Abstract

Long cylindrical objects have been observed to align their central axis with the propagation axis of the illuminating laser beam through the action of radiation-pressure-generated force and torque. A cylindrically shaped microactuator based on this principle and suitable for micromachine applications is examined theoretically. When four in-plane laser beams converging at a common point centered on the cylinder are used, the cylinder can be made to rotate about a pivot point. In one mode, smooth, continuous, and reversible rotation is possible, whereas the other cylinder can be step rotated and locked, similar to the operation of conventional stepping motors. The properties of the device are analyzed based on obtaining either a constant rotation rate with variable beam power levels or a quasi-constant rotation rate with constant beam power levels or on using a fixed beam sequence rate that matches the system parameters and produces smooth or stepped operation.

© 1999 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. G. Roosen, C. Imbert, “Optical levitation by means of two horizontal laser beams: a theoretical and experimental study,” Phys. Lett. 59A, 6–8 (1976).
  3. A. Ashkin, J. M. Dziedzic, “Observation of radiation pressure trapping of particles by alternating light beams,” Phys. Rev. Lett. 54, 1245–1248 (1985).
    [CrossRef] [PubMed]
  4. 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, 288–298 (1986).
    [CrossRef] [PubMed]
  5. E. Sidick, S. D. Collins, A. Knoesen, “Trapping forces in a multiple-beam fiber-optic trap,” Appl. Opt. 36, 6423–6433 (1997).
    [CrossRef]
  6. W. H. Wright, G. J. Sonek, M. W. Berns, “Parametric study of the forces on microspheres held by optical tweezers,” Appl. Opt. 33, 1735–1748 (1994).
    [CrossRef] [PubMed]
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    [CrossRef]
  8. 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]
  9. R. C. Gauthier, M. Ashman, “Simulated dynamic behavior of single and multiple spheres in the trap region of focused laser beams,” Appl. Opt. 37, 6421–6431 (1998).
    [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. 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]
  12. D. R. Koehler, “Optical actuation of micromechanical components,” J. Opt. Soc. Am. B 14, 2197–2203 (1997).
    [CrossRef]

1998 (2)

1997 (5)

1994 (1)

1986 (1)

1985 (1)

A. Ashkin, J. M. Dziedzic, “Observation of radiation pressure trapping of particles by alternating light beams,” Phys. Rev. Lett. 54, 1245–1248 (1985).
[CrossRef] [PubMed]

1976 (1)

G. Roosen, C. Imbert, “Optical levitation by means of two horizontal laser beams: a theoretical and experimental study,” Phys. Lett. 59A, 6–8 (1976).

1970 (1)

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

Ashkin, A.

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, 288–298 (1986).
[CrossRef] [PubMed]

A. Ashkin, J. M. Dziedzic, “Observation of radiation pressure trapping of particles by alternating light beams,” Phys. Rev. Lett. 54, 1245–1248 (1985).
[CrossRef] [PubMed]

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

Ashman, M.

Berns, M. W.

Bjorkholm, J. E.

Chu, S.

Collins, S. D.

Dziedzic, J. M.

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, 288–298 (1986).
[CrossRef] [PubMed]

A. Ashkin, J. M. Dziedzic, “Observation of radiation pressure trapping of particles by alternating light beams,” Phys. Rev. Lett. 54, 1245–1248 (1985).
[CrossRef] [PubMed]

Gauthier, R. C.

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]

Imbert, C.

G. Roosen, C. Imbert, “Optical levitation by means of two horizontal laser beams: a theoretical and experimental study,” Phys. Lett. 59A, 6–8 (1976).

Knoesen, A.

Koehler, D. R.

Nemoto, S.

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]

Roosen, G.

G. Roosen, C. Imbert, “Optical levitation by means of two horizontal laser beams: a theoretical and experimental study,” Phys. Lett. 59A, 6–8 (1976).

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]

Sidick, E.

Sonek, G. J.

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]

Togo, H.

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]

Wright, W. H.

Appl. Opt. (4)

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. Opt. Soc. Am. B (3)

Opt. Lett. (1)

Phys. Lett. (1)

G. Roosen, C. Imbert, “Optical levitation by means of two horizontal laser beams: a theoretical and experimental study,” Phys. Lett. 59A, 6–8 (1976).

