Abstract

The characteristics of the optical trapping force, optical torque, and viscous drag force for a newly proposed cylindrical optical rotator are analyzed. The optical trapping force and torque are evaluated by use of a ray optics model for both parallel and focused laser beam illumination. The drag force is calculated from computational fluid dynamics to be the sum of the components of both the pressure and the shearing stress on all the surfaces of the rotator. We analyze the rotation rate by balancing the optical torque with the drag force. A cylindrical optical rotator is expected to rotate at a high speed because of its highly efficient generation of optical torque and its small viscous drag force.

© 2003 Optical Society of America

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References

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  1. E. Higurashi, H. Ukita, H. Tanaka, O. Ohguchi, “Optically induced rotation of micro-objects fabricated by surface micromachining,” Appl. Phys. Lett. 64, 2209–2210 (1994).
    [CrossRef]
  2. R. C. Gauthier, “Ray optics model and numerical computation for the radiation pressure micromotor,” Appl. Phys. Lett. 67, 2269–2271 (1995).
    [CrossRef]
  3. Y. Ohmachi, K. Baba, E. Higurashi, “Numerical analysis of an optical motor based on the radiation pressure,” in Micromachined Devices and Components II, K. Chao, M. Roop, eds., Proc. SPIE2882, 333–338 (1996).
    [CrossRef]
  4. H. Ukita, K. Nagatomi, “Theoretical demonstration of a micro-rotator driven by optical pressure on the light incident surface,” Opt. Rev. 4, 447–449 (1997).
    [CrossRef]
  5. 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]
  6. P. Galajda, P. Ormos, “Complex micromachines produced and driven by light,” Appl. Phys. Lett. 78, 249–251 (2001).
    [CrossRef]
  7. M. E. J. Friese, H. Rubinsztein-Dunlop, “Optically driven micromachine elements,” Appl. Phys. Lett. 78, 547–549 (2001).
    [CrossRef]
  8. S. Maruo, K. Ikuta, K. Hayato, “Light-driven MEMS made by high-speed two-photon microstereolithography,” presented at the Meeting on Micro Electro Mechanical Systems, Interlaken, Switzerland, 21–25 January, 2001.
  9. H. Ukita, M. Kanehira, “A shuttlecock optical rotator—its design, fabrication and evaluation for a micro-fluidic mixer,” IEEE J. Sel. Top. Quantum Electron. 8, 111–117 (2002).
    [CrossRef]
  10. K. Nagatomi, H. Ukita, “Improvement in optical rotation rate of a cylindrical micro-objects by incident beam profiles,” presented at the Conference on Optical MEMS and Their Applications (MOEMS ’97), Nara, Japan, 18–21 November 1997.
  11. K. Nagumo, Y. Ogami, K. Nagatomi, H. Ukita, “Investigation on mixing performance by a shuttlecock optical micro-rotor,” presented at the 8th International Symposium on Transport Phenomena and Dynamics of Rotating Machinery, ISROMAC-8, Honolulu, Hawaii, 26–30 March 2000.

2002 (1)

H. Ukita, M. Kanehira, “A shuttlecock optical rotator—its design, fabrication and evaluation for a micro-fluidic mixer,” IEEE J. Sel. Top. Quantum Electron. 8, 111–117 (2002).
[CrossRef]

2001 (2)

P. Galajda, P. Ormos, “Complex micromachines produced and driven by light,” Appl. Phys. Lett. 78, 249–251 (2001).
[CrossRef]

M. E. J. Friese, H. Rubinsztein-Dunlop, “Optically driven micromachine elements,” Appl. Phys. Lett. 78, 547–549 (2001).
[CrossRef]

1997 (2)

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]

H. Ukita, K. Nagatomi, “Theoretical demonstration of a micro-rotator driven by optical pressure on the light incident surface,” Opt. Rev. 4, 447–449 (1997).
[CrossRef]

1995 (1)

R. C. Gauthier, “Ray optics model and numerical computation for the radiation pressure micromotor,” Appl. Phys. Lett. 67, 2269–2271 (1995).
[CrossRef]

1994 (1)

E. Higurashi, H. Ukita, H. Tanaka, O. Ohguchi, “Optically induced rotation of micro-objects fabricated by surface micromachining,” Appl. Phys. Lett. 64, 2209–2210 (1994).
[CrossRef]

Baba, K.

