Abstract

A theoretical examination of off-axial trapping in non-paraxial Laguerre–Gaussian beams is presented for both the Rayleigh and Mie regimes. It is well known that the force acting on a particle may be divided into a term proportional to the intensity gradient and another representing the scattering force. The latter term may be further sub-divided into a dissipative radiation force and a term dependent on the electric field gradient. For Rayleigh particles in Laguerre–Gaussian beams, it is shown that the field gradient term contributes exactly half of the scattering force. This may be compared with a plane wave, in which it makes zero contribution. The off-axis trapping positions for spheres with radii varying from 0.1 to 0.5μm and a range of refractive indices are calculated numerically in the Mie regime, using a conjugate gradient approach. Azimuthal forces and orbital torques are presented for particles in their trapping positions, for beams with different orbital angular momentum and polarization states. The components of a “spin” torque, acting through the center of the particle, are also computed for absorbing particles in the Mie regime.

© 2010 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. J. F. Nye and M. V. Berry, “Dislocations in wave trains,” Proc. R. Soc. London, Ser. A 336, 165–190 (1974).
    [CrossRef]
  2. M.Vasnetsov and K.Staliunas, eds., Optical Vortices, Vol. 228 of Horizons in World Physics (Nova Science, 1999).
  3. L.Allen, S.M.Barnett, and M.J.Padgett, eds., Optical Angular Momentum (IOP, 2003).
    [CrossRef]
  4. D.L.Andrews, ed., Structured Light and Its Applications: An Introduction to Phase-Structured Beams and Nanoscale Optical Forces (Academic, 2008).
    [PubMed]
  5. T. A. Nieminen, S. Parkin, T. Asavei, V. L. Y. Loke, N. R. Heckenberg, and H. Rubinsztein-Dunlop, in Structured Light and Its Applications: An Introduction to Phase-Structured Beams and Nanoscale Optical Forces, D.L.Andrews, ed. (Academic, 2008), Chap. 8, pp. 195–236.
  6. S. H. Simpson and S. Hanna, “Optical angular momentum transfer by Laguerre–Gaussian beams,” J. Opt. Soc. Am. A 26, 625–638 (2009).
    [CrossRef]
  7. 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]
  8. V. Garcés-Chávez, K. Volke-Sepulveda, S. Chávez-Cerda, W. Sibbett, and K. Dholakia, “Transfer of orbital angular momentum to an optically trapped low-index particle,” Phys. Rev. A 66, 063402 (2002).
    [CrossRef]
  9. J. E. Curtis and D. G. Grier, “Structure of optical vortices,” Phys. Rev. Lett. 90, 133901 (2003).
    [CrossRef] [PubMed]
  10. N. R. Heckenberg, M. E. J. Friese, T. A. Nieminen, and H. Rubinsztein-Dunlop, “Mechanical effects of optical vortices,” in Optical Vortices, Vol. 228 of Horizons in World Physics, M.Vasnetsov and K.Staliunas, eds. (Nova Science, 1999), pp. 75–105.
  11. S. H. Simpson and S. Hanna, “Rotation of absorbing spheres in Laguerre–Gaussian beams,” J. Opt. Soc. Am. A 26, 173–183 (2009).
    [CrossRef]
  12. D. Benito, S. H. Simpson, and S. Hanna, “FDTD simulations of forces on particles during holographic assembly,” Opt. Express 16, 2942–2957 (2008).
    [CrossRef] [PubMed]
  13. S. H. Simpson and S. Hanna, “Holographic optical trapping of microrods and nanowires,” J. Opt. Soc. Am. A 27, 1255–1264 (2010).
    [CrossRef]
  14. B. Sun, Y. Roichman, and D. G. Grier, “Theory of holographic optical trapping,” Opt. Express 16, 15765–15776 (2008).
    [CrossRef] [PubMed]
  15. S. M. Barnett and L. Allen, “Orbital angular-momentum and nonparaxial light-beams,” Opt. Commun. 110, 670–678 (1994).
    [CrossRef]
  16. S. M. Barnett, “Optical angular-momentum flux,” J. Opt. B: Quantum Semiclassical Opt. 4, S7–S16 (2002).
    [CrossRef]
  17. 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]
  18. L. Allen and M. Padgett, “The Poynting vector in Laguerre–Gaussian beams and the interpretation of their angular momentum density,” Opt. Commun. 184, 67–71 (2000).
    [CrossRef]
  19. J. P. Gordon and A. Ashkin, “Motion of atoms in a radiation trap,” Phys. Rev. A 21, 1606–1617 (1980).
    [CrossRef]
  20. P. C. Chaumet and M. Nieto-Vesperinas, “Time-averaged total force on a dipolar sphere in an electromagnetic field,” Opt. Lett. 25, 1065–1067 (2000).
    [CrossRef]
  21. V. Wong and M. A. Ratner, “Gradient and nongradient contributions to plasmon-enhanced optical forces on silver nanoparticles,” Phys. Rev. B 73, 075416 (2006).
    [CrossRef]
  22. B. T. Draine, “The discrete-dipole approximation and its application to interstellar graphite grains,” Astrophys. J. 333, 848–872 (1988).
    [CrossRef]
  23. M. J. Collinge and B. T. Draine, “Discrete-dipole approximation with polarizabilities that account for both finite wavelength and target geometry,” J. Opt. Soc. Am. A 21, 2023–2028 (2004).
    [CrossRef]
  24. T. A. Nieminen, H. Rubinsztein-Dunlop, and N. R. Heckenberg, “Calculation and optical measurement of laser trapping forces on non-spherical particles,” J. Quant. Spectrosc. Radiat. Transf. 70, 627–637 (2001).
    [CrossRef]
  25. T. A. Nieminen, H. Rubinsztein-Dunlop, N. R. Heckenberg, and A. I. Bishop, “Numerical modelling of optical trapping,” Comput. Phys. Commun. 142, 468–471 (2001).
    [CrossRef]
  26. M. I. Mishchenko, L. D. Travis, and A. A. Lacis, Scattering, Absorption and Emission of Light by Small Particles (Cambridge University Press, 2002).
  27. S. H. Simpson and S. Hanna, “Numerical calculation of inter-particle forces arising in association with holographic assembly,” J. Opt. Soc. Am. A 23, 1419–1431 (2006).
    [CrossRef]
  28. S. H. Simpson, D. C. Benito, and S. Hanna, “Polarization-induced torque in optical traps,” Phys. Rev. A 76, 043408 (2007).
    [CrossRef]
  29. S. H. Simpson and S. Hanna, “Optical trapping of spheroidal particles in Gaussian beams,” J. Opt. Soc. Am. A 24, 430–443 (2007).
    [CrossRef]
  30. A. S. van de Nes and P. Török, “Rigorous analysis of spheres in Gauss–Laguerre beams,” Opt. Express 15, 13360–13374 (2007).
    [CrossRef] [PubMed]
  31. J. P. Barton, D. R. Alexander, and S. A. Schaub, “Theoretical determination of net radiation force and torque for a spherical particle illuminated by a focused laser beam,” J. Appl. Phys. 66, 4594–4602 (1989).
    [CrossRef]
  32. W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes: The Art of Scientific Programming, 3rd ed. (Cambridge University Press, 2007).
  33. J. F. Nye and J. V. Hajnal, “The wave structure of monochromatic electromagnetic-radiation,” Proc. R. Soc. London, Ser. A 409, 21–36 (1987).
    [CrossRef]
  34. A. B. Stilgoe, T. A. Nieminen, G. Knoner, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “The effect of Mie resonances on trapping in optical tweezers,” Opt. Express 16, 15039–15051 (2008).
    [CrossRef] [PubMed]
  35. M. V. Berry, “Optical currents,” J. Opt. A, Pure Appl. Opt. 11, 094001 (2009).
    [CrossRef]
  36. http://www.bris.ac.uk/acrc/.

