Abstract

We examine the rotational dynamics of spheroidal particles in an optical trap comprising counter-propagating Gaussian beams of opposing helicity. Isolated spheroids undergo continuous rotation with frequencies determined by their size and aspect ratio, whilst pairs of spheroids display phase locking behaviour. The introduction of additional particles leads to yet more complex behaviour. Experimental results are supported by numerical calculations.

© 2015 Optical Society of America

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    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref]
  46. J. A. Champion, Y. K. Katare, and S. Mitragotri, “Making polymeric micro- and nanoparticles of complex shapes,” Proc. Natl. Acad. Sci. USA 104, 11901–11904 (2007).
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    [Crossref]
  50. O. Brzobohatý, V. Karásek, M. Šiler, J. Trojek, and P. Zemánek, “Static and dynamic behavior of two optically bound microparticles in a standing wave,” Opt. Express 19, 19613–19626 (2011).
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2014 (5)

J. Millen, T. Deesuwan, P. Barker, and J. Anders, “Nanoscale temperature measurements using non-equilibrium Brownian dynamics of a levitated nanosphere,” Nature Nanotech. 9, 425–429 (2014).
[Crossref]

A. Arzola, P. Jákl, L. Chvátal, and P. Zemánek, “Rotation, oscillation and hydrodynamic synchronization of optically trapped oblate spheroidal microparticles,” Opt. Express 22, 16207–16221 (2014).
[Crossref] [PubMed]

B. Mihiretie, P. Snabre, J.-C. Loudet, and B. Pouligny, “Optically driven oscillations of ellipsoidal particles. Part I: Experimental observations,” Eur. Phys. J. E 37, 124 (2014).
[Crossref]

D. Phillips, M. Padgett, S. Hanna, Y.-L. Ho, D. Carberry, M. Miles, and S. Simpson, “Shape-induced force fields in optical trapping,” Nature Photon. 8, 400–405 (2014).
[Crossref]

S. H. Simpson, “Inhomogeneous and anisotropic particles in optical traps: Physical behaviour and applications,” J. Quant. Spectrosc. Radiat. Transf. 146, 81–99 (2014).
[Crossref]

2013 (3)

D. Palima and J. Glückstad, “Generalized phase contrast matched to Gaussian illumination,” Laser Photon. Rev. 7, 478–494 (2013).
[Crossref]

Y. Arita, M. Mazilu, and K. Dholakia, “Laser-induced rotation and cooling of a trapped microgyroscope in vacuum,” Nature Commun. 4, 2374 (2013).
[Crossref]

M. Aas, A. Jonáš, A. Kiraz, O. Brzobohatý, J. Ježek, Z. Pilát, and P. Zemánek, “Spectral tuning of lasing emission from optofluidic droplet microlasers using optical stretching,” Opt. Express 21, 21381–21394 (2013).
[Crossref]

2012 (2)

B. M. Mihiretie, P. Snabre, J. C. Loudet, and B. Pouligny, “Radiation pressure makes ellipsoidal particles tumble,” Europhys. Lett. 100, 48005 (2012).
[Crossref]

J. Trojek, L. Chvátal, and P. Zemánek, “Optical alignment and confinement of an ellipsoidal nanorod in optical tweezers: a theoretical study,” J. Opt. Soc. Am. A 29, 1224–1236 (2012).
[Crossref]

2011 (7)

O. Brzobohatý, V. Karásek, T. Čižmár, and P. Zemánek, “Dynamic size tuning of multidimensional optically bound matter,” Appl. Phys. Lett. 99, 101105 (2011).
[Crossref]

S. H. Simpson and S. Hanna, “Computational study of the optical trapping of ellipsoidal particles,” Phys. Rev. A 84, 053808 (2011).
[Crossref]

T. Čižmár, O. Brzobohatý, K. Dholakia, and P. Zemánek, “The holographic optical micro-manipulation system based on counter-propagating beams,” Laser Phys. Lett. 8, 50–56 (2011).
[Crossref]

C.-L. Lin, G. Vitrant, M. Bouriau, R. Casalegno, and P. L. Baldeck, “Optically driven Archimedes micro-screws for micropump application,” Opt. Express 19, 8267–8276 (2011).
[Crossref] [PubMed]

M. Padgett and R. Bowman, “Tweezers with a twist,” Nature Photon. 5, 343–348 (2011).
[Crossref]

M. Šiler and P. Zemánek, “Parametric study of optical forces acting upon nanoparticles in a single, or a standing, evanescent wave,” J. Opt. 13, 044016 (2011).
[Crossref]

