Abstract

Cylindrical micro-objects with inclined end surfaces have been observed to be optically trapped in a focused laser beam and to rotate about the beam’s propagation direction. A simplified vector model is developed that accounts for the observed effect; the enhanced ray-optics model is used to simulate the behavior of time evolution for the cylindrical object in the beam. Experimental laser trap configurations are presented, along with a video image sequence of the cylinder’s precession.

© 2001 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, 156–159 (1970).
    [CrossRef]
  2. A. Ashkin, J. M. Dziedzic, J. E. Bjorkholm, S. Chu, “Observation of a single-beam gradient force optical trap for dielectric particles,” Opt. Lett. 11, 288–290 (1986).
    [CrossRef] [PubMed]
  3. S. C. Kuo, M. P. Sheetz, “Optical tweezers in cell biology,” Trends Cell Biol. 2, 117–118 (1992).
  4. S. Sato, H. Inaba, “Optical trapping and manipulation of microscopic particles and biological cells by laser beams,” Opt. Quantum Electron. 28, 1–16 (1996).
    [CrossRef]
  5. A. Ashkin, “Optical trapping and manipulation of neutral particles using lasers,” Opt. Photon. News 10(5), 41–46 (1999).
    [CrossRef]
  6. T. Tlusty, A. Meller, R. Bar-Ziv, “Optical gradient forces of strongly localized fields,” Phys. Rev. Lett. 81, 1738–1741 (1998).
    [CrossRef]
  7. K. D. Crawford, K. D. Hughes, “Raman vibrational evidence for the presence of conjugated regions in individual micron diameter polystyrene particles irradiated with visible radiation,” J. Phys. Chem. B 102, 2325–2328 (1998).
    [CrossRef]
  8. E. Higurashi, O. Ohguchi, H. Ukita, “Optical trapping of low-refractive-index microfabricated objects using radiation pressure exerted on their inner walls,” Opt. Lett. 20, 1931–1933 (1995).
    [CrossRef] [PubMed]
  9. E. Higurashi, O. Ohguchi, T. Tamamura, H. Ukita, R. Sawada, “Optically induced rotation of dissymmetrically shaped fluorinated polyimide micro-objects in optical traps,” J. Appl. Phys. 82, 2773–2779 (1997).
    [CrossRef]
  10. R. C. Gauthier, “Theoretical investigation of the optical trapping force and torque on cylindrical micro-objects,” J. Opt. Soc. Am. B 14, 3323–3333 (1997).
    [CrossRef]
  11. R. C. Gauthier, M. Ashman, A. Frangioudakis, H. Mende, S. Ma, “Radiation-pressure-based cylindrically shaped microactuator capable of smooth, continuous, reversible, and stepped rotation,” Appl. Opt. 38, 4850–4860 (1999).
    [CrossRef]
  12. R. C. Gauthier, M. Ashman, C. P. Grover, “Experimental confirmation of the optical-trapping properties of cylindrical objects,” Appl. Opt. 38, 4861–4869 (1999).
    [CrossRef]
  13. E. Higurashi, H. Ukita, H. Tanaka, O. Ochguchi, “Rotational control of anisotropic micro-objects by radiation pressure,” in Proceedings of IEEE Micro Electro Mechanical Systems ’94 (Institute of Electrical and Electronics Engineers, New York, 1994), pp. 291–296.
  14. K. F. Ren, G. Gréhan, G. Gouesbet, “Prediction of the reverse radiation pressure by generalized Lorenz–Mie theory,” Appl. Opt. 35, 2702–2710 (1996).
    [CrossRef] [PubMed]
  15. A. Ashkin, “Forces of a single-beam gradient laser trap on a dielectric sphere in the ray optics regime,” J. Biophys. 61, 569–582 (1992).
    [CrossRef]
  16. R. C. Gauthier, S. Wallace, “Optical levitation of spheres: analytical development and numerical computations of the force equations,” J. Opt. Soc. Am. B 12, 1680–1685 (1995).
    [CrossRef]
  17. R. C. Gauthier, “Trapping model for the low-index ring-shaped micro-object in a focused, lowest-order Gaussian laser-beam profile,” J. Opt. Soc. Am. B 14, 782–789 (1997).
    [CrossRef]
  18. R. C. Gauthier, M. Ashman, “Simulated dynamic behavior of single and multiple spheres in the trap region of focused laser beams,” Appl. Opt. 37, 6421–6430 (1998).
    [CrossRef]
  19. B. E. A. Saleh, M. C. Teich, Fundamentals of Photonics (Wiley, New York, 1991).
    [CrossRef]
  20. P. L. Marston, J. H. Crichton, “Radiation torque on a sphere caused by a circularly-polarized electromagnetic wave,” Phys. Rev. A 30, 2508–2516 (1985).
    [CrossRef]
  21. R. C. Gauthier, A. Frangioudakis, “Optical levitation particle delivery system for a dual beam fiber optic trap,” Appl. Opt. 39, 26–33 (2000).
    [CrossRef]
  22. R. C. Gauthier, A. Frangioudakis, “Theoretical investigation of the optical trapping properties of a micro-optic cube glass structure,” Appl. Opt. 39, 3060–3070 (2000).
    [CrossRef]
  23. J. S. Kim, S. W. Kim, “Dynamic motion analysis of optically trapped nonspherical particles with off-axis position and arbitrary orientation,” Appl. Opt. 39, 4327–4332 (2000).
    [CrossRef]
  24. I. A. Kholeif, M. H. Kamel, M. A. Atwa, “The deceleration of a cylinder in an infinite viscous fluid,” Energy Convers. Manage. 34, 235–237 (1993).
    [CrossRef]
  25. I. A. Kholeif, M. H. Kamel, “The deceleration of a sphere in an infinite viscous fluid,” Energy Convers. Manage. 34, 239–241 (1993).
    [CrossRef]
  26. M. H. Kamel, “The deceleration of two hollow concentric infinite cylinders submerged in three fluids with different viscosities,” Energy Convers. Manage. 34, 1319–1322 (1993).
    [CrossRef]