2010 (1)

2009 (3)

2008 (3)

2007 (3)

2006 (2)

V. Wong and M. A. Ratner, “Gradient and nongradient contributions to plasmon-enhanced optical forces on silver nanoparticles,” Phys. Rev. B 73, 075416 (2006).
[CrossRef]

S. H. Simpson and S. Hanna, “Numerical calculation of inter-particle forces arising in association with holographic assembly,” J. Opt. Soc. Am. A 23, 1419–1431 (2006).
[CrossRef]

2004 (1)

2003 (1)

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

2002 (3)

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]

V. Garcés-Chávez, K. Volke-Sepulveda, S. Chávez-Cerda, W. Sibbett, and K. Dholakia, “Transfer of orbital angular momentum to an optically trapped low-index particle,” Phys. Rev. A 66, 063402 (2002).
[CrossRef]

S. M. Barnett, “Optical angular-momentum flux,” J. Opt. B: Quantum Semiclassical Opt. 4, S7–S16 (2002).
[CrossRef]

2001 (2)

T. A. Nieminen, H. Rubinsztein-Dunlop, and N. R. Heckenberg, “Calculation and optical measurement of laser trapping forces on non-spherical particles,” J. Quant. Spectrosc. Radiat. Transf. 70, 627–637 (2001).
[CrossRef]

T. A. Nieminen, H. Rubinsztein-Dunlop, N. R. Heckenberg, and A. I. Bishop, “Numerical modelling of optical trapping,” Comput. Phys. Commun. 142, 468–471 (2001).
[CrossRef]

