Abstract

Optical traps use the forces exerted by structured beams of light to confine and manipulate microscopic objects in three dimensions. A popular implementation involves structuring the trap-forming beam with computer-generated holograms before focusing it into traps with a high-numerical-aperture optical train. Here, we present a fully vectorial theory for the forces and torques exerted by such systems.

© 2008 Optical Society of America

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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
  33. Y. Roichman and D. G. Grier, "Holographic assembly of quasicrystalline photonic heterostructures," Opt. Express 13, 5434-5439 (2005).
    [CrossRef] [PubMed]
  34. H. He, N. R. Heckenberg, and H. Rubinsztein-Dunlop, "Optical particle trapping with higher-order doughnut beams produced using high efficiency computer generated holograms," J. Mod. Opt. 42, 217-223 (1995).
    [CrossRef]
  35. N. B. Simpson, L. Allen, and M. J. Padgett, "Optical tweezers and optical spanners with Laguerre-Gaussian modes," J. Mod. Opt. 43, 2485-2491 (1996).
    [CrossRef]
  36. K. T. Gahagan and G. A. Swartzlander, "Optical vortex trapping of particles," Opt. Lett. 21, 827-829 (1996).
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  37. J. E. Curtis and D. G. Grier, "Structure of optical vortices," Phys. Rev. Lett. 90, 133901 (2003).
    [CrossRef] [PubMed]
  38. J. E. Curtis and D. G. Grier, "Modulated optical vortices," Opt. Lett. 28, 872-874 (2003).
    [CrossRef] [PubMed]
  39. S. Sundbeck, I. Gruzberg, and D. G. Grier, "Structure and scaling of helical modes of light," Opt. Lett. 30, 477-479 (2005).
    [CrossRef] [PubMed]
  40. A. T. O???Neil, I. MacVicar, 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] [PubMed]
  41. M. Babiker, C. R. Bennet, D. L. Andrews, and L. C. D???avila Romero, "Orbital angular momentum exchange in the interaction of twisted light with molecules," Phys. Rev. Lett. 89, 143601 (2002).
    [CrossRef] [PubMed]
  42. 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]
  43. L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, "Orbital angular-momentum of light and the transformation of Laguerre-Gaussian laser modes," Phys. Rev. A 45, 8185-8189 (1992).
    [CrossRef] [PubMed]
  44. J. Leach, M. J. Padgett, S. M. Barnett, S. Franke-Arnold, and J. Courtial, "Measuring the orbital angular momentum of a single photon," Phys. Rev. Lett. 88, 257901 (2002).
    [CrossRef] [PubMed]
  45. N. B. Simpson, K. Dholakia, L. Allen, and M. J. Padgett, "Mechanical equivalence of spin and orbital angular momentum of light: An optical spanner," Opt. Lett. 22, 52-54 (1997).
    [CrossRef] [PubMed]
  46. Y. Roichman and D. G. Grier, "Three-dimensional holographic ring traps," Proc. SPIE 6483, 64830F (2007).
    [CrossRef]
  47. K. Ladavac and D. G. Grier, "Microoptomechanical pump assembled and driven by holographic optical vortex arrays," Opt. Express 12, 1144-1149 (2004).
    [CrossRef] [PubMed]

2008 (4)

Y. Roichman, B. Sun, Y. Roichman, J. Amato-Grill, and D. G. Grier, "Optical forces arising from phase gradients," Phys. Rev. Lett. 100, 013602 (2008).
[CrossRef] [PubMed]

D. C. Benito, S. H. Simpson, and H. Simon, "FDTD simulations of forces on particles during holographic assembly," Opt. Express 16, 2942-2957 (2008).
[CrossRef] [PubMed]

S. S. Sherif, M. R. Foreman, and P. Torok, "Eigenfunction expansion of the electric fields in the focal region of a high numerical aperture focusing system," Opt. Express 16, 3397-3407 (2008).
[CrossRef] [PubMed]

Y. Zhang, Y. Lie, J. Qi, G. Cui, H. Lui, J. Chen, L. Zhao, J. Xu, and Q. Sun, "Influence of absorption on optical trapping force of spherical particles in a focussed Gaussian beam," J. Opt. A 10, 085001 (2008).
[CrossRef]

2007 (3)

P. R. T. Munro and P. Torok, "Calculation of the image of an arbitrary vectorial electromagnetic field," Opt. Express 15, 9293-9307 (2007).
[CrossRef] [PubMed]

T. A. Nieminen, L. V. L. Y., A. B. Stilgoe, G. Knoner, A. M. Branczyk, N. R. Heckenberg, and H. Rubinsztein- Dunlop, "Optical tweezers computational toolbox," J. Opt. A 9, S196-S203 (2007).
[CrossRef]

Y. Roichman and D. G. Grier, "Three-dimensional holographic ring traps," Proc. SPIE 6483, 64830F (2007).
[CrossRef]

2006 (3)

2005 (4)

2004 (2)

2003 (4)

A. Mazolli, P. A. Maia Neto, and H. M. Nussenzveig, "Theory of trapping forces in optical tweezers," Proc. Royal Soc. London A 459, 3021-3041 (2003).
[CrossRef]

