Optical vortices: the concept of topological potential and analogies with two-dimensional electrostatics

TL;DR

This paper introduces the concept of a Topological Potential to describe optical vortices, drawing analogies with 2D electrostatics, and explores their stability and applications in optical communications and tweezers.

Contribution

It proposes the Topological Potential as a new framework to analyze optical vortices and their multipoles, enabling tailored applications in optics.

Findings

TC multipoles are topologically stable during propagation

2D distributions can control transverse forces in optical tweezers

The formalism allows designing OV for specific applications

Abstract

We show how the phase profile of a distribution of topological charges (TC) of an optical vortex (OV) can be described by a potential analogous to the Coulomb's potential for a distribution of electric charges in two-dimensional electrostatics. From what we call the Topological Potential (TP), the properties of TC multipoles and a 2D radial distribution were analyzed. The TC multipoles have a transverse profile that is topologically stable under propagation and may be exploited in optical communications; on the other hand, the 2D distributions can be used to tune the transverse forces in optical tweezers. Considering the analogies with the electrostatics formalism, it is also expected that the TP allows the tailoring of OV for specific applications.