2000 (2)

P. C. Chaumet and M. Nieto-Vesperinas, “Time-averaged total force on a dipolar sphere in an electromagnetic field,” Opt. Lett. 25, 1065–1067 (2000).
[CrossRef]

L. Allen and M. Padgett, “The Poynting vector in Laguerre–Gaussian beams and the interpretation of their angular momentum density,” Opt. Commun. 184, 67–71 (2000).
[CrossRef]

1994 (1)

S. M. Barnett and L. Allen, “Orbital angular-momentum and nonparaxial light-beams,” Opt. Commun. 110, 670–678 (1994).
[CrossRef]

1992 (1)

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]

1989 (1)

J. P. Barton, D. R. Alexander, and S. A. Schaub, “Theoretical determination of net radiation force and torque for a spherical particle illuminated by a focused laser beam,” J. Appl. Phys. 66, 4594–4602 (1989).
[CrossRef]

1988 (1)

B. T. Draine, “The discrete-dipole approximation and its application to interstellar graphite grains,” Astrophys. J. 333, 848–872 (1988).
[CrossRef]

1987 (1)

J. F. Nye and J. V. Hajnal, “The wave structure of monochromatic electromagnetic-radiation,” Proc. R. Soc. London, Ser. A 409, 21–36 (1987).
[CrossRef]

1980 (1)

J. P. Gordon and A. Ashkin, “Motion of atoms in a radiation trap,” Phys. Rev. A 21, 1606–1617 (1980).
[CrossRef]

1974 (1)

J. F. Nye and M. V. Berry, “Dislocations in wave trains,” Proc. R. Soc. London, Ser. A 336, 165–190 (1974).
[CrossRef]

Alexander, D. R.

J. P. Barton, D. R. Alexander, and S. A. Schaub, “Theoretical determination of net radiation force and torque for a spherical particle illuminated by a focused laser beam,” J. Appl. Phys. 66, 4594–4602 (1989).
[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]

L. Allen and M. Padgett, “The Poynting vector in Laguerre–Gaussian beams and the interpretation of their angular momentum density,” Opt. Commun. 184, 67–71 (2000).
[CrossRef]

S. M. Barnett and L. Allen, “Orbital angular-momentum and nonparaxial light-beams,” Opt. Commun. 110, 670–678 (1994).
[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]

Asavei, T.

T. A. Nieminen, S. Parkin, T. Asavei, V. L. Y. Loke, N. R. Heckenberg, and H. Rubinsztein-Dunlop, in Structured Light and Its Applications: An Introduction to Phase-Structured Beams and Nanoscale Optical Forces, D.L.Andrews, ed. (Academic, 2008), Chap. 8, pp. 195–236.

Ashkin, A.

J. P. Gordon and A. Ashkin, “Motion of atoms in a radiation trap,” Phys. Rev. A 21, 1606–1617 (1980).
[CrossRef]

Barnett, S. M.

S. M. Barnett, “Optical angular-momentum flux,” J. Opt. B: Quantum Semiclassical Opt. 4, S7–S16 (2002).
[CrossRef]

S. M. Barnett and L. Allen, “Orbital angular-momentum and nonparaxial light-beams,” Opt. Commun. 110, 670–678 (1994).
[CrossRef]

Barton, J. P.

J. P. Barton, D. R. Alexander, and S. A. Schaub, “Theoretical determination of net radiation force and torque for a spherical particle illuminated by a focused laser beam,” J. Appl. Phys. 66, 4594–4602 (1989).
[CrossRef]

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.

Benito, D. C.

S. H. Simpson, D. C. Benito, and S. Hanna, “Polarization-induced torque in optical traps,” Phys. Rev. A 76, 043408 (2007).
[CrossRef]

Berry, M. V.

M. V. Berry, “Optical currents,” J. Opt. A, Pure Appl. Opt. 11, 094001 (2009).
[CrossRef]

J. F. Nye and M. V. Berry, “Dislocations in wave trains,” Proc. R. Soc. London, Ser. A 336, 165–190 (1974).
[CrossRef]

Bishop, A. I.

T. A. Nieminen, H. Rubinsztein-Dunlop, N. R. Heckenberg, and A. I. Bishop, “Numerical modelling of optical trapping,” Comput. Phys. Commun. 142, 468–471 (2001).
[CrossRef]

Chaumet, P. C.

Chávez-Cerda, S.

V. Garcés-Chávez, K. Volke-Sepulveda, S. Chávez-Cerda, W. Sibbett, and K. Dholakia, “Transfer of orbital angular momentum to an optically trapped low-index particle,” Phys. Rev. A 66, 063402 (2002).
[CrossRef]

Collinge, M. J.

Curtis, J. E.

