Abstract

Dynamic simulation is a powerful tool to observe the behavior of arbitrary shaped particles trapped in a focused laser beam. Here we develop a method to find equilibrium positions and orientations using dynamic simulation. This general method is applied to micro- and nano-cylinders as a demonstration of its predictive power. Orientation landscapes for particles trapped with beams of differing polarisation are presented. The torque efficiency of micro-cylinders at equilibrium in a plane is also calculated as a function of tilt angle. This systematic investigation elucidates in both the function and properties of micro- and nano-cylinders trapped in optical tweezers.

©2012 Optical Society of America

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References

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    [PubMed]
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    [PubMed]
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2011 (2)

T. A. Nieminen, V. L. Y. Loke, A. B. Stilgoe, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “T-matrix method for modelling optical tweezers,” J. Mod. Opt. 58, 528–544 (2011).

S. H. Simpson and S. Hanna, “Application of the discrete dipole approximation to optical trapping calculations of inhomogeneous and anisotropic particles,” Opt. Express 19(17), 16526–16541 (2011).
[PubMed]

2010 (4)

2009 (6)

P. H. Jones, F. Palmisano, F. Bonaccorso, P. G. Gucciardi, G. Calogero, A. C. Ferrari, and O. M. Maragó, “Rotation Detection in Light-Driven Nanorotors,” ACS Nano 3(10), 3077–3084 (2009).
[PubMed]

T. A. Nieminen, T. Asavei, V. L. Y. Loke, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Symmetry and the generation and measurement of optical torque,” J. Quant. Spectrosc. Radiat. Transf. 110, 1472–1482 (2009).

S. Albaladejo, M. I. Marqués, M. Laroche, and J. J. Sáenz, “Scattering forces from the curl of the spin angular momentum of a light field,” Phys. Rev. Lett. 102(11), 113602 (2009).
[PubMed]

V. L. Y. Loke, T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “T-matrix calculation via discrete dipole approximation, point matching and exploiting symmetry,” J. Quant. Spectrosc. Radiat. Transf. 110, 1460–1471 (2009).

M. Rodriguez-Otazo, A. Augier-Calderin, J. P. Galaup, J. F. Lamère, and S. Fery-Forgues, “High rotation speed of single molecular microcrystals in an optical trap with elliptically polarized light,” Appl. Opt. 48(14), 2720–2730 (2009).
[PubMed]

M. C. Zhong, J. H. Zhou, Y. X. Ren, Y. M. Li, and Z. Q. Wang, “Rotation of birefringent particles in optical tweezers with spherical aberration,” Appl. Opt. 48(22), 4397–4402 (2009).
[PubMed]

2008 (4)

J. Harris and G. McConnell, “Optical trapping and manipulation of live T cells with a low numerical aperture lens,” Opt. Express 16(18), 14036–14043 (2008).
[PubMed]

A. B. Stilgoe, T. A. Nieminen, G. Knöener, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “The effect of Mie resonances on trapping in optical tweezers,” Opt. Express 16(19), 15039–15051 (2008).
[PubMed]

F. Borghese, P. Denti, R. Saija, M. A. Iatì, and O. M. Maragò, “Radiation torque and force on optically trapped linear nanostructures,” Phys. Rev. Lett. 100(16), 163903 (2008).
[PubMed]

M. Dienerowitz, M. Mazilu, and K. Dholakia, “Optical manipulation of nanoparticles: a review,” J. Nanophoton. 2, 021875 (2008).

2007 (3)

T. A. Nieminen, V. L. Y. Loke, A. B. Stilgoe, G. Knöner, A. M. Brańczyk, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Optical tweezers computational toolbox,” J. Opt. A 9, S196–S203 (2007).

P. C. Chaumet and C. Billaudeau, “Coupled dipole method to compute optical torque: Application to a micro-propeller,” J. Appl. Phys. 101, 023106 (2007).

Y. Nakayama, P. J. Pauzauskie, A. Radenovic, R. M. Onorato, R. J. Saykally, J. Liphardt, and P. D. Yang, “Tunable nanowire nonlinear optical probe,” Nature 447(7148), 1098–1101 (2007).
[PubMed]

2006 (3)

J. L. Zhang, T. G. Kim, S. C. Jeoung, F. F. Yao, H. Lee, and X. D. Sun, “Controlled trapping and rotation of carbon nanotube bundle with optical tweezers,” Opt. Commun. 267, 260–263 (2006).

A. A. R. Neves, A. Fontes, Lde. Y. Pozzo, A. A. de Thomaz, E. Chillce, E. Rodriguez, L. C. Barbosa, and C. L. Cesar, “Electromagnetic forces for an arbitrary optical trapping of a spherical dielectric,” Opt. Express 14(26), 13101–13106 (2006).
[PubMed]

G. Knöner, T. A. Nieminen, S. Parkin, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Calculation of optical trapping landscapes,” Proc. SPIE 6326, U119–U127 (2006).