D. G. Grier, "A revolution in optical manipulation," Nature 424, 810-816 (2003).
[CrossRef] [PubMed]

J. E. Curtis and D. G. Grier, "Structure of optical vortices," Phys. Rev. Lett. 90, 133901 (2003).
[CrossRef] [PubMed]

J. E. Curtis and D. G. Grier, "Modulated optical vortices," Opt. Lett. 28, 872-874 (2003).
[CrossRef] [PubMed]

2002 (6)

A. Rohrbach and E. H. K. Stelzer, "Three-dimensional position detection of optical trapped dielectric particles," J. Appl. Phys. 91, 5474-5488 (2002).
[CrossRef]

A. Rohrbach and E. H. K. Stelzer, "Trapping forces, force constants, and potential depths for dielectric spheres in the presence of spherical aberrations," Appl. Opt. 41, 2494-2507 (2002).
[CrossRef] [PubMed]

J. E. Curtis, B. A. Koss, and D. G. Grier, "Dynamic holographic optical tweezers," Opt. Commun. 207, 169-175 (2002).
[CrossRef]

J. Leach, M. J. Padgett, S. M. Barnett, S. Franke-Arnold, and J. Courtial, "Measuring the orbital angular momentum of a single photon," Phys. Rev. Lett. 88, 257901 (2002).
[CrossRef] [PubMed]

A. T. O???Neil, I. MacVicar, 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] [PubMed]

M. Babiker, C. R. Bennet, D. L. Andrews, and L. C. D???avila Romero, "Orbital angular momentum exchange in the interaction of twisted light with molecules," Phys. Rev. Lett. 89, 143601 (2002).
[CrossRef] [PubMed]

2000 (2)

J. Liesener, M. Reicherter, T. Haist, and H. J. Tiziani, "Multi-functional optical tweezers using computergenerated holograms," Opt. Commun. 185, 77-82 (2000).
[CrossRef]

P. A. Maia Neto and H. M. Nussenzveig, "Theory of optical tweezers," Europhys. Lett. 50, 702-708 (2000).
[CrossRef]

1998 (1)

E. R. Dufresne and D. G. Grier, "Optical tweezer arrays and optical substrates created with diffractive optical elements," Rev. Sci. Instrum. 69, 1974-1977 (1998).
[CrossRef]

1997 (1)

1996 (3)

1995 (2)

H. He, N. R. Heckenberg, and H. Rubinsztein-Dunlop, "Optical particle trapping with higher-order doughnut beams produced using high efficiency computer generated holograms," J. Mod. Opt. 42, 217-223 (1995).
[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]

1992 (2)

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

A. Ashkin, "Forces of a single-beam gradient laser trap on a dielectric sphere in the ray optics regime," Biophys. J. 61, 569-582 (1992).
[CrossRef] [PubMed]

1986 (1)

1984 (1)

P. L. Marston and J. H. Crichton, "Radiation torque on a sphere caused by a circularly polarized electromagnetic wave," Phys. Rev. A 30, 2508-2516 (1984).
[CrossRef]

1980 (2)

W. J. Wiscombe, "Improved Mie scattering algorithms," Appl. Opt. 19, 1505-1509 (1980).
[CrossRef] [PubMed]

A. Ashkin, "Applications of laser radiation pressure," Science 210, 1081-1088 (1980).
[CrossRef] [PubMed]

1976 (1)

1970 (1)

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

1959 (1)

E. Wolf, "Electromagnetic diffraction in optical systems. I. An integral representation of the image field," Proc. Royal Soc. London A 253, 349-357 (1959).
[CrossRef]

Allen, L.

A. T. O???Neil, I. MacVicar, 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] [PubMed]

N. B. Simpson, K. Dholakia, L. Allen, and M. J. Padgett, "Mechanical equivalence of spin and orbital angular momentum of light: An optical spanner," Opt. Lett. 22, 52-54 (1997).
[CrossRef] [PubMed]

N. B. Simpson, L. Allen, and M. J. Padgett, "Optical tweezers and optical spanners with Laguerre-Gaussian modes," J. Mod. Opt. 43, 2485-2491 (1996).
[CrossRef]

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

Amato-Grill, J.

Y. Roichman, B. Sun, Y. Roichman, J. Amato-Grill, and D. G. Grier, "Optical forces arising from phase gradients," Phys. Rev. Lett. 100, 013602 (2008).
[CrossRef] [PubMed]

Andrews, D. L.

M. Babiker, C. R. Bennet, D. L. Andrews, and L. C. D???avila Romero, "Orbital angular momentum exchange in the interaction of twisted light with molecules," Phys. Rev. Lett. 89, 143601 (2002).
[CrossRef] [PubMed]

Ashkin, A.

