Abstract

The torque exerted by an astigmatic optical beam on small transparent isotropic particles was dynamically measured observing the angular motion of the particles under a microscope. The data confirmed that torque was originated by the transfer of orbital angular momentum associated with the spatial changes in the phase of the optical field induced by the moving particle. This mechanism for angular momentum transfer works also with incident light beams with no net angular momentum.

© 2002 Optical Society of America

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References

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    [CrossRef]
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Amer. J. Phys.

P. J. Allen, “A radiation torque experiment,” Amer. J. Phys. 74, 1185–1192 (1966).
[CrossRef]

Appl. Phys. Lett.

S. Juodkazis, M. Shikata, T. Takahashi, S. Matsuo, and H. Misawa, “Fast optical switching by a laser-manipulated microdroplet of liquid crystal,” Appl. Phys. Lett. 74, 3627–3629 (1999).
[CrossRef]

Electron. Lett.

S. Sato and M. Ishigure, “Optical rapping and manipulation of microscopic particles and biological cells using higher-order mode Nd:YAG laser beams,” Electron. Lett. 27 1831-1832 (1991).
[CrossRef]

J. Opt. B: Quantum Semiclass. Opt.

K. Volke-Sepulveda, V. Garces-Chavez, S. Chavez-Cerda, J. Arlt, and K. Dholakia, “Orbital angular momentum of a high-order Bessel light beam,” J. Opt. B: Quantum Semiclass. Opt. 4 S82 (2002).
[CrossRef]

Mol. Cryst. Liq. Cryst.

E. Santamato, B. Daino, M. Romagnoli, M. Settembre, and Y. R. Shen, “Collective rotation of the molecules of a nematic liquid crystal driven by the angular momentum of light,” Mol. Cryst. Liq. Cryst. 143, 89–100 (1987).
[CrossRef]

Nature

M. E. J. Friese, T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Optical alignment and spinning of laser trapped microscopic particles,” Nature 394, 348–350 (1998).
[CrossRef]

Opt. Commun.

A. E. Chiou, W. Wang, G. J. Sonek, J. Hong, and M. W. Berns, “Interferometric optical tweezers,” Opt. Commun. 133 7-10 (1997).
[CrossRef]

S. J. van Enk and G. Nienhuis, “Eigenfunction description of laser beams and orbital angular momentum of light,” Opt. Commun. 94, 147–158 (1992).
[CrossRef]

Opt. Lett.

Phys. Rev.

R. A. Beth, “Mechanical detection and measurement of the angular momentum of light,” Phys. Rev. 50, 115–125 (1936).
[CrossRef]

Phys. Rev. A

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P.Woerdman, “Orbital angular momenum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45, 8185–8189 (1992).
[CrossRef] [PubMed]

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, 1593–1596 (1996).
[CrossRef] [PubMed]

Phys. Rev. Lett.

A. T. O’Neil, I. Mac Vicar, L. Allen, and M. J. Padgett, “Intrinsic and extrinsic nature of the orbital angular momentum of a light beam,” Phys. Rev. Lett. 88 053601 (2002).
[CrossRef]

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, 826–829 (1995).
[CrossRef] [PubMed]

E. Santamato, B. Daino, M. Romagnoli, M. Settembre, and Y. R. Shen, “Collective rotation of molecules driven by the angular momentum of light in a nematic film,” Phys. Rev. Lett. 57, 2423–2426 (1986).
[CrossRef] [PubMed]

E. Santamato, M. Romagnoli, M. Settembre, B. Daino, and Y. R. Shen, “Self-Induced Stimulated Light Scattering,” Phys. Rev. Lett. 61, 113–116 (1988).
[CrossRef] [PubMed]

Science

L. Paterson, M. P. MacDonald, J. Arlt, W. Sibbet, P. E. Bryant, and K. Dholakia, “Controlled rotation of optically trapped microscopic particles,” Science 292, 912–914 (2001).
[CrossRef] [PubMed]

Supplementary Material (1)

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Figures (4)

Fig. 1.
Fig. 1.

Rotational dragging of three trapped latex spheres each 14 μm in diameter.

Fig. 2.
Fig. 2.

Movie showing the laser-induced spinning of a trapped small glass rod (length 13 μm, diameter 2 μm). [Media 1]

Fig. 3.
Fig. 3.

Nine frames of a trapped glass rods showing the alignment motion along the major axis of the trapping beam shape. As the optical torque acting on the particle depends on its orientation [see Eq. (8)], the rotation speed is not constant. The frames are 200 ms apart. The scale bar is 10 μm.

Fig. 4.
Fig. 4.

The angular position of the particle as a function of time during its motion. The laser power at the sample position was P = 200 mW.

Equations (14)

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ψ r α = k r 2 4 f k r 2 4 a cos [ 2 ( ϕ α ) ]
E r ϕ α = p = 0 l = c p , l ( α ) exp [ il ( ϕ α ) ] f p , l ( r ) ,
f p , l ( x ) = ( 1 ) p 2 p ! π w 2 ( p + l ) ! x l exp ( x 2 ) L p l ( x 2 )
c ˙ p , l ( t ) = il α ˙ c p , l ( k w 2 α ˙ 8 a ) [ ( p + l ) ( p + l 1 ) c p , l 2 2 ( p + l ) ( p + 1 ) c p + 1 , l 2
+ ( p + 1 ) ( p + 2 ) c p + 2 , l 2 ( p + l + 1 ) ( p + l + 2 ) c p , l + 2
+ 2 p ( p + l + 1 ) c p 1 , l + 2 p ( p 1 ) c p 2 , l + 2 ] .
( l = 0,2,4 , ) ( p = 0,1,2 , )
c ˙ p , 0 ( t ) = ( k w 2 α ˙ 8 a ) [ ( p + 1 ) ( p + 2 ) c p , 2 2 p ( p + 1 ) c p 1 , 2 + p ( p 1 ) c p 2 , 2
+ 2 p ( p + 1 ) c p 1,2 ( p + 1 ) ( p + 2 ) c p , 2 p ( p 1 ) c p 2,2 ] .
γ α ˙ = M z ( t ) = ( cn 8 πω ) p = 0 l = l c p , l ( t ) 2 =
= ( P ω ) p = 0 l = l c p , l ( t ) 2 p = 0 l = c p , l ( t ) 2
M z ( t ) = ( cn 8 πω ) Im ( E * ϕ E ) d x d y
= A sin 2 α ( t )
tan α ( t ) = e t τ tan α ( 0 )

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