Phys. Rev. Lett. (2)

A. Ashkin, J. M. Dziedzic, “Observation of radiation pressure trapping of particles by alternating light beams,” Phys. Rev. Lett. 54, 1245–1248 (1985).
[CrossRef] [PubMed]

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

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Figures (11)

Fig. 1
Fig. 1

Video images taken through the optics of a conventional laser trapping system. The cylinder in (a) is shown resting on the base of the sample holder. When illuminated with the focused laser beam, it experiences a torque that induces it to rotate and align with the laser beam propagation axis [(b)–(d)].

Fig. 2
Fig. 2

Plot of torque on a 70-µm-long, 10-µm-radius cylinder as a function of the orientation angle between the cylinder axis and the beam propagation axis. The 0° and the 90° orientations are unstable orientations, whereas the 11° orientation is stable. The 45° window between 13° and 58° is the orientation window used for the design of the microactuator and has the largest average torque.

Fig. 3
Fig. 3

Four-beam design of the cylinder-based microactuator. The beams are contained in the same plane as the cylinder axis, converge on the cylinder’s central position, and equally incline by 45° to each other. Beam 1 defines the 0° direction of the polar coordinates used in the discussion. The inset shows a six-beam configuration for a shorter-length actuator.

Fig. 4
Fig. 4

Plot of torque on a 20-µm-long, 10-µm-radius cylinder as a function of the orientation angle between the cylinder axis and the beam propagation axis. The 0° and the 90° orientations are unstable orientations, whereas the 45° orientation is stable. Based on this curve, a 30° window for device activation can be selected but requires six beams for inducing full rotation, as shown in the inset of Fig. 3.

Fig. 5
Fig. 5

Available laser beam power as a function of time when a rotation rate of 2 rev/s is desired. The available power has been limited to 100 mW. For damping factors less than or equal to 1000 I, the available power is limited to the 100 mW and the rotation rate can be maintained for those times only when the power falls below 100 mW.

Fig. 6
Fig. 6

Cylinder orientation angle as a function of time for damping factors above 1000 I. The available power is limited to 100 mW and a 2-rev/s rotation rate is desired and represented by the straight line in the figure. Only in those regions on the curves with straight lines of slope equal to the reference line can the desired rotation rate be maintained. The 20,000 I damping factor curve indicates that the desired rotation rate cannot be achieved.

Fig. 7
Fig. 7

Rotation rate as a function of time and damping factor when the actuator is operated in constant power mode at 1 mW. The smaller the damping factor, the smoother the rotation and the higher the rotation rate.

Fig. 8
Fig. 8

Same as Fig. 7 but for a power of 10 mW. When compared with Fig. 7, smoother and higher rotation rates are possible for similar damping factors.

Fig. 9
Fig. 9

Orientation angle as a function of time for the microactuator operated in a constant laser power level of 1 mW. The nearly uniform slopes of these curves indicate that the actuator can run at nearly a constant rotation rate.

Fig. 10
Fig. 10

Orientation angle of the cylinder as a function of time when a constant cycle rate of one four-beam sequence per second is used. The cylinder snaps into alignment with the on beam and holds its orientation until another beam is switched on. Operation is similar to that of conventional stepping motors.

Fig. 11
Fig. 11

Orientation angle of the cylinder as a function of time when the cylinder is operated in constant beam cycle mode. The damping factor and the beam power have been selected to provide a nearly constant rotation rate. The device acts similarly to the constant torque and constant power modes but does not require information on cylinder orientation.

Tables (1)

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Table 1 Microactuator System Parameters

Equations (10)

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τ=Iα+bω+kθ
θ=τk1-exp-bt2Icos4kI-b21/22I t+b4kI-b21/2sin4kI-b21/22I t,
ω=2τ exp-bt2Isin4kI-b21/22I t4kI-b21/2.
τ=bωc1-exp-btI.
Prequired=ττcomputed 100 mW.
available power=Prequired, when Prequired100 mW100 mW100 mWPrequired, when Prequired>100 mW.
α=τI-bI ω.
ωt=τ/b.
ωt+dt=ωt+αtt.
θt+dt=θt+t+12αtt2.

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