A. Ashkin, "Forces of a single-beam gradient laser trap on a dielectric sphere in the ray optics regime," Biophys. J. 61, 569-582 (1992).
[CrossRef] [PubMed]

A. Ashkin, J. M. Dziedzic, J. E. Bjorkholm, and S. Chu, "Observation of a single-beam gradient force optical trap for dielectric particles," Opt. Lett. 11, 288-290 (1986).
[CrossRef] [PubMed]

A. Ashkin, "Applications of laser radiation pressure," Science 210, 1081-1088 (1980).
[CrossRef] [PubMed]

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

Babiker, M.

M. Babiker, C. R. Bennet, D. L. Andrews, and L. C. D???avila Romero, "Orbital angular momentum exchange in the interaction of twisted light with molecules," Phys. Rev. Lett. 89, 143601 (2002).
[CrossRef] [PubMed]

Barnett, S. M.

J. Leach, M. J. Padgett, S. M. Barnett, S. Franke-Arnold, and J. Courtial, "Measuring the orbital angular momentum of a single photon," Phys. Rev. Lett. 88, 257901 (2002).
[CrossRef] [PubMed]

Beijersbergen, M. W.

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

Benito, D. C.

Bennet, C. R.

M. Babiker, C. R. Bennet, D. L. Andrews, and L. C. D???avila Romero, "Orbital angular momentum exchange in the interaction of twisted light with molecules," Phys. Rev. Lett. 89, 143601 (2002).
[CrossRef] [PubMed]

Bjorkholm, J. E.

Chaumet, P. C.

P. C. Chaumet, A. Rahmani, and M. Nieto-Vesperinas, "Photonic force spectroscopy on metallic and absorbing nanoparticles," Phys. Rev. B 71, 045425 (2005).
[CrossRef]

Chen, J.

Y. Zhang, Y. Lie, J. Qi, G. Cui, H. Lui, J. Chen, L. Zhao, J. Xu, and Q. Sun, "Influence of absorption on optical trapping force of spherical particles in a focussed Gaussian beam," J. Opt. A 10, 085001 (2008).
[CrossRef]

Chu, S.

Courtial, J.

J. Leach, M. J. Padgett, S. M. Barnett, S. Franke-Arnold, and J. Courtial, "Measuring the orbital angular momentum of a single photon," Phys. Rev. Lett. 88, 257901 (2002).
[CrossRef] [PubMed]

Crichton, J. H.

P. L. Marston and J. H. Crichton, "Radiation torque on a sphere caused by a circularly polarized electromagnetic wave," Phys. Rev. A 30, 2508-2516 (1984).
[CrossRef]

Cui, G.

Y. Zhang, Y. Lie, J. Qi, G. Cui, H. Lui, J. Chen, L. Zhao, J. Xu, and Q. Sun, "Influence of absorption on optical trapping force of spherical particles in a focussed Gaussian beam," J. Opt. A 10, 085001 (2008).
[CrossRef]

Curtis, J. E.

J. E. Curtis and D. G. Grier, "Structure of optical vortices," Phys. Rev. Lett. 90, 133901 (2003).
[CrossRef] [PubMed]

J. E. Curtis and D. G. Grier, "Modulated optical vortices," Opt. Lett. 28, 872-874 (2003).
[CrossRef] [PubMed]

J. E. Curtis, B. A. Koss, and D. G. Grier, "Dynamic holographic optical tweezers," Opt. Commun. 207, 169-175 (2002).
[CrossRef]

Dholakia, K.

Dufresne, E. R.

E. R. Dufresne and D. G. Grier, "Optical tweezer arrays and optical substrates created with diffractive optical elements," Rev. Sci. Instrum. 69, 1974-1977 (1998).
[CrossRef]

Dziedzic, J. M.

Foreman, M. R.

Franke-Arnold, S.

J. Leach, M. J. Padgett, S. M. Barnett, S. Franke-Arnold, and J. Courtial, "Measuring the orbital angular momentum of a single photon," Phys. Rev. Lett. 88, 257901 (2002).
[CrossRef] [PubMed]

Friese, M. E. J.

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]

Gahagan, K. T.

Gardel, E.

Gouesbet, G.

Grehan, G.

Grier, D. G.

Y. Roichman, B. Sun, Y. Roichman, J. Amato-Grill, and D. G. Grier, "Optical forces arising from phase gradients," Phys. Rev. Lett. 100, 013602 (2008).
[CrossRef] [PubMed]

Y. Roichman and D. G. Grier, "Three-dimensional holographic ring traps," Proc. SPIE 6483, 64830F (2007).
[CrossRef]

Y. Roichman, A. S. Waldron, E. Gardel, and D. G. Grier, "Performance of optical traps with geometric aberrations," Appl. Opt. 45, 3425-3429 (2006).
[CrossRef] [PubMed]

Y. Roichman and D. G. Grier, "Projecting extended optical traps with shape-phase holography," Opt. Lett. 31, 1675-1677 (2006).
[CrossRef] [PubMed]

M. Polin, K. Ladavac, S.-H. Lee, Y. Roichman, and D. G. Grier, "Optimized holographic optical traps," Opt. Express 13, 5831-5845 (2005).
[CrossRef] [PubMed]

Y. Roichman and D. G. Grier, "Holographic assembly of quasicrystalline photonic heterostructures," Opt. Express 13, 5434-5439 (2005).
[CrossRef] [PubMed]

