Abstract

We describe a way to determine the total angular momentum, both spin and orbital, transferred to a particle trapped in optical tweezers. As an example an LG02 mode of a laser beam with varying degrees of circular polarisation is used to trap and rotate an elongated particle with a well defined geometry. The method successfully estimates the total optical torque applied to the particle. For this technique, there is no need to measure the viscous drag on the particle, as it is an optical measurement. Therefore, knowledge of the particle’s size and shape, as well as the fluid’s viscosity, is not required.

© 2006 Optical Society of America

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  1. A. Ashkin, J. M. Dziedzic, J. E. Bjorkholm, and S. Chu, "Observation of Single-Beam Gradient Force Optical Trap for Dielectric Particles," Opt. Lett. 11,288-290 (1986).
    [CrossRef] [PubMed]
  2. S. M. Block, D. F. Blair, and H. C. Berg, "Compliance of bacterial flagella measured with optical tweezers," Nature 338,514-518 (1989).
    [CrossRef] [PubMed]
  3. A. Ashkin, K. Schutze, J. M. Dziedzic, U. Euteneuer, and M. Schliwa, "Force generation of organelle transport measured in vivo by an infrared laser trap," Nature 348,346-348 (1990).
    [CrossRef] [PubMed]
  4. K. Svoboda, C. F. Schmidt, B. J. Schnapp, and S. M. Block, "Direct observation of kinesin stepping by optical trapping interferometry," Nature 365,721-727 (1993).
    [CrossRef] [PubMed]
  5. J. T. Finer, R. M. Simmons, and J. A. Spudich, "Single myosin molecule mechanics: piconewton forces and nanometre steps," Nature 368,113-119 (1994).
    [CrossRef] [PubMed]
  6. H. Yin, M. D. Wang, K. Svoboda, R. Landick, S. M. Block, and J. Gelles, "Transcription Against an Applied Force," Science 270,1653-1657 (1995).
    [CrossRef] [PubMed]
  7. M. S. Z. Kellermayer, S. B. Smith, H. L. Granzier, and C. Bustamante, "Folding-Unfolding Transitions in Single Titin Molecules Characterized with Laser Tweezers," Science 276,1112-1116 (1997).
    [CrossRef] [PubMed]
  8. L. Tskhovrebova, J. Trinick, J. A. Sleep, and R. M. Simmons, "Elasticity and unfolding of single molecules of the giant muscle protein titin," Nature 387,308-312 (1997).
    [CrossRef] [PubMed]
  9. D. E. Smith, S. J. Tans, S. B. Smith, S. Grimes, D. L. Anderson, and C. Bustamante, "The bacteriophage theta 29 portal motor can package DNA against a larger internal force," Nature 413,748-752 (2001).
    [CrossRef] [PubMed]
  10. 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]
  11. 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]
  12. 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]
  13. T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, "Optical measurement of microscopic torques," J. Mod. Opt. 48,405-413 (2001).
  14. A. I. Bishop, T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, "Optical Microrheology Using Rotating Laser-Trapped Particles," Phys. Rev. Lett. 92,198104 (2004).
    [CrossRef] [PubMed]
  15. L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, "Orbital angular momentum and the transformation of Laguerre-Gaussian laser modes," Phys. Rev. A 45,8185-8189 (1992).
    [CrossRef] [PubMed]
  16. K. D. Bonin and B. Kourmanov, "Light torque nanocontrol, nanomotors and nanorockers," Opt. Express 10,984-989 (2002).
    [PubMed]
  17. A. I. Bishop, T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, "Optical application and measurement of torque on microparticles of isotropic nonabsorbing material," Phys. Rev. A 68,033802 (2003).
    [CrossRef]
  18. P. Galajda and P. Ormos, "Complex micromachines produced and driven by light," Appl. Phys. Lett. 78,249-251 (2001).
    [CrossRef]
  19. A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, "Entanglement of the orbital angular momentum states of photons," Nature 412,313-316 (2001).
    [CrossRef] [PubMed]
  20. S. J. Parkin, T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, "Optical measurement of torque exerted on an elongated object by a noncircular laser beam," Phys. Rev. A 70,023816 (2004).
    [CrossRef]
  21. J. Courtial, D. A. Robertson, K. Dholakia, L. Allen, and M. J. Padgett, "Rotational Frequency Shift of a Light Beam," Phys. Rev. Lett. 81,4828-4830 (1998).
    [CrossRef]
  22. I. V. Basistiy, V. V. Slyusar, M. S. Soskin, and M. V. Vasnetsov, "Manifestation of the rotational Doppler effect by use of an off axis optical vortex beam," Opt. Lett. 28,1185-1187 (2003).
    [CrossRef] [PubMed]
  23. J. Leach, J. Courtial, K. Skeldon, S. M. Barnett, S. Franke-Arnold, and M. J. Padgett, "Interferometric Methods to Measure Orbital and Spin, or the Total Angular Momentum of a Single Photon," Phys. Rev. Lett. 92,013601 (2004).
    [CrossRef] [PubMed]
  24. G. Knöner, S. Parkin, N. R. Heckenberg, and H. Rubinsztein-Dunlop, "Characterization of optically driven fluid stress fields with optical tweezers," Phys. Rev. E 72,031507 (2005).
    [CrossRef]
  25. W. S. Ryu, R. M. Berry, and H. C. Berg, "Torque-generating units of the flagellar motor of Escherichia coli have a high duty ratio," Nature 403,444-447 (2000).
    [CrossRef] [PubMed]