2004 (1)

S. D. Tan, H. A. Lopez, C. W. Cai, and Y. G. Zhang, “Optical trapping of single-walled carbon nanotubes,” Nano Lett. 4, 1415–1419 (2004).

2003 (4)

O. A. Bauchau and L. Trainelli, “The vectorial parameterization of rotation,” Nonlinear Dyn. 32, 71–92 (2003).

A. Mazolli, P. A. Maia Neto, and H. M. Nussenzveig, “Theory of trapping forces in optical tweezers,” Proc. R. Soc. Lond. A 459, 3021–3041 (2003).

T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Calculation of the T-matrix: general considerations and application of the point-matching method,” J. Quant. Spectrosc. Radiat. Transf. 79–80, 1019–1029 (2003).

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

2001 (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).

2000 (1)

1999 (1)

C. H. Choi, J. Ivanic, M. S. Gordon, and K. Ruedenberg, “Rapid and stable determination of rotation matrices between spherical harmonics by direct recursion,” J. Chem. Phys. 111, 8825–8831 (1999).

1997 (2)

1986 (1)

1981 (1)

J. G. Garcia de la Torre and V. A. Bloomfield, “Hydrodynamic properties of complex, rigid, biological macromolecules: theory and applications,” Q. Rev. Biophys. 14(1), 81–139 (1981).
[PubMed]

1977 (1)

E. M. Purcell, “Life at low Reynolds-number,” Am. J. Phys. 45, 3–11 (1977).

1970 (1)

A. Ashkin, “Acceleration and trapping of particles by radiation pressure,” Phys. Rev. Lett. 24, 156–159 (1970).

Albaladejo, S.

S. Albaladejo, M. I. Marqués, M. Laroche, and J. J. Sáenz, “Scattering forces from the curl of the spin angular momentum of a light field,” Phys. Rev. Lett. 102(11), 113602 (2009).
[PubMed]

Asavei, T.

T. A. Nieminen, T. Asavei, V. L. Y. Loke, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Symmetry and the generation and measurement of optical torque,” J. Quant. Spectrosc. Radiat. Transf. 110, 1472–1482 (2009).

Ashkin, A.

Augier-Calderin, A.

Barbosa, L. C.

Bauchau, O. A.

O. A. Bauchau and L. Trainelli, “The vectorial parameterization of rotation,” Nonlinear Dyn. 32, 71–92 (2003).

Billaudeau, C.

P. C. Chaumet and C. Billaudeau, “Coupled dipole method to compute optical torque: Application to a micro-propeller,” J. Appl. Phys. 101, 023106 (2007).

Bishop, A. I.

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

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).

Bjorkholm, J. E.

Bloomfield, V. A.

J. G. Garcia de la Torre and V. A. Bloomfield, “Hydrodynamic properties of complex, rigid, biological macromolecules: theory and applications,” Q. Rev. Biophys. 14(1), 81–139 (1981).
[PubMed]

Bonaccorso, F.

P. H. Jones, F. Palmisano, F. Bonaccorso, P. G. Gucciardi, G. Calogero, A. C. Ferrari, and O. M. Maragó, “Rotation Detection in Light-Driven Nanorotors,” ACS Nano 3(10), 3077–3084 (2009).
[PubMed]

Borghese, F.

A. A. R. Neves, A. Camposeo, S. Pagliara, R. Saija, F. Borghese, P. Denti, M. A. Iatì, R. Cingolani, O. M. Maragò, and D. Pisignano, “Rotational dynamics of optically trapped nanofibers,” Opt. Express 18(2), 822–830 (2010).
[PubMed]

F. Borghese, P. Denti, R. Saija, M. A. Iatì, and O. M. Maragò, “Radiation torque and force on optically trapped linear nanostructures,” Phys. Rev. Lett. 100(16), 163903 (2008).
[PubMed]

Branczyk, A. M.

T. A. Nieminen, V. L. Y. Loke, A. B. Stilgoe, G. Knöner, A. M. Brańczyk, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Optical tweezers computational toolbox,” J. Opt. A 9, S196–S203 (2007).

Cai, C. W.

S. D. Tan, H. A. Lopez, C. W. Cai, and Y. G. Zhang, “Optical trapping of single-walled carbon nanotubes,” Nano Lett. 4, 1415–1419 (2004).

Calogero, G.

P. H. Jones, F. Palmisano, F. Bonaccorso, P. G. Gucciardi, G. Calogero, A. C. Ferrari, and O. M. Maragó, “Rotation Detection in Light-Driven Nanorotors,” ACS Nano 3(10), 3077–3084 (2009).
[PubMed]

Camposeo, A.

