Abstract

It is well known that Laguerre–Gaussian beams carry angular momentum and that this angular momentum has a mechanical effect when such beams are incident on particles whose refractive indices differ from those of the background medium. Under conditions of tight focusing, intensity gradients arise that are sufficiently large to trap micrometer-sized particles, permitting these mechanical effects to be observed directly. In particular, when the particles are spherical and absorbing, they rotate steadily at a rate that is directly proportional to the theoretical angular momentum flux of the incident beam. We note that this behavior is peculiar to absorbing spheres. For arbitrary, axially placed particles the induced torque for rotation angle ζ is shown to be Γz=Asin(2ζ+δ)+B, where A, B, and δ are constants that are determined by the mechanisms coupling optical and mechanical angular momentum. The resulting behavior need not be directly related to the total angular momentum in the beam but can, nonetheless, be understood in terms of an appropriate torque density. This observation is illustrated by calculations of the torque induced in optically and geometrically anisotropic particles using a T-matrix approach.

© 2009 Optical Society of America

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    [CrossRef]
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2009 (1)

2008 (1)

S. Franke-Arnold, L. Allen, and M. Padgett, “Advances in optical angular momentum,” Laser Photonics Rev. 2, 299-313 (2008).
[CrossRef]

2007 (4)

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

R. N. C. Pfeifer, T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Colloquium: Momentum of an electromagnetic wave in dielectric media,” Rev. Mod. Phys. 79, 1197-1216 (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]

2006 (1)

2005 (1)

W. A. Shelton, K. D. Bonin, and T. G. Walker, “Nonlinear motion of optically torqued nano-rods,” Phys. Rev. E 71, 036204 (2005).
[CrossRef]

2004 (5)

Z. F. Lin and S. T. Chui, “Electromagnetic scattering by optically anisotropic magnetic particle,” Phys. Rev. E 69, 056614 (2004).
[CrossRef]

A. La Porta and M. D. Wang, “Optical torque wrench: Angular trapping, rotation, and torque detection of quartz microparticles,” Phys. Rev. Lett. 92, 190801 (2004).
[CrossRef] [PubMed]

T. A. Nieminen, “Comment on 'Geometric absorption of electromagnetic angular momentum,' C. Konz, G. Benford,” Opt. Commun. 235, 227-229 (2004).
[CrossRef]

G. Benford and C. Konz, “Reply to comment on 'Geometric absorption of electromagnetic angular momentum,'” Opt. Commun. 235, 231-232 (2004).
[CrossRef]

T. A. Nieminen, S. J. W. Parkin, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Optical torque and symmetry,” Proc. SPIE 5514, 254-263(2004).
[CrossRef]

2003 (2)

C. Konz and G. Benford, “Geometric absorption of electromagnetic angular momentum,” Opt. Commun. 226, 249-254 (2003).
[CrossRef]

M. J. Padgett, S. M. Barnett, and R. Loudon, “The angular momentum of light inside a dielectric,” J. Mod. Opt. 50, 1555-1562 (2003).
[CrossRef]

2002 (3)

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

J. E. Molloy and M. J. Padgett, “Lights, action: optical tweezers,” Contemp. Phys. 43, 241-258 (2002).
[CrossRef]

K. D. Bonin, B. Kourmanov, and T. G. Walker, “Light torque nanocontrol, nanomotors and nanorockers,” Opt. Express 10, 984-989 (2002).
[PubMed]

2001 (3)

R. C. Gauthier, “Optical levitation and trapping of a micro-optic inclined end-surface cylindrical spinner,” Appl. Opt. 40, 1961-1973 (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]

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)

J.-S. Kim and S.-W. Kim, “Dynamic motion analysis of optically trapped nonspherical particles with off-axis position and arbitrary orientation,” Appl. Opt. 39, 4327-4332 (2000).
[CrossRef]

A. T. O'Neil and M. J. Padgett, “Three-dimensional optical confinement of micron-sized metal particles and the decoupling of the spin and orbital angular momentum within an optical spanner,” Opt. Commun. 185, 139-143 (2000).
[CrossRef]

1997 (2)

