfect are Perfect Vortex Beams?

## TL;DR

This paper derives and experimentally confirms an explicit formula for the width of quasi-perfect vortex beams, revealing it scales with the square root of the orbital angular momentum, which is crucial for applications in optical trapping and communications.

## Contribution

It provides the first explicit analytic expression for the width of quasi-perfect vortex beams and confirms it experimentally, clarifying their OAM dependence.

## Key findings

- Width scales as √ℓ, similar to regular vortex modes
- Experimental confirmation of the derived width expression
- Quasi-PV beams have a smaller proportionality constant

## Abstract

Perfect (optical) vortex (PV) beams are fields which are mooted to be independent of the orbital angular momentum (OAM) they carry. To date, the best experimental approximation of these modes is obtained from passing Bessel-Gaussian beams through a Fourier lens. However, the OAM-dependent width of these quasi-PVs is not precisely known and is often understated. We address this here by deriving and experimentally confirming an explicit analytic expression for the second moment width of quasi-PVs. We show that the width scales in proportion to $\sqrt{\ell}$ in the best case, the same as most "regular" vortex modes albeit with a much smaller proportionality constant. Our work will be of interest to the large community who seek to use such structured light fields in various applications, including optical trapping, tweezing and communications.