S. Sundbeck, I. Gruzberg, and D. G. Grier, "Structure and scaling of helical modes of light," Opt. Lett. 30, 477-479 (2005).
[CrossRef] [PubMed]

K. Ladavac and D. G. Grier, "Microoptomechanical pump assembled and driven by holographic optical vortex arrays," Opt. Express 12, 1144-1149 (2004).
[CrossRef] [PubMed]

J. E. Curtis and D. G. Grier, "Modulated optical vortices," Opt. Lett. 28, 872-874 (2003).
[CrossRef] [PubMed]

J. E. Curtis and D. G. Grier, "Structure of optical vortices," Phys. Rev. Lett. 90, 133901 (2003).
[CrossRef] [PubMed]

D. G. Grier, "A revolution in optical manipulation," Nature 424, 810-816 (2003).
[CrossRef] [PubMed]

J. E. Curtis, B. A. Koss, and D. G. Grier, "Dynamic holographic optical tweezers," Opt. Commun. 207, 169-175 (2002).
[CrossRef]

E. R. Dufresne and D. G. Grier, "Optical tweezer arrays and optical substrates created with diffractive optical elements," Rev. Sci. Instrum. 69, 1974-1977 (1998).
[CrossRef]

Gruzberg, I.

Grzegorczyk, T. M.

B. A. Kemp, T. M. Grzegorczyk, and J. A. Kong, "Optical momentum transfer to absorbing Mie particles," Phys. Rev. Lett. 97, 133902 (2006).
[CrossRef] [PubMed]

Haist, T.

J. Liesener, M. Reicherter, T. Haist, and H. J. Tiziani, "Multi-functional optical tweezers using computergenerated holograms," Opt. Commun. 185, 77-82 (2000).
[CrossRef]

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]

H. He, N. R. Heckenberg, and H. Rubinsztein-Dunlop, "Optical particle trapping with higher-order doughnut beams produced using high efficiency computer generated holograms," J. Mod. Opt. 42, 217-223 (1995).
[CrossRef]

Heckenberg, N. R.

H. He, N. R. Heckenberg, and H. Rubinsztein-Dunlop, "Optical particle trapping with higher-order doughnut beams produced using high efficiency computer generated holograms," J. Mod. Opt. 42, 217-223 (1995).
[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]

Kemp, B. A.

B. A. Kemp, T. M. Grzegorczyk, and J. A. Kong, "Optical momentum transfer to absorbing Mie particles," Phys. Rev. Lett. 97, 133902 (2006).
[CrossRef] [PubMed]

Kong, J. A.

B. A. Kemp, T. M. Grzegorczyk, and J. A. Kong, "Optical momentum transfer to absorbing Mie particles," Phys. Rev. Lett. 97, 133902 (2006).
[CrossRef] [PubMed]

Koss, B. A.

J. E. Curtis, B. A. Koss, and D. G. Grier, "Dynamic holographic optical tweezers," Opt. Commun. 207, 169-175 (2002).
[CrossRef]

Ladavac, K.

Leach, J.

J. Leach, M. J. Padgett, S. M. Barnett, S. Franke-Arnold, and J. Courtial, "Measuring the orbital angular momentum of a single photon," Phys. Rev. Lett. 88, 257901 (2002).
[CrossRef] [PubMed]

Lee, S.-H.

Lentz, W. J.

Lie, Y.

Y. Zhang, Y. Lie, J. Qi, G. Cui, H. Lui, J. Chen, L. Zhao, J. Xu, and Q. Sun, "Influence of absorption on optical trapping force of spherical particles in a focussed Gaussian beam," J. Opt. A 10, 085001 (2008).
[CrossRef]

Liesener, J.

J. Liesener, M. Reicherter, T. Haist, and H. J. Tiziani, "Multi-functional optical tweezers using computergenerated holograms," Opt. Commun. 185, 77-82 (2000).
[CrossRef]

Loudon, R.

R. Loudon, "Radiation pressure and momentum in dielectrics," Fortschr. Phys. 52, 1134-1140 (2004).
[CrossRef]

Lui, H.

Y. Zhang, Y. Lie, J. Qi, G. Cui, H. Lui, J. Chen, L. Zhao, J. Xu, and Q. Sun, "Influence of absorption on optical trapping force of spherical particles in a focussed Gaussian beam," J. Opt. A 10, 085001 (2008).
[CrossRef]

MacVicar, I.

A. T. O???Neil, I. MacVicar, 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] [PubMed]

Maia Neto, P. A.

A. Mazolli, P. A. Maia Neto, and H. M. Nussenzveig, "Theory of trapping forces in optical tweezers," Proc. Royal Soc. London A 459, 3021-3041 (2003).
[CrossRef]

P. A. Maia Neto and H. M. Nussenzveig, "Theory of optical tweezers," Europhys. Lett. 50, 702-708 (2000).
[CrossRef]

Marston, P. L.

P. L. Marston and J. H. Crichton, "Radiation torque on a sphere caused by a circularly polarized electromagnetic wave," Phys. Rev. A 30, 2508-2516 (1984).
[CrossRef]

Mazolli, A.

