Abstract

Laser light can exert forces on matter by exchanging momentum in form of radiation pressure and refraction. Although these forces are small, they are sufficient to trap and manipulate microscopic particles [Phys. Rev. Lett. 24, 156 (1970)]. In this paper, we study the optical trapping phenomena by using computer simulation to show a detailed account of the process of momentum exchange between a focused light and a microscopic particle in an optical trapping by use of the finite difference time domain method. This approach provides a practical routine to predict the magnitude of the exchanged momentum, track the particle in a trapping process, and determine a trapping point, where dynamic equilibrium happens. Here we also theoretically describe the transfer procedure of orbital angular momentum from a focused optical vortex to the particle.

©2004 Optical Society of America

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References

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  1. A. Ashkin, “Acceleration and trapping of particles by radiation pressure,” Phys. Rev. Lett. 24, 156 (1970).
    [Crossref]
  2. D.G. Grier, “A revolution in optical manipulation,” Nature 424, 810(2003).
    [Crossref] [PubMed]
  3. L. Novotny, R. X. Bian, and X. S. Xie, “Theory of Nanometric Optical Tweezers,” Phys. Rev. Lett. 79, 645(1997).
    [Crossref]
  4. a. Taflove, Computation Electrodynamics: The Finite Difference Time Domain Method (Norwood, MA, Artech House, 1995).
  5. J. D. Jackson, Classical Electrodynamics (Wiley, New York, 1962).
  6. J. P. Berenger, “Three-dimensional perfectly matched layer for the absorption of electromagnetic waves,” J. Comput. Phys. 127, 363(1996).
    [Crossref]
  7. M. E. J. Friese, J. Enger, H. Rubinsztein-Dunlop, and N. R. Heckenberg, “Optical angular-momentum transfer to trapped absorbing particles,” Phys. Rev. A 54, 1593(1996).
    [Crossref] [PubMed]
  8. M. E. J. Friese, T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Optical alignment and spinning of laser-trapped microscopic particles,” Nature 395, 621(1998).
    [Crossref]
  9. H. He, M. E. J. Friese, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Direct Observation of Transfer of Angular Momentum to Absorptive Particles from a Laser Beam with a Phase Singularity,” Phys. Rev. Lett. 75, 826(1995).
    [Crossref] [PubMed]

2003 (1)

D.G. Grier, “A revolution in optical manipulation,” Nature 424, 810(2003).
[Crossref] [PubMed]

1998 (1)

M. E. J. Friese, T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Optical alignment and spinning of laser-trapped microscopic particles,” Nature 395, 621(1998).
[Crossref]

1997 (1)

L. Novotny, R. X. Bian, and X. S. Xie, “Theory of Nanometric Optical Tweezers,” Phys. Rev. Lett. 79, 645(1997).
[Crossref]

1996 (2)

J. P. Berenger, “Three-dimensional perfectly matched layer for the absorption of electromagnetic waves,” J. Comput. Phys. 127, 363(1996).
[Crossref]

M. E. J. Friese, J. Enger, H. Rubinsztein-Dunlop, and N. R. Heckenberg, “Optical angular-momentum transfer to trapped absorbing particles,” Phys. Rev. A 54, 1593(1996).
[Crossref] [PubMed]

1995 (1)

H. He, M. E. J. Friese, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Direct Observation of Transfer of Angular Momentum to Absorptive Particles from a Laser Beam with a Phase Singularity,” Phys. Rev. Lett. 75, 826(1995).
[Crossref] [PubMed]

1970 (1)

A. Ashkin, “Acceleration and trapping of particles by radiation pressure,” Phys. Rev. Lett. 24, 156 (1970).
[Crossref]

Ashkin, A.

A. Ashkin, “Acceleration and trapping of particles by radiation pressure,” Phys. Rev. Lett. 24, 156 (1970).
[Crossref]

Berenger, J. P.

J. P. Berenger, “Three-dimensional perfectly matched layer for the absorption of electromagnetic waves,” J. Comput. Phys. 127, 363(1996).
[Crossref]

Bian, R. X.