M. S. Soskin, V. N. Gorshkov, M. V. Vasnetsov, J. T. Malos, and N. R. Heckenberg, “Topological charge and angular momentum of light beams carrying optical vortices,” Phys. Rev. A 56, 4064-4075 (1997).
[CrossRef]

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]

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 (1)

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 (2)

S. J. van Enk and G. Nienhuis, “Spin and orbital angular-momentum of photons,” Europhys. Lett. 25, 497-501 (1994).
[CrossRef]

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]

1979 (1)

I. Brevik, “Experiments in phenomenological electrodynamics and the electromagnetic energy-momentum tensor,” Phys. Rep., Phys. Lett. 52, 133-201 (1979).
[CrossRef]

1936 (2)

R. A. Beth, “Mechanical detection and measurement of the angular momentum of light,” Phys. Rev. 50, 115-125 (1936).
[CrossRef]

A. H. S. Holbourn, “Angular momentum of circularly polarised light,” Nature (London) 137, 31 (1936).
[CrossRef]

1909 (1)

J. H. Poynting, “The wave motion of a revolving shaft, and a suggestion as to the angular momentum in a beam of circularly polarised light,” Proc. R. Soc. London, Ser. A 82, 560-567 (1909).
[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.

S. Franke-Arnold, L. Allen, and M. Padgett, “Advances in optical angular momentum,” Laser Photonics Rev. 2, 299-313 (2008).
[CrossRef]

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]

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, “Optical vortex trapping and the dynamics of particle rotation,” 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.

Barnett, S. M.

M. J. Padgett, S. M. Barnett, and R. Loudon, “The angular momentum of light inside a dielectric,” J. Mod. Opt. 50, 1555-1562 (2003).
[CrossRef]

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]

Benford, G.

G. Benford and C. Konz, “Reply to comment on 'Geometric absorption of electromagnetic angular momentum,'” Opt. Commun. 235, 231-232 (2004).
[CrossRef]

C. Konz and G. Benford, “Geometric absorption of electromagnetic angular momentum,” Opt. Commun. 226, 249-254 (2003).
[CrossRef]

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]

Beth, R. A.

R. A. Beth, “Mechanical detection and measurement of the angular momentum of light,” Phys. Rev. 50, 115-125 (1936).
[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]

Bohren, C. F.

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

Bonin, K. D.

W. A. Shelton, K. D. Bonin, and T. G. Walker, “Nonlinear motion of optically torqued nano-rods,” Phys. Rev. E 71, 036204 (2005).
[CrossRef]

K. D. Bonin, B. Kourmanov, and T. G. Walker, “Light torque nanocontrol, nanomotors and nanorockers,” Opt. Express 10, 984-989 (2002).
[PubMed]

Brevik, I.

I. Brevik, “Experiments in phenomenological electrodynamics and the electromagnetic energy-momentum tensor,” Phys. Rep., Phys. Lett. 52, 133-201 (1979).
[CrossRef]

Chui, S. T.

Z. F. Lin and S. T. Chui, “Electromagnetic scattering by optically anisotropic magnetic particle,” Phys. Rev. E 69, 056614 (2004).
[CrossRef]

Dholakia, K.

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]

Franke-Arnold, S.

S. Franke-Arnold, L. Allen, and M. Padgett, “Advances in optical angular momentum,” Laser Photonics Rev. 2, 299-313 (2008).
[CrossRef]

Friese, M. E. 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]

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]

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.

Gauthier, R. C.

Gorshkov, V. N.

M. S. Soskin, V. N. Gorshkov, M. V. Vasnetsov, J. T. Malos, and N. R. Heckenberg, “Topological charge and angular momentum of light beams carrying optical vortices,” Phys. Rev. A 56, 4064-4075 (1997).
[CrossRef]

Hanna, S.

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.

R. N. C. Pfeifer, T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Colloquium: Momentum of an electromagnetic wave in dielectric media,” Rev. Mod. Phys. 79, 1197-1216 (2007).
[CrossRef]

T. A. Nieminen, S. J. W. Parkin, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Optical torque and symmetry,” Proc. SPIE 5514, 254-263(2004).
[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]

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]

M. S. Soskin, V. N. Gorshkov, M. V. Vasnetsov, J. T. Malos, and N. R. Heckenberg, “Topological charge and angular momentum of light beams carrying optical vortices,” Phys. Rev. A 56, 4064-4075 (1997).
[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]

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, “Optical vortex trapping and the dynamics of particle rotation,” 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.

