# An upper limit to the orbital angular momentum of a vortex-carrying ultrashort pulse

## TL;DR

This paper establishes a fundamental upper limit on the orbital angular momentum of vortex-carrying ultrashort pulses based on their spectral properties, linking pulse duration and topological charge.

## Contribution

It introduces a theoretical limit on the topological charge of ultrashort vortex pulses derived from spectral characteristics, revealing fundamental constraints.

## Key findings

- Topological charge is limited by the pulse's spectral mean and variance.
- An upper bound exists for the orbital angular momentum of ultrashort pulses.
- A minimum pulse duration is required to carry any orbital angular momentum.

## Abstract

The magnitude of the topological charge of the vortex of a ring-shaped pulse is found to be limited by the squared mean frequency of the pulse spectrum at the ring relative to its variance. This limitation implies a upper bound to the orbital angular momentum carried by a pulse, and a lower bound to the duration for a pulse to carry any orbital angular momentum.