2000 (3)

1999 (3)

1998 (3)

T. Tlusty, A. Meller, R. Bar-Ziv, “Optical gradient forces of strongly localized fields,” Phys. Rev. Lett. 81, 1738–1741 (1998).
[CrossRef]

K. D. Crawford, K. D. Hughes, “Raman vibrational evidence for the presence of conjugated regions in individual micron diameter polystyrene particles irradiated with visible radiation,” J. Phys. Chem. B 102, 2325–2328 (1998).
[CrossRef]

R. C. Gauthier, M. Ashman, “Simulated dynamic behavior of single and multiple spheres in the trap region of focused laser beams,” Appl. Opt. 37, 6421–6430 (1998).
[CrossRef]

1997 (3)

1996 (2)

K. F. Ren, G. Gréhan, G. Gouesbet, “Prediction of the reverse radiation pressure by generalized Lorenz–Mie theory,” Appl. Opt. 35, 2702–2710 (1996).
[CrossRef] [PubMed]

S. Sato, H. Inaba, “Optical trapping and manipulation of microscopic particles and biological cells by laser beams,” Opt. Quantum Electron. 28, 1–16 (1996).
[CrossRef]

1995 (2)

1993 (3)

I. A. Kholeif, M. H. Kamel, M. A. Atwa, “The deceleration of a cylinder in an infinite viscous fluid,” Energy Convers. Manage. 34, 235–237 (1993).
[CrossRef]

I. A. Kholeif, M. H. Kamel, “The deceleration of a sphere in an infinite viscous fluid,” Energy Convers. Manage. 34, 239–241 (1993).
[CrossRef]

M. H. Kamel, “The deceleration of two hollow concentric infinite cylinders submerged in three fluids with different viscosities,” Energy Convers. Manage. 34, 1319–1322 (1993).
[CrossRef]

1992 (2)

A. Ashkin, “Forces of a single-beam gradient laser trap on a dielectric sphere in the ray optics regime,” J. Biophys. 61, 569–582 (1992).
[CrossRef]

S. C. Kuo, M. P. Sheetz, “Optical tweezers in cell biology,” Trends Cell Biol. 2, 117–118 (1992).

1986 (1)

1985 (1)

P. L. Marston, J. H. Crichton, “Radiation torque on a sphere caused by a circularly-polarized electromagnetic wave,” Phys. Rev. A 30, 2508–2516 (1985).
[CrossRef]

1970 (1)

A. Ashkin, “Acceleration and trapping of particles by radiation pressure,” Phys. Rev. Lett. 24, 156–159 (1970).
[CrossRef]

Ashkin, A.