2005 (1)

G. Knöner, S. Parkin, N. R. Heckenberg, and H. Rubinsztein-Dunlop, "Characterization of optically driven fluid stress fields with optical tweezers," Phys. Rev. E 72,031507 (2005).
[CrossRef]

2004 (3)

S. J. Parkin, T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, "Optical measurement of torque exerted on an elongated object by a noncircular laser beam," Phys. Rev. A 70,023816 (2004).
[CrossRef]

J. Leach, J. Courtial, K. Skeldon, S. M. Barnett, S. Franke-Arnold, and M. J. Padgett, "Interferometric Methods to Measure Orbital and Spin, or the Total Angular Momentum of a Single Photon," Phys. Rev. Lett. 92,013601 (2004).
[CrossRef] [PubMed]

A. I. Bishop, T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, "Optical Microrheology Using Rotating Laser-Trapped Particles," Phys. Rev. Lett. 92,198104 (2004).
[CrossRef] [PubMed]

2003 (2)

A. I. Bishop, T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, "Optical application and measurement of torque on microparticles of isotropic nonabsorbing material," Phys. Rev. A 68,033802 (2003).
[CrossRef]

I. V. Basistiy, V. V. Slyusar, M. S. Soskin, and M. V. Vasnetsov, "Manifestation of the rotational Doppler effect by use of an off axis optical vortex beam," Opt. Lett. 28,1185-1187 (2003).
[CrossRef] [PubMed]

2002 (1)

2001 (4)

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

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, "Entanglement of the orbital angular momentum states of photons," Nature 412,313-316 (2001).
[CrossRef] [PubMed]

T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, "Optical measurement of microscopic torques," J. Mod. Opt. 48,405-413 (2001).

D. E. Smith, S. J. Tans, S. B. Smith, S. Grimes, D. L. Anderson, and C. Bustamante, "The bacteriophage theta 29 portal motor can package DNA against a larger internal force," Nature 413,748-752 (2001).
[CrossRef] [PubMed]

2000 (1)

W. S. Ryu, R. M. Berry, and H. C. Berg, "Torque-generating units of the flagellar motor of Escherichia coli have a high duty ratio," Nature 403,444-447 (2000).
[CrossRef] [PubMed]

1998 (2)

J. Courtial, D. A. Robertson, K. Dholakia, L. Allen, and M. J. Padgett, "Rotational Frequency Shift of a Light Beam," Phys. Rev. Lett. 81,4828-4830 (1998).
[CrossRef]

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]

1997 (2)

M. S. Z. Kellermayer, S. B. Smith, H. L. Granzier, and C. Bustamante, "Folding-Unfolding Transitions in Single Titin Molecules Characterized with Laser Tweezers," Science 276,1112-1116 (1997).
[CrossRef] [PubMed]

