Figure 1: Momentum and spin in a circularly-polarized propagating plane wave.

The complex wave electric field is given by equation (1) with m=i, that is σ=1. (a) Instantaneous electric and magnetic fields, (r,t)=Re[E(r)e^−iωt] and (r,t)=Re[H(r)e^−iωt], form helical distributions (see also Supplementary Note 2 and Supplementary Fig. 1). As the wave propagates along the z axis, the fields rotate in the transverse (x,y) plane. This rotation generates the spin AM density , which is represented in (b) by multiple loops of the (zero-net) spin-momentum p^S=∇ × s/2 in the transverse plane. At the same time, the wave propagation produces the canonical (orbital) momentum density . (c) Orbital momentum and spin AM are locally transferred to a probe particle, thereby exerting a radiation force F∝p^O and torque T∝s on it, equation (6).