L. Novotny, R. X. Bian, and X. S. Xie, “Theory of Nanometric Optical Tweezers,” Phys. Rev. Lett. 79, 645(1997).
[Crossref]

Enger, J.

M. E. J. Friese, J. Enger, H. Rubinsztein-Dunlop, and N. R. Heckenberg, “Optical angular-momentum transfer to trapped absorbing particles,” Phys. Rev. A 54, 1593(1996).
[Crossref] [PubMed]

Friese, M. E. J.

M. E. J. Friese, T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Optical alignment and spinning of laser-trapped microscopic particles,” Nature 395, 621(1998).
[Crossref]

M. E. J. Friese, J. Enger, H. Rubinsztein-Dunlop, and N. R. Heckenberg, “Optical angular-momentum transfer to trapped absorbing particles,” Phys. Rev. A 54, 1593(1996).
[Crossref] [PubMed]

H. He, M. E. J. Friese, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Direct Observation of Transfer of Angular Momentum to Absorptive Particles from a Laser Beam with a Phase Singularity,” Phys. Rev. Lett. 75, 826(1995).
[Crossref] [PubMed]

Grier, D.G.

D.G. Grier, “A revolution in optical manipulation,” Nature 424, 810(2003).
[Crossref] [PubMed]

He, H.

H. He, M. E. J. Friese, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Direct Observation of Transfer of Angular Momentum to Absorptive Particles from a Laser Beam with a Phase Singularity,” Phys. Rev. Lett. 75, 826(1995).
[Crossref] [PubMed]

Heckenberg, N. R.

M. E. J. Friese, T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Optical alignment and spinning of laser-trapped microscopic particles,” Nature 395, 621(1998).
[Crossref]

M. E. J. Friese, J. Enger, H. Rubinsztein-Dunlop, and N. R. Heckenberg, “Optical angular-momentum transfer to trapped absorbing particles,” Phys. Rev. A 54, 1593(1996).
[Crossref] [PubMed]

H. He, M. E. J. Friese, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Direct Observation of Transfer of Angular Momentum to Absorptive Particles from a Laser Beam with a Phase Singularity,” Phys. Rev. Lett. 75, 826(1995).
[Crossref] [PubMed]

Jackson, J. D.

J. D. Jackson, Classical Electrodynamics (Wiley, New York, 1962).

Nieminen, T. A.

M. E. J. Friese, T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Optical alignment and spinning of laser-trapped microscopic particles,” Nature 395, 621(1998).
[Crossref]

Novotny, L.

L. Novotny, R. X. Bian, and X. S. Xie, “Theory of Nanometric Optical Tweezers,” Phys. Rev. Lett. 79, 645(1997).
[Crossref]

Rubinsztein-Dunlop, H.

M. E. J. Friese, T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Optical alignment and spinning of laser-trapped microscopic particles,” Nature 395, 621(1998).
[Crossref]

M. E. J. Friese, J. Enger, H. Rubinsztein-Dunlop, and N. R. Heckenberg, “Optical angular-momentum transfer to trapped absorbing particles,” Phys. Rev. A 54, 1593(1996).
[Crossref] [PubMed]

H. He, M. E. J. Friese, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Direct Observation of Transfer of Angular Momentum to Absorptive Particles from a Laser Beam with a Phase Singularity,” Phys. Rev. Lett. 75, 826(1995).
[Crossref] [PubMed]

Taflove, a.

a. Taflove, Computation Electrodynamics: The Finite Difference Time Domain Method (Norwood, MA, Artech House, 1995).

Xie, X. S.