Cesar, C. L.

Chaumet, P. C.

P. C. Chaumet and C. Billaudeau, “Coupled dipole method to compute optical torque: Application to a micro-propeller,” J. Appl. Phys. 101, 023106 (2007).

Chillce, E.

Choi, C. H.

C. H. Choi, J. Ivanic, M. S. Gordon, and K. Ruedenberg, “Rapid and stable determination of rotation matrices between spherical harmonics by direct recursion,” J. Chem. Phys. 111, 8825–8831 (1999).

Chu, S.

Cingolani, R.

de Thomaz, A. A.

Denti, P.

A. A. R. Neves, A. Camposeo, S. Pagliara, R. Saija, F. Borghese, P. Denti, M. A. Iatì, R. Cingolani, O. M. Maragò, and D. Pisignano, “Rotational dynamics of optically trapped nanofibers,” Opt. Express 18(2), 822–830 (2010).
[PubMed]

F. Borghese, P. Denti, R. Saija, M. A. Iatì, and O. M. Maragò, “Radiation torque and force on optically trapped linear nanostructures,” Phys. Rev. Lett. 100(16), 163903 (2008).
[PubMed]

Dholakia, K.

M. Dienerowitz, M. Mazilu, and K. Dholakia, “Optical manipulation of nanoparticles: a review,” J. Nanophoton. 2, 021875 (2008).

Dienerowitz, M.

M. Dienerowitz, M. Mazilu, and K. Dholakia, “Optical manipulation of nanoparticles: a review,” J. Nanophoton. 2, 021875 (2008).

Dziedzic, J. M.

Ferrari, A. C.

P. H. Jones, F. Palmisano, F. Bonaccorso, P. G. Gucciardi, G. Calogero, A. C. Ferrari, and O. M. Maragó, “Rotation Detection in Light-Driven Nanorotors,” ACS Nano 3(10), 3077–3084 (2009).
[PubMed]

Fery-Forgues, S.

Fontes, A.

Frangioudakis, A.

Galaup, J. P.

Garcia de la Torre, J. G.

J. G. Garcia de la Torre and V. A. Bloomfield, “Hydrodynamic properties of complex, rigid, biological macromolecules: theory and applications,” Q. Rev. Biophys. 14(1), 81–139 (1981).
[PubMed]

Gauthier, R. C.

Gordon, M. S.

C. H. Choi, J. Ivanic, M. S. Gordon, and K. Ruedenberg, “Rapid and stable determination of rotation matrices between spherical harmonics by direct recursion,” J. Chem. Phys. 111, 8825–8831 (1999).

Gucciardi, P. G.

P. H. Jones, F. Palmisano, F. Bonaccorso, P. G. Gucciardi, G. Calogero, A. C. Ferrari, and O. M. Maragó, “Rotation Detection in Light-Driven Nanorotors,” ACS Nano 3(10), 3077–3084 (2009).
[PubMed]

Hanna, S.

Hanstorp, D.

K. Ramser and D. Hanstorp, “Optical manipulation for single-cell studies,” J Biophoton. 3(4), 187–206 (2010).
[PubMed]

Harris, J.

Heckenberg, N. R.

T. A. Nieminen, V. L. Y. Loke, A. B. Stilgoe, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “T-matrix method for modelling optical tweezers,” J. Mod. Opt. 58, 528–544 (2011).

T. A. Nieminen, T. Asavei, V. L. Y. Loke, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Symmetry and the generation and measurement of optical torque,” J. Quant. Spectrosc. Radiat. Transf. 110, 1472–1482 (2009).

V. L. Y. Loke, T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “T-matrix calculation via discrete dipole approximation, point matching and exploiting symmetry,” J. Quant. Spectrosc. Radiat. Transf. 110, 1460–1471 (2009).

A. B. Stilgoe, T. A. Nieminen, G. Knöener, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “The effect of Mie resonances on trapping in optical tweezers,” Opt. Express 16(19), 15039–15051 (2008).
[PubMed]

T. A. Nieminen, V. L. Y. Loke, A. B. Stilgoe, G. Knöner, A. M. Brańczyk, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Optical tweezers computational toolbox,” J. Opt. A 9, S196–S203 (2007).

G. Knöner, T. A. Nieminen, S. Parkin, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Calculation of optical trapping landscapes,” Proc. SPIE 6326, U119–U127 (2006).

T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Calculation of the T-matrix: general considerations and application of the point-matching method,” J. Quant. Spectrosc. Radiat. Transf. 79–80, 1019–1029 (2003).

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

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).

Iatì, M. A.