O. Brzobohatý, V. Karásek, M. Šiler, J. Trojek, and P. Zemánek, “Static and dynamic behavior of two optically bound microparticles in a standing wave,” Opt. Express 19, 19613–19626 (2011).
[Crossref] [PubMed]

2010 (1)

B. Gutierrez-Medina, J. O. Andreasson, W. J. Greenleaf, A. LaPorta, and S. M. Block, “An optical apparatus for rotation and trapping,” Methods Enzymol. 475, 377–404 (2010).
[Crossref] [PubMed]

2009 (3)

2008 (4)

D. M. Gherardi, A. E. Carruthers, T. Čižmár, E. M. Wright, and K. Dholakia, “A dual beam photonic crystal fibre trap for microscopic particles,” Appl. Phys. Lett. 93, 041110 (2008).
[Crossref]

R. Gordon, M. Kawano, J. T. Blakely, and D. Sinton, “Optohydrodynamic theory of particles in a dual-beam optical trap,” Phys. Rev. B 77, 245125 (2008).
[Crossref]

M. Šiler, T. Čižmár, A. Jonáš, and P. Zemánek, “Surface delivery of a single nanoparticle under moving evanescent standing-wave illumination,” New. J. Phys. 10, 113010 (2008).
[Crossref]

F. Xu, J. A. Lock, G. Gouesbet, and C. Tropea, “Radiation torque exerted on a spheroid: Analytical solution,” Phys. Rev. A 78, 013843 (2008).
[Crossref]

2007 (4)

S. H. Simpson and S. Hanna, “Optical trapping of spheroidal particles in Gaussian beams,” J. Opt. Soc. Am. A 24, 430 (2007).
[Crossref]

F. Xu, K. Ren, G. Gouesbet, X. Cai, and G. Gréhan, “Theoretical prediction of radiation pressure force exerted on a spheroid by an arbitrarily shaped beam,” Phys. Rev. E 75, 026613 (2007).
[Crossref]

J. A. Champion, Y. K. Katare, and S. Mitragotri, “Making polymeric micro- and nanoparticles of complex shapes,” Proc. Natl. Acad. Sci. USA 104, 11901–11904 (2007).
[Crossref] [PubMed]

S. Parkin, G. Knöner, W. Singer, T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Optical torque on microscopic objects,” Methods Cell. Biol. 82, 525–561 (2007).
[Crossref] [PubMed]

2006 (5)

Y. Han, A. Alsayed, M. Nobili, J. Zhang, T. Lubensky, and A. Yodh, “Brownian motion of an ellipsoid,” Science 314, 626–630 (2006).
[Crossref] [PubMed]

L. Oroszi, P. Galajda, H. Kirei, S. Bottka, and P. Ormos, “Direct measurement of torque in an optical trap and its application to double-strand DNA,” Phys. Rev. Lett. 97, 058301 (2006).
[Crossref] [PubMed]

P. J. Rodrigo, I. R. Perch-Nielsen, C. A. Alonzo, and J. Glueckstad, “GPC-based optical micromanipulation in 3D real-time using a single spatial light modulator,” Opt. Express 14, 13107–13112 (2006).
[Crossref] [PubMed]

P. Jess, V. Garcés-Chávez, D. Smith, M. Mazilu, L. Paterson, A. Riches, C. Herrington, W. Sibbett, and K. Dholakia, “Dual beam fibre trap for Raman microspectroscopy of single cells,” Opt. Express 14, 5779–5791 (2006).
[Crossref] [PubMed]

T. Čižmár, M. Šiler, and P. Zemánek, “An optical nanotrap array movable over a milimetre range,” Appl. Phys. B 84, 197–203 (2006).
[Crossref]

2005 (1)

T. Čižmár, V. Garcés-Chávez, K. Dholakia, and P. Zemánek, “Optical conveyor belt for delivery of submicron objects,” Appl. Phys. Lett. 86, 174101 (2005).
[Crossref]

2004 (1)

A. Bishop, T. Nieminen, N. Heckenberg, and H. Rubinsztein-Dunlop, “Optical microrheology using rotating laser-trapped particles,” Phys. Rev. Lett. 92, 198104 (2004).
[Crossref] [PubMed]

2003 (4)

Z. Cheng and T. Mason, “Rotational diffusion microrheology,” Phys. Rev. Lett. 90, 018304 (2003).
[Crossref] [PubMed]

P. Zemánek, A. Jonáš, P. Jákl, M. Šerý, J. Ježek, and M. Liška, “Theoretical comparison of optical traps created by standing wave and single beam,” Opt. Commun. 220, 401–412 (2003).
[Crossref]

