Abstract

The recent advent of angular optical trapping techniques has allowed for rotational control and direct torque measurement on biological substrates. Here we present a method that increases the versatility and flexibility of these techniques. We demonstrate that a single beam with a rapidly rotating linear polarization can be utilized to apply a constant controllable torque to a trapped particle without active feedback, while simultaneously measuring the particle angular position. In addition, this device can rapidly switch between a torque wrench and an angular trap. These features should make possible torsional measurements across a wide range of biological systems.

© 2010 Optical Society of America

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References

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    [CrossRef] [PubMed]
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    [CrossRef]
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2009 (2)

2008 (2)

T. A. Wood, G. S. Roberts, S. Eaimkhong, and P. Bartlett, Faraday Discuss. 137, 319 (2008).
[CrossRef] [PubMed]

S. Forth, C. Deufel, M. Y. Sheinin, B. Daniels, J. P. Sethna, and M. D. Wang, Phys. Rev. Lett. 100, 148301 (2008).
[CrossRef] [PubMed]

2007 (2)

C. Deufel, S. Forth, C. R. Simmons, S. Dejgosha, and M. D. Wang, Nat. Meth. 4, 223 (2007).
[CrossRef]

B. H. McNaughton, R. R. Agayan, R. Clarke, R. G. Smith, and R. Kopelman, Appl. Phys. Lett. 91, 224105 (2007).
[CrossRef]

2004 (1)

A. La Porta and M. D. Wang, Phys. Rev. Lett. 92, 190801 (2004).
[CrossRef] [PubMed]

2003 (2)

P. Galajda and P. Ormos, Opt. Express 11, 446 (2003).
[CrossRef] [PubMed]

C. Bustamante, Z. Bryant, and S. B. Smith, Nature 421, 423 (2003).
[CrossRef] [PubMed]

2002 (1)

2001 (1)

L. Paterson, M. P. MacDonald, J. Arlt, W. Sibbett, P. E. Bryant, and K. Dholakia, Science 292, 912 (2001).
[CrossRef] [PubMed]

1998 (2)

M. D. Wang, M. J. Schnitzer, H. Yin, R. Landick, J. Gelles, and S. M. Block, Science 282, 902 (1998).
[CrossRef] [PubMed]

M. E. J. Friese, T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, Nature 394, 348 (1998).
[CrossRef]

Agayan, R. R.

B. H. McNaughton, R. R. Agayan, R. Clarke, R. G. Smith, and R. Kopelman, Appl. Phys. Lett. 91, 224105 (2007).
[CrossRef]

Arlt, J.

L. Paterson, M. P. MacDonald, J. Arlt, W. Sibbett, P. E. Bryant, and K. Dholakia, Science 292, 912 (2001).
[CrossRef] [PubMed]

Bartlett, P.

T. A. Wood, G. S. Roberts, S. Eaimkhong, and P. Bartlett, Faraday Discuss. 137, 319 (2008).
[CrossRef] [PubMed]

Block, S. M.

M. D. Wang, M. J. Schnitzer, H. Yin, R. Landick, J. Gelles, and S. M. Block, Science 282, 902 (1998).
[CrossRef] [PubMed]

Bonin, K. D.

Bryant, P. E.

L. Paterson, M. P. MacDonald, J. Arlt, W. Sibbett, P. E. Bryant, and K. Dholakia, Science 292, 912 (2001).
[CrossRef] [PubMed]

Bryant, Z.

C. Bustamante, Z. Bryant, and S. B. Smith, Nature 421, 423 (2003).
[CrossRef] [PubMed]

Bustamante, C.

C. Bustamante, Z. Bryant, and S. B. Smith, Nature 421, 423 (2003).
[CrossRef] [PubMed]

Clarke, R.

B. H. McNaughton, R. R. Agayan, R. Clarke, R. G. Smith, and R. Kopelman, Appl. Phys. Lett. 91, 224105 (2007).
[CrossRef]

Daniels, B.

S. Forth, C. Deufel, M. Y. Sheinin, B. Daniels, J. P. Sethna, and M. D. Wang, Phys. Rev. Lett. 100, 148301 (2008).
[CrossRef] [PubMed]

Dejgosha, S.

C. Deufel, S. Forth, C. R. Simmons, S. Dejgosha, and M. D. Wang, Nat. Meth. 4, 223 (2007).
[CrossRef]

Deufel, C.

S. Forth, C. Deufel, M. Y. Sheinin, B. Daniels, J. P. Sethna, and M. D. Wang, Phys. Rev. Lett. 100, 148301 (2008).
[CrossRef] [PubMed]

C. Deufel, S. Forth, C. R. Simmons, S. Dejgosha, and M. D. Wang, Nat. Meth. 4, 223 (2007).
[CrossRef]

Dholakia, K.