A. A. R. Neves, A. Camposeo, S. Pagliara, R. Saija, F. Borghese, P. Denti, M. A. Iatì, R. Cingolani, O. M. Maragò, and D. Pisignano, “Rotational dynamics of optically trapped nanofibers,” Opt. Express 18(2), 822–830 (2010).
[PubMed]

F. Borghese, P. Denti, R. Saija, M. A. Iatì, and O. M. Maragò, “Radiation torque and force on optically trapped linear nanostructures,” Phys. Rev. Lett. 100(16), 163903 (2008).
[PubMed]

Ivanic, J.

C. H. Choi, J. Ivanic, M. S. Gordon, and K. Ruedenberg, “Rapid and stable determination of rotation matrices between spherical harmonics by direct recursion,” J. Chem. Phys. 111, 8825–8831 (1999).

Jeoung, S. C.

J. L. Zhang, T. G. Kim, S. C. Jeoung, F. F. Yao, H. Lee, and X. D. Sun, “Controlled trapping and rotation of carbon nanotube bundle with optical tweezers,” Opt. Commun. 267, 260–263 (2006).

Jones, P. H.

P. H. Jones, F. Palmisano, F. Bonaccorso, P. G. Gucciardi, G. Calogero, A. C. Ferrari, and O. M. Maragó, “Rotation Detection in Light-Driven Nanorotors,” ACS Nano 3(10), 3077–3084 (2009).
[PubMed]

Kawashima, H.

Kim, T. G.

J. L. Zhang, T. G. Kim, S. C. Jeoung, F. F. Yao, H. Lee, and X. D. Sun, “Controlled trapping and rotation of carbon nanotube bundle with optical tweezers,” Opt. Commun. 267, 260–263 (2006).

Knöener, G.

Knöner, G.

T. A. Nieminen, V. L. Y. Loke, A. B. Stilgoe, G. Knöner, A. M. Brańczyk, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Optical tweezers computational toolbox,” J. Opt. A 9, S196–S203 (2007).

G. Knöner, T. A. Nieminen, S. Parkin, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Calculation of optical trapping landscapes,” Proc. SPIE 6326, U119–U127 (2006).

Lamère, J. F.

Laroche, M.

S. Albaladejo, M. I. Marqués, M. Laroche, and J. J. Sáenz, “Scattering forces from the curl of the spin angular momentum of a light field,” Phys. Rev. Lett. 102(11), 113602 (2009).
[PubMed]

Lee, H.

J. L. Zhang, T. G. Kim, S. C. Jeoung, F. F. Yao, H. Lee, and X. D. Sun, “Controlled trapping and rotation of carbon nanotube bundle with optical tweezers,” Opt. Commun. 267, 260–263 (2006).

Li, Y. M.

Liphardt, J.

Y. Nakayama, P. J. Pauzauskie, A. Radenovic, R. M. Onorato, R. J. Saykally, J. Liphardt, and P. D. Yang, “Tunable nanowire nonlinear optical probe,” Nature 447(7148), 1098–1101 (2007).
[PubMed]

Loke, V. L. Y.

T. A. Nieminen, V. L. Y. Loke, A. B. Stilgoe, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “T-matrix method for modelling optical tweezers,” J. Mod. Opt. 58, 528–544 (2011).

V. L. Y. Loke, T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “T-matrix calculation via discrete dipole approximation, point matching and exploiting symmetry,” J. Quant. Spectrosc. Radiat. Transf. 110, 1460–1471 (2009).

T. A. Nieminen, T. Asavei, V. L. Y. Loke, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Symmetry and the generation and measurement of optical torque,” J. Quant. Spectrosc. Radiat. Transf. 110, 1472–1482 (2009).

T. A. Nieminen, V. L. Y. Loke, A. B. Stilgoe, G. Knöner, A. M. Brańczyk, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Optical tweezers computational toolbox,” J. Opt. A 9, S196–S203 (2007).

Lopez, H. A.

S. D. Tan, H. A. Lopez, C. W. Cai, and Y. G. Zhang, “Optical trapping of single-walled carbon nanotubes,” Nano Lett. 4, 1415–1419 (2004).

Maia Neto, P. A.

A. Mazolli, P. A. Maia Neto, and H. M. Nussenzveig, “Theory of trapping forces in optical tweezers,” Proc. R. Soc. Lond. A 459, 3021–3041 (2003).

Maragó, O. M.

P. H. Jones, F. Palmisano, F. Bonaccorso, P. G. Gucciardi, G. Calogero, A. C. Ferrari, and O. M. Maragó, “Rotation Detection in Light-Driven Nanorotors,” ACS Nano 3(10), 3077–3084 (2009).
[PubMed]

Maragò, O. M.