Holbourn, A. H. S.

A. H. S. Holbourn, “Angular momentum of circularly polarised light,” Nature (London) 137, 31 (1936).
[CrossRef]

Huffman, D. R.

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

Kim, J.-S.

Kim, S.-W.

Konz, C.

G. Benford and C. Konz, “Reply to comment on 'Geometric absorption of electromagnetic angular momentum,'” Opt. Commun. 235, 231-232 (2004).
[CrossRef]

C. Konz and G. Benford, “Geometric absorption of electromagnetic angular momentum,” Opt. Commun. 226, 249-254 (2003).
[CrossRef]

Kourmanov, B.

Lacis, A. A.

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

Lin, Z. F.

Z. F. Lin and S. T. Chui, “Electromagnetic scattering by optically anisotropic magnetic particle,” Phys. Rev. E 69, 056614 (2004).
[CrossRef]

Loke, V. L. Y.

T. A. Nieminen, S. Parkin, T. Asavei, V. L. Y. Loke, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Optical vortex trapping and the dynamics of particle rotation,” 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.

Loudon, R.

M. J. Padgett, S. M. Barnett, and R. Loudon, “The angular momentum of light inside a dielectric,” J. Mod. Opt. 50, 1555-1562 (2003).
[CrossRef]

Malos, J. T.

M. S. Soskin, V. N. Gorshkov, M. V. Vasnetsov, J. T. Malos, and N. R. Heckenberg, “Topological charge and angular momentum of light beams carrying optical vortices,” Phys. Rev. A 56, 4064-4075 (1997).
[CrossRef]

Mishchenko, M. I.

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

Molloy, J. E.

J. E. Molloy and M. J. Padgett, “Lights, action: optical tweezers,” Contemp. Phys. 43, 241-258 (2002).
[CrossRef]

Nieminen, T. A.

R. N. C. Pfeifer, T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Colloquium: Momentum of an electromagnetic wave in dielectric media,” Rev. Mod. Phys. 79, 1197-1216 (2007).
[CrossRef]

T. A. Nieminen, S. J. W. Parkin, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Optical torque and symmetry,” Proc. SPIE 5514, 254-263(2004).
[CrossRef]

T. A. Nieminen, “Comment on 'Geometric absorption of electromagnetic angular momentum,' C. Konz, G. Benford,” Opt. Commun. 235, 227-229 (2004).
[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]

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, “Optical vortex trapping and the dynamics of particle rotation,” 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.

Nienhuis, G.

S. J. van Enk and G. Nienhuis, “Spin and orbital angular-momentum of photons,” Europhys. Lett. 25, 497-501 (1994).
[CrossRef]

O'Neil, A. T.

A. T. O'Neil and M. J. Padgett, “Three-dimensional optical confinement of micron-sized metal particles and the decoupling of the spin and orbital angular momentum within an optical spanner,” Opt. Commun. 185, 139-143 (2000).
[CrossRef]

Padgett, M.

S. Franke-Arnold, L. Allen, and M. Padgett, “Advances in optical angular momentum,” Laser Photonics Rev. 2, 299-313 (2008).
[CrossRef]

Padgett, M. J.

M. J. Padgett, S. M. Barnett, and R. Loudon, “The angular momentum of light inside a dielectric,” J. Mod. Opt. 50, 1555-1562 (2003).
[CrossRef]

J. E. Molloy and M. J. Padgett, “Lights, action: optical tweezers,” Contemp. Phys. 43, 241-258 (2002).
[CrossRef]

A. T. O'Neil and M. J. Padgett, “Three-dimensional optical confinement of micron-sized metal particles and the decoupling of the spin and orbital angular momentum within an optical spanner,” Opt. Commun. 185, 139-143 (2000).
[CrossRef]

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]

Parkin, S.

T. A. Nieminen, S. Parkin, T. Asavei, V. L. Y. Loke, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Optical vortex trapping and the dynamics of particle rotation,” 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.

Parkin, S. J. W.

