Fig. 4: NOT on homogeneous isotropic spheres in perfect vortex beams.

a Calculated field distribution on the focal plane of a perfect vortex beam (λ = 1.064 μm) with left-handed circular polarization and a topological charge ℓ = 10. The field quantities are normalized to the maximum of their absolute values. Magenta arrows in the intensity map indicate the direction of transverse momentum density. b Calculated longitudinal SAM-induced and momentum-curl torques on a gold particle (r = 0.75 μm) placed at varying radial positions. Their sum is also presented, which agrees with Lorenz-Mie results for the net torque Tz. NOT occurs when Tz is negative, i.e., against the incident angular momentum. The blue circle indicates the radial trapping position. c Calculated net longitudinal torques for different topological charges.