L. Tskhovrebova, J. Trinick, J. A. Sleep, and R. M. Simmons, "Elasticity and unfolding of single molecules of the giant muscle protein titin," Nature 387,308-312 (1997).
[CrossRef] [PubMed]

1996 (1)

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]

1995 (2)

H. Yin, M. D. Wang, K. Svoboda, R. Landick, S. M. Block, and J. Gelles, "Transcription Against an Applied Force," Science 270,1653-1657 (1995).
[CrossRef] [PubMed]

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]

1994 (1)

J. T. Finer, R. M. Simmons, and J. A. Spudich, "Single myosin molecule mechanics: piconewton forces and nanometre steps," Nature 368,113-119 (1994).
[CrossRef] [PubMed]

1993 (1)

K. Svoboda, C. F. Schmidt, B. J. Schnapp, and S. M. Block, "Direct observation of kinesin stepping by optical trapping interferometry," Nature 365,721-727 (1993).
[CrossRef] [PubMed]

1992 (1)

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

1990 (1)

A. Ashkin, K. Schutze, J. M. Dziedzic, U. Euteneuer, and M. Schliwa, "Force generation of organelle transport measured in vivo by an infrared laser trap," Nature 348,346-348 (1990).
[CrossRef] [PubMed]

1989 (1)

S. M. Block, D. F. Blair, and H. C. Berg, "Compliance of bacterial flagella measured with optical tweezers," Nature 338,514-518 (1989).
[CrossRef] [PubMed]

1986 (1)

Allen, L.

J. Courtial, D. A. Robertson, K. Dholakia, L. Allen, and M. J. Padgett, "Rotational Frequency Shift of a Light Beam," Phys. Rev. Lett. 81,4828-4830 (1998).
[CrossRef]

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

Anderson, D. L.

D. E. Smith, S. J. Tans, S. B. Smith, S. Grimes, D. L. Anderson, and C. Bustamante, "The bacteriophage theta 29 portal motor can package DNA against a larger internal force," Nature 413,748-752 (2001).
[CrossRef] [PubMed]

Ashkin, A.

A. Ashkin, K. Schutze, J. M. Dziedzic, U. Euteneuer, and M. Schliwa, "Force generation of organelle transport measured in vivo by an infrared laser trap," Nature 348,346-348 (1990).
[CrossRef] [PubMed]

A. Ashkin, J. M. Dziedzic, J. E. Bjorkholm, and S. Chu, "Observation of Single-Beam Gradient Force Optical Trap for Dielectric Particles," Opt. Lett. 11,288-290 (1986).
[CrossRef] [PubMed]

Barnett, S. M.

J. Leach, J. Courtial, K. Skeldon, S. M. Barnett, S. Franke-Arnold, and M. J. Padgett, "Interferometric Methods to Measure Orbital and Spin, or the Total Angular Momentum of a Single Photon," Phys. Rev. Lett. 92,013601 (2004).
[CrossRef] [PubMed]

Basistiy, I. V.

Beijersbergen, M. W.

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

Berg, H. C.

W. S. Ryu, R. M. Berry, and H. C. Berg, "Torque-generating units of the flagellar motor of Escherichia coli have a high duty ratio," Nature 403,444-447 (2000).
[CrossRef] [PubMed]

S. M. Block, D. F. Blair, and H. C. Berg, "Compliance of bacterial flagella measured with optical tweezers," Nature 338,514-518 (1989).
[CrossRef] [PubMed]

Berry, R. M.

W. S. Ryu, R. M. Berry, and H. C. Berg, "Torque-generating units of the flagellar motor of Escherichia coli have a high duty ratio," Nature 403,444-447 (2000).
[CrossRef] [PubMed]

Bishop, A. I.

A. I. Bishop, T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, "Optical Microrheology Using Rotating Laser-Trapped Particles," Phys. Rev. Lett. 92,198104 (2004).
[CrossRef] [PubMed]

A. I. Bishop, T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, "Optical application and measurement of torque on microparticles of isotropic nonabsorbing material," Phys. Rev. A 68,033802 (2003).
[CrossRef]

Bjorkholm, J. E.

Blair, D. F.

S. M. Block, D. F. Blair, and H. C. Berg, "Compliance of bacterial flagella measured with optical tweezers," Nature 338,514-518 (1989).
[CrossRef] [PubMed]

Block, S. M.

