Fig. 1. Concepts of (a) conventional optical tweezers for manipulating mass-point particles and (b) rigid-body emulated structured light tweezers for manipulating irregular objects with full-degree-of-freedom six-axis motion.

Fig. 2. Schematic of six independent DoFs of the rigid-body mechanics with the structured light trapped particle, including surge, sway, heave, roll, pitch, and yaw.

Fig. 3. Schematic of the experimental setup. L1, concave lens; L2–L5, convex lenses; P1, P2, polarizers; A1, A2, apertures; SLM, spatial light modulator; M1–M4, mirrors; CCD, charge-coupled device; MO1, MO2, micro-objectives. (a) Phase mask diagram, (b) intensity image of captured particle at z=0 plane, and (c) 3D state model diagram of the captured particle.

Fig. 4. Steering ability of the beam was verified by manipulating the yeast cells. (a1)–(a5) Images recorded during the experiment, and the parameter of the beam is the spin angle φ=0–2π. (b1)–(b5) Schematics of the 3D model corresponding to the first row. (c1)–(c5) Images recorded when the yeast cells were manipulated by the spin angle φ=0–2π and displacement along the z axis Δz=0–15  μm. (d1)–(d5) Schematics of the 3D model corresponding to the third row. (e1)–(e5) Images recorded during the experiment of performing a 180º flip of the yeast cells, and the parameter of the beam is the nutation angle θ=0–2π. (f1)–(f5) Schematics of the 3D model corresponding to the fifth row.

Fig. 5. (a) 3D model schematic of the TOMOTRAP method. (b) 3D model schematic of the rigid-body emulated optical tweezers. (c) Schematic of the operation of a 3D model of rigid-body optical tweezers. (d) Yeast cells are manipulated by the spin angle φ=0–2π, nutation angle θ=7π/4−π/4, and displacement along the x axis Δx=0–20  μm.

Fig. 6. CHG of phase masks designed and used in Figs. 4, 5, and 7 shown in sub-figures (a1)–(a5), (b1)–(b5), and (c1)–(c5), respectively.

Fig. 7. Yeast capture and flip experiment. (a1)–(a5) Images recorded during the experiment of yeast were captured by changing the precession angle; (b1)–(b5) schematic diagrams of the 3D model corresponding to (a1)–(a5). (c1)–(c5) Images recorded during the experiment of yeast perform a 360° flip; (d1)–(d5) schematic diagrams of the 3D model corresponding to (c1)–(c5).

Fig. 8. (a1)–(a4) Stokes drag force test to determine the trapping force and stiffness of the proposed 6D optical tweezers. (b) Optical trap stiffness versus input power. A polystyrene sphere with a diameter of 3 μm was employed in the experiments.