Y. Ohmachi, K. Baba, E. Higurashi, “Numerical analysis of an optical motor based on the radiation pressure,” in Micromachined Devices and Components II, K. Chao, M. Roop, eds., Proc. SPIE2882, 333–338 (1996).
[CrossRef]

Friese, M. E. J.

M. E. J. Friese, H. Rubinsztein-Dunlop, “Optically driven micromachine elements,” Appl. Phys. Lett. 78, 547–549 (2001).
[CrossRef]

Galajda, P.

P. Galajda, P. Ormos, “Complex micromachines produced and driven by light,” Appl. Phys. Lett. 78, 249–251 (2001).
[CrossRef]

Gauthier, R. C.

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]

R. C. Gauthier, “Ray optics model and numerical computation for the radiation pressure micromotor,” Appl. Phys. Lett. 67, 2269–2271 (1995).
[CrossRef]

Hayato, K.

S. Maruo, K. Ikuta, K. Hayato, “Light-driven MEMS made by high-speed two-photon microstereolithography,” presented at the Meeting on Micro Electro Mechanical Systems, Interlaken, Switzerland, 21–25 January, 2001.

Higurashi, E.

E. Higurashi, H. Ukita, H. Tanaka, O. Ohguchi, “Optically induced rotation of micro-objects fabricated by surface micromachining,” Appl. Phys. Lett. 64, 2209–2210 (1994).
[CrossRef]

Y. Ohmachi, K. Baba, E. Higurashi, “Numerical analysis of an optical motor based on the radiation pressure,” in Micromachined Devices and Components II, K. Chao, M. Roop, eds., Proc. SPIE2882, 333–338 (1996).
[CrossRef]

Ikuta, K.

S. Maruo, K. Ikuta, K. Hayato, “Light-driven MEMS made by high-speed two-photon microstereolithography,” presented at the Meeting on Micro Electro Mechanical Systems, Interlaken, Switzerland, 21–25 January, 2001.

Kanehira, M.

H. Ukita, M. Kanehira, “A shuttlecock optical rotator—its design, fabrication and evaluation for a micro-fluidic mixer,” IEEE J. Sel. Top. Quantum Electron. 8, 111–117 (2002).
[CrossRef]

Maruo, S.

S. Maruo, K. Ikuta, K. Hayato, “Light-driven MEMS made by high-speed two-photon microstereolithography,” presented at the Meeting on Micro Electro Mechanical Systems, Interlaken, Switzerland, 21–25 January, 2001.

Nagatomi, K.

H. Ukita, K. Nagatomi, “Theoretical demonstration of a micro-rotator driven by optical pressure on the light incident surface,” Opt. Rev. 4, 447–449 (1997).
[CrossRef]

K. Nagumo, Y. Ogami, K. Nagatomi, H. Ukita, “Investigation on mixing performance by a shuttlecock optical micro-rotor,” presented at the 8th International Symposium on Transport Phenomena and Dynamics of Rotating Machinery, ISROMAC-8, Honolulu, Hawaii, 26–30 March 2000.

K. Nagatomi, H. Ukita, “Improvement in optical rotation rate of a cylindrical micro-objects by incident beam profiles,” presented at the Conference on Optical MEMS and Their Applications (MOEMS ’97), Nara, Japan, 18–21 November 1997.

Nagumo, K.

K. Nagumo, Y. Ogami, K. Nagatomi, H. Ukita, “Investigation on mixing performance by a shuttlecock optical micro-rotor,” presented at the 8th International Symposium on Transport Phenomena and Dynamics of Rotating Machinery, ISROMAC-8, Honolulu, Hawaii, 26–30 March 2000.

Ogami, Y.

K. Nagumo, Y. Ogami, K. Nagatomi, H. Ukita, “Investigation on mixing performance by a shuttlecock optical micro-rotor,” presented at the 8th International Symposium on Transport Phenomena and Dynamics of Rotating Machinery, ISROMAC-8, Honolulu, Hawaii, 26–30 March 2000.

Ohguchi, O.

E. Higurashi, H. Ukita, H. Tanaka, O. Ohguchi, “Optically induced rotation of micro-objects fabricated by surface micromachining,” Appl. Phys. Lett. 64, 2209–2210 (1994).
[CrossRef]

Ohmachi, Y.