A. A. R. Neves, A. Camposeo, S. Pagliara, R. Saija, F. Borghese, P. Denti, M. A. Iatì, R. Cingolani, O. M. Maragò, and D. Pisignano, “Rotational dynamics of optically trapped nanofibers,” Opt. Express 18(2), 822–830 (2010).
[PubMed]

F. Borghese, P. Denti, R. Saija, M. A. Iatì, and O. M. Maragò, “Radiation torque and force on optically trapped linear nanostructures,” Phys. Rev. Lett. 100(16), 163903 (2008).
[PubMed]

Marqués, M. I.

S. Albaladejo, M. I. Marqués, M. Laroche, and J. J. Sáenz, “Scattering forces from the curl of the spin angular momentum of a light field,” Phys. Rev. Lett. 102(11), 113602 (2009).
[PubMed]

Mazilu, M.

M. Dienerowitz, M. Mazilu, and K. Dholakia, “Optical manipulation of nanoparticles: a review,” J. Nanophoton. 2, 021875 (2008).

Mazolli, A.

A. Mazolli, P. A. Maia Neto, and H. M. Nussenzveig, “Theory of trapping forces in optical tweezers,” Proc. R. Soc. Lond. A 459, 3021–3041 (2003).

McConnell, G.

Nakayama, Y.

Y. Nakayama, P. J. Pauzauskie, A. Radenovic, R. M. Onorato, R. J. Saykally, J. Liphardt, and P. D. Yang, “Tunable nanowire nonlinear optical probe,” Nature 447(7148), 1098–1101 (2007).
[PubMed]

Neves, A. A. R.

Nieminen, T. A.

T. A. Nieminen, V. L. Y. Loke, A. B. Stilgoe, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “T-matrix method for modelling optical tweezers,” J. Mod. Opt. 58, 528–544 (2011).

V. L. Y. Loke, T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “T-matrix calculation via discrete dipole approximation, point matching and exploiting symmetry,” J. Quant. Spectrosc. Radiat. Transf. 110, 1460–1471 (2009).

T. A. Nieminen, T. Asavei, V. L. Y. Loke, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Symmetry and the generation and measurement of optical torque,” J. Quant. Spectrosc. Radiat. Transf. 110, 1472–1482 (2009).

A. B. Stilgoe, T. A. Nieminen, G. Knöener, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “The effect of Mie resonances on trapping in optical tweezers,” Opt. Express 16(19), 15039–15051 (2008).
[PubMed]

T. A. Nieminen, V. L. Y. Loke, A. B. Stilgoe, G. Knöner, A. M. Brańczyk, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Optical tweezers computational toolbox,” J. Opt. A 9, S196–S203 (2007).

G. Knöner, T. A. Nieminen, S. Parkin, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Calculation of optical trapping landscapes,” Proc. SPIE 6326, U119–U127 (2006).

T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Calculation of the T-matrix: general considerations and application of the point-matching method,” J. Quant. Spectrosc. Radiat. Transf. 79–80, 1019–1029 (2003).

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

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).

Nussenzveig, H. M.

A. Mazolli, P. A. Maia Neto, and H. M. Nussenzveig, “Theory of trapping forces in optical tweezers,” Proc. R. Soc. Lond. A 459, 3021–3041 (2003).

Onorato, R. M.

Y. Nakayama, P. J. Pauzauskie, A. Radenovic, R. M. Onorato, R. J. Saykally, J. Liphardt, and P. D. Yang, “Tunable nanowire nonlinear optical probe,” Nature 447(7148), 1098–1101 (2007).
[PubMed]

Pagliara, S.

Palmisano, F.

P. H. Jones, F. Palmisano, F. Bonaccorso, P. G. Gucciardi, G. Calogero, A. C. Ferrari, and O. M. Maragó, “Rotation Detection in Light-Driven Nanorotors,” ACS Nano 3(10), 3077–3084 (2009).
[PubMed]

Parkin, S.

G. Knöner, T. A. Nieminen, S. Parkin, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Calculation of optical trapping landscapes,” Proc. SPIE 6326, U119–U127 (2006).

Pauzauskie, P. J.

Y. Nakayama, P. J. Pauzauskie, A. Radenovic, R. M. Onorato, R. J. Saykally, J. Liphardt, and P. D. Yang, “Tunable nanowire nonlinear optical probe,” Nature 447(7148), 1098–1101 (2007).
[PubMed]

Pisignano, D.

Pozzo, Lde. Y.

Purcell, E. M.

E. M. Purcell, “Life at low Reynolds-number,” Am. J. Phys. 45, 3–11 (1977).

Radenovic, A.

Y. Nakayama, P. J. Pauzauskie, A. Radenovic, R. M. Onorato, R. J. Saykally, J. Liphardt, and P. D. Yang, “Tunable nanowire nonlinear optical probe,” Nature 447(7148), 1098–1101 (2007).
[PubMed]

Ramser, K.