L. Novotny, R. X. Bian, and X. S. Xie, “Theory of Nanometric Optical Tweezers,” Phys. Rev. Lett. 79, 645(1997).
[Crossref]

J. Comput. Phys. (1)

J. P. Berenger, “Three-dimensional perfectly matched layer for the absorption of electromagnetic waves,” J. Comput. Phys. 127, 363(1996).
[Crossref]

Nature (2)

M. E. J. Friese, T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Optical alignment and spinning of laser-trapped microscopic particles,” Nature 395, 621(1998).
[Crossref]

D.G. Grier, “A revolution in optical manipulation,” Nature 424, 810(2003).
[Crossref] [PubMed]

Phys. Rev. A (1)

M. E. J. Friese, J. Enger, H. Rubinsztein-Dunlop, and N. R. Heckenberg, “Optical angular-momentum transfer to trapped absorbing particles,” Phys. Rev. A 54, 1593(1996).
[Crossref] [PubMed]

Phys. Rev. Lett. (3)

H. He, M. E. J. Friese, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Direct Observation of Transfer of Angular Momentum to Absorptive Particles from a Laser Beam with a Phase Singularity,” Phys. Rev. Lett. 75, 826(1995).
[Crossref] [PubMed]

L. Novotny, R. X. Bian, and X. S. Xie, “Theory of Nanometric Optical Tweezers,” Phys. Rev. Lett. 79, 645(1997).
[Crossref]

A. Ashkin, “Acceleration and trapping of particles by radiation pressure,” Phys. Rev. Lett. 24, 156 (1970).
[Crossref]

Other (2)

a. Taflove, Computation Electrodynamics: The Finite Difference Time Domain Method (Norwood, MA, Artech House, 1995).

J. D. Jackson, Classical Electrodynamics (Wiley, New York, 1962).

Supplementary Material (7)

» Media 1: GIF (200 KB)     
» Media 2: GIF (163 KB)     
» Media 3: GIF (134 KB)     
» Media 4: GIF (177 KB)     
» Media 5: GIF (178 KB)     
» Media 6: GIF (45 KB)     
» Media 7: GIF (355 KB)     

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Figures (7)

Fig. 1.
Fig. 1. The modal of laser trapping for computer simulations.

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Fig. 2.
Fig. 2. (a) The incident wave form. (b) The main electric field component E y in sequential time steps with the propagation of a focused negative single sine pulse wave in water. (c) The two vector components S x and S z of momentum flux of the incident single sine pulse passed through the MTR.

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Fig. 3.
Fig. 3. (a) The main electric field component E y of a focused negative single sine pulse wave in the water when it strikes on a sphere particle with a higher refractive index than that of environment. (b) The two vector components S x and S z of momentum flux of the incident single sine pulse passing through the MTR. [Media 1]

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Fig. 4.
Fig. 4. (a) The main electric field component E y of a focused negative single sine pulse wave in water when it strikes on an air bubble. [Media 2] (b) The two vector components S x and S z of momentum flux of the incident single sine pulse passing through the MTR.

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Fig. 5.
Fig. 5. (a) The main electric field component E y of a focused negative single sine pulse wave in water strikes on a sphere particle with a high reflection coefficient. [Media 3] (b) The two vector components S x and S z of momentum flux of the incident single sine pulse passing through the MTR.

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Fig. 6.
Fig. 6. (a) Incident Gaussian optical vortex pulse. (b) Propagation of Poynting Vector in the x-z plane (y = 0), (b-1) for topological index l=1 [Media 4] and (b-2) l=3. [Media 5] (c) Continuous rotation movement of Poynting vector on the focusing plane in sequential time steps. [Media 6]

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Fig. 7.
Fig. 7. (a) The main electric field E y varies in the sequential time steps when a focused optical vortex shines in the high refractive index sphere particle. Here the topological index of optical vortex is taken to 1. [Media 7] (b) The three vector components S x, S y and S z of momentum flux of the incident light with the different topological index l passing through the MTR.

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Tables (3)

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Table 1. Momentum transfer in the laser trapping of the focused single sine wave

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Table 2. Momentum transfer between the E y polarized incident optical vortex with the different topological order l and the sphere particle in a fixed position (685nm, 0nm, 959nm).

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Table 3. Momentum exchange between the E y polarized incident optical vortex and the sphere particle in the three different positions of laser trapping space.

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Equations (2)

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d P d A = ( n c ) S ,
F = n c ∫ ∫ Δ S · dA ,

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