Poynting vector and orbital angular momentum density of superpositions of Bessel beams

Igor A. Litvin,Andrew Forbes,Angela Dudley

doi:10.1364/oe.19.016760

Abstract

We study theoretically the orbital angular momentum (OAM) density in arbitrary scalar optical fields, and outline a simple approach using only a spatial light modulator to measure this density. We demonstrate the theory in the laboratory by creating superpositions of non-diffracting Bessel beams with digital holograms, and find that the OAM distribution in the superposition field matches the predicted values. Knowledge of the OAM distribution has relevance in optical trapping and tweezing, and quantum information processing.

Highlights

It has been well known for some time that photons carry spin angular momentum of + ħ (–ħ) per photon for left circularly polarised light, and that the transfer of this momentum can be measured in the laboratory when the light passes through a birefringent plate [1]
Applying Eq (12), we calculate the dependence of the orbital angular momentum (OAM) density of a superposition of Bessel beams (BBs), where the two components differ in their radial wave numbers
We find that while the global OAM is zero, the local OAM spectrum changes radially across the beam, and can be made to oscillate from positive to negative values by a suitable choice of the parameters making up the superposition

Summary

Introduction

It has been well known for some time that photons carry spin angular momentum of + ħ (–ħ) per photon for left (right) circularly polarised light, and that the transfer of this momentum can be measured in the laboratory when the light passes through a birefringent plate [1]. More recently [2,3] it has been realised that light may carry an extrinsic component of angular momentum, orbital angular momentum (OAM), when the electric field or mode has an azimuthal angular dependence of exp(ilφ), where l is the azimuthal mode index. Such fields carry OAM of lħ per photon, and may be found as beams expressed in several basis functions, including Laguerre-Gaussian beams [2], Bessel-Gaussian beams [4] and Airy beams [5] to name but a few. One is interested in the superposition of OAM carrying fields, both at the classical [18,19,20] and quantum levels [7]

Methods

Results

Conclusion