H. Yin, M. D. Wang, K. Svoboda, R. Landick, S. M. Block, and J. Gelles, "Transcription Against an Applied Force," Science 270,1653-1657 (1995).
[CrossRef] [PubMed]

K. Svoboda, C. F. Schmidt, B. J. Schnapp, and S. M. Block, "Direct observation of kinesin stepping by optical trapping interferometry," Nature 365,721-727 (1993).
[CrossRef] [PubMed]

S. M. Block, D. F. Blair, and H. C. Berg, "Compliance of bacterial flagella measured with optical tweezers," Nature 338,514-518 (1989).
[CrossRef] [PubMed]

Bonin, K. D.

Bustamante, C.

D. E. Smith, S. J. Tans, S. B. Smith, S. Grimes, D. L. Anderson, and C. Bustamante, "The bacteriophage theta 29 portal motor can package DNA against a larger internal force," Nature 413,748-752 (2001).
[CrossRef] [PubMed]

M. S. Z. Kellermayer, S. B. Smith, H. L. Granzier, and C. Bustamante, "Folding-Unfolding Transitions in Single Titin Molecules Characterized with Laser Tweezers," Science 276,1112-1116 (1997).
[CrossRef] [PubMed]

Chu, S.

Courtial, J.

J. Leach, J. Courtial, K. Skeldon, S. M. Barnett, S. Franke-Arnold, and M. J. Padgett, "Interferometric Methods to Measure Orbital and Spin, or the Total Angular Momentum of a Single Photon," Phys. Rev. Lett. 92,013601 (2004).
[CrossRef] [PubMed]

J. Courtial, D. A. Robertson, K. Dholakia, L. Allen, and M. J. Padgett, "Rotational Frequency Shift of a Light Beam," Phys. Rev. Lett. 81,4828-4830 (1998).
[CrossRef]

Dholakia, K.

J. Courtial, D. A. Robertson, K. Dholakia, L. Allen, and M. J. Padgett, "Rotational Frequency Shift of a Light Beam," Phys. Rev. Lett. 81,4828-4830 (1998).
[CrossRef]

Dziedzic, J. M.

A. Ashkin, K. Schutze, J. M. Dziedzic, U. Euteneuer, and M. Schliwa, "Force generation of organelle transport measured in vivo by an infrared laser trap," Nature 348,346-348 (1990).
[CrossRef] [PubMed]

A. Ashkin, J. M. Dziedzic, J. E. Bjorkholm, and S. Chu, "Observation of Single-Beam Gradient Force Optical Trap for Dielectric Particles," Opt. Lett. 11,288-290 (1986).
[CrossRef] [PubMed]

Enger, J.

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]

Euteneuer, U.

A. Ashkin, K. Schutze, J. M. Dziedzic, U. Euteneuer, and M. Schliwa, "Force generation of organelle transport measured in vivo by an infrared laser trap," Nature 348,346-348 (1990).
[CrossRef] [PubMed]

Finer, J. T.

J. T. Finer, R. M. Simmons, and J. A. Spudich, "Single myosin molecule mechanics: piconewton forces and nanometre steps," Nature 368,113-119 (1994).
[CrossRef] [PubMed]

Franke-Arnold, S.

J. Leach, J. Courtial, K. Skeldon, S. M. Barnett, S. Franke-Arnold, and M. J. Padgett, "Interferometric Methods to Measure Orbital and Spin, or the Total Angular Momentum of a Single Photon," Phys. Rev. Lett. 92,013601 (2004).
[CrossRef] [PubMed]

Friese, M. E. J.

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]

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]

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]

Galajda, P.

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

Gelles, J.

H. Yin, M. D. Wang, K. Svoboda, R. Landick, S. M. Block, and J. Gelles, "Transcription Against an Applied Force," Science 270,1653-1657 (1995).
[CrossRef] [PubMed]

Granzier, H. L.

M. S. Z. Kellermayer, S. B. Smith, H. L. Granzier, and C. Bustamante, "Folding-Unfolding Transitions in Single Titin Molecules Characterized with Laser Tweezers," Science 276,1112-1116 (1997).
[CrossRef] [PubMed]

Grimes, S.