A. Ashkin, “Optical trapping and manipulation of neutral particles using lasers,” Opt. Photon. News 10(5), 41–46 (1999).
[CrossRef]

A. Ashkin, “Forces of a single-beam gradient laser trap on a dielectric sphere in the ray optics regime,” J. Biophys. 61, 569–582 (1992).
[CrossRef]

A. Ashkin, J. M. Dziedzic, J. E. Bjorkholm, S. Chu, “Observation of a single-beam gradient force optical trap for dielectric particles,” Opt. Lett. 11, 288–290 (1986).
[CrossRef] [PubMed]

A. Ashkin, “Acceleration and trapping of particles by radiation pressure,” Phys. Rev. Lett. 24, 156–159 (1970).
[CrossRef]

Ashman, M.

Atwa, M. A.

I. A. Kholeif, M. H. Kamel, M. A. Atwa, “The deceleration of a cylinder in an infinite viscous fluid,” Energy Convers. Manage. 34, 235–237 (1993).
[CrossRef]

Bar-Ziv, R.

T. Tlusty, A. Meller, R. Bar-Ziv, “Optical gradient forces of strongly localized fields,” Phys. Rev. Lett. 81, 1738–1741 (1998).
[CrossRef]

Bjorkholm, J. E.

Chu, S.

Crawford, K. D.

K. D. Crawford, K. D. Hughes, “Raman vibrational evidence for the presence of conjugated regions in individual micron diameter polystyrene particles irradiated with visible radiation,” J. Phys. Chem. B 102, 2325–2328 (1998).
[CrossRef]

Crichton, J. H.

P. L. Marston, J. H. Crichton, “Radiation torque on a sphere caused by a circularly-polarized electromagnetic wave,” Phys. Rev. A 30, 2508–2516 (1985).
[CrossRef]

Dziedzic, J. M.

Frangioudakis, A.

Gauthier, R. C.

Gouesbet, G.

Gréhan, G.

Grover, C. P.

Higurashi, E.

E. Higurashi, O. Ohguchi, T. Tamamura, H. Ukita, R. Sawada, “Optically induced rotation of dissymmetrically shaped fluorinated polyimide micro-objects in optical traps,” J. Appl. Phys. 82, 2773–2779 (1997).
[CrossRef]

E. Higurashi, O. Ohguchi, H. Ukita, “Optical trapping of low-refractive-index microfabricated objects using radiation pressure exerted on their inner walls,” Opt. Lett. 20, 1931–1933 (1995).
[CrossRef] [PubMed]

E. Higurashi, H. Ukita, H. Tanaka, O. Ochguchi, “Rotational control of anisotropic micro-objects by radiation pressure,” in Proceedings of IEEE Micro Electro Mechanical Systems ’94 (Institute of Electrical and Electronics Engineers, New York, 1994), pp. 291–296.

Hughes, K. D.

K. D. Crawford, K. D. Hughes, “Raman vibrational evidence for the presence of conjugated regions in individual micron diameter polystyrene particles irradiated with visible radiation,” J. Phys. Chem. B 102, 2325–2328 (1998).
[CrossRef]

Inaba, H.

S. Sato, H. Inaba, “Optical trapping and manipulation of microscopic particles and biological cells by laser beams,” Opt. Quantum Electron. 28, 1–16 (1996).
[CrossRef]

Kamel, M. H.

I. A. Kholeif, M. H. Kamel, “The deceleration of a sphere in an infinite viscous fluid,” Energy Convers. Manage. 34, 239–241 (1993).
[CrossRef]

M. H. Kamel, “The deceleration of two hollow concentric infinite cylinders submerged in three fluids with different viscosities,” Energy Convers. Manage. 34, 1319–1322 (1993).
[CrossRef]

I. A. Kholeif, M. H. Kamel, M. A. Atwa, “The deceleration of a cylinder in an infinite viscous fluid,” Energy Convers. Manage. 34, 235–237 (1993).
[CrossRef]

Kholeif, I. A.