W. Singer, M. Frick, S. Bernet, and M. Ritsch-Marte, “Self-organized array of regularly spaced microbeads in a fiber-optical trap,” J. Opt. Soc. Am. B 20, 1568–1574 (2003).
[Crossref]

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

2002 (2)

Z. Cheng, P. Chaikin, and T. Mason, “Light streak tracking of optically trapped thin microdisks,” Phys. Rev. Lett. 89, 108303 (2002).
[Crossref] [PubMed]

S. A. Tatarkova, A. E. Carruthers, and K. Dholakia, “One-Dimensional Optically Bound Arrays of Microscopic Particles,” Phys. Rev. Lett. 89, 283901 (2002).
[Crossref]

2001 (1)

J. Guck, R. Ananthakrishnan, H. Mahmood, T. Moon, C. Cunningham, and J. Kas, “The optical stretcher: A novel laser tool to micromanipulate cells,” Biophys. J. 1, 767–784 (2001).
[Crossref]

1998 (1)

P. Zemánek, A. Jonáš, L. Šrámek, and M. Liška, “Optical trapping of Rayleigh particles using a Gaussian standing wave,” Opt. Commun. 151, 273–285 (1998).
[Crossref]

1994 (1)

1993 (1)

C. C. Ho, A. Keller, J. A. Odell, and R. H. Ottewill, “Preparation of monodisperse ellipsoidal polystyrene particles,” Colloid Polym. Sci. 271, 469–479 (1993).
[Crossref]

1986 (1)

1970 (1)

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

1936 (1)

F. Perrin, “Mouvement brownien d’un ellipsoide (II). rotation libre et d’polarisation des fluorescences. translation et diffusion de molecules ellipsoidales,” J. Phys. Radium 7, 1–11 (1936).
[Crossref]

1934 (1)

F. Perrin, “Mouvement brownien d’un ellipsoide - i. dispersion dielectrique pour des molecules ellipsoidales,” J. Phys. Radium 5, 497–511 (1934).
[Crossref]

Aas, M.

M. Aas, A. Jonáš, A. Kiraz, O. Brzobohatý, J. Ježek, Z. Pilát, and P. Zemánek, “Spectral tuning of lasing emission from optofluidic droplet microlasers using optical stretching,” Opt. Express 21, 21381–21394 (2013).
[Crossref]

Alonzo, C. A.

Alsayed, A.

Y. Han, A. Alsayed, M. Nobili, J. Zhang, T. Lubensky, and A. Yodh, “Brownian motion of an ellipsoid,” Science 314, 626–630 (2006).
[Crossref] [PubMed]

Ananthakrishnan, R.

J. Guck, R. Ananthakrishnan, H. Mahmood, T. Moon, C. Cunningham, and J. Kas, “The optical stretcher: A novel laser tool to micromanipulate cells,” Biophys. J. 1, 767–784 (2001).
[Crossref]

Anders, J.

J. Millen, T. Deesuwan, P. Barker, and J. Anders, “Nanoscale temperature measurements using non-equilibrium Brownian dynamics of a levitated nanosphere,” Nature Nanotech. 9, 425–429 (2014).
[Crossref]

Andreasson, J. O.

B. Gutierrez-Medina, J. O. Andreasson, W. J. Greenleaf, A. LaPorta, and S. M. Block, “An optical apparatus for rotation and trapping,” Methods Enzymol. 475, 377–404 (2010).
[Crossref] [PubMed]

Arita, Y.

Y. Arita, M. Mazilu, and K. Dholakia, “Laser-induced rotation and cooling of a trapped microgyroscope in vacuum,” Nature Commun. 4, 2374 (2013).
[Crossref]

Arzola, A.

Ashkin, A.

Baldeck, P. L.

Barker, P.

J. Millen, T. Deesuwan, P. Barker, and J. Anders, “Nanoscale temperature measurements using non-equilibrium Brownian dynamics of a levitated nanosphere,” Nature Nanotech. 9, 425–429 (2014).
[Crossref]

Bernet, S.

Bishop, A.

A. Bishop, T. Nieminen, N. Heckenberg, and H. Rubinsztein-Dunlop, “Optical microrheology using rotating laser-trapped particles,” Phys. Rev. Lett. 92, 198104 (2004).
[Crossref] [PubMed]

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

Bjorkholm, J. E.

Blakely, J. T.