K. Ramser and D. Hanstorp, “Optical manipulation for single-cell studies,” J Biophoton. 3(4), 187–206 (2010).
[PubMed]

Ren, Y. X.

Rodriguez, E.

Rodriguez-Otazo, M.

Rubinsztein-Dunlop, H.

T. A. Nieminen, V. L. Y. Loke, A. B. Stilgoe, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “T-matrix method for modelling optical tweezers,” J. Mod. Opt. 58, 528–544 (2011).

T. A. Nieminen, T. Asavei, V. L. Y. Loke, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Symmetry and the generation and measurement of optical torque,” J. Quant. Spectrosc. Radiat. Transf. 110, 1472–1482 (2009).

V. L. Y. Loke, T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “T-matrix calculation via discrete dipole approximation, point matching and exploiting symmetry,” J. Quant. Spectrosc. Radiat. Transf. 110, 1460–1471 (2009).

A. B. Stilgoe, T. A. Nieminen, G. Knöener, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “The effect of Mie resonances on trapping in optical tweezers,” Opt. Express 16(19), 15039–15051 (2008).
[PubMed]

T. A. Nieminen, V. L. Y. Loke, A. B. Stilgoe, G. Knöner, A. M. Brańczyk, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Optical tweezers computational toolbox,” J. Opt. A 9, S196–S203 (2007).

G. Knöner, T. A. Nieminen, S. Parkin, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Calculation of optical trapping landscapes,” Proc. SPIE 6326, U119–U127 (2006).

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

T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Calculation of the T-matrix: general considerations and application of the point-matching method,” J. Quant. Spectrosc. Radiat. Transf. 79–80, 1019–1029 (2003).

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).

Ruedenberg, K.

C. H. Choi, J. Ivanic, M. S. Gordon, and K. Ruedenberg, “Rapid and stable determination of rotation matrices between spherical harmonics by direct recursion,” J. Chem. Phys. 111, 8825–8831 (1999).

Sáenz, J. J.

S. Albaladejo, M. I. Marqués, M. Laroche, and J. J. Sáenz, “Scattering forces from the curl of the spin angular momentum of a light field,” Phys. Rev. Lett. 102(11), 113602 (2009).
[PubMed]

Saija, R.

A. A. R. Neves, A. Camposeo, S. Pagliara, R. Saija, F. Borghese, P. Denti, M. A. Iatì, R. Cingolani, O. M. Maragò, and D. Pisignano, “Rotational dynamics of optically trapped nanofibers,” Opt. Express 18(2), 822–830 (2010).
[PubMed]

F. Borghese, P. Denti, R. Saija, M. A. Iatì, and O. M. Maragò, “Radiation torque and force on optically trapped linear nanostructures,” Phys. Rev. Lett. 100(16), 163903 (2008).
[PubMed]

Saykally, R. J.

Y. Nakayama, P. J. Pauzauskie, A. Radenovic, R. M. Onorato, R. J. Saykally, J. Liphardt, and P. D. Yang, “Tunable nanowire nonlinear optical probe,” Nature 447(7148), 1098–1101 (2007).
[PubMed]

Simpson, S. H.

Stilgoe, A. B.

T. A. Nieminen, V. L. Y. Loke, A. B. Stilgoe, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “T-matrix method for modelling optical tweezers,” J. Mod. Opt. 58, 528–544 (2011).

A. B. Stilgoe, T. A. Nieminen, G. Knöener, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “The effect of Mie resonances on trapping in optical tweezers,” Opt. Express 16(19), 15039–15051 (2008).
[PubMed]

T. A. Nieminen, V. L. Y. Loke, A. B. Stilgoe, G. Knöner, A. M. Brańczyk, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Optical tweezers computational toolbox,” J. Opt. A 9, S196–S203 (2007).

Sun, X. D.

J. L. Zhang, T. G. Kim, S. C. Jeoung, F. F. Yao, H. Lee, and X. D. Sun, “Controlled trapping and rotation of carbon nanotube bundle with optical tweezers,” Opt. Commun. 267, 260–263 (2006).

Tan, S. D.

S. D. Tan, H. A. Lopez, C. W. Cai, and Y. G. Zhang, “Optical trapping of single-walled carbon nanotubes,” Nano Lett. 4, 1415–1419 (2004).

Trainelli, L.

O. A. Bauchau and L. Trainelli, “The vectorial parameterization of rotation,” Nonlinear Dyn. 32, 71–92 (2003).

Ukita, H.

Wang, Z. Q.

Yang, P. D.

Y. Nakayama, P. J. Pauzauskie, A. Radenovic, R. M. Onorato, R. J. Saykally, J. Liphardt, and P. D. Yang, “Tunable nanowire nonlinear optical probe,” Nature 447(7148), 1098–1101 (2007).
[PubMed]

Yao, F. F.

