Figure 3: Numerically calculated forces and torques on a Mie particle in an evanescent field.

(a,c) Schematics of a proposed experiment (see also Supplementary Fig. 3). A polarized propagating wave undergoes total internal reflection at the glass–water interface, thereby generating the evanescent wave (7) in water. A gold spherical particle of radius a is placed in water on the glass surface, and its observable linear and spinning motion is proportional to the forces and torques exerted by the evanescent wave. (b,d) Normalized torque and force components for circular ( m=±i, σ=±1) and diagonal (m=χ=±1) polarizations versus the particle size ka (the Rayleigh dipole region ka≪1 is indicated by the orange circles). (b) The longitudinal helicity-dependent torque T_z∝s_z∝σ indicates the usual spin. The transverse torque is helicity independent and signals the appearance of the transverse spin (9): T_y∝s_y∝(κ/k_z)w. The vertical torque for the diagonal polarizations χ=±1 appears because of the strong electric–magnetic (dual) asymmetry of the particle. It is caused by the non-zero electric part (10) of the (zero-net) vertical spin density: , s_ex=−s_mx. (d) The orbital momentum density (8) produces mostly polarization-independent longitudinal radiation pressure force: . At the same time, the transverse force vanishes in the Rayleigh region, but becomes non-zero for larger Mie particles with ka~1, see equation (11). This transverse force has the helicity-dependent part proportional to the transverse spin momentum (8): , and also the χ-dependent part proportional to the ‘imaginary’ Poynting momentum (12) .