T. A. Nieminen, S. J. W. Parkin, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Optical torque and symmetry,” Proc. SPIE 5514, 254-263(2004).
[CrossRef]

Pfeifer, R. N. C.

R. N. C. Pfeifer, T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Colloquium: Momentum of an electromagnetic wave in dielectric media,” Rev. Mod. Phys. 79, 1197-1216 (2007).
[CrossRef]

Porta, A. La

A. La Porta and M. D. Wang, “Optical torque wrench: Angular trapping, rotation, and torque detection of quartz microparticles,” Phys. Rev. Lett. 92, 190801 (2004).
[CrossRef] [PubMed]

Poynting, J. H.

J. H. Poynting, “The wave motion of a revolving shaft, and a suggestion as to the angular momentum in a beam of circularly polarised light,” Proc. R. Soc. London, Ser. A 82, 560-567 (1909).
[CrossRef]

Rubinsztein-Dunlop, H.

R. N. C. Pfeifer, T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Colloquium: Momentum of an electromagnetic wave in dielectric media,” Rev. Mod. Phys. 79, 1197-1216 (2007).
[CrossRef]

T. A. Nieminen, S. J. W. Parkin, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Optical torque and symmetry,” Proc. SPIE 5514, 254-263(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. 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]

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, “Optical vortex trapping and the dynamics of particle rotation,” 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]

Shelton, W. A.

W. A. Shelton, K. D. Bonin, and T. G. Walker, “Nonlinear motion of optically torqued nano-rods,” Phys. Rev. E 71, 036204 (2005).
[CrossRef]

Simpson, N. B.

Simpson, S. H.

Soskin, M. S.

M. S. Soskin, V. N. Gorshkov, M. V. Vasnetsov, J. T. Malos, and N. R. Heckenberg, “Topological charge and angular momentum of light beams carrying optical vortices,” Phys. Rev. A 56, 4064-4075 (1997).
[CrossRef]

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]

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 U. Press, 2002).

van Bladel, J.

J. van Bladel, Singular Electromagnetic Fields and Sources (Clarendon Press, 1991).

van de Nes, A. S.

van Enk, S. J.

S. J. van Enk and G. Nienhuis, “Spin and orbital angular-momentum of photons,” Europhys. Lett. 25, 497-501 (1994).
[CrossRef]

Vasnetsov, M. V.

M. S. Soskin, V. N. Gorshkov, M. V. Vasnetsov, J. T. Malos, and N. R. Heckenberg, “Topological charge and angular momentum of light beams carrying optical vortices,” Phys. Rev. A 56, 4064-4075 (1997).
[CrossRef]

Walker, T. G.

W. A. Shelton, K. D. Bonin, and T. G. Walker, “Nonlinear motion of optically torqued nano-rods,” Phys. Rev. E 71, 036204 (2005).
[CrossRef]

K. D. Bonin, B. Kourmanov, and T. G. Walker, “Light torque nanocontrol, nanomotors and nanorockers,” Opt. Express 10, 984-989 (2002).
[PubMed]

Wang, M. D.

A. La Porta and M. D. Wang, “Optical torque wrench: Angular trapping, rotation, and torque detection of quartz microparticles,” Phys. Rev. Lett. 92, 190801 (2004).
[CrossRef] [PubMed]

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]

Appl. Opt. (2)

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]

Contemp. Phys. (1)

J. E. Molloy and M. J. Padgett, “Lights, action: optical tweezers,” Contemp. Phys. 43, 241-258 (2002).
[CrossRef]

Europhys. Lett. (1)

S. J. van Enk and G. Nienhuis, “Spin and orbital angular-momentum of photons,” Europhys. Lett. 25, 497-501 (1994).
[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. Mod. Opt. (1)

M. J. Padgett, S. M. Barnett, and R. Loudon, “The angular momentum of light inside a dielectric,” J. Mod. Opt. 50, 1555-1562 (2003).
[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 (3)

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]

Laser Photonics Rev. (1)

S. Franke-Arnold, L. Allen, and M. Padgett, “Advances in optical angular momentum,” Laser Photonics Rev. 2, 299-313 (2008).
[CrossRef]

Nature (London) (1)

A. H. S. Holbourn, “Angular momentum of circularly polarised light,” Nature (London) 137, 31 (1936).
[CrossRef]

Opt. Commun. (5)