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

Dholakia, K.

V. Garcés-Chávez, K. Volke-Sepulveda, S. Chávez-Cerda, W. Sibbett, and K. Dholakia, “Transfer of orbital angular momentum to an optically trapped low-index particle,” Phys. Rev. A 66, 063402 (2002).
[CrossRef]

Draine, B. T.

M. J. Collinge and B. T. Draine, “Discrete-dipole approximation with polarizabilities that account for both finite wavelength and target geometry,” J. Opt. Soc. Am. A 21, 2023–2028 (2004).
[CrossRef]

B. T. Draine, “The discrete-dipole approximation and its application to interstellar graphite grains,” Astrophys. J. 333, 848–872 (1988).
[CrossRef]

Flannery, B. P.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes: The Art of Scientific Programming, 3rd ed. (Cambridge University Press, 2007).

Friese, M. E. J.

N. R. Heckenberg, M. E. J. Friese, T. A. Nieminen, and H. Rubinsztein-Dunlop, “Mechanical effects of optical vortices,” in Optical Vortices, Vol. 228 of Horizons in World Physics, M.Vasnetsov and K.Staliunas, eds. (Nova Science, 1999), pp. 75–105.

Garcés-Chávez, V.

V. Garcés-Chávez, K. Volke-Sepulveda, S. Chávez-Cerda, W. Sibbett, and K. Dholakia, “Transfer of orbital angular momentum to an optically trapped low-index particle,” Phys. Rev. A 66, 063402 (2002).
[CrossRef]

Gordon, J. P.

J. P. Gordon and A. Ashkin, “Motion of atoms in a radiation trap,” Phys. Rev. A 21, 1606–1617 (1980).
[CrossRef]

Grier, D. G.

Hajnal, J. V.

J. F. Nye and J. V. Hajnal, “The wave structure of monochromatic electromagnetic-radiation,” Proc. R. Soc. London, Ser. A 409, 21–36 (1987).
[CrossRef]

Hanna, S.

Heckenberg, N. R.

A. B. Stilgoe, T. A. Nieminen, G. Knoner, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “The effect of Mie resonances on trapping in optical tweezers,” Opt. Express 16, 15039–15051 (2008).
[CrossRef] [PubMed]

T. A. Nieminen, H. Rubinsztein-Dunlop, and N. R. Heckenberg, “Calculation and optical measurement of laser trapping forces on non-spherical particles,” J. Quant. Spectrosc. Radiat. Transf. 70, 627–637 (2001).
[CrossRef]

T. A. Nieminen, H. Rubinsztein-Dunlop, N. R. Heckenberg, and A. I. Bishop, “Numerical modelling of optical trapping,” Comput. Phys. Commun. 142, 468–471 (2001).
[CrossRef]

N. R. Heckenberg, M. E. J. Friese, T. A. Nieminen, and H. Rubinsztein-Dunlop, “Mechanical effects of optical vortices,” in Optical Vortices, Vol. 228 of Horizons in World Physics, M.Vasnetsov and K.Staliunas, eds. (Nova Science, 1999), pp. 75–105.

T. A. Nieminen, S. Parkin, T. Asavei, V. L. Y. Loke, N. R. Heckenberg, and H. Rubinsztein-Dunlop, in Structured Light and Its Applications: An Introduction to Phase-Structured Beams and Nanoscale Optical Forces, D.L.Andrews, ed. (Academic, 2008), Chap. 8, pp. 195–236.

Knoner, G.

Lacis, A. A.

M. I. Mishchenko, L. D. Travis, and A. A. Lacis, Scattering, Absorption and Emission of Light by Small Particles (Cambridge University Press, 2002).

Loke, V. L. Y.

T. A. Nieminen, S. Parkin, T. Asavei, V. L. Y. Loke, N. R. Heckenberg, and H. Rubinsztein-Dunlop, in Structured Light and Its Applications: An Introduction to Phase-Structured Beams and Nanoscale Optical Forces, D.L.Andrews, ed. (Academic, 2008), Chap. 8, pp. 195–236.

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]

Mishchenko, M. I.

M. I. Mishchenko, L. D. Travis, and A. A. Lacis, Scattering, Absorption and Emission of Light by Small Particles (Cambridge University Press, 2002).

Nieminen, T. A.