A. Mazolli, P. A. Maia Neto, and H. M. Nussenzveig, "Theory of trapping forces in optical tweezers," Proc. Royal Soc. London A 459, 3021-3041 (2003).
[CrossRef]

Munro, P. R. T.

Nieminen, T. A.

T. A. Nieminen, L. V. L. Y., A. B. Stilgoe, G. Knoner, A. M. Branczyk, N. R. Heckenberg, and H. Rubinsztein- Dunlop, "Optical tweezers computational toolbox," J. Opt. A 9, S196-S203 (2007).
[CrossRef]

Nieto-Vesperinas, M.

P. C. Chaumet, A. Rahmani, and M. Nieto-Vesperinas, "Photonic force spectroscopy on metallic and absorbing nanoparticles," Phys. Rev. B 71, 045425 (2005).
[CrossRef]

Nussenzveig, H. M.

A. Mazolli, P. A. Maia Neto, and H. M. Nussenzveig, "Theory of trapping forces in optical tweezers," Proc. Royal Soc. London A 459, 3021-3041 (2003).
[CrossRef]

P. A. Maia Neto and H. M. Nussenzveig, "Theory of optical tweezers," Europhys. Lett. 50, 702-708 (2000).
[CrossRef]

O???Neil, A. T.

A. T. O???Neil, I. MacVicar, 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] [PubMed]

Padgett, M. J.

A. T. O???Neil, I. MacVicar, 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] [PubMed]

J. Leach, M. J. Padgett, S. M. Barnett, S. Franke-Arnold, and J. Courtial, "Measuring the orbital angular momentum of a single photon," Phys. Rev. Lett. 88, 257901 (2002).
[CrossRef] [PubMed]

N. B. Simpson, K. Dholakia, L. Allen, and M. J. Padgett, "Mechanical equivalence of spin and orbital angular momentum of light: An optical spanner," Opt. Lett. 22, 52-54 (1997).
[CrossRef] [PubMed]

N. B. Simpson, L. Allen, and M. J. Padgett, "Optical tweezers and optical spanners with Laguerre-Gaussian modes," J. Mod. Opt. 43, 2485-2491 (1996).
[CrossRef]

Polin, M.

Qi, J.

Y. Zhang, Y. Lie, J. Qi, G. Cui, H. Lui, J. Chen, L. Zhao, J. Xu, and Q. Sun, "Influence of absorption on optical trapping force of spherical particles in a focussed Gaussian beam," J. Opt. A 10, 085001 (2008).
[CrossRef]

Rahmani, A.

P. C. Chaumet, A. Rahmani, and M. Nieto-Vesperinas, "Photonic force spectroscopy on metallic and absorbing nanoparticles," Phys. Rev. B 71, 045425 (2005).
[CrossRef]

Reicherter, M.

J. Liesener, M. Reicherter, T. Haist, and H. J. Tiziani, "Multi-functional optical tweezers using computergenerated holograms," Opt. Commun. 185, 77-82 (2000).
[CrossRef]

Ren, K. F.

Rohrbach, A.

A. Rohrbach and E. H. K. Stelzer, "Trapping forces, force constants, and potential depths for dielectric spheres in the presence of spherical aberrations," Appl. Opt. 41, 2494-2507 (2002).
[CrossRef] [PubMed]

A. Rohrbach and E. H. K. Stelzer, "Three-dimensional position detection of optical trapped dielectric particles," J. Appl. Phys. 91, 5474-5488 (2002).
[CrossRef]

Roichman, Y.

Rubinsztein-Dunlop, H.

H. He, N. R. Heckenberg, and H. Rubinsztein-Dunlop, "Optical particle trapping with higher-order doughnut beams produced using high efficiency computer generated holograms," J. Mod. Opt. 42, 217-223 (1995).
[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]

Sherif, S. S.

Simon, H.

Simpson, N. B.

N. B. Simpson, K. Dholakia, L. Allen, and M. J. Padgett, "Mechanical equivalence of spin and orbital angular momentum of light: An optical spanner," Opt. Lett. 22, 52-54 (1997).
[CrossRef] [PubMed]

N. B. Simpson, L. Allen, and M. J. Padgett, "Optical tweezers and optical spanners with Laguerre-Gaussian modes," J. Mod. Opt. 43, 2485-2491 (1996).
[CrossRef]

Simpson, S. H.

Spreeuw, R. J. C.

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

Stelzer, E. H. K.

A. Rohrbach and E. H. K. Stelzer, "Trapping forces, force constants, and potential depths for dielectric spheres in the presence of spherical aberrations," Appl. Opt. 41, 2494-2507 (2002).
[CrossRef] [PubMed]

A. Rohrbach and E. H. K. Stelzer, "Three-dimensional position detection of optical trapped dielectric particles," J. Appl. Phys. 91, 5474-5488 (2002).
[CrossRef]

Sun, B.