J. L. Zhang, T. G. Kim, S. C. Jeoung, F. F. Yao, H. Lee, and X. D. Sun, “Controlled trapping and rotation of carbon nanotube bundle with optical tweezers,” Opt. Commun. 267, 260–263 (2006).

Zhang, J. L.

J. L. Zhang, T. G. Kim, S. C. Jeoung, F. F. Yao, H. Lee, and X. D. Sun, “Controlled trapping and rotation of carbon nanotube bundle with optical tweezers,” Opt. Commun. 267, 260–263 (2006).

Zhang, Y. G.

S. D. Tan, H. A. Lopez, C. W. Cai, and Y. G. Zhang, “Optical trapping of single-walled carbon nanotubes,” Nano Lett. 4, 1415–1419 (2004).

Zhong, M. C.

Zhou, J. H.

ACS Nano (1)

P. H. Jones, F. Palmisano, F. Bonaccorso, P. G. Gucciardi, G. Calogero, A. C. Ferrari, and O. M. Maragó, “Rotation Detection in Light-Driven Nanorotors,” ACS Nano 3(10), 3077–3084 (2009).
[PubMed]

Am. J. Phys. (1)

E. M. Purcell, “Life at low Reynolds-number,” Am. J. Phys. 45, 3–11 (1977).

Appl. Opt. (4)

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).

J Biophoton. (1)

K. Ramser and D. Hanstorp, “Optical manipulation for single-cell studies,” J Biophoton. 3(4), 187–206 (2010).
[PubMed]

J. Appl. Phys. (1)

P. C. Chaumet and C. Billaudeau, “Coupled dipole method to compute optical torque: Application to a micro-propeller,” J. Appl. Phys. 101, 023106 (2007).

J. Chem. Phys. (1)

C. H. Choi, J. Ivanic, M. S. Gordon, and K. Ruedenberg, “Rapid and stable determination of rotation matrices between spherical harmonics by direct recursion,” J. Chem. Phys. 111, 8825–8831 (1999).

J. Mod. Opt. (1)

T. A. Nieminen, V. L. Y. Loke, A. B. Stilgoe, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “T-matrix method for modelling optical tweezers,” J. Mod. Opt. 58, 528–544 (2011).

J. Nanophoton. (1)

M. Dienerowitz, M. Mazilu, and K. Dholakia, “Optical manipulation of nanoparticles: a review,” J. Nanophoton. 2, 021875 (2008).

J. Opt. A (1)

T. A. Nieminen, V. L. Y. Loke, A. B. Stilgoe, G. Knöner, A. M. Brańczyk, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Optical tweezers computational toolbox,” J. Opt. A 9, S196–S203 (2007).

J. Opt. Soc. Am. A (1)

J. Opt. Soc. Am. B (2)

J. Quant. Spectrosc. Radiat. Transf. (3)

T. A. Nieminen, T. Asavei, V. L. Y. Loke, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Symmetry and the generation and measurement of optical torque,” J. Quant. Spectrosc. Radiat. Transf. 110, 1472–1482 (2009).

V. L. Y. Loke, T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “T-matrix calculation via discrete dipole approximation, point matching and exploiting symmetry,” J. Quant. Spectrosc. Radiat. Transf. 110, 1460–1471 (2009).

T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Calculation of the T-matrix: general considerations and application of the point-matching method,” J. Quant. Spectrosc. Radiat. Transf. 79–80, 1019–1029 (2003).

Nano Lett. (1)

S. D. Tan, H. A. Lopez, C. W. Cai, and Y. G. Zhang, “Optical trapping of single-walled carbon nanotubes,” Nano Lett. 4, 1415–1419 (2004).

Nature (1)

Y. Nakayama, P. J. Pauzauskie, A. Radenovic, R. M. Onorato, R. J. Saykally, J. Liphardt, and P. D. Yang, “Tunable nanowire nonlinear optical probe,” Nature 447(7148), 1098–1101 (2007).
[PubMed]

Nonlinear Dyn. (1)

O. A. Bauchau and L. Trainelli, “The vectorial parameterization of rotation,” Nonlinear Dyn. 32, 71–92 (2003).

Opt. Commun. (1)

J. L. Zhang, T. G. Kim, S. C. Jeoung, F. F. Yao, H. Lee, and X. D. Sun, “Controlled trapping and rotation of carbon nanotube bundle with optical tweezers,” Opt. Commun. 267, 260–263 (2006).