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

A. T. O'Neil and M. J. Padgett, “Three-dimensional optical confinement of micron-sized metal particles and the decoupling of the spin and orbital angular momentum within an optical spanner,” Opt. Commun. 185, 139-143 (2000).
[CrossRef]

C. Konz and G. Benford, “Geometric absorption of electromagnetic angular momentum,” Opt. Commun. 226, 249-254 (2003).
[CrossRef]

T. A. Nieminen, “Comment on 'Geometric absorption of electromagnetic angular momentum,' C. Konz, G. Benford,” Opt. Commun. 235, 227-229 (2004).
[CrossRef]

G. Benford and C. Konz, “Reply to comment on 'Geometric absorption of electromagnetic angular momentum,'” Opt. Commun. 235, 231-232 (2004).
[CrossRef]

Opt. Express (2)

Opt. Lett. (1)

Phys. Rep., Phys. Lett. (1)

I. Brevik, “Experiments in phenomenological electrodynamics and the electromagnetic energy-momentum tensor,” Phys. Rep., Phys. Lett. 52, 133-201 (1979).
[CrossRef]

Phys. Rev. (1)

R. A. Beth, “Mechanical detection and measurement of the angular momentum of light,” Phys. Rev. 50, 115-125 (1936).
[CrossRef]

Phys. Rev. A (4)

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]

M. S. Soskin, V. N. Gorshkov, M. V. Vasnetsov, J. T. Malos, and N. R. Heckenberg, “Topological charge and angular momentum of light beams carrying optical vortices,” Phys. Rev. A 56, 4064-4075 (1997).
[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]

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

Phys. Rev. E (2)

W. A. Shelton, K. D. Bonin, and T. G. Walker, “Nonlinear motion of optically torqued nano-rods,” Phys. Rev. E 71, 036204 (2005).
[CrossRef]

Z. F. Lin and S. T. Chui, “Electromagnetic scattering by optically anisotropic magnetic particle,” Phys. Rev. E 69, 056614 (2004).
[CrossRef]

Phys. Rev. Lett. (2)

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]

A. La Porta and M. D. Wang, “Optical torque wrench: Angular trapping, rotation, and torque detection of quartz microparticles,” Phys. Rev. Lett. 92, 190801 (2004).
[CrossRef] [PubMed]

Proc. R. Soc. London, Ser. A (1)

J. H. Poynting, “The wave motion of a revolving shaft, and a suggestion as to the angular momentum in a beam of circularly polarised light,” Proc. R. Soc. London, Ser. A 82, 560-567 (1909).
[CrossRef]

Proc. SPIE (1)

T. A. Nieminen, S. J. W. Parkin, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Optical torque and symmetry,” Proc. SPIE 5514, 254-263(2004).
[CrossRef]

Rev. Mod. Phys. (1)

R. N. C. Pfeifer, T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Colloquium: Momentum of an electromagnetic wave in dielectric media,” Rev. Mod. Phys. 79, 1197-1216 (2007).
[CrossRef]

Other (6)

J. van Bladel, Singular Electromagnetic Fields and Sources (Clarendon Press, 1991).

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

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

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.

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

T. A. Nieminen, S. Parkin, T. Asavei, V. L. Y. Loke, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Optical vortex trapping and the dynamics of particle rotation,” 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.

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Figures (12)

Fig. 1
Fig. 1

Horizontal sections through the intensity distributions of LG 03 beams with (a) σ z = + 1 , (b) σ z = 0 (x polarization) and (c) σ z = 1 . (d) A vertical section through the LG 03 beam with σ z = + 1 .

Fig. 2
Fig. 2

Plot of the radius of the first intense ring occurring in LG beams, R max , as a function of l.

Fig. 3
Fig. 3

Induced forces as a function of the position of the center of the sphere for (a) a 2 μ m diameter sphere in a LG 02 , σ z = 0 beam, (b) a 1 μ m diameter sphere in a LG 02 , σ z = 0 beam, and (c) a 4 μ m diameter sphere in a LG 05 , σ z = 0 beam. Approximate trapping positions are indicated with small solid circles; the open circle in (b) marks a saddle point in the underlying potential.