Y. Roichman, B. Sun, Y. Roichman, J. Amato-Grill, and D. G. Grier, "Optical forces arising from phase gradients," Phys. Rev. Lett. 100, 013602 (2008).
[CrossRef] [PubMed]

Sun, Q.

Y. Zhang, Y. Lie, J. Qi, G. Cui, H. Lui, J. Chen, L. Zhao, J. Xu, and Q. Sun, "Influence of absorption on optical trapping force of spherical particles in a focussed Gaussian beam," J. Opt. A 10, 085001 (2008).
[CrossRef]

Sundbeck, S.

Swartzlander, G. A.

Tiziani, H. J.

J. Liesener, M. Reicherter, T. Haist, and H. J. Tiziani, "Multi-functional optical tweezers using computergenerated holograms," Opt. Commun. 185, 77-82 (2000).
[CrossRef]

Torok, P.

Waldron, A. S.

Wiscombe, W. J.

Woerdman, J. P.

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

Wolf, E.

E. Wolf, "Electromagnetic diffraction in optical systems. I. An integral representation of the image field," Proc. Royal Soc. London A 253, 349-357 (1959).
[CrossRef]

Xu, J.

Y. Zhang, Y. Lie, J. Qi, G. Cui, H. Lui, J. Chen, L. Zhao, J. Xu, and Q. Sun, "Influence of absorption on optical trapping force of spherical particles in a focussed Gaussian beam," J. Opt. A 10, 085001 (2008).
[CrossRef]

Zhang, Y.

Y. Zhang, Y. Lie, J. Qi, G. Cui, H. Lui, J. Chen, L. Zhao, J. Xu, and Q. Sun, "Influence of absorption on optical trapping force of spherical particles in a focussed Gaussian beam," J. Opt. A 10, 085001 (2008).
[CrossRef]

Zhao, L.

Y. Zhang, Y. Lie, J. Qi, G. Cui, H. Lui, J. Chen, L. Zhao, J. Xu, and Q. Sun, "Influence of absorption on optical trapping force of spherical particles in a focussed Gaussian beam," J. Opt. A 10, 085001 (2008).
[CrossRef]

Appl. Opt. (5)

Biophys. J. (1)

A. Ashkin, "Forces of a single-beam gradient laser trap on a dielectric sphere in the ray optics regime," Biophys. J. 61, 569-582 (1992).
[CrossRef] [PubMed]

Europhys. Lett. (1)

P. A. Maia Neto and H. M. Nussenzveig, "Theory of optical tweezers," Europhys. Lett. 50, 702-708 (2000).
[CrossRef]

Fortschr. Phys. (1)

R. Loudon, "Radiation pressure and momentum in dielectrics," Fortschr. Phys. 52, 1134-1140 (2004).
[CrossRef]

J. Appl. Phys. (1)

A. Rohrbach and E. H. K. Stelzer, "Three-dimensional position detection of optical trapped dielectric particles," J. Appl. Phys. 91, 5474-5488 (2002).
[CrossRef]

J. Mod. Opt. (2)

H. He, N. R. Heckenberg, and H. Rubinsztein-Dunlop, "Optical particle trapping with higher-order doughnut beams produced using high efficiency computer generated holograms," J. Mod. Opt. 42, 217-223 (1995).
[CrossRef]

N. B. Simpson, L. Allen, and M. J. Padgett, "Optical tweezers and optical spanners with Laguerre-Gaussian modes," J. Mod. Opt. 43, 2485-2491 (1996).
[CrossRef]

J. Opt. A (2)

T. A. Nieminen, L. V. L. Y., A. B. Stilgoe, G. Knoner, A. M. Branczyk, N. R. Heckenberg, and H. Rubinsztein- Dunlop, "Optical tweezers computational toolbox," J. Opt. A 9, S196-S203 (2007).
[CrossRef]

Y. Zhang, Y. Lie, J. Qi, G. Cui, H. Lui, J. Chen, L. Zhao, J. Xu, and Q. Sun, "Influence of absorption on optical trapping force of spherical particles in a focussed Gaussian beam," J. Opt. A 10, 085001 (2008).
[CrossRef]

Nature (1)

D. G. Grier, "A revolution in optical manipulation," Nature 424, 810-816 (2003).
[CrossRef] [PubMed]

Opt. Commun. (2)

J. Liesener, M. Reicherter, T. Haist, and H. J. Tiziani, "Multi-functional optical tweezers using computergenerated holograms," Opt. Commun. 185, 77-82 (2000).
[CrossRef]

J. E. Curtis, B. A. Koss, and D. G. Grier, "Dynamic holographic optical tweezers," Opt. Commun. 207, 169-175 (2002).
[CrossRef]

Opt. Express (6)

Opt. Lett. (6)

Phys. Rev. A (2)

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

P. L. Marston and J. H. Crichton, "Radiation torque on a sphere caused by a circularly polarized electromagnetic wave," Phys. Rev. A 30, 2508-2516 (1984).
[CrossRef]

Phys. Rev. B (1)

P. C. Chaumet, A. Rahmani, and M. Nieto-Vesperinas, "Photonic force spectroscopy on metallic and absorbing nanoparticles," Phys. Rev. B 71, 045425 (2005).
[CrossRef]

