Journal of East China Normal University(Natural Science) >

2022 , Vol. 2022 >Issue 2: 106 - 113

DOI: https://doi.org/10.3969/j.issn.1000-5641.2022.02.012

Physics and Electronics

Calculation of particle motion trajectories in optical force fields

  • Hailei XIE ,
  • Junjie DU
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  • School of Physics and Electronic Science, East China Normal University, Shanghai　200241 China

Received date: 2021-03-11

  Online published: 2022-03-28

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Abstract

In this paper, the motion trajectory of micro-nanoparticles is calculated based on the Euler-Richardson algorithm after the optical force exerted on the particles is determined using Mie scattering theory. The Euler-Richardson algorithm has better calculation accuracy and faster convergence speed than the Euler algorithm and the Euler-Kromer algorithm, and thus is an appropriate approach to describe the trajectory of particles. Hence, the motion trajectory of a nanoparticle in a periodic conservative optical force field is calculated based on the Euler-Kromer algorithm; the results confirm consistency with the physical analysis, further verifying the effectiveness and stability of the approach. The calculation method shown in this paper provides a high-efficiency approach to study optical trapping, transport, sorting of colloidal particles, and biological macromolecules as well as the cooling of macroscopic particles in optical micro-manipulation.

Key words： Euler-Richardson algorithm; optical force field; particle motion trajectory

Cite this article

Hailei XIE , Junjie DU . Calculation of particle motion trajectories in optical force fields[J]. Journal of East China Normal University(Natural Science), 2022 , 2022(2) : 106 -113 . DOI: 10.3969/j.issn.1000-5641.2022.02.012

References

1 LEBEDEW P. Untersuchungen über die druckkrfte des lichtes. Annalen Der Physik, 1901, 311 (11): 433- 458.
2 NICHOLS E F, HULL G F. A preliminary communication on the pressure of heat and light radiation. Physical Review, 1901, 13 (5): 307- 320.
3 ASHKIN A. Acceleration and trapping of particles by radiation pressure [J]. Physical Review Letters, 1970, 24(4): 156-159.
4 ASHKIN A. Stability of optical levitation by radiation pressure. Applied Physics Letters, 1974, 24 (12): 586- 588.
5 GHISLAIN L P, SWITZ N A, WEBB W W. Measurement of small forces using an optical trap. Review of Scientific Instruments, 1994, 65 (9): 2762- 2768.
6 ROHRBACH A, STELZER E H K. Trapping forces, force constants, and potential depths for dielectric spheres in the presence of spherical aberrations. Applied Optics, 2002, 41 (13): 2494- 2507.
7 LITVINOV R I, SHUMAN H, BENNETT J S, et al. Binding strength and activation state of single fibrinogen-integrin pairs on living cells. Proceedings of the National Academy of Sciences, 2002, 99 (11): 7426- 7431.
8 GITTES F, SCHMIDT C F. Signals and noise in micromechanical measurements. Methods in Cell Biology, 1998, 55 (55): 129- 156.
9 GITTES F, SCHMIDT C F. Interference model for back-focal-plane displacement detection in optical tweezers. Optics Letters, 1998, 23 (1): 7- 9.
10 PRALLE A, PRUMMER M, FLORIN E L, et al. Three-dimensional high-resolution particle tracking for optical tweezers by forward scattered light. Microscopy Research and Technique, 2015, 44 (5): 378- 386.
11 SVOBODA K, BLOCK S M. Optical trapping of metallic Rayleigh particles. Optics Letters, 1994, 19 (13): 930- 932.
12 KE P C, GU M. Characterization of trapping force on metallic mie particles. Applied Optics, 1999, 38 (1): 160- 167.
13 ASHKIN A. History of optical trapping and manipulation of small-neutral particle, atoms, and molecules. IEEE Journal of Selected Topics in Quantum Electronics, 2000, 6 (6): 841- 856.
14 SVOBODA K, MITRA P P, BLOCK S M. Fluctuation analysis of motor protein movement and single enzyme kinetics. Proceedings of the National Academy of Sciences of the United States of America, 1994, 91 (25): 11782- 11786.
15 BUSTAMANTE C, SMITH S B, LIPHARDT J, et al. Single-molecule studies of DNA mechanics. Current Opinion in Structural Biology, 2000, 10 (3): 279- 285.
16 TATARKOVA S A, SIBBETT W, DHOLAKIA K. Brownian particle in an optical potential of the washboard type. Physical Review Letters, 2003, 91 (3): 038101.
17 GAHAGAN K T, SWARTZLANDER G A. Optical vortex trapping of particles. Optics Letters, 1996, 21 (11): 827- 829.
18 O’NEIL A T, PADGETT M J. Three-dimensional optical confinement of micron-sized metal particles and the decoupling of the spin and orbital angular momentum within an optical spanner. Optics Communications, 2000, 185 (1/2/3): 139- 143.
19 HE H, FRIESE M E J, HECKENBERG N R, et al. Direct observation of transfer of angular momentum to absorptive particles from a laser beam with a phase singularity. Physical Review Letters, 1995, 75 (5): 826- 829.
20 ALLEN L, PADGETT M J, BABIKER M. IV the orbital angular momentum of light. Progress in Optics, 1999, 39, 291- 372.
21 O’NEIL A T, MACVICAR I, ALLEN L, et al. Intrinsic and extrinsic nature of the orbital angular momentum of a light beam. Physical Review Letters, 2002, 88, 053601.
22 CURTIS J E, GRIER D G. Structure of optical vortices. Physical Review Letters, 2003, 90 (13): 133901.
23 SIMPSON N B, DHOLAKIA K, ALLEN L, et al. Mechanical equivalence of spin and orbital angular momentum of light: An optical spanner. Optics Letters, 1997, 22 (1): 52- 54.
24 KORDA P T, SPALDING G C, GRIER D G. Evolution of a colloidal critical state in an optical pinning potential landscape. Physical Review B, 2002, 66, 024504.
25 MANGOLD K, LEIDERER P, BECHINGER C. Phase transitions of colloidal monolayers in periodic pinning arrays. Physical Review Letters, 2003, 90 (15): 158302.
26 BROWN S E, MOZURKEWICH G, GRüNER G. Subharmonic shapiro steps and devil’s-staircase behavior in driven charge-density-wave systems. Physical Review Letters, 1984, 52 (25): 2277- 2280.
27 WIERSIG J, AHN K H. Devil’s staircase in magnetoresistance of a periodic array of scatterers. Physical Review Letters, 2001, 87 (2): 026803.
28 PIERRE-LOUIS O, HAFTEL M. Oscillatory driving of crystal surfaces: A route to controlled pattern formation. Physical Review Letters, 2001, 87 (4): 048701.
29 REICHHARDT C, NORI F. Phase locking, devil’s staircases, farey trees, and arnold tongues in driven vortex lattices with periodic pinning. Physical Review Letters, 1998, 82 (2): 414- 417.
30 GOULD H, TOBOCHNIK J CHRISTIAN W. 计算机模拟方法在物理学中的应用 [M]. 影印版. 3版. 北京, 高等教育出版社, 2006.
31 DU J J, YUEN C H, LI X, et al. Tailoring optical gradient force and optical scattering and absorption force. Scientific Reports, 2017, 7 (1): 18042.
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