Fig. 1. Generation of GPOVs. (a) Different optical conveyor belt models based on the generation of GPOVs. (b) Tightly focusing structure to generate customized GPOVs; the inset shows focus intensity distribution. (c) Isometric uniform sampling eliminates redundancy in the optical pattern at the inflection points.

Fig. 2. Schematic optical setup of holographic optical tweezers for rotating and transporting metallic particles with GPOVs. (a) GPOV phase mask addressed on SLM. (b) Dynamics details of the optical trapping, including the scattering force Fs, and the gradient forces F∇1 and F∇2. Additionally, the axial scattering force is balanced by the cover-slip pressure Fc and the self-gravitational force mg of the particles. F, filter; L1–L5, lenses; M1–M5, mirrors; O1, O2, objectives; DM, dichroic mirror; TR, triangle reflector; HWP, half-wave plate; PBS, polarizing beam splitter; SLM, spatial light modulator; CCD, charged coupled device.

Fig. 3. Generation of GPOVs (ℓ=12) with different curvilinear structures. Intensity and phase portrait of the GPOVs by our method (a) and the integral method (b). (c) and (d) show the distribution of the intensity concerning the transmission length for our proposed method and the integral technique, respectively, with I, II, III, and IV representing the different optical patterns in (a), which are distinguished by different colors. (e) and (f) Phase and phase gradient distributions in GPOVs of different structures as a function of curve length. (e) corresponds to our method, and (f) is the integral method. (g) Comparison of the intensity and phase gradient uniformity of the two methods based on mean squared error (MSE).

Fig. 4. Numerical results of optical forces exerted on a gold particle by the focused hypocycloid hexagonal POV with topological charge ℓ=20. (a) Transverse optical force exerted on a gold particle (R=0.5  μm) in a background of light field intensity. Arrows indicate the direction and magnitude of the force. An inset provides an enlarged view of the force distribution within the delineated red box region. (b) Profile of the optical force along the x-direction at the center of the red box region in (a), with black points representing trapping positions. (c) Phase diagram of optical forces Fx on a gold particle arising from the hexagonal optical field, as a function of the particle radius R and the horizontal position x. (d) Particle transport force versus laser power. (e) Particle transport force versus topological charge.

Fig. 5. Single-shot and time-lapse images of 1.4-μm-diameter gold particles manipulated by GPOV conveyor belts. (a) Rhombic and (b) pentagonal conveyors implement effectively rotational conveyance of the gold particles, as indicated by the white dashed lines representing the position of the optical field. The time intervals between consecutive frames in the time-lapse images are 0.08 s for case (a) and 0.12 s for case (b). (c) The integral method for generating a pentagonal conveyor belt transporting the particle and the transverse optical force distribution in the field.

Fig. 6. Long-distance transport of gold particles (0.58 μm in diameter) by the Archimedean spiral optical trap. (a) Counterclockwise rotation of a particle at the topological charge ℓ=50. The white dashed lines indicate the position of the optical field. (b) Time-lapse image of the gold particle rotation with the color bar indicating time.

Fig. 7. Manipulation of gold particles using a three-orbit external pendulum hexagonal optical trap. (a) Counterclockwise rotation of particles with topological charge ℓ=15, 25, and 35 from the inside to outside. (b) Clockwise rotation as the topological charge changes to −15,−25, and −35. The white dashed lines indicate the positions of the optical field, and the round arrows depict the directions of rotation. Red, blue, and yellow rings represent the dynamic positions of the specific particles in different orbits.

Fig. 8. Transport of large-sized particles using the GPOV double-conveyor belt. (a) Double-wavy conveyor belt, time-lapse, and single-frame images of unidirectional transport of a single gold particle. (b) Rotational transport of a single aluminum particle by the dual-track pentagon conveyor with counterclockwise rotation in the dark region of the orbit. The white dashed line represents the position of optical belts, and the arrows represent the direction of motion of the microparticle.