A general theorem on the divergence of vortex beams

TL;DR

This paper establishes a fundamental limit on the divergence of vortex beams carrying orbital angular momentum, linking mean OAM to minimum divergence and applicable across various optical and quantum systems.

Contribution

It introduces a general theorem that relates OAM to beam divergence, providing a unified framework and a generalized uncertainty principle for optical beam analysis.

Findings

Mean absolute OAM sets a lower bound on beam divergence.

Derived a generalized uncertainty principle for divergence.

Applicable to long-range communication, microscopy, and quantum systems.

Abstract

The propagation and divergence properties of beams carrying orbital angular momentum (OAM) play a crucial role in many applications. Here we present a general study on the divergence of optical beams with OAM. We show that the mean absolute value of the OAM imposes a lower bound on the value of the beam divergence. We discuss our results for two different definitions of the divergence, the so called rms or encircled-energy. The bound on the rms divergence can be expressed as a generalized uncertainty principle, with applications in long-range communication, microscopy and 2D quantum systems.