I. A. Kholeif, M. H. Kamel, “The deceleration of a sphere in an infinite viscous fluid,” Energy Convers. Manage. 34, 239–241 (1993).
[CrossRef]

I. A. Kholeif, M. H. Kamel, M. A. Atwa, “The deceleration of a cylinder in an infinite viscous fluid,” Energy Convers. Manage. 34, 235–237 (1993).
[CrossRef]

Kim, J. S.

Kim, S. W.

Kuo, S. C.

S. C. Kuo, M. P. Sheetz, “Optical tweezers in cell biology,” Trends Cell Biol. 2, 117–118 (1992).

Ma, S.

Marston, P. L.

P. L. Marston, J. H. Crichton, “Radiation torque on a sphere caused by a circularly-polarized electromagnetic wave,” Phys. Rev. A 30, 2508–2516 (1985).
[CrossRef]

Meller, A.

T. Tlusty, A. Meller, R. Bar-Ziv, “Optical gradient forces of strongly localized fields,” Phys. Rev. Lett. 81, 1738–1741 (1998).
[CrossRef]

Mende, H.

Ochguchi, O.

E. Higurashi, H. Ukita, H. Tanaka, O. Ochguchi, “Rotational control of anisotropic micro-objects by radiation pressure,” in Proceedings of IEEE Micro Electro Mechanical Systems ’94 (Institute of Electrical and Electronics Engineers, New York, 1994), pp. 291–296.

Ohguchi, O.

E. Higurashi, O. Ohguchi, T. Tamamura, H. Ukita, R. Sawada, “Optically induced rotation of dissymmetrically shaped fluorinated polyimide micro-objects in optical traps,” J. Appl. Phys. 82, 2773–2779 (1997).
[CrossRef]

E. Higurashi, O. Ohguchi, H. Ukita, “Optical trapping of low-refractive-index microfabricated objects using radiation pressure exerted on their inner walls,” Opt. Lett. 20, 1931–1933 (1995).
[CrossRef] [PubMed]

Ren, K. F.

Saleh, B. E. A.

B. E. A. Saleh, M. C. Teich, Fundamentals of Photonics (Wiley, New York, 1991).
[CrossRef]

Sato, S.

S. Sato, H. Inaba, “Optical trapping and manipulation of microscopic particles and biological cells by laser beams,” Opt. Quantum Electron. 28, 1–16 (1996).
[CrossRef]

Sawada, R.

E. Higurashi, O. Ohguchi, T. Tamamura, H. Ukita, R. Sawada, “Optically induced rotation of dissymmetrically shaped fluorinated polyimide micro-objects in optical traps,” J. Appl. Phys. 82, 2773–2779 (1997).
[CrossRef]

Sheetz, M. P.

S. C. Kuo, M. P. Sheetz, “Optical tweezers in cell biology,” Trends Cell Biol. 2, 117–118 (1992).

Tamamura, T.

E. Higurashi, O. Ohguchi, T. Tamamura, H. Ukita, R. Sawada, “Optically induced rotation of dissymmetrically shaped fluorinated polyimide micro-objects in optical traps,” J. Appl. Phys. 82, 2773–2779 (1997).
[CrossRef]

Tanaka, H.

E. Higurashi, H. Ukita, H. Tanaka, O. Ochguchi, “Rotational control of anisotropic micro-objects by radiation pressure,” in Proceedings of IEEE Micro Electro Mechanical Systems ’94 (Institute of Electrical and Electronics Engineers, New York, 1994), pp. 291–296.

Teich, M. C.

B. E. A. Saleh, M. C. Teich, Fundamentals of Photonics (Wiley, New York, 1991).
[CrossRef]

Tlusty, T.

T. Tlusty, A. Meller, R. Bar-Ziv, “Optical gradient forces of strongly localized fields,” Phys. Rev. Lett. 81, 1738–1741 (1998).
[CrossRef]

Ukita, H.

