Fig. 1. (a) Schematic of basic optical tweezers. A single laser beam is focused by a high numerical aperture objective lens to form a stable optical trap for microscale particle. (b) and (c) illustrate the calculated optical force acting on a micro-sphere when it moves along the x-axis and z-axis, respectively, in the optical tweezers at the laser power P = 10 mW. Here, the two most important features of optical tweezers are shown: the maximum reverse axial force that characterizes the strength of the trap, and spring constants (the slope of the fit line). (d) and (e) display the calculated optical torque acting on a micro-sphere when it moves along the x-axis and z-axis, respectively.

Fig. 2. The dynamic process of the micro-sphere in an optical tweezers. Plots of the (a) position, (b) velocity, (c) angular velocity, and (d) optical force versus time under the initial condition of r₀=[0,0,1] μm, v₀=[0,0,0] μm/s, ϕ₀=[0,0,0] rad, and ω₀=[0,0,0] rad/s.

Fig. 3. Mechanical motion dynamics of the micro-sphere at different initial positions in the horizontal trapping plane. (a) The x-directional trajectories of the micro-sphere at different initial positions in the x-axis in the optical tweezers with r_0x=0.5, 1.0, 1.5, 1.8, 1.9, and 2.0 μm. (b)−(d) display the temporal evolution of the x- and y- and z- directional trajectory, optical force, drag force, and resultant force, respectively, when the micro-sphere is set at the initial position r_0x=1.9 μm. (e) and (f) display the temporal evolution of the optical force and the drag force, and the resultant force, respectively, when r_0x=2.0 μm.

Fig. 4. The 3D trajectories of the micro-sphere in the optical tweezers at different initial positions in the x-axis with r_0x= 0.5, 1.0, 1.5, 1.8, 1.9, and 2 μm.

Fig. 5. Mechanical motion dynamics of the micro-sphere at different initial positions along the optical axis. (a) The z-directional trajectories of the micro-sphere at different initial positions in the z-axis in the optical tweezers with r_0x=−2.0, −1.5, −1.0, −0.5, 1.0, 1.4, 1.6, 1.7, 1.75 and 1.9 μm. (b) and (c) The sketches of the optical force and the drag force, and the resultant force over time, respectively, when the micro-sphere is set at the initial position r_0x=1.7 μm.

Fig. 6. The 3D trajectories of the micro-sphere at different initial velocities in the x-axis in the optical tweezers with v_0x=100, 1×10⁴, 1×10⁶, 5×10⁶, 7.5×10⁶, 7.75×10⁶, and 8×10⁶ μm/s.

Fig. 7. (a) The 3D trajectories of a micro-sphere at different initial velocities in the z-axis with v_0x=1×10⁶, 5×10⁶, 6×10⁶, and 6.5×10⁶ μm/s, when the initial position is r_0x=[1,0,0] μm. The plots of (b) the optical force and drag force, and (c) the resultant force over time of the micro-sphere when v₀=[6.5 × 10⁶,0,0] μm/s, and r_0x=[1,0,0] μm.