Y. Ohmachi, K. Baba, E. Higurashi, “Numerical analysis of an optical motor based on the radiation pressure,” in Micromachined Devices and Components II, K. Chao, M. Roop, eds., Proc. SPIE2882, 333–338 (1996).
[CrossRef]

Ormos, P.

P. Galajda, P. Ormos, “Complex micromachines produced and driven by light,” Appl. Phys. Lett. 78, 249–251 (2001).
[CrossRef]

Rubinsztein-Dunlop, H.

M. E. J. Friese, H. Rubinsztein-Dunlop, “Optically driven micromachine elements,” Appl. Phys. Lett. 78, 547–549 (2001).
[CrossRef]

Tanaka, H.

E. Higurashi, H. Ukita, H. Tanaka, O. Ohguchi, “Optically induced rotation of micro-objects fabricated by surface micromachining,” Appl. Phys. Lett. 64, 2209–2210 (1994).
[CrossRef]

Ukita, H.

H. Ukita, M. Kanehira, “A shuttlecock optical rotator—its design, fabrication and evaluation for a micro-fluidic mixer,” IEEE J. Sel. Top. Quantum Electron. 8, 111–117 (2002).
[CrossRef]

H. Ukita, K. Nagatomi, “Theoretical demonstration of a micro-rotator driven by optical pressure on the light incident surface,” Opt. Rev. 4, 447–449 (1997).
[CrossRef]

E. Higurashi, H. Ukita, H. Tanaka, O. Ohguchi, “Optically induced rotation of micro-objects fabricated by surface micromachining,” Appl. Phys. Lett. 64, 2209–2210 (1994).
[CrossRef]

K. Nagumo, Y. Ogami, K. Nagatomi, H. Ukita, “Investigation on mixing performance by a shuttlecock optical micro-rotor,” presented at the 8th International Symposium on Transport Phenomena and Dynamics of Rotating Machinery, ISROMAC-8, Honolulu, Hawaii, 26–30 March 2000.

K. Nagatomi, H. Ukita, “Improvement in optical rotation rate of a cylindrical micro-objects by incident beam profiles,” presented at the Conference on Optical MEMS and Their Applications (MOEMS ’97), Nara, Japan, 18–21 November 1997.

Appl. Phys. Lett. (4)

E. Higurashi, H. Ukita, H. Tanaka, O. Ohguchi, “Optically induced rotation of micro-objects fabricated by surface micromachining,” Appl. Phys. Lett. 64, 2209–2210 (1994).
[CrossRef]

R. C. Gauthier, “Ray optics model and numerical computation for the radiation pressure micromotor,” Appl. Phys. Lett. 67, 2269–2271 (1995).
[CrossRef]

P. Galajda, P. Ormos, “Complex micromachines produced and driven by light,” Appl. Phys. Lett. 78, 249–251 (2001).
[CrossRef]

M. E. J. Friese, H. Rubinsztein-Dunlop, “Optically driven micromachine elements,” Appl. Phys. Lett. 78, 547–549 (2001).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron. (1)

H. Ukita, M. Kanehira, “A shuttlecock optical rotator—its design, fabrication and evaluation for a micro-fluidic mixer,” IEEE J. Sel. Top. Quantum Electron. 8, 111–117 (2002).
[CrossRef]

J. Opt. Soc. Am. B (1)

Opt. Rev. (1)

H. Ukita, K. Nagatomi, “Theoretical demonstration of a micro-rotator driven by optical pressure on the light incident surface,” Opt. Rev. 4, 447–449 (1997).
[CrossRef]

Other (4)

K. Nagatomi, H. Ukita, “Improvement in optical rotation rate of a cylindrical micro-objects by incident beam profiles,” presented at the Conference on Optical MEMS and Their Applications (MOEMS ’97), Nara, Japan, 18–21 November 1997.

K. Nagumo, Y. Ogami, K. Nagatomi, H. Ukita, “Investigation on mixing performance by a shuttlecock optical micro-rotor,” presented at the 8th International Symposium on Transport Phenomena and Dynamics of Rotating Machinery, ISROMAC-8, Honolulu, Hawaii, 26–30 March 2000.

S. Maruo, K. Ikuta, K. Hayato, “Light-driven MEMS made by high-speed two-photon microstereolithography,” presented at the Meeting on Micro Electro Mechanical Systems, Interlaken, Switzerland, 21–25 January, 2001.

