Fig. 3: Simulation of 3D optical spin torques.

a Illustration of the single-beam configuration for vectorial SAM transfer. A 45° LP beam incidents on an SLM. The wavefront of the x-polarized component is modulated as dictated by the phase on the SLM, while the y-component remains a uniform plane wave. Their superposition creates the light field given by Eq. (7). b Phase profile for generating a T-spin along the x-axis. c, d Intensity and SAM density distributions of the individual field components for the T-spin beam. e–g Simulation results corresponding to the SAM about an oblique axis of (60^°, 45^°). h, i 3D orientation plot of the calculated torques acting on a spinning birefringent spherical particle with the SAM vector in the transverse or oblique (60^°, 45^°) direction, respectively. The insert shows the orientations of the torque and the SAM vector in the spherical coordinate system.