Spin and Orbital Angular Momenta of Electromagnetic Waves in Free Space

TL;DR

This paper derives exact Fourier integral expressions for the energy, momentum, and angular momentum of free-space electromagnetic pulses, clarifying the distinct roles and orientations of spin and orbital angular momentum components.

Contribution

It provides a novel, exact formulation of electromagnetic angular momentum in free space, distinguishing intrinsic and extrinsic orbital angular momentum contributions.

Findings

Spin angular momentum aligns with the wavevector.

Orbital angular momentum is orthogonal to the wavevector.

The total orbital angular momentum includes intrinsic and extrinsic parts.

Abstract

We derive exact expressions, in the form of Fourier integrals over the (k,w) domain, for the energy, momentum, and angular momentum of a light pulse propagating in free space. The angular momentum is seen to split naturally into two parts. The spin contribution of each plane-wave constituent of the pulse, representing the difference between its right- and left-circular polarization content, is aligned with the corresponding k-vector. In contrast, the orbital angular momentum associated with each plane-wave is orthogonal to its k-vector. In general, the orbital angular momentum content of the wavepacket is the sum of an intrinsic part, due, for example, to phase vorticity, and an extrinsic part, r_CM x p, produced by the linear motion of the center-of-mass r_CM of the light pulse in the direction of its linear momentum p.