Y. Ohmachi, K. Baba, E. Higurashi, “Numerical analysis of an optical motor based on the radiation pressure,” in Micromachined Devices and Components II, K. Chao, M. Roop, eds., Proc. SPIE2882, 333–338 (1996).
[CrossRef]

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Figures (19)

Fig. 1
Fig. 1

Fundamental 3D image of shuttlecock (left) and cylindrical (right) types of optical rotator.

Fig. 2
Fig. 2

Rotation relative to the optical pressure exerted on the slopes of the cylindrical rotator.

Fig. 3
Fig. 3

Dependence of trapping efficiency on slope angle. Incident beam power, P = 100 mW; rotator diameter, 2r = 3 μm; length, h = 10 μm.

Fig. 4
Fig. 4

Dependence of rotation rate on slope angle.

Fig. 5
Fig. 5

(a) Ray tracing for the rotator illuminated with a focused beam and (b) trapping efficiency along the light beam’s axis.

Fig. 6
Fig. 6

Ray optics model of a focused laser beam, showing the beam waist. Ray tW(z) passes tW 0 at the beam waist (z = z f ), where 0 ≤ t ≤ 1.

Fig. 7
Fig. 7

Dependence of trapping efficiency Q on beam waist position z f for several NAs and slope angles a, where P = 100 mW, 2r = 3 μm, and h = 10 μm.

Fig. 8
Fig. 8

Relation between torque efficiency Q t on beam waist position z f for several NAs and slope angles a.

Fig. 9
Fig. 9

Top view of a region illuminated by a focused beam for three NAs.

Fig. 10
Fig. 10

Relationship between rotation rate and slope angle of a focused beam for the approximation M opt = 4πμr 2 hω, where M opt is the optical torque, μ is the medium’s viscosity, r is the radius, h is the length of the rotator, and ω is the angular velocity.

Fig. 11
Fig. 11

Relationship between torque efficiency Q t and beam waist position z f for several beam profiles.

Fig. 12
Fig. 12

Relationship between rotation rate and focused beam power for several profiles; diameter 2r = 3 μm and height h = 10 μm.

Fig. 13
Fig. 13

Flow chart of a drag force analysis by the finite-volume method.

Fig. 14
Fig. 14

Velocity vectors in the plane at 0.5 μm before the center plane for an optical rotator: a = 45°, 2r = 3 μm, h = 10 μm.

Fig. 15
Fig. 15

Streamlines about the rotator.

Fig. 16
Fig. 16

3D images of (a) the pressure distribution and (b) the shearing stress distribution.

Fig. 17
Fig. 17

Comparison of drag force in the CFD and approximation method with rotator length as a parameter.

Fig. 18
Fig. 18

Comparison of rotation rates for CFD and approximation methods with parallel beam illumination for a = 45°, 2r = 3 μm, and h = 10 μm with rotator length as a parameter.

Fig. 19
Fig. 19

Comparison of rotation rates for the CFD and the approximation methods, with slope angle as a parameter.

Tables (2)

Tables Icon

Table 1 Comparison of Drag Force of 3000-rpm Optical Rotators for a = 45°, 2r = 3 μm, and h = 3 μm

Tables Icon

Table 2 Drag Forces of Surfaces on a 3000-rpm Optical Rotator Simulated by CFD for 2r = 3 μm and h = 3 μm

Equations (17)

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

F=1+Rsina-n2/n1T sina2n1P/c=n1PQ/c,
R= 12Rs+Rp= 12tan2a2-a1tan2a2+a1+ sin2a2-a1sin2a2+a1,
T=1-R,
Fs=F cosa,
Ft=Fg sinθ=F sinasinθ.
Tq=rFt=n1PQt/c,
Fb=n2/n11+Rsina-a2-T sina3×n2P/c,
Ftrap= Fs+FbdS,
Mopt= n1c P  QtdS.
Wz=W01+z-zfZ021/2,
Wzcos θ, Wzsin θ, z.
I=tWzcos θ, tWzsin θ, z,
Ir=I-2I·nn,
It=I+I·ntana2tana1-1n,
·U-u=0,
Ut+U-u·U=-P+ν2U,
Mdrag= r2Pt+Stdrdθ,

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