Electromagnetic angular momentum of quantized wavepackets in free space

TL;DR

This paper investigates the electromagnetic angular momentum of quantized wavepackets in free space, emphasizing the complexities of calculating spin and orbital angular momentum through discretization methods.

Contribution

It clarifies how angular momentum arises from interference of plane-waves and discusses the challenges of discretizing (k,ω) space for calculations.

Findings

Angular momentum arises from interference of plane-waves with same frequency but different k-vectors.

Discretizing (k,ω) space complicates the calculation of angular momentum.

Fourier transformation facilitates evaluation of wavepacket angular momentum.

Abstract

A single electromagnetic plane-wave propagating in free space possesses neither spin nor orbital angular momentum. Both types of angular momentum arise from interference between pairs of plane-waves having the same temporal frequency {\omega} but differing k-vectors k_1 and k_2. While it is fairly straightforward to evaluate a wavepacket's spin and orbital angular momenta in the (k,{\omega}) continuum by means of Fourier transformation, obtaining the same results by discretizing the (k,{\omega}) space, then attempting to approach the continuum limit via an infinite enlargement of the spatial volume under consideration, is fraught with danger.