L. Paterson, M. P. MacDonald, J. Arlt, W. Sibbett, P. E. Bryant, and K. Dholakia, Science 292, 912 (2001).
[CrossRef] [PubMed]

Eaimkhong, S.

T. A. Wood, G. S. Roberts, S. Eaimkhong, and P. Bartlett, Faraday Discuss. 137, 319 (2008).
[CrossRef] [PubMed]

Forth, S.

S. Forth, C. Deufel, M. Y. Sheinin, B. Daniels, J. P. Sethna, and M. D. Wang, Phys. Rev. Lett. 100, 148301 (2008).
[CrossRef] [PubMed]

C. Deufel, S. Forth, C. R. Simmons, S. Dejgosha, and M. D. Wang, Nat. Meth. 4, 223 (2007).
[CrossRef]

Friese, M. E. J.

M. E. J. Friese, T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, Nature 394, 348 (1998).
[CrossRef]

Funk, M.

Galajda, P.

Gelles, J.

M. D. Wang, M. J. Schnitzer, H. Yin, R. Landick, J. Gelles, and S. M. Block, Science 282, 902 (1998).
[CrossRef] [PubMed]

Heckenberg, N. R.

Kopelman, R.

B. H. McNaughton, R. R. Agayan, R. Clarke, R. G. Smith, and R. Kopelman, Appl. Phys. Lett. 91, 224105 (2007).
[CrossRef]

Kourmanov, B.

La Porta, A.

A. La Porta and M. D. Wang, Phys. Rev. Lett. 92, 190801 (2004).
[CrossRef] [PubMed]

Landick, R.

M. D. Wang, M. J. Schnitzer, H. Yin, R. Landick, J. Gelles, and S. M. Block, Science 282, 902 (1998).
[CrossRef] [PubMed]

MacDonald, M. P.

L. Paterson, M. P. MacDonald, J. Arlt, W. Sibbett, P. E. Bryant, and K. Dholakia, Science 292, 912 (2001).
[CrossRef] [PubMed]

McNaughton, B. H.

B. H. McNaughton, R. R. Agayan, R. Clarke, R. G. Smith, and R. Kopelman, Appl. Phys. Lett. 91, 224105 (2007).
[CrossRef]

Nieminen, T. A.

Ormos, P.

Parkin, S. J.

Paterson, L.

L. Paterson, M. P. MacDonald, J. Arlt, W. Sibbett, P. E. Bryant, and K. Dholakia, Science 292, 912 (2001).
[CrossRef] [PubMed]

Roberts, G. S.

T. A. Wood, G. S. Roberts, S. Eaimkhong, and P. Bartlett, Faraday Discuss. 137, 319 (2008).
[CrossRef] [PubMed]

Rubinsztein-Dunlop, H.

Schnitzer, M. J.

M. D. Wang, M. J. Schnitzer, H. Yin, R. Landick, J. Gelles, and S. M. Block, Science 282, 902 (1998).
[CrossRef] [PubMed]

Sethna, J. P.

S. Forth, C. Deufel, M. Y. Sheinin, B. Daniels, J. P. Sethna, and M. D. Wang, Phys. Rev. Lett. 100, 148301 (2008).
[CrossRef] [PubMed]

Sheinin, M. Y.

M. Y. Sheinin and M. D. Wang, Phys. Chem. Chem. Phys. 11, 4800 (2009).
[CrossRef] [PubMed]

S. Forth, C. Deufel, M. Y. Sheinin, B. Daniels, J. P. Sethna, and M. D. Wang, Phys. Rev. Lett. 100, 148301 (2008).
[CrossRef] [PubMed]

Sibbett, W.

L. Paterson, M. P. MacDonald, J. Arlt, W. Sibbett, P. E. Bryant, and K. Dholakia, Science 292, 912 (2001).
[CrossRef] [PubMed]

Simmons, C. R.

C. Deufel, S. Forth, C. R. Simmons, S. Dejgosha, and M. D. Wang, Nat. Meth. 4, 223 (2007).
[CrossRef]

Smith, R. G.

B. H. McNaughton, R. R. Agayan, R. Clarke, R. G. Smith, and R. Kopelman, Appl. Phys. Lett. 91, 224105 (2007).
[CrossRef]

Smith, S. B.

C. Bustamante, Z. Bryant, and S. B. Smith, Nature 421, 423 (2003).
[CrossRef] [PubMed]

Stilgoe, A. B.

Strogatz, S. H.

S. H. Strogatz, Nonlinear Dynamics and Chaos (Addison-Wesley, 1994).

Walker, T. G.

Wang, M. D.

