Divergence of an orbital-angular-momentum-carrying beam upon propagation

TL;DR

This paper investigates how the divergence of light beams carrying orbital angular momentum (OAM) scales with OAM, clarifying the conditions under which divergence increases linearly or with the square root of OAM, impacting free-space optical communication.

Contribution

It clarifies the conditions under which OAM beam divergence scales linearly or with the square root, resolving existing confusion in the field.

Findings

Divergence scales linearly when the beam waist radius is constant.

Divergence scales with the square root when the rms intensity is constant.

Both scaling laws are valid depending on the constant parameter.

Abstract

There is recent interest in the use of light beams carrying orbital angular momentum (OAM) for creating multiple channels within free-space optical communication systems. One limiting issue is that, for a given beam size at the transmitter, the beam divergence angle increases with increasing OAM, thus requiring a larger aperture at the receiving optical system if the efficiency of detection is to be maintained. Confusion exists as to whether this divergence scales linarly with, or with the square root of, the beam's OAM. We clarify how both these scaling laws are valid, depending upon whether it is the radius of the Gaussian beam waist or the rms intensity which is kept constant while varying the OAM.