D. E. Smith, S. J. Tans, S. B. Smith, S. Grimes, D. L. Anderson, and C. Bustamante, "The bacteriophage theta 29 portal motor can package DNA against a larger internal force," Nature 413,748-752 (2001).
[CrossRef] [PubMed]

He, H.

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]

Heckenberg, N. R.

G. Knöner, S. Parkin, N. R. Heckenberg, and H. Rubinsztein-Dunlop, "Characterization of optically driven fluid stress fields with optical tweezers," Phys. Rev. E 72,031507 (2005).
[CrossRef]

S. J. Parkin, T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, "Optical measurement of torque exerted on an elongated object by a noncircular laser beam," Phys. Rev. A 70,023816 (2004).
[CrossRef]

A. I. Bishop, T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, "Optical Microrheology Using Rotating Laser-Trapped Particles," Phys. Rev. Lett. 92,198104 (2004).
[CrossRef] [PubMed]

A. I. Bishop, T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, "Optical application and measurement of torque on microparticles of isotropic nonabsorbing material," Phys. Rev. A 68,033802 (2003).
[CrossRef]

T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, "Optical measurement of microscopic torques," J. Mod. Opt. 48,405-413 (2001).

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]

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]

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]

Kellermayer, M. S. Z.

M. S. Z. Kellermayer, S. B. Smith, H. L. Granzier, and C. Bustamante, "Folding-Unfolding Transitions in Single Titin Molecules Characterized with Laser Tweezers," Science 276,1112-1116 (1997).
[CrossRef] [PubMed]

Knöner, G.

G. Knöner, S. Parkin, N. R. Heckenberg, and H. Rubinsztein-Dunlop, "Characterization of optically driven fluid stress fields with optical tweezers," Phys. Rev. E 72,031507 (2005).
[CrossRef]

Kourmanov, B.

Landick, R.

H. Yin, M. D. Wang, K. Svoboda, R. Landick, S. M. Block, and J. Gelles, "Transcription Against an Applied Force," Science 270,1653-1657 (1995).
[CrossRef] [PubMed]

Leach, J.

J. Leach, J. Courtial, K. Skeldon, S. M. Barnett, S. Franke-Arnold, and M. J. Padgett, "Interferometric Methods to Measure Orbital and Spin, or the Total Angular Momentum of a Single Photon," Phys. Rev. Lett. 92,013601 (2004).
[CrossRef] [PubMed]

Mair, A.

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, "Entanglement of the orbital angular momentum states of photons," Nature 412,313-316 (2001).
[CrossRef] [PubMed]

Nieminen, T. A.

A. I. Bishop, T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, "Optical Microrheology Using Rotating Laser-Trapped Particles," Phys. Rev. Lett. 92,198104 (2004).
[CrossRef] [PubMed]

S. J. Parkin, T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, "Optical measurement of torque exerted on an elongated object by a noncircular laser beam," Phys. Rev. A 70,023816 (2004).
[CrossRef]

A. I. Bishop, T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, "Optical application and measurement of torque on microparticles of isotropic nonabsorbing material," Phys. Rev. A 68,033802 (2003).
[CrossRef]

T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, "Optical measurement of microscopic torques," J. Mod. Opt. 48,405-413 (2001).

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]

Ormos, P.

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

Padgett, M. J.

J. Leach, J. Courtial, K. Skeldon, S. M. Barnett, S. Franke-Arnold, and M. J. Padgett, "Interferometric Methods to Measure Orbital and Spin, or the Total Angular Momentum of a Single Photon," Phys. Rev. Lett. 92,013601 (2004).
[CrossRef] [PubMed]

J. Courtial, D. A. Robertson, K. Dholakia, L. Allen, and M. J. Padgett, "Rotational Frequency Shift of a Light Beam," Phys. Rev. Lett. 81,4828-4830 (1998).
[CrossRef]

Parkin, S.

G. Knöner, S. Parkin, N. R. Heckenberg, and H. Rubinsztein-Dunlop, "Characterization of optically driven fluid stress fields with optical tweezers," Phys. Rev. E 72,031507 (2005).
[CrossRef]

Parkin, S. J.