M. Y. Sheinin and M. D. Wang, Phys. Chem. Chem. Phys. 11, 4800 (2009).
[CrossRef] [PubMed]

S. Forth, C. Deufel, M. Y. Sheinin, B. Daniels, J. P. Sethna, and M. D. Wang, Phys. Rev. Lett. 100, 148301 (2008).
[CrossRef] [PubMed]

C. Deufel, S. Forth, C. R. Simmons, S. Dejgosha, and M. D. Wang, Nat. Meth. 4, 223 (2007).
[CrossRef]

A. La Porta and M. D. Wang, Phys. Rev. Lett. 92, 190801 (2004).
[CrossRef] [PubMed]

M. D. Wang, M. J. Schnitzer, H. Yin, R. Landick, J. Gelles, and S. M. Block, Science 282, 902 (1998).
[CrossRef] [PubMed]

Wood, T. A.

T. A. Wood, G. S. Roberts, S. Eaimkhong, and P. Bartlett, Faraday Discuss. 137, 319 (2008).
[CrossRef] [PubMed]

Yin, H.

M. D. Wang, M. J. Schnitzer, H. Yin, R. Landick, J. Gelles, and S. M. Block, Science 282, 902 (1998).
[CrossRef] [PubMed]

Appl. Phys. Lett. (1)

B. H. McNaughton, R. R. Agayan, R. Clarke, R. G. Smith, and R. Kopelman, Appl. Phys. Lett. 91, 224105 (2007).
[CrossRef]

Faraday Discuss. (1)

T. A. Wood, G. S. Roberts, S. Eaimkhong, and P. Bartlett, Faraday Discuss. 137, 319 (2008).
[CrossRef] [PubMed]

Nat. Meth. (1)

C. Deufel, S. Forth, C. R. Simmons, S. Dejgosha, and M. D. Wang, Nat. Meth. 4, 223 (2007).
[CrossRef]

Nature (2)

C. Bustamante, Z. Bryant, and S. B. Smith, Nature 421, 423 (2003).
[CrossRef] [PubMed]

M. E. J. Friese, T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, Nature 394, 348 (1998).
[CrossRef]

Opt. Express (2)

Opt. Lett. (1)

Phys. Chem. Chem. Phys. (1)

M. Y. Sheinin and M. D. Wang, Phys. Chem. Chem. Phys. 11, 4800 (2009).
[CrossRef] [PubMed]

Phys. Rev. Lett. (2)

S. Forth, C. Deufel, M. Y. Sheinin, B. Daniels, J. P. Sethna, and M. D. Wang, Phys. Rev. Lett. 100, 148301 (2008).
[CrossRef] [PubMed]

A. La Porta and M. D. Wang, Phys. Rev. Lett. 92, 190801 (2004).
[CrossRef] [PubMed]

Science (2)

L. Paterson, M. P. MacDonald, J. Arlt, W. Sibbett, P. E. Bryant, and K. Dholakia, Science 292, 912 (2001).
[CrossRef] [PubMed]

M. D. Wang, M. J. Schnitzer, H. Yin, R. Landick, J. Gelles, and S. M. Block, Science 282, 902 (1998).
[CrossRef] [PubMed]

Other (1)

S. H. Strogatz, Nonlinear Dynamics and Chaos (Addison-Wesley, 1994).

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Figures (3)

Fig. 1
Fig. 1

Method of constant optical torque generation and angular position detection. (a) Simplified schematic of the passive optical torque wrench. The optical setup is similar to what has been previously described [6] but with the important addition of a lock-in amplifier. (b) The lock-in amplifier uses I x ( t ) as a reference signal and the torque detector signal τ ( t ) as the input signal. The phase difference between these two signals provides the angular position θ of the cylinder. (c) Comparison of detected angular position of a quartz dust particle as simultaneously determined by the lock-in method (red curve) and video-tracking method (blue points). For both (b) and (c), f critical = 9 Hz and f = 1 kHz .

Fig. 2
Fig. 2

Demonstration of the passive torque wrench mode. (a) Single traces of cylinder angular position versus time for various polarization rotation rates and the corresponding measured torque. f critical = 13 Hz . (b) Direct measurement of the torque versus polarization rotation rate for various laser powers on a quartz cylinder. Solid curves are global fits to the expected mean torque.

Fig. 3
Fig. 3

Demonstration of rapid switching between an angular trapping mode and a torque wrench mode. f critical = 9 Hz . Polarization rate was set to + 5 Hz at t = 0 (angular trapping mode), 1 kHz at t = 1 s (torque wrench mode), and 5 Hz at t = 6 s (angular trapping mode).

Equations (1)

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γ d θ d t = τ 0 sin [ 2 ( ω t θ ) ] ,

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