Orbital motion of optically trapped particles in Laguerre–Gaussian beams

doi:10.1364/JOSAA.27.002061

Orbital motion of optically trapped particles in Laguerre–Gaussian beams

Stephen H. Simpson and Simon Hanna »View Author Affiliations

JOSA A, Vol. 27, Issue 9, pp. 2061-2071 (2010)
http://dx.doi.org/10.1364/JOSAA.27.002061

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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 $0.5 μ m$ 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.

OCIS Codes
(290.4020) Scattering : Mie theory
(290.5870) Scattering : Scattering, Rayleigh
(350.4855) Other areas of optics : Optical tweezers or optical manipulation
(050.4865) Diffraction and gratings : Optical vortices

ToC Category:
Scattering

History
Original Manuscript: April 1, 2010
Revised Manuscript: July 22, 2010
Manuscript Accepted: July 26, 2010
Published: August 24, 2010

Virtual Issues
Vol. 5, Iss. 13 Virtual Journal for Biomedical Optics

Citation
Stephen H. Simpson and Simon Hanna, "Orbital motion of optically trapped particles in Laguerre–Gaussian beams," J. Opt. Soc. Am. A 27, 2061-2071 (2010)
http://www.opticsinfobase.org/vjbo/abstract.cfm?URI=josaa-27-9-2061

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References

J. F. Nye and M. V. Berry, “Dislocations in wave trains,” Proc. R. Soc. London, Ser. A 336, 165–190 (1974). [CrossRef]
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.
S. H. Simpson and S. Hanna, “Optical angular momentum transfer by Laguerre–Gaussian beams,” J. Opt. Soc. Am. A 26, 625–638 (2009). [CrossRef]
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]
J. E. Curtis and D. G. Grier, “Structure of optical vortices,” Phys. Rev. Lett. 90, 133901 (2003). [CrossRef] [PubMed]
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.
S. H. Simpson and S. Hanna, “Rotation of absorbing spheres in Laguerre–Gaussian beams,” J. Opt. Soc. Am. A 26, 173–183 (2009). [CrossRef]
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]
S. H. Simpson and S. Hanna, “Holographic optical trapping of microrods and nanowires,” J. Opt. Soc. Am. A 27, 1255–1264 (2010). [CrossRef]
B. Sun, Y. Roichman, and D. G. Grier, “Theory of holographic optical trapping,” Opt. Express 16, 15765–15776 (2008). [CrossRef] [PubMed]
S. M. Barnett and L. Allen, “Orbital angular-momentum and nonparaxial light-beams,” Opt. Commun. 110, 670–678 (1994). [CrossRef]
S. M. Barnett, “Optical angular-momentum flux,” J. Opt. B: Quantum Semiclassical Opt. 4, S7–S16 (2002). [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]
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]
J. P. Gordon and A. Ashkin, “Motion of atoms in a radiation trap,” Phys. Rev. A 21, 1606–1617 (1980). [CrossRef]
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]
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]
B. T. Draine, “The discrete-dipole approximation and its application to interstellar graphite grains,” Astrophys. J. 333, 848–872 (1988). [CrossRef]
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]
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]
M. I. Mishchenko, L. D. Travis, and A. A. Lacis, Scattering, Absorption and Emission of Light by Small Particles (Cambridge University Press, 2002).
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]
S. H. Simpson, D. C. Benito, and S. Hanna, “Polarization-induced torque in optical traps,” Phys. Rev. A 76, 043408 (2007). [CrossRef]
S. H. Simpson and S. Hanna, “Optical trapping of spheroidal particles in Gaussian beams,” J. Opt. Soc. Am. A 24, 430–443 (2007). [CrossRef]
A. S. van de Nes and P. Török, “Rigorous analysis of spheres in Gauss–Laguerre beams,” Opt. Express 15, 13360–13374 (2007). [CrossRef] [PubMed]
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]
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).
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]
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]
M. V. Berry, “Optical currents,” J. Opt. A, Pure Appl. Opt. 11, 094001 (2009). [CrossRef]
http://www.bris.ac.uk/acrc/.

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[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/.

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Orbital motion of optically trapped particles in Laguerre–Gaussian beams