Fig. 1. Calculation of the pupil field to obtain a focused beam with arbitrary photonic spin orientation through coherent superposition of the radiation patterns from electric dipoles.

Fig. 2. (a), (c), and (e) Intensity distribution superimposed with polarization map. (b), (d), and (f) Histogram of ellipticity of the ideal incident pupil field for generating (a) photonic spin orientated along (α,β,γ)=(60°,60°,45°), (c) photonic spin with ellipticity of 2 and orientation along (α,β,γ)=(20°,80°,73°), and (e) photonic spin with elevation angle of −45° and orientation along (α,β,γ)=(110°,20°,90°).

Fig. 3. (a) Normalized intensity distribution. (b)–(d) Stokes images. (e)–(g) Spin density distribution in the vicinity of the focus of the highly focused light given in Fig. 2(a).

Fig. 4. (a) Normalized intensity. (b)–(d) Stokes images. (e)–(g) Spin density distribution in the vicinity of the focus of the highly focused light given in Fig. 2(c).

Fig. 5. (a) Normalized intensity. (b)–(d) Stokes images. (e)–(g) Spin density distribution in the vicinity of the focus of the highly focused light given in Fig. 2(e).

Fig. 6. Diagram of the experimental setup. HWP, half-wave plate; P, polarizer; BS, beam splitter; L, lens; M, mirror; SF, spatial filter.

Fig. 7. Experimental results of the (a), (c), and (e) intensity distribution with polarization map and (b), (d), and (f) histogram of ellipticity corresponding to the incident pupil field presented in Figs. 2(a), 2(c), and 2(e), respectively.

Fig. 8. Spatial orientation of the spheroid.

Fig. 9. Optical force on the dielectric spheroidal particle located near the focus of the photonic spin presented in Fig. 3(a). Equilibrium position is indicated by the asterisk.

Fig. 10. Distribution of the optical torque in the (a) x′–y′, (b) y′–z′, and (c) x′–z′ planes. (d) Corresponding rotation diagram of a spheroid with orientation at (Θ0=45°,ϕ0=45°). Equilibrium position is indicated by the asterisk.

Fig. 11. Torque exerted on the spheroid at the equilibrium position versus (a) the polar angle Θ0 and (b) the azimuthal angle ϕ0.

Fig. 12. Optical force along (a) x′, (b) y′, and (c) z′ axes exerted on the 50 nm absorbing nanoparticle located near the focus of the photonic spin presented in Fig. 3(a). Equilibrium position is indicated by the asterisk.

Fig. 13. Distribution of the optical torque in the (a) x′–y′, (b) y′–z′, and (c) x′–z′ planes for absorbing spherical nanoparticle. The equilibrium position is indicated by the asterisk.

Fig. 14. Particle rotation as a result of the torque from elliptically polarized light. (a) Torque and (b) rotation frequency for absorbing nanoparticles are shown as a function of Δϕ, the phase difference that determines the ellipticity of the focal field.

Table 1. Theoretical and Experimental Pi Values for the Incident Light Presented in Figs. 2 and 7