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 OSA

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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).

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).

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).

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).

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).

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).

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).

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)

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, 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)

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).

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]

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)

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