A. B. Stilgoe, T. A. Nieminen, G. Knoner, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “The effect of Mie resonances on trapping in optical tweezers,” Opt. Express 16, 15039–15051 (2008).
[CrossRef] [PubMed]

T. A. Nieminen, H. Rubinsztein-Dunlop, N. R. Heckenberg, and A. I. Bishop, “Numerical modelling of optical trapping,” Comput. Phys. Commun. 142, 468–471 (2001).
[CrossRef]

T. A. Nieminen, H. Rubinsztein-Dunlop, and N. R. Heckenberg, “Calculation and optical measurement of laser trapping forces on non-spherical particles,” J. Quant. Spectrosc. Radiat. Transf. 70, 627–637 (2001).
[CrossRef]

N. R. Heckenberg, M. E. J. Friese, T. A. Nieminen, and H. Rubinsztein-Dunlop, “Mechanical effects of optical vortices,” in Optical Vortices, Vol. 228 of Horizons in World Physics, M.Vasnetsov and K.Staliunas, eds. (Nova Science, 1999), pp. 75–105.

T. A. Nieminen, S. Parkin, T. Asavei, V. L. Y. Loke, N. R. Heckenberg, and H. Rubinsztein-Dunlop, in Structured Light and Its Applications: An Introduction to Phase-Structured Beams and Nanoscale Optical Forces, D.L.Andrews, ed. (Academic, 2008), Chap. 8, pp. 195–236.

Nieto-Vesperinas, M.

Nye, J. F.

J. F. Nye and J. V. Hajnal, “The wave structure of monochromatic electromagnetic-radiation,” Proc. R. Soc. London, Ser. A 409, 21–36 (1987).
[CrossRef]

J. F. Nye and M. V. Berry, “Dislocations in wave trains,” Proc. R. Soc. London, Ser. A 336, 165–190 (1974).
[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.

L. Allen and M. Padgett, “The Poynting vector in Laguerre–Gaussian beams and the interpretation of their angular momentum density,” Opt. Commun. 184, 67–71 (2000).
[CrossRef]

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]

Parkin, S.

T. A. Nieminen, S. Parkin, T. Asavei, V. L. Y. Loke, N. R. Heckenberg, and H. Rubinsztein-Dunlop, in Structured Light and Its Applications: An Introduction to Phase-Structured Beams and Nanoscale Optical Forces, D.L.Andrews, ed. (Academic, 2008), Chap. 8, pp. 195–236.

Press, W. H.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes: The Art of Scientific Programming, 3rd ed. (Cambridge University Press, 2007).

Ratner, M. A.

V. Wong and M. A. Ratner, “Gradient and nongradient contributions to plasmon-enhanced optical forces on silver nanoparticles,” Phys. Rev. B 73, 075416 (2006).
[CrossRef]

Roichman, Y.

Rubinsztein-Dunlop, H.

A. B. Stilgoe, T. A. Nieminen, G. Knoner, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “The effect of Mie resonances on trapping in optical tweezers,” Opt. Express 16, 15039–15051 (2008).
[CrossRef] [PubMed]

T. A. Nieminen, H. Rubinsztein-Dunlop, N. R. Heckenberg, and A. I. Bishop, “Numerical modelling of optical trapping,” Comput. Phys. Commun. 142, 468–471 (2001).
[CrossRef]

T. A. Nieminen, H. Rubinsztein-Dunlop, and N. R. Heckenberg, “Calculation and optical measurement of laser trapping forces on non-spherical particles,” J. Quant. Spectrosc. Radiat. Transf. 70, 627–637 (2001).
[CrossRef]

N. R. Heckenberg, M. E. J. Friese, T. A. Nieminen, and H. Rubinsztein-Dunlop, “Mechanical effects of optical vortices,” in Optical Vortices, Vol. 228 of Horizons in World Physics, M.Vasnetsov and K.Staliunas, eds. (Nova Science, 1999), pp. 75–105.

T. A. Nieminen, S. Parkin, T. Asavei, V. L. Y. Loke, N. R. Heckenberg, and H. Rubinsztein-Dunlop, in Structured Light and Its Applications: An Introduction to Phase-Structured Beams and Nanoscale Optical Forces, D.L.Andrews, ed. (Academic, 2008), Chap. 8, pp. 195–236.

Schaub, S. A.

J. P. Barton, D. R. Alexander, and S. A. Schaub, “Theoretical determination of net radiation force and torque for a spherical particle illuminated by a focused laser beam,” J. Appl. Phys. 66, 4594–4602 (1989).
[CrossRef]

Sibbett, W.

V. Garcés-Chávez, K. Volke-Sepulveda, S. Chávez-Cerda, W. Sibbett, and K. Dholakia, “Transfer of orbital angular momentum to an optically trapped low-index particle,” Phys. Rev. A 66, 063402 (2002).
[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]

Stilgoe, A. B.

Sun, B.

Teukolsky, S. A.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes: The Art of Scientific Programming, 3rd ed. (Cambridge University Press, 2007).

Török, P.

Travis, L. D.

M. I. Mishchenko, L. D. Travis, and A. A. Lacis, Scattering, Absorption and Emission of Light by Small Particles (Cambridge University Press, 2002).

van de Nes, A. S.