S. J. Parkin, T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, "Optical measurement of torque exerted on an elongated object by a noncircular laser beam," Phys. Rev. A 70,023816 (2004).
[CrossRef]

Robertson, D. A.

J. Courtial, D. A. Robertson, K. Dholakia, L. Allen, and M. J. Padgett, "Rotational Frequency Shift of a Light Beam," Phys. Rev. Lett. 81,4828-4830 (1998).
[CrossRef]

Rubinsztein-Dunlop, H.

G. Knöner, S. Parkin, N. R. Heckenberg, and H. Rubinsztein-Dunlop, "Characterization of optically driven fluid stress fields with optical tweezers," Phys. Rev. E 72,031507 (2005).
[CrossRef]

S. J. Parkin, T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, "Optical measurement of torque exerted on an elongated object by a noncircular laser beam," Phys. Rev. A 70,023816 (2004).
[CrossRef]

A. I. Bishop, T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, "Optical Microrheology Using Rotating Laser-Trapped Particles," Phys. Rev. Lett. 92,198104 (2004).
[CrossRef] [PubMed]

A. I. Bishop, T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, "Optical application and measurement of torque on microparticles of isotropic nonabsorbing material," Phys. Rev. A 68,033802 (2003).
[CrossRef]

T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, "Optical measurement of microscopic torques," J. Mod. Opt. 48,405-413 (2001).

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]

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]

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]

Ryu, W. S.

W. S. Ryu, R. M. Berry, and H. C. Berg, "Torque-generating units of the flagellar motor of Escherichia coli have a high duty ratio," Nature 403,444-447 (2000).
[CrossRef] [PubMed]

Schliwa, M.

A. Ashkin, K. Schutze, J. M. Dziedzic, U. Euteneuer, and M. Schliwa, "Force generation of organelle transport measured in vivo by an infrared laser trap," Nature 348,346-348 (1990).
[CrossRef] [PubMed]

Schmidt, C. F.

K. Svoboda, C. F. Schmidt, B. J. Schnapp, and S. M. Block, "Direct observation of kinesin stepping by optical trapping interferometry," Nature 365,721-727 (1993).
[CrossRef] [PubMed]

Schnapp, B. J.

K. Svoboda, C. F. Schmidt, B. J. Schnapp, and S. M. Block, "Direct observation of kinesin stepping by optical trapping interferometry," Nature 365,721-727 (1993).
[CrossRef] [PubMed]

Schutze, K.

A. Ashkin, K. Schutze, J. M. Dziedzic, U. Euteneuer, and M. Schliwa, "Force generation of organelle transport measured in vivo by an infrared laser trap," Nature 348,346-348 (1990).
[CrossRef] [PubMed]

Simmons, R. M.

L. Tskhovrebova, J. Trinick, J. A. Sleep, and R. M. Simmons, "Elasticity and unfolding of single molecules of the giant muscle protein titin," Nature 387,308-312 (1997).
[CrossRef] [PubMed]

J. T. Finer, R. M. Simmons, and J. A. Spudich, "Single myosin molecule mechanics: piconewton forces and nanometre steps," Nature 368,113-119 (1994).
[CrossRef] [PubMed]

Skeldon, K.

J. Leach, J. Courtial, K. Skeldon, S. M. Barnett, S. Franke-Arnold, and M. J. Padgett, "Interferometric Methods to Measure Orbital and Spin, or the Total Angular Momentum of a Single Photon," Phys. Rev. Lett. 92,013601 (2004).
[CrossRef] [PubMed]

Sleep, J. A.

L. Tskhovrebova, J. Trinick, J. A. Sleep, and R. M. Simmons, "Elasticity and unfolding of single molecules of the giant muscle protein titin," Nature 387,308-312 (1997).
[CrossRef] [PubMed]

Slyusar, V. V.

Smith, D. E.

D. E. Smith, S. J. Tans, S. B. Smith, S. Grimes, D. L. Anderson, and C. Bustamante, "The bacteriophage theta 29 portal motor can package DNA against a larger internal force," Nature 413,748-752 (2001).
[CrossRef] [PubMed]

Smith, S. B.