Phys. Rev. Lett. (8)

B. A. Kemp, T. M. Grzegorczyk, and J. A. Kong, "Optical momentum transfer to absorbing Mie particles," Phys. Rev. Lett. 97, 133902 (2006).
[CrossRef] [PubMed]

J. E. Curtis and D. G. Grier, "Structure of optical vortices," Phys. Rev. Lett. 90, 133901 (2003).
[CrossRef] [PubMed]

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

Y. Roichman, B. Sun, Y. Roichman, J. Amato-Grill, and D. G. Grier, "Optical forces arising from phase gradients," Phys. Rev. Lett. 100, 013602 (2008).
[CrossRef] [PubMed]

J. Leach, M. J. Padgett, S. M. Barnett, S. Franke-Arnold, and J. Courtial, "Measuring the orbital angular momentum of a single photon," Phys. Rev. Lett. 88, 257901 (2002).
[CrossRef] [PubMed]

A. T. O???Neil, I. MacVicar, 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] [PubMed]

M. Babiker, C. R. Bennet, D. L. Andrews, and L. C. D???avila Romero, "Orbital angular momentum exchange in the interaction of twisted light with molecules," Phys. Rev. Lett. 89, 143601 (2002).
[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]

Proc. Royal Soc. London A (2)

E. Wolf, "Electromagnetic diffraction in optical systems. I. An integral representation of the image field," Proc. Royal Soc. London A 253, 349-357 (1959).
[CrossRef]

A. Mazolli, P. A. Maia Neto, and H. M. Nussenzveig, "Theory of trapping forces in optical tweezers," Proc. Royal Soc. London A 459, 3021-3041 (2003).
[CrossRef]

Proc. SPIE (1)

Y. Roichman and D. G. Grier, "Three-dimensional holographic ring traps," Proc. SPIE 6483, 64830F (2007).
[CrossRef]

Rev. Sci. Instrum. (1)

E. R. Dufresne and D. G. Grier, "Optical tweezer arrays and optical substrates created with diffractive optical elements," Rev. Sci. Instrum. 69, 1974-1977 (1998).
[CrossRef]

Science (1)

A. Ashkin, "Applications of laser radiation pressure," Science 210, 1081-1088 (1980).
[CrossRef] [PubMed]

Other (3)

M. I. Mishchenko, L. D. Travis, and A. A. Lacis, Scattering, Absorption and Emission of Light by Small Particles (Cambridge University Press, Cambridge, 2001).

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley Interscience, New York, 1983).

P. W. Barber and S. C. Hill, Light Scattering by Particles: Computational Methods, vol. 2 of Advanced Series in Applied Physics (World Scientific, New Jersey, 1990).
[CrossRef]

Cited By

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Figures (5)

Fig. 1.
Fig. 1.

Schematic representation of a holographic optical trapping system. A laser beam propagating from the left is imprinted with a computer-generated hologram by a diffractive optical element (DOE). The modified beam is relayed to an objective lens that focuses it onto the sample. The figure shows one of the plane waves projected from one of the DOE’s pixels at r j .

Fig. 2.
Fig. 2.

(a) Magnitude Q max and (b) range r max of the axial trapping force for a sphere of radius a and relative refractive index n p /n m in an optical tweezer created from light of wavenumber k. The solid curve denotes marginal trapping conditions with Q max=0. The dashed curve in (b) indicates conditions for which the trap’s axial well extends 1 µm.

Fig. 3.
Fig. 3.

(a) Computed intensity distribution in the focal plane, z=0 of an optical vortex of radius R . (b) In-plane force distribution, F ( r ), including six representative trajectories whose starting points are represented by dots. Hue indicates direction in the (x,y) plane according to the inset color wheel. Color saturation indicates relative magnitude. (c) In plane torque distribution. (d) Intensity distribution in the (x, z) plane along the optical axis, y=0. (e) Force distribution, with unbounded trajectories showing absence of stable axial trapping. (f) Axial torque distribution. Scale bars indicates 1 µm.

Fig. 4.
Fig. 4.

(a) Intensity distribution of a holographic ring trap of radius R in the focal plane, z=0. (b) In-plane force distribution, with representative trajectories. Hue indicates direction in the (x,y) plane according to the inset color wheel. Saturation indicates relative magnitude. (c) In plane torque distribution. (d) Intensity distribution in the (x, z) plane along the optical axis, y=0. (e) Axial force distribution with representative trajectories showing strong axial trapping near the focal plane. (f) Axial torque distribution. Scale bars indicates 1 µm.

Fig. 5.
Fig. 5.

(a) Intensity of a uniformly bright holographic line trap in the (x,y) plane. (b) Inplane force distribution, showing the influence of a parabolic phase profile. Superimposed trajectories converge at stable equilibrium point. Hue indicates direction of the force according to the color wheel, and saturation indicates magnitude. Full saturation corresponds to Q max=0.06. (c) In-plane component of the torque with τ max=2×10-5. (d) Intensity in the (x, z) plane showing diffraction-limited focusing. (e) Associated axial force distribution with superimposed trajectories demonstrating stable three-dimensional trapping. Q max=0.05 (f) Axial torque distribution. τ max=6×10-7.

