Spin and orbital angular momenta of electromagnetic waves in classical and quantum electrodynamics

TL;DR

This paper explores the distinctions and calculations of spin and orbital angular momenta in electromagnetic waves within classical and quantum electrodynamics, highlighting the complexities and nuances involved in their analysis.

Contribution

It provides a detailed analysis of how spin and orbital angular momenta can be computed for finite wavepackets in both classical and quantum frameworks, addressing subtle theoretical issues.

Findings

Spin angular momentum of plane waves is difficult to evaluate without limits.

Both classical and quantum methods can compute angular momenta for finite wavepackets.

Quantum analysis involves subtle arguments related to multimodal structures.

Abstract

A plane, monochromatic electromagnetic wave propagating in free space can have a certain amount of spin angular momentum but cannot possess any orbital angular momentum. Even the spin angular momentum of the plane-wave is difficult to evaluate without resort to certain mathematical limit arguments. Both spin and orbital angular momenta can be computed for a wavepacket of finite duration and finite cross-sectional area using standard methods of classical electrodynamics. Extending these results to finite wavepackets in quantum electrodynamics requires subtle arguments in conjunction with the multimodal structure of the wavepacket. This paper presents some of the nuances of classical as well as quantum-optical methods for analyzing the spin and orbital angular momenta of electromagnetic waves.