E. Higurashi, O. Ohguchi, T. Tamamura, H. Ukita, R. Sawada, “Optically induced rotation of dissymmetrically shaped fluorinated polyimide micro-objects in optical traps,” J. Appl. Phys. 82, 2773–2779 (1997).
[CrossRef]

E. Higurashi, O. Ohguchi, H. Ukita, “Optical trapping of low-refractive-index microfabricated objects using radiation pressure exerted on their inner walls,” Opt. Lett. 20, 1931–1933 (1995).
[CrossRef] [PubMed]

E. Higurashi, H. Ukita, H. Tanaka, O. Ochguchi, “Rotational control of anisotropic micro-objects by radiation pressure,” in Proceedings of IEEE Micro Electro Mechanical Systems ’94 (Institute of Electrical and Electronics Engineers, New York, 1994), pp. 291–296.

Wallace, S.

Appl. Opt. (7)

Energy Convers. Manage. (3)

I. A. Kholeif, M. H. Kamel, M. A. Atwa, “The deceleration of a cylinder in an infinite viscous fluid,” Energy Convers. Manage. 34, 235–237 (1993).
[CrossRef]

I. A. Kholeif, M. H. Kamel, “The deceleration of a sphere in an infinite viscous fluid,” Energy Convers. Manage. 34, 239–241 (1993).
[CrossRef]

M. H. Kamel, “The deceleration of two hollow concentric infinite cylinders submerged in three fluids with different viscosities,” Energy Convers. Manage. 34, 1319–1322 (1993).
[CrossRef]

J. Appl. Phys. (1)

E. Higurashi, O. Ohguchi, T. Tamamura, H. Ukita, R. Sawada, “Optically induced rotation of dissymmetrically shaped fluorinated polyimide micro-objects in optical traps,” J. Appl. Phys. 82, 2773–2779 (1997).
[CrossRef]

J. Biophys. (1)

A. Ashkin, “Forces of a single-beam gradient laser trap on a dielectric sphere in the ray optics regime,” J. Biophys. 61, 569–582 (1992).
[CrossRef]

J. Opt. Soc. Am. B (3)

J. Phys. Chem. B (1)

K. D. Crawford, K. D. Hughes, “Raman vibrational evidence for the presence of conjugated regions in individual micron diameter polystyrene particles irradiated with visible radiation,” J. Phys. Chem. B 102, 2325–2328 (1998).
[CrossRef]

Opt. Lett. (2)

Opt. Photon. News (1)

A. Ashkin, “Optical trapping and manipulation of neutral particles using lasers,” Opt. Photon. News 10(5), 41–46 (1999).
[CrossRef]

Opt. Quantum Electron. (1)

S. Sato, H. Inaba, “Optical trapping and manipulation of microscopic particles and biological cells by laser beams,” Opt. Quantum Electron. 28, 1–16 (1996).
[CrossRef]

Phys. Rev. A (1)

P. L. Marston, J. H. Crichton, “Radiation torque on a sphere caused by a circularly-polarized electromagnetic wave,” Phys. Rev. A 30, 2508–2516 (1985).
[CrossRef]

Phys. Rev. Lett. (2)

A. Ashkin, “Acceleration and trapping of particles by radiation pressure,” Phys. Rev. Lett. 24, 156–159 (1970).
[CrossRef]

T. Tlusty, A. Meller, R. Bar-Ziv, “Optical gradient forces of strongly localized fields,” Phys. Rev. Lett. 81, 1738–1741 (1998).
[CrossRef]

Trends Cell Biol. (1)

S. C. Kuo, M. P. Sheetz, “Optical tweezers in cell biology,” Trends Cell Biol. 2, 117–118 (1992).

Other (2)

E. Higurashi, H. Ukita, H. Tanaka, O. Ochguchi, “Rotational control of anisotropic micro-objects by radiation pressure,” in Proceedings of IEEE Micro Electro Mechanical Systems ’94 (Institute of Electrical and Electronics Engineers, New York, 1994), pp. 291–296.

B. E. A. Saleh, M. C. Teich, Fundamentals of Photonics (Wiley, New York, 1991).
[CrossRef]

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Figures (14)

Fig. 1
Fig. 1

Cylinder illuminated with a focused laser beam. The surface normals for the top and bottom end surfaces are shown, along with the direction cosines of the cylinder’s central axis. Inset, the reflection and refraction process at one intercept point. The angles of incidence and refraction are shown, along with the direction cosine related to each photon stream.