Equations (31)

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

μ 0 T μ ν = F μ ρ F ρ ν + 1 4 F ρ σ F ρ σ δ μ ν ,
F μ ν = μ A ν ν A μ ,
F μ = Σ T μ ν d S ν .
M μ = 1 2 Σ ε i j μ M i j k d S k
M i j k = r i T j k r j T i k
Q ν = c n m P F ν
τ ν = ω P M ν .
A j , μ D ( r ) = a j 2 π c exp ( i φ j ) exp ( i k r r j ) r r j P μ ,
s ̂ 1 = ( sin θ 1 cos ϕ 1 , sin θ 1 sin ϕ 1 , cos θ 1 ) .
p = s ̂ 1 × ( z ̂ × ε ̂ ) ,
A μ D ( r ) = j = 1 N A j , μ D ( r )
A μ O ( r 2 ) = Ω 2 B μ ( s ̂ 2 ) exp ( i k s ̂ 2 · r 2 ) d Ω 2 ,
B μ ( s ̂ 2 ) = f 2 2 π c G μ ν ( s ̂ 2 ) p ν j = 1 N a j exp ( i φ j ) exp ( i k s ̂ 1 · r j ) .
𝔾 ( s ̂ 2 ) = cos θ 2 cos θ 1 1 ( ϕ 1 ) 𝕃 ( π θ 2 ) 𝕃 ( π θ 1 ) ( θ 1 ) ,
( ϕ ) = ( cos ϕ sin ϕ 0 sin ϕ cos ϕ 0 0 0 1 )         and         𝕃 ( θ ) = ( cos θ 0 sin θ 0 1 0 sin θ 0 cos θ ) .
A μ I ( r , s ̂ ) = A μ I ( s ̂ ) exp ( i n m k s ̂ · r )
A μ I ( s ̂ ) = Ω 2 H μ ν ( s ̂ , s ̂ 2 ) B ν ( s ̂ 2 ) exp ( i n m k s ̂ · Δ r ) d Ω 2 ,
( s ̂ , s ̂ 2 ) = i π s ̂ · s ̂ 2 n m 1 1 ( s ̂ · s ̂ 2 ) 2 { ( s ̂ × s ̂ 2 ) ( s ̂ × s ̂ 2 ) + [ s ̂ 2 s ̂ ( s ̂ · s ̂ 2 ) ] [ s ̂ + s ̂ 2 ( s ̂ · s ̂ 2 ) ] } .
A S ( r ) = μ = 1 2 Ω A μ S ( r , s ̂ ) d Ω
A ( r ) = A I ( r ) + A S ( r ) .
A S ( r , z ̂ ) = 𝕃 𝕄 1 ( r ) A 1 I ( r , z ̂ ) ,
𝕃 𝕄 1 ( r ) = n = 1 ( i a n N e l n ( 3 ) ( r ) b n M o l n ( 3 ) ( r ) ) ,
M o l n ( 3 ) ( r ) = cos ϕ sin θ P n 1 ( cos θ ) j n ( k r ) θ ̂ sin ϕ d P n 1 ( cos θ ) d θ j n ( k r ) ϕ ̂
N e l n ( 3 ) ( r ) = n ( n + 1 ) cos ϕ P n 1 ( cos θ ) j n ( k r ) k r r ̂
+ cos ϕ d p n 1 ( cos θ ) d θ 1 k r d d r [ r j n ( k r ) ] θ ̂
sin ϕ sin θ P n 1 ( cos θ ) 1 k r d d r [ r j n ( k r ) ] ϕ ̂ .
a n = m 2 j n ( m x ) [ x j n ( x ) ] j n ( x ) [ m x j n ( m x ) ] m 2 j n ( m x ) [ x h n ( 1 ) ( x ) ] h n ( 1 ) ( x ) [ m x j n ( m x ) ] ,
b n = j n ( m x ) [ x j n ( x ) ] j n ( x ) [ m x j n ( m x ) ] j n ( m x ) [ x h n ( 1 ) ( x ) ] h n ( 1 ) ( x ) [ m x j n ( m x ) ] .
𝔼 ( s ̂ ) = ( ( cos θ s 1 ) cos 2 ϕ s + 1 sin ϕ s cos ϕ s ( cos θ s 1 ) sin θ s cos ϕ s sin ϕ s cos ϕ s ( cos ϕ s 1 ) sin 2 ϕ s ( cos θ s 1 ) + 1 sin θ s sin ϕ s sin θ s cos ϕ s sin 2 ϕ s ( cos θ s 1 ) + 1 cos θ s ) ,
A S ( r , s ̂ ) = 𝔼 1 ( s ̂ ) 𝕃 𝕄 ( 𝔼 ( s ̂ ) r ) 𝔼 ( s ̂ ) A I ( s ̂ )
a j = J ( k R r j 2 f )         and         φ j = [ θ j + π H ( J ( k R r j 2 f ) ) ] mod 2 π ,

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