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Liu J, Zheng M, Xiong ZJ, Li ZY. 3D dynamic motion of a dielectric micro-sphere within optical tweezers. Opto-Electron Adv 4, 200015 (2021).. doi: 10.29026/oea.2021.200015
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3D dynamic motion of a dielectric micro-sphere within optical tweezers
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Abstract
Known as laser trapping, optical tweezers, with nanometer accuracy and pico-newton precision, plays a pivotal role in single bio-molecule measurements and controllable motions of micro-machines. In order to advance the flourishing applications for those achievements, it is necessary to make clear the three-dimensional dynamic process of micro-particles stepping into an optical field. In this paper, we utilize the ray optics method to calculate the optical force and optical torque of a micro-sphere in optical tweezers. With the influence of viscosity force and torque taken into account, we numerically solve and analyze the dynamic process of a dielectric micro-sphere in optical tweezers on the basis of Newton mechanical equations under various conditions of initial positions and velocity vectors of the particle. The particle trajectory over time can demonstrate whether the particle can be successfully trapped into the optical tweezers center and reveal the subtle details of this trapping process. Even in a simple pair of optical tweezers, the dielectric micro-sphere exhibits abundant phases of mechanical motions including acceleration, deceleration, and turning. These studies will be of great help to understand the particle-laser trap interaction in various situations and promote exciting possibilities for exploring novel ways to control the mechanical dynamics of microscale particles. -
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References
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Supplementary Information
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Video S2: 2Rz.avi
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Liu J, Zheng M, Xiong ZJ, Li ZY. 3D dynamic motion of a dielectric micro-sphere within optical tweezers. Opto-Electron Adv 4, 200015 (2021).. doi: 10.29026/oea.2021.200015
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Figure 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.
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Figure 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.
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Figure 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 r0x=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 r0x=1.9 μm. (e) and (f) display the temporal evolution of the optical force and the drag force, and the resultant force, respectively, when r0x=2.0 μm.
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Figure 4.
The 3D trajectories of the micro-sphere in the optical tweezers at different initial positions in the x-axis with r0x=0.5, 1.0, 1.5, 1.8, 1.9, and 2 μm.
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Figure 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 r0x=−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 r0x=1.7 μm.
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Figure 6.
The 3D trajectories of the micro-sphere at different initial velocities in the x-axis in the optical tweezers with v0x=100, 1×104, 1×106, 5×106, 7.5×106, 7.75×106, and 8×106 μm/s.
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Figure 7.
(a) The 3D trajectories of a micro-sphere at different initial velocities in the z-axis with v0x=1×106, 5×106, 6×106, and 6.5×106 μm/s, when the initial position is r0x=[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 r0x=[1,0,0] μm.