Opt. Express (5)

Opt. Lett. (1)

Phys. Rev. A (1)

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

Phys. Rev. Lett. (3)

F. Borghese, P. Denti, R. Saija, M. A. Iatì, and O. M. Maragò, “Radiation torque and force on optically trapped linear nanostructures,” Phys. Rev. Lett. 100(16), 163903 (2008).
[PubMed]

S. Albaladejo, M. I. Marqués, M. Laroche, and J. J. Sáenz, “Scattering forces from the curl of the spin angular momentum of a light field,” Phys. Rev. Lett. 102(11), 113602 (2009).
[PubMed]

A. Ashkin, “Acceleration and trapping of particles by radiation pressure,” Phys. Rev. Lett. 24, 156–159 (1970).

Proc. R. Soc. Lond. A (1)

A. Mazolli, P. A. Maia Neto, and H. M. Nussenzveig, “Theory of trapping forces in optical tweezers,” Proc. R. Soc. Lond. A 459, 3021–3041 (2003).

Proc. SPIE (1)

G. Knöner, T. A. Nieminen, S. Parkin, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Calculation of optical trapping landscapes,” Proc. SPIE 6326, U119–U127 (2006).

Q. Rev. Biophys. (1)

J. G. Garcia de la Torre and V. A. Bloomfield, “Hydrodynamic properties of complex, rigid, biological macromolecules: theory and applications,” Q. Rev. Biophys. 14(1), 81–139 (1981).
[PubMed]

Other (1)

H. K. Moffat, “Six Lectures on General Fluid Dynamics and Two on Hydromagnetic Dynamo Theory,” in Fluid Dynamics, R. Balian and J.-L. Peube eds., (Gordon and Breach, 1977), pp. 149–234.

Supplementary Material (1)

» Media 1: MOV (2552 KB)     

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Figures (5)

Fig. 1
Fig. 1

Trajectories of a glass microcylinder with D = 500 nm and L = 2000 nm in a linearly polarized beam. AB is starting position and orientation of the microcylinder, A2B2 is the trapped position and final orientation. The starting positions are (a) (−0.5, 0.5, −0.5)λ, (b) (0, 1, 0)λ, (c) (0.5, −0.5, −0.5)λ and (d) (−0.5, 0, 1)λ. The initial orientations are (a) (90°, 90°), (b) (45°, 270°), (c) (0°, 0°) and (d) (45°, 180°). The solid curve and arrow show the trajectory of one top center of the cylinder. The cylinder was finally trapped vertically at (0, 0, 0.94) λ (Media 1).

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Fig. 2
Fig. 2

Rotations and translations of beam coefficients from initial Cartesian coordinate system x1y1z1 to an arbitrary coordinate system x3y3z3 through translated coordinate system x2y2z2. (A) and (B) are translations of beam coefficients along O1O2 direction. R1 and R2 are rotations of beam coefficients.

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Fig. 3
Fig. 3

Trajectories of a simulated glass nanowire with D = 50 nm and L = 2000 nm in (a) linearly and (b) circularly polarized beams. AB is initial position and orientation of the nanowire, A2B2 is the trapped position and orientation. The solid curve and arrow show the trajectory of one top center of the cylinder. The linear polarisation contributed to the horizontal torque component which would make the nanowire lie down. But the circular polarisation made the time-averaged horizontal torque component so weak that the nanowire could stand up.

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Fig. 4
Fig. 4

Orientations landscapes of nanowires and microcylinders in (a) linearly polarized and (b) circularly polarized beams. The coordinate system is Cartesian coordinate system centred at cylinder position. The rectangular shapes in (a) show the orientations of cylinders in each region. Four regimes in the orientation landscapes are the untrapped region, vertical region, horizontal region, and the intermediate region between the vertical and horizontal regions. The “circle” means the longest nanowire or microcylinder trapped horizontally for each diameter. The “asterisk” represents the shortest nanowire or microcylinder trapped vertically for each diameter. The “star” indicates the longest nanowire or microcylinder for each diameter, which can be trapped (vertically). The fitting curves are used to distinguish different regions.

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Fig. 5
Fig. 5

Torque efficiencies, Qτt, for cylinders with diameter of 300 nm and different lengths located in polarisation plane of (a) a linearly polarized beam and in a plane parallel to the beam axis in (b) a circularly polarized beam as a function of tilt angle.

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Equations (13)

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

U inc = ∑ n ∞ a n Ψ n inc ,
U scat = ∑ k ∞ p k Ψ k scat .
P ˜ =T A ˜ ,
a= R 2 ( R 1 −1 A R 1 a 0 + R 1 −1 B R 1 b 0 ),
b= R 2 ( R 1 −1 B R 1 a 0 + R 1 −1 A R 1 b 0 ).
R 2,3,t+dt =ΔR R 2,3,t .
ΔR= I+sinφ(u×)+(1−cosφ) (u×) 2
F= n m P inc Q c ,
Γ= P inc τ ω .
v= γ t −1 F,
ω= γ r −1 Γ,
r( t+dt )=r( t )+vdt,
dt= α P inc (1+β| ω t |)

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