Fig. 4
Fig. 4

Axial torque induced in weakly absorbing spheres on the axis of LG beams with 1 l 5 and σ z = 1 , 0 and + 1 for spheres of diameter (a) 0.5, (b) 1.0, (c) 2.0, (d) 4.0 μ m .

Fig. 5
Fig. 5

Comparison between the axial torque induced in weakly absorbing spheres calculated from the approximate formula in Eq. (27) and the rigorous VSWF formula in Eq. (21). The plot shows the fractional error in Eq. (27) as a function of sphere radius for LG beams with 1 < l < 4 .

Fig. 6
Fig. 6

Contributions to the torque on prolate spheroids of different aspect ratio and an equivalent radius of 1 μ m lying with unique axis perpendicular to the axis of linearly polarized LG beams with l = 1 , 2, and 3: (a) variation in A for nonabsorbing spheroids, (b) variation in B for nonabsorbing spheroids, and (c) variation in B for weakly absorbing spheroids.

Fig. 7
Fig. 7

Contributions to the torque on prolate spheroids with different equivalent radii and an aspect ratio of 2 lying with unique axis perpendicular to the the axis of linearly polarized LG beams with l = 1 , 2, and 3: (a) variation in A for nonabsorbing spheroids, (b) variation in B for nonabsorbing spheroids, and (c) variation in B for weakly absorbing spheroids.

Fig. 8
Fig. 8

Variation in B for spheroids in circularly polarized LG beams: (a) variation with aspect ratio for nonabsorbing particles with 1 μ m equivalent radius and l = 1 , 2, and 3; (b) variation with equivalent radius for nonabsorbing particles with an aspect ratio of 2 in LG 01 beams; (c) same as (b) but using LG 02 beams; (d) variation in B with equivalent radius for weakly absorbing spheroids with aspect ratio = 2 and l = 1 , 2, and 3.

Fig. 9
Fig. 9

Variation in A for anisotropic spheres in linearly polarized LG beams with l = 1 , 2, and 3. (a) Variation in A with radius for spheres with n o = 1.41 and n e = 1.51 . (b) Variation in A with n e for spheres with n o = 1.41 and radius of 1 μ m .

Fig. 10
Fig. 10

Variation in B for anisotropic spheres in circularly polarized LG beams with l = 1 , 2, and 3 and σ z = ± 1 . (a) Variation in B with radius for spheres with n o = 1.41 and n e = 1.51 . (b) Variation in B with n e for spheres with n o = 1.41 and a radius of 1 μ m .

Fig. 11
Fig. 11

Section through a prolate spheroid showing the position vector to a point on the surface r, the surface normal n, and the direction of the torque density t.

Fig. 12
Fig. 12

Torque induced in birefringent spheres ( n o = 1.41 , n e = 1.51 ) of large radius by LG beams with σ z = + 1 and l = 1 and 2.

Equations (40)