D. E. Smith, S. J. Tans, S. B. Smith, S. Grimes, D. L. Anderson, and C. Bustamante, "The bacteriophage theta 29 portal motor can package DNA against a larger internal force," Nature 413,748-752 (2001).
[CrossRef] [PubMed]

M. S. Z. Kellermayer, S. B. Smith, H. L. Granzier, and C. Bustamante, "Folding-Unfolding Transitions in Single Titin Molecules Characterized with Laser Tweezers," Science 276,1112-1116 (1997).
[CrossRef] [PubMed]

Soskin, M. S.

Spreeuw, R. J. C.

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

Spudich, J. A.

J. T. Finer, R. M. Simmons, and J. A. Spudich, "Single myosin molecule mechanics: piconewton forces and nanometre steps," Nature 368,113-119 (1994).
[CrossRef] [PubMed]

Svoboda, K.

H. Yin, M. D. Wang, K. Svoboda, R. Landick, S. M. Block, and J. Gelles, "Transcription Against an Applied Force," Science 270,1653-1657 (1995).
[CrossRef] [PubMed]

K. Svoboda, C. F. Schmidt, B. J. Schnapp, and S. M. Block, "Direct observation of kinesin stepping by optical trapping interferometry," Nature 365,721-727 (1993).
[CrossRef] [PubMed]

Tans, S. J.

D. E. Smith, S. J. Tans, S. B. Smith, S. Grimes, D. L. Anderson, and C. Bustamante, "The bacteriophage theta 29 portal motor can package DNA against a larger internal force," Nature 413,748-752 (2001).
[CrossRef] [PubMed]

Trinick, J.

L. Tskhovrebova, J. Trinick, J. A. Sleep, and R. M. Simmons, "Elasticity and unfolding of single molecules of the giant muscle protein titin," Nature 387,308-312 (1997).
[CrossRef] [PubMed]

Tskhovrebova, L.

L. Tskhovrebova, J. Trinick, J. A. Sleep, and R. M. Simmons, "Elasticity and unfolding of single molecules of the giant muscle protein titin," Nature 387,308-312 (1997).
[CrossRef] [PubMed]

Vasnetsov, M. V.

Vaziri, A.

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, "Entanglement of the orbital angular momentum states of photons," Nature 412,313-316 (2001).
[CrossRef] [PubMed]

Wang, M. D.

H. Yin, M. D. Wang, K. Svoboda, R. Landick, S. M. Block, and J. Gelles, "Transcription Against an Applied Force," Science 270,1653-1657 (1995).
[CrossRef] [PubMed]

Weihs, G.

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, "Entanglement of the orbital angular momentum states of photons," Nature 412,313-316 (2001).
[CrossRef] [PubMed]

Woerdman, J. P.

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

Yin, H.

H. Yin, M. D. Wang, K. Svoboda, R. Landick, S. M. Block, and J. Gelles, "Transcription Against an Applied Force," Science 270,1653-1657 (1995).
[CrossRef] [PubMed]

Zeilinger, A.

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, "Entanglement of the orbital angular momentum states of photons," Nature 412,313-316 (2001).
[CrossRef] [PubMed]

Appl. Phys. Lett. (1)

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

J. Mod. Opt. (1)

T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, "Optical measurement of microscopic torques," J. Mod. Opt. 48,405-413 (2001).

Nature (9)

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, "Entanglement of the orbital angular momentum states of photons," Nature 412,313-316 (2001).
[CrossRef] [PubMed]

S. M. Block, D. F. Blair, and H. C. Berg, "Compliance of bacterial flagella measured with optical tweezers," Nature 338,514-518 (1989).
[CrossRef] [PubMed]

A. Ashkin, K. Schutze, J. M. Dziedzic, U. Euteneuer, and M. Schliwa, "Force generation of organelle transport measured in vivo by an infrared laser trap," Nature 348,346-348 (1990).
[CrossRef] [PubMed]

K. Svoboda, C. F. Schmidt, B. J. Schnapp, and S. M. Block, "Direct observation of kinesin stepping by optical trapping interferometry," Nature 365,721-727 (1993).
[CrossRef] [PubMed]

J. T. Finer, R. M. Simmons, and J. A. Spudich, "Single myosin molecule mechanics: piconewton forces and nanometre steps," Nature 368,113-119 (1994).
[CrossRef] [PubMed]

