On Small Beams with Large Topological Charge

TL;DR

This paper investigates the limitations of using large orbital angular momentum beams for high-resolution imaging, showing that non-paraxial effects reduce visibility and challenge the advantages predicted by paraxial theory.

Contribution

It provides a non-paraxial analysis of beams with large topological charge, revealing the impact on resolution and visibility, which was not addressed in previous paraxial solutions.

Findings

Larger OAM can resolve smaller distances but with reduced visibility.

Non-paraxial effects introduce a field component along the propagation direction.

Maintaining constant visibility negates the advantage of larger OAM for resolution.

Abstract

Light beams can carry a discrete, in principle unbounded amount of angular momentum. Examples of such beams, the Laguerre-Gauss modes, are frequently expressed as solutions of the paraxial wave equation. There, they are eigenstates of the orbital angular momentum (OAM) operator. The paraxial solutions predict that beams with large OAM could be used to resolve arbitrarily small distances - a dubious situation. Here we show how to solve that situation by calculating the properties of beams free from the paraxial approximation. We find the surprising result that indeed one can resolve smaller distances with larger OAM, although with decreased visibility. If the visibility is kept constant (for instance at the Rayleigh criterion, the limit where two points are reasonably distinguishable), larger OAM does not provide an advantage. The drop in visibility is due to a field in the direction of propagation, which is neglected within the paraxial limit.