Fig. 1: Concept of a dynamic 3D rotation by time-varying 3D SAM transfer.

a Transverse spin (T-spin) by two-wave interference (classic). The superposition of the left-hand and right-hand circularly polarized beams (LCP and RCP) leads to a T-spin (yellow arrow), which can be transferred to particles to drive transverse rotation (red arrow). b Time-varying 3D SAM control via a single-beam configuration (our work). The incident beam is 45° linearly polarized (LP), and its x-polarized component is shaped with asymptotic spiral phases to manipulate various SAM vectors (yellow arrows). The spiral phase masks labeled t₁, t₂, and t₃ correspond to a sequence of phase masks at times t₁, t₂, and t₃, resulting in SAM₁, SAM₂, and SAM₃, respectively. c Dynamic 3D optical spanner via time-varying vectorial transfer of the SAM to microparticles in an optical trap. Experimental images of a spinning cubic calcite particle demonstrate controlled rotations around an arbitrary axis in 3D space. The rotation axes are defined by the corresponding SAM₁, SAM₂, and SAM₃ in (b).