L. Tskhovrebova, J. Trinick, J. A. Sleep, and R. M. Simmons, "Elasticity and unfolding of single molecules of the giant muscle protein titin," Nature 387,308-312 (1997).
[CrossRef] [PubMed]

D. E. Smith, S. J. Tans, S. B. Smith, S. Grimes, D. L. Anderson, and C. Bustamante, "The bacteriophage theta 29 portal motor can package DNA against a larger internal force," Nature 413,748-752 (2001).
[CrossRef] [PubMed]

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]

W. S. Ryu, R. M. Berry, and H. C. Berg, "Torque-generating units of the flagellar motor of Escherichia coli have a high duty ratio," Nature 403,444-447 (2000).
[CrossRef] [PubMed]

Opt. Express (1)

Opt. Lett. (2)

Phys. Rev. A (4)

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]

S. J. Parkin, T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, "Optical measurement of torque exerted on an elongated object by a noncircular laser beam," Phys. Rev. A 70,023816 (2004).
[CrossRef]

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

A. I. Bishop, T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, "Optical application and measurement of torque on microparticles of isotropic nonabsorbing material," Phys. Rev. A 68,033802 (2003).
[CrossRef]

Phys. Rev. E (1)

G. Knöner, S. Parkin, N. R. Heckenberg, and H. Rubinsztein-Dunlop, "Characterization of optically driven fluid stress fields with optical tweezers," Phys. Rev. E 72,031507 (2005).
[CrossRef]

Phys. Rev. Lett. (4)

A. I. Bishop, T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, "Optical Microrheology Using Rotating Laser-Trapped Particles," Phys. Rev. Lett. 92,198104 (2004).
[CrossRef] [PubMed]

J. Courtial, D. A. Robertson, K. Dholakia, L. Allen, and M. J. Padgett, "Rotational Frequency Shift of a Light Beam," Phys. Rev. Lett. 81,4828-4830 (1998).
[CrossRef]

J. Leach, J. Courtial, K. Skeldon, S. M. Barnett, S. Franke-Arnold, and M. J. Padgett, "Interferometric Methods to Measure Orbital and Spin, or the Total Angular Momentum of a Single Photon," Phys. Rev. Lett. 92,013601 (2004).
[CrossRef] [PubMed]

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]

Science (2)

H. Yin, M. D. Wang, K. Svoboda, R. Landick, S. M. Block, and J. Gelles, "Transcription Against an Applied Force," Science 270,1653-1657 (1995).
[CrossRef] [PubMed]

M. S. Z. Kellermayer, S. B. Smith, H. L. Granzier, and C. Bustamante, "Folding-Unfolding Transitions in Single Titin Molecules Characterized with Laser Tweezers," Science 276,1112-1116 (1997).
[CrossRef] [PubMed]

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Figures (3)

Fig. 1.
Fig. 1.

The optical tweezers setup used to make measurements of optical torque applied to a trapped object. The two polystyrene spheres that were trapped and rotated are shown in the inset. The phase hologram created a LG02 beam in the first diffraction order, which was used as the trapping beam. The three detectors measured the rotation rate of the particle and the change in polarisation of the trapping beam.

Fig. 2.
Fig. 2.

(a) Typical signal from photo-detector 3, from which the rotation rate of the particle was found. The solid line (—) is the actual signal from the detector and the dashed line (––) is a sinusoidal fit of the data. (b) Typical signals from photo-detectors 1 and 2 for the case when no particle is trapped and also the case when the particles are trapped by the optical tweezers. The ‘ripple’ visible in the signal with the particle trapped is due to the rotation of the particle in the trap and has the same frequency as measured by photo-detector 3.

Fig. 3.
Fig. 3.

The rotation rate, Ω, of the trapped particle (two polystrene spheres) as a function of the optically applied torque due to the spin angular momentum of the trapping beam, τspin. The torque transfer of the orbital component is found from the slope (1/K) and intercept (Ω0) of the fit.

Equations (3)

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

τ total = τ orbital + τ spin = Ω K
τ orbital = K Ω 0 = Ω 0 slope = 0.017 ± 0.003 h ̄ .
τ D = 12 πη a 3 Ω

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