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

ρ t = j .
t V ρ d V = V j d V = S j d σ ,
E inc = n = 1 m = n n [ a n m ( 1 ) Rg M n m ( k 1 r ) + a n m ( 2 ) Rg N n m ( k 1 r ) ] ,
E scat = n = 1 m = n n [ p n m ( 1 ) M n m ( 1 ) ( k 1 r ) + p n m ( 2 ) N n m ( 1 ) ( k 1 r ) ] .
E inc = a ̃ Rg Ψ ,
E scat = p ̃ Ψ ( 1 ) ,
a ̃ = { a 1 , 1 ( 1 ) , a 1 , 0 ( 1 ) , a 1 , 1 ( 1 ) , , a n max , n max ( 1 ) , a 1 , 1 ( 2 ) , , a n max , n max ( 2 ) } ,
Rg Ψ = { Rg M 1 , 1 , Rg M 1 , 0 , Rg M 1 , 1 , , Rg M n max , n max , Rg N 1 , 1 , , Rg N n max , n max } .
p ̃ = T a ̃ .
E = α E ( ρ , z ) e i l ϕ i ̂ + β E ( ρ , z ) e i l ϕ j ̂ + E z ( ρ , ϕ , z ) k ̂ ,
E ( ρ , z ) = 0 k d κ f ( κ ) exp ( i k 2 κ 2 z ) J l ( κ ρ ) ,
E z ( ρ , ϕ , z ) = 0 k d κ f ( κ ) e i l ϕ exp ( i k 2 κ 2 z ) κ 2 k 2 κ 2 × [ ( i α β ) e i ϕ J l 1 ( κ ρ ) ( i α + β ) e i ϕ J l + 1 ( κ ρ ) ] ,
f ( κ ) = exp [ k κ 2 z r 2 ( k 2 κ 2 ) ] ( κ 2 k 2 κ 2 ) ( 2 p + l + 1 ) 2 × ( k 2 k 2 κ 2 ) 1 2 .
ϵ = [ ϵ 0 0 0 ϵ 0 0 0 ϵ ] ϵ [ a 0 0 0 a 0 0 0 1 ] ϵ A ,
× × A 1 D = k 2 D ,
k 2 = ω 2 ϵ μ .
D = d ̃ Rg Ψ .
A 1 D = e ̃ Rg Ψ + = [ d ̃ T G ] Rg Ψ + .
T i j = E i D j + H i B j 1 2 ( E D + B H ) δ i j .
f i = T i k x k = ρ E i + ε i j k j j B k 1 2 E j E k ϵ j k x i + 1 2 H j H k μ j k x i + ε i j k ( D j E k ) t ,
ϵ i j = ( ϵ i j sphere ϵ i j medium ) δ ( n ) n ̂ .
f = 1 2 Re [ ( B × j * ) + E j E k * Δ ϵ j k δ ( n ) n ̂ ] .
m i k = ( r × T ) i k = ε i p q x p T q k ,
t i = ( m ) i = ε i p q x p T q k x k = ε i p q x p T q k x k + ε i p q T q k x p x k = ε i p q x p f q + ε i p q T q p .
t = ( r × f ) + ( D × E ) + ( B × H ) ,
t = r × f + 1 2 Re ( D × E * ) + 1 2 Re ( B × H * ) .
Γ z = ϵ ext 2 k 1 3 k = 1 2 n = 1 m = n n m [ p n m ( k ) 2 + Re ( p n m ( k ) a n m * ( k ) ) ] ,
a ̃ ( ζ ) = a ̃ 0 + e i ( l + 1 ) ζ + a ̃ 0 e i ( l 1 ) ζ ,
p ̃ ( ζ ) = T a ̃ ( ζ ) = e i ( l + 1 ) ζ T a ̃ 0 + + e i ( l 1 ) ζ T a ̃ 0 e i ( l + 1 ) ζ p ̃ 0 + + e i ( l 1 ) ζ p ̃ 0 .
c ( ζ ) = e i ( l + 1 ) ζ c 0 + + e i ( l 1 ) ζ c 0
c ( ζ ) [ d ( ζ ) ] * = [ e i ( l + 1 ) ζ c 0 + + e i ( l 1 ) ζ c 0 + ] [ e i ( l + 1 ) ζ d 0 + + e i ( l 1 ) ζ d 0 + ] * = c 0 + [ d 0 + ] * + c 0 [ d 0 ] * + e 2 i ζ c 0 + [ d 0 ] * + e 2 i ζ c 0 [ d 0 + ] * .
Γ z = A sin ( 2 ζ + δ ) + B ,
Γ z P 2 a n c ( l + σ z ) ( n n 1 + n 1 n ) ,
t = ( r × f ) = r × 1 2 Re ( B × j * ) .
t = r × 1 2 E 2 Δ ϵ δ ( r r s ) n ̂ ,
E = α e i l ϕ e i δ x i ̂ + β e i l ϕ e i δ y j ̂ ,
D = α n x 2 e i l ϕ e i δ x i ̂ + β n y 2 e i l ϕ e i δ y j ̂ ,
δ x = k 0 n x L ,
δ y = k 0 n y L .
t z = 1 2 Re ( D × E * ) k = { 1 4 Δ n 2 cos [ k 0 L ( n x n y ) ] sin ( 2 ζ ) , σ z = 0 1 4 Δ n 2 sin [ k 0 L ( n x n y ) ] , σ z = + 1 . 1 4 Δ n 2 sin [ k 0 L ( n x n y ) ] , σ z = 1 }

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