Vetterling, W. T.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes: The Art of Scientific Programming, 3rd ed. (Cambridge University Press, 2007).

Volke-Sepulveda, K.

V. Garcés-Chávez, K. Volke-Sepulveda, S. Chávez-Cerda, W. Sibbett, and K. Dholakia, “Transfer of orbital angular momentum to an optically trapped low-index particle,” Phys. Rev. A 66, 063402 (2002).
[CrossRef]

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]

Wong, V.

V. Wong and M. A. Ratner, “Gradient and nongradient contributions to plasmon-enhanced optical forces on silver nanoparticles,” Phys. Rev. B 73, 075416 (2006).
[CrossRef]

Astrophys. J. (1)

B. T. Draine, “The discrete-dipole approximation and its application to interstellar graphite grains,” Astrophys. J. 333, 848–872 (1988).
[CrossRef]

Comput. Phys. Commun. (1)

T. A. Nieminen, H. Rubinsztein-Dunlop, N. R. Heckenberg, and A. I. Bishop, “Numerical modelling of optical trapping,” Comput. Phys. Commun. 142, 468–471 (2001).
[CrossRef]

J. Appl. Phys. (1)

J. P. Barton, D. R. Alexander, and S. A. Schaub, “Theoretical determination of net radiation force and torque for a spherical particle illuminated by a focused laser beam,” J. Appl. Phys. 66, 4594–4602 (1989).
[CrossRef]

J. Opt. A, Pure Appl. Opt. (1)

M. V. Berry, “Optical currents,” J. Opt. A, Pure Appl. Opt. 11, 094001 (2009).
[CrossRef]

J. Opt. B: Quantum Semiclassical Opt. (1)

S. M. Barnett, “Optical angular-momentum flux,” J. Opt. B: Quantum Semiclassical Opt. 4, S7–S16 (2002).
[CrossRef]

J. Opt. Soc. Am. A (6)

J. Quant. Spectrosc. Radiat. Transf. (1)

T. A. Nieminen, H. Rubinsztein-Dunlop, and N. R. Heckenberg, “Calculation and optical measurement of laser trapping forces on non-spherical particles,” J. Quant. Spectrosc. Radiat. Transf. 70, 627–637 (2001).
[CrossRef]

Opt. Commun. (2)

L. Allen and M. Padgett, “The Poynting vector in Laguerre–Gaussian beams and the interpretation of their angular momentum density,” Opt. Commun. 184, 67–71 (2000).
[CrossRef]

S. M. Barnett and L. Allen, “Orbital angular-momentum and nonparaxial light-beams,” Opt. Commun. 110, 670–678 (1994).
[CrossRef]

Opt. Express (4)

Opt. Lett. (1)

Phys. Rev. A (4)

S. H. Simpson, D. C. Benito, and S. Hanna, “Polarization-induced torque in optical traps,” Phys. Rev. A 76, 043408 (2007).
[CrossRef]

V. Garcés-Chávez, K. Volke-Sepulveda, S. Chávez-Cerda, W. Sibbett, and K. Dholakia, “Transfer of orbital angular momentum to an optically trapped low-index particle,” Phys. Rev. A 66, 063402 (2002).
[CrossRef]

J. P. Gordon and A. Ashkin, “Motion of atoms in a radiation trap,” Phys. Rev. A 21, 1606–1617 (1980).
[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]

Phys. Rev. B (1)

V. Wong and M. A. Ratner, “Gradient and nongradient contributions to plasmon-enhanced optical forces on silver nanoparticles,” Phys. Rev. B 73, 075416 (2006).
[CrossRef]

Phys. Rev. Lett. (2)

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

Proc. R. Soc. London, Ser. A (2)

J. F. Nye and M. V. Berry, “Dislocations in wave trains,” Proc. R. Soc. London, Ser. A 336, 165–190 (1974).
[CrossRef]

J. F. Nye and J. V. Hajnal, “The wave structure of monochromatic electromagnetic-radiation,” Proc. R. Soc. London, Ser. A 409, 21–36 (1987).
[CrossRef]

Other (8)

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes: The Art of Scientific Programming, 3rd ed. (Cambridge University Press, 2007).

http://www.bris.ac.uk/acrc/.

M.Vasnetsov and K.Staliunas, eds., Optical Vortices, Vol. 228 of Horizons in World Physics (Nova Science, 1999).

L.Allen, S.M.Barnett, and M.J.Padgett, eds., Optical Angular Momentum (IOP, 2003).
[CrossRef]

D.L.Andrews, ed., Structured Light and Its Applications: An Introduction to Phase-Structured Beams and Nanoscale Optical Forces (Academic, 2008).
[PubMed]

T. A. Nieminen, S. Parkin, T. Asavei, V. L. Y. Loke, N. R. Heckenberg, and H. Rubinsztein-Dunlop, in Structured Light and Its Applications: An Introduction to Phase-Structured Beams and Nanoscale Optical Forces, D.L.Andrews, ed. (Academic, 2008), Chap. 8, pp. 195–236.