Fig. 2
Fig. 2

Cylinders with inclined end surfaces. The axis of the cylinder is in the (X, Z) plane: (a) inclined end surfaces are in the same direction and produce torque components that add, inducing the cylinder to precess the Z axis; (b) the inclined end surfaces are in opposite directions and produce torque components that cancel, and no precession about the Z axis is possible.

Fig. 3
Fig. 3

Z-axis torque versus relative rotation angle of 45-deg inclined end surface cylinders. The Z-axis torque value is taken when the cylinder’s rotation about the Z axis is uniform.

Fig. 4
Fig. 4

Z-axis torque computed with the enhanced ray-optics model versus end-surface inclination angle when the relative rotation angle is 90 deg. From 0 to 60 deg the Z-axis torque curve follows that of the cosine of the inclination angle curve. For angles larger than 60 deg the simplified vector model description is no longer valid, and deviations from model predictions are observed.

Fig. 5
Fig. 5

Precession angle versus time and damping factor for the cylinder with 45-deg inclined end surfaces and 90-deg relative rotation angle. The damping factor range covers those expected in experiments.

Fig. 6
Fig. 6

Precession angular velocity versus time for the cylinder of Fig. 5.

Fig. 7
Fig. 7

Precession angular acceleration versus time for the cylinder of Fig. 5. For damping factors b ≥ 30I the acceleration of the cylinder stops, and a constant rotation rate is expected afterward.

Fig. 8
Fig. 8

X-, Y-, and Z-axis direction cosines for the central axis of the cylinder of Fig. 5. The cylinder precesses at a constant rate in the CW direction.

Fig. 9
Fig. 9

Same as Fig. 8, except that the relative rotation angle is -90 deg between the end surfaces. This cylinder rotates in the CCW direction.

Fig. 10
Fig. 10

Typical micro-optic cylinders used in the experiments. Cylinders are of various lengths, and a fracture process dictates the end-surface finish.

Fig. 11
Fig. 11

Block diagram of the experimental top-down configuration.

Fig. 12
Fig. 12

Sequence of video images showing the rotation of one of the special inclined end-surface cylinders in the CCW direction. In (a) the cylinder is shown on edge; in (b)–(p) the cylinder has aligned diagonally to the laser beam axis and is set to precess the Z axis. It drags along the larger cylinder as it rotates.

Fig. 13
Fig. 13

Block diagram of the experimental bottom-up configuration.

Fig. 14
Fig. 14

Sequence of video images showing the stable levitation and precession of a cylindrical object. The scattered light is observed to sweep 360 deg in the plane of the sample chamber’s base. The direction of rotation is CW. The optical fibers are components of a dual-beam optical fiber trap and were not used in these experiments.

Equations (18)

Equations on this page are rendered with MathJax. Learn more.

RTE=|rTE|2=nin cosθin-nout cosθoutnin cosθin+nout cosθout2, TTE=|tTE|2=1-|rTE|2, RTM=|rTM|2=nout cosθin-nin cosθoutnout cosθin+nin cosθout2, TTM=|tTM|2=1-|rTM|2,
Rave=RTE+RTM/2.
dPr=hλo ninlo-lrxˆ+mo-mryˆ+no-nrzˆ,
dPt=hλo ninlo-noutnin ltxˆ+mo-noutnin mtyˆ+no-noutnin ntzˆ.
Ix, y, z=2PπWz2exp-2x2+y2Wz2,
Ni=Ix, y, zdAE,
F=APIdFi=API NiRavedPr+1-RavedPt.
ri=xi-xoxˆ+yi-yoyˆ+zi-zozˆ.
τ=APIdτi=APIri×dFi.
τT=RT×FT=L/2FTMoCT-NoBT, NoAT-LoCT, LoBT-MoAT
τB=RB×FB=L/2FBNoBB-MoCB, LoCB-NoAB, MoAB-LoBB
τ=τbody+τT+τB.
τz=L/2LoFTBT-FBBB+MoFBAB-FTAT.
τz=L/2LoFTBT-FBBB.
2θtt2+bIθtt-τzI=0.
θt=τztb+τzIb2exp-btI-1
ωt=τzb1-exp-btI
αt=τzIexp-btI

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