Fig. 1. Schematic of the focusing geometry.

Fig. 2. Simulated field distribution E→f=(Efx,Efy,Efz) of the focal plane: (rows 1, 2, and 3) three elliptical DC-OVBs designed by setting q=(1,1,2,10,6,6), and distinct R0 values of 0.1 and 0.5 for the inner and outer ellipses, respectively. α=1 is set for the first and third rows and α=8 for the second row. The luminance and color of the colormap refer to the absolute (Abs) value and phase of the focal field components, respectively. The green line in the plot shows the profile of absolute value along the x-axis.

Fig. 3. Simulated momentum density distribution corresponding to the tightly focused focal field shown in Fig. 2, depicted in four columns from left to right: (first column) intensity, (second column) ϕ-component of momentum density, (third column) ρ-component of momentum density, and (fourth column) optical force distribution of LRI particles. The white dotted line indicates a local zoom.

Fig. 4. Simulated angular momentum density distribution corresponding to the tightly focused focal field shown in Fig. 2, depicted in three columns from left to right: (first column) z-component of the total angular momentum density, (second column) z-component of the orbital angular momentum density, and (third column) z-component of the spin angular momentum density.

Fig. 5. Configuration of the inverted optical trapping microscope. CGH, computer-generated hologram; SLM, spatial light modulator; BS, beam splitter; P, polarizer; LP, linear polarization; L1, L2, lenses.

Fig. 6. Schematic diagram of silver-coated hollow glass spheres, showcasing overall (left) appearance and structural dissection (right).

Fig. 7. Observation of a silver-coated hollow glass sphere manipulated by DC-OVBs with different topological charges. (a) Snap-shot image of a silver-coated hollow glass sphere trapped in the annular dark region enclosed between the two bright rings outlined by dashed yellow lines. Inner ring: 2.7 µm in diameter; outer ring: 13.6 µm in diameter; Fϕ: tangent force, Fp: radial force. (b) Particle motion velocity along the annular trajectory.

Fig. 8. Experimental results demonstrate simultaneous manipulation of both HRI and LRI particles using circular DC-OVBs: five sequential snapshots throughout one complete revolution of LRI particles’ motion. The first, second, and third rows show the cases of uniform OFD distribution (α=1) with different values of m1 and m2 for the inner and outer loops, respectively. Specifically, the values of m1 and m2 are −5 and −40 for the first row, −5 and −30 for the second row, and −5 and 40 for the third row [see Visualization 1 for a comprehensive video recording illustrating particle motion for different parameter pairs (m1, m2), arranged sequentially].

Fig. 9. Experimental results demonstrating simultaneous manipulation of both HRI and LRI particles using elliptical DC-OVBs. The first, second, and third rows show the cases of uniform OFD distribution (α=1) with different values of m1 and m2 for the inner and outer loops, respectively. The values are 5 and 40 for the first row, −5 and −30 for the second row, and −5 and 40 for the third row [see Visualization 2 for a comprehensive video recording illustrating particle motion for different parameter pairs (m1, m2), arranged sequentially].

Fig. 10. Experimental results demonstrating simultaneous manipulation of both HRI and LRI particles using quadrilateral DC-OVBs. The first, second, and third rows show the cases of uniform OFD distribution (α=1) with different values of m1 and m2 for the inner and outer rings, respectively. The values are −5 and −40 for the first row, −5 and −30 for the second row, and −5 and 40 for the third row [see Visualization 3 for a comprehensive video recording illustrating particle motion for different parameter pairs (m1, m2), arranged sequentially].

Fig. 11. Experimental results demonstrating variable speed motion of particles along quadrilateral DC-OVB, defined by m1=5 and m2=40 for inner and outer loops. The three rows display DC-OVBs with phase change control parameters α=1, 0.7, and 1.2. Time periods for LRI particles to complete one revolution are represented by τ1, τ2, and τ3 (see Visualization 4 for a video recording illustrating motion transitions of particles for different values of the parameter α).