N. R. Heckenberg, M. E. J. Friese, T. A. Nieminen, and H. Rubinsztein-Dunlop, “Mechanical effects of optical vortices,” in Optical Vortices, Vol. 228 of Horizons in World Physics, M.Vasnetsov and K.Staliunas, eds. (Nova Science, 1999), pp. 75–105.

M. I. Mishchenko, L. D. Travis, and A. A. Lacis, Scattering, Absorption and Emission of Light by Small Particles (Cambridge University Press, 2002).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (7)

Fig. 1
Fig. 1

(a) The maximum peak intensity and (b) the radius of the bright ring, ρ max , for LG 0 l beams with σ z = ± 1 as functions of the beam helicity l.

Fig. 2
Fig. 2

(a) The trapping radius ρ eqm and (b) height z eqm of silica spheres in LG 0 l beams with σ z = + 1 as functions of sphere radius R. (c) The trapping coordinates of spheres in the same beams. (d) A comparison of the trapping coordinates for LG 03 beams with σ z = ± 1 .

Fig. 3
Fig. 3

(a) The azimuthal force f ϕ and (b) orbital torque τ z = ρ eqm f ϕ acting on silica spheres in LG 0 l beams as functions of sphere radius. (c) The azimuthal force and (d) orbital torque acting on silica spheres in LG 03 beams with σ z = ± 1 . The forces and torques are presented at the equilibrium trapping position ( ρ eqm , z eqm ) for each sphere.

Fig. 4
Fig. 4

(a) The equilibrium trapping radius, (b) trapping height, (c) azimuthal force, and (d) orbital torque acting on non-absorbing dielectric spheres in a LG 03 ( σ z = + 1 ) beam as functions of sphere refractive index, for three sizes of sphere: R = 0.1 , 0.25, and 0.5 μ m . The forces and torques are presented at the equilibrium trapping position ( ρ eqm , z eqm ) for each sphere.

Fig. 5
Fig. 5

Components of the spin torque acting on absorbing particles, with Im ( n ) = 10 4 , as a function of particle radius, parallel to the (a) x, (b) y, and (c) z directions. The torques were evaluated about the center of the particle, with the particle at the point on its orbit with y = 0 and x positive. The forces and torques are presented at the equilibrium trapping position ( ρ eqm , z eqm ) for each sphere.

Fig. 6
Fig. 6

(a) The azimuthal forces and (b) vertical spin torque acting on absorbing spheres in LG 03 beams as functions of the imaginary part of the refractive index of the sphere. The forces and torques are presented at the equilibrium trapping position ( ρ eqm , z eqm ) for each sphere.

Fig. 7
Fig. 7

(a) The equilibrium trapping radius ρ eqm , (b) trapping height z eqm , (c) azimuthal force f ϕ , and (d) orbital torque τ z , acting on silica spheres in a LG 03 ( σ z = + 1 ) beam as functions of beam parameter z R for spheres with R = 0.1 , 0.25, and 0.5 μ m . The forces and torques are presented at the equilibrium trapping position ( ρ eqm , z eqm ) for each sphere.

Equations (37)

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

E = ( a i ̂ + b j ̂ ) E 1 ( ρ , z ) e i l ϕ + E z ( ρ , ϕ , z ) k ̂ ,
E z ( ρ , ϕ , z ) = ( a i b ) e i ( l + 1 ) ϕ E z , + ( ρ , z ) + ( a + i b ) e i ( l 1 ) ϕ E z , ( ρ , z ) ,
E 1 ( ρ , z ) = 0 k d κ F ( κ ) exp ( i k 2 κ 2 z ) J l ( κ ρ ) ,
E z ± ( ρ , z ) = i 0 k d κ F ( κ ) exp ( i k 2 κ 2 z ) κ 2 k 2 κ 2 J l ± 1 ( κ ρ ) ,
F ( κ ) = exp ( k κ 2 z R 2 ( k 2 κ 2 ) ) ( k 2 k 2 κ 2 ) 1 / 2 ( κ 2 k 2 κ 2 ) ( 2 p + l + 1 ) / 2 .
f i = 2 π ϵ   Re [ α E j i E j ] ,
f i = π ϵ α re i | E | 2 + 2 π ϵ α im   Im [ E j i E j ] .
f i scat = 2 π ϵ α im { 2 ω μ S + Im [ ( E ) E ] } ,
f i diss = 4 π ϵ α im ω μ S ,
f i grad = 2 π ϵ α im   Im [ ( E ) E ] .
α = α CM 1 i 2 3 k 3 α CM ,
α CM = R 3 ( ϵ s ϵ m ) ( ϵ s + 2 ϵ m ) ,
α α CM + i 2 3 k 3 α CM 2 ,
f = 1 2 Re [ ( B × j ) + 1 2 | E | 2 Δ ϵ δ ( n ) n ̂ ] ,
t = r × f .
f ϕ = 2 π ϵ ρ × { α im ( l | E | 2 + | E z | 2 ) : σ z = + 1 α im ( l | E | 2 | E z | 2 ) : σ z = 1 α im ( l | E | 2 + | E z + | 2 | E z | 2 ) + 2 α re   Im ( E z + E z e 2 i ϕ ) : σ z = 0. }
S ϕ = 1 2 ω μ × { l 2 ρ ( | E | 2 + | E z | 2 ) Re ( E z + z E 1 ) 1 4 ρ | E 1 | 2 + 1 ρ | E z | 2 : σ z = + 1 l 2 ρ ( | E | 2 + | E z | 2 ) + Re ( E z z E 1 ) + 1 4 ρ | E 1 | 2 1 ρ | E z | 2 : σ z = 1 l ρ ( | E | 2 | E 1 | 2 sin 2 ( ϕ ) ) + 1 ρ ( | E z + | 2 | E z | 2 ) sin ( ϕ ) Im [ ( e i ϕ E z + + e i ϕ E z ) z E 1 ] sin ( ϕ ) cos ( ϕ ) Im ( E 1 ρ E 1 ) : σ z = 0. }
f ϕ diss = π ϵ α im ρ l | E | 2 = 1 2 f ϕ .
E x = 1 2 E 1 ( ρ , z ) e i l ϕ ,
E y = i 2 E 1 ( ρ , z ) e i l ϕ ,
E z = 2 E z , + ( ρ , z ) e i ( l + 1 ) ϕ ,
| E | 2 = | E 1 | 2 + 2 | E z , + | 2 = | E 1 | 2 + | E z | 2 .
f ϕ diss = 2 π ϵ α im   Im [ ( E × × E ) x ] .
( E × × E ) x = ( E y x E y + E z x E z ) ( E y y E x + E z z E x ) .
E y x E y = 1 2 ( cos ( ϕ ) E 1 ρ E 1 + i l | E 1 | 2 ρ sin ( ϕ ) ) ,
E z x E z = 2 ( cos ( ϕ ) E z , + ρ E z , + + i ( l + 1 ) | E z , + | 2 ρ sin ( ϕ ) ) ,
E y y E x = 1 2 ( i   sin ( ϕ ) E 1 ρ E 1 + l | E 1 | 2 ρ cos ( ϕ ) ) ,
E z z E x = exp ( i ϕ ) E z , + z E 1 ,
( E × × E ) ϕ = i l 2 ρ ( | E 1 | 2 + 4 | E z , + | 2 ) 2 i | E z , + | 2 ρ + i 2 E 1 ρ E 1 + i E z , + z E 1 = i l 2 ρ ( | E | 2 + | E z | 2 ) + i E z , + z E 1 + i 2 E 1 ρ E 1 i | E z | 2 ρ .
f ϕ diss = π ϵ α im [ l ρ ( | E | 2 + | E z | 2 ) 2   Re ( E z , + z E 1 ) 1 2 ρ | E 1 | 2 + 2 | E z | 2 ρ ] π ϵ α im l ρ | E | 2 .
f x grad = 2 π ϵ α im   Im [ ( E E ) x ] = 2 π ϵ α im   Im [ E x x E x + E y y E x + E z z E x ] .
E x x E x = 1 2 ( cos ( ϕ ) E 1 ρ E 1 i l | E 1 | 2 ρ sin ( ϕ ) ) ,
E y y E x = 1 2 ( l | E 1 | 2 ρ cos ( ϕ ) i E 1 ρ E 1   sin ( ϕ ) ) ,
E z z E x = exp ( i ϕ ) E z , + z E 1 .
f ϕ grad = π ϵ α im   Re [ l | E 1 | 2 ρ + E 1 ρ E ρ + 2 E z , + z E 1 ] = π ϵ α im [ l ρ ( | E | 2 | E z | 2 ) + 1 2 ρ | E 1 | 2 + 2   Re ( E z , + z E 1 ) ] π ϵ α im l ρ | E | 2 .
E ( r ) = exp i k r u ,
f i grad = 2 π ϵ α im   Im ( E j j E i ) = 2 π ϵ α im   Im ( e i k r u j j u i e i k r ) = 2 π ϵ α im u i u j k j = 2 π ϵ α im u i k u = 0.

Metrics