R. Gordon, M. Kawano, J. T. Blakely, and D. Sinton, “Optohydrodynamic theory of particles in a dual-beam optical trap,” Phys. Rev. B 77, 245125 (2008).
[Crossref]

Block, S. M.

B. Gutierrez-Medina, J. O. Andreasson, W. J. Greenleaf, A. LaPorta, and S. M. Block, “An optical apparatus for rotation and trapping,” Methods Enzymol. 475, 377–404 (2010).
[Crossref] [PubMed]

Bottka, S.

L. Oroszi, P. Galajda, H. Kirei, S. Bottka, and P. Ormos, “Direct measurement of torque in an optical trap and its application to double-strand DNA,” Phys. Rev. Lett. 97, 058301 (2006).
[Crossref] [PubMed]

Bouriau, M.

Bowman, R.

M. Padgett and R. Bowman, “Tweezers with a twist,” Nature Photon. 5, 343–348 (2011).
[Crossref]

Brenner, H.

J. Happel and H. Brenner, Low Reynolds number hydrodynamics (Prentice–Hall, 1965).

Brzobohatý, O.

M. Aas, A. Jonáš, A. Kiraz, O. Brzobohatý, J. Ježek, Z. Pilát, and P. Zemánek, “Spectral tuning of lasing emission from optofluidic droplet microlasers using optical stretching,” Opt. Express 21, 21381–21394 (2013).
[Crossref]

O. Brzobohatý, V. Karásek, T. Čižmár, and P. Zemánek, “Dynamic size tuning of multidimensional optically bound matter,” Appl. Phys. Lett. 99, 101105 (2011).
[Crossref]

T. Čižmár, O. Brzobohatý, K. Dholakia, and P. Zemánek, “The holographic optical micro-manipulation system based on counter-propagating beams,” Laser Phys. Lett. 8, 50–56 (2011).
[Crossref]

O. Brzobohatý, V. Karásek, M. Šiler, J. Trojek, and P. Zemánek, “Static and dynamic behavior of two optically bound microparticles in a standing wave,” Opt. Express 19, 19613–19626 (2011).
[Crossref] [PubMed]

Cai, X.

F. Xu, K. Ren, G. Gouesbet, X. Cai, and G. Gréhan, “Theoretical prediction of radiation pressure force exerted on a spheroid by an arbitrarily shaped beam,” Phys. Rev. E 75, 026613 (2007).
[Crossref]

Carberry, D.

D. Phillips, M. Padgett, S. Hanna, Y.-L. Ho, D. Carberry, M. Miles, and S. Simpson, “Shape-induced force fields in optical trapping,” Nature Photon. 8, 400–405 (2014).
[Crossref]

Carruthers, A. E.

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Frick, M.

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L. Oroszi, P. Galajda, H. Kirei, S. Bottka, and P. Ormos, “Direct measurement of torque in an optical trap and its application to double-strand DNA,” Phys. Rev. Lett. 97, 058301 (2006).
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D. M. Gherardi, A. E. Carruthers, T. Čižmár, E. M. Wright, and K. Dholakia, “A dual beam photonic crystal fibre trap for microscopic particles,” Appl. Phys. Lett. 93, 041110 (2008).
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O. Brzobohatý, V. Karásek, T. Čižmár, and P. Zemánek, “Dynamic size tuning of multidimensional optically bound matter,” Appl. Phys. Lett. 99, 101105 (2011).
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O. Brzobohatý, V. Karásek, M. Šiler, J. Trojek, and P. Zemánek, “Static and dynamic behavior of two optically bound microparticles in a standing wave,” Opt. Express 19, 19613–19626 (2011).
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J. Guck, R. Ananthakrishnan, H. Mahmood, T. Moon, C. Cunningham, and J. Kas, “The optical stretcher: A novel laser tool to micromanipulate cells,” Biophys. J. 1, 767–784 (2001).
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J. A. Champion, Y. K. Katare, and S. Mitragotri, “Making polymeric micro- and nanoparticles of complex shapes,” Proc. Natl. Acad. Sci. USA 104, 11901–11904 (2007).
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L. Oroszi, P. Galajda, H. Kirei, S. Bottka, and P. Ormos, “Direct measurement of torque in an optical trap and its application to double-strand DNA,” Phys. Rev. Lett. 97, 058301 (2006).
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S. Parkin, G. Knöner, W. Singer, T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Optical torque on microscopic objects,” Methods Cell. Biol. 82, 525–561 (2007).
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B. Gutierrez-Medina, J. O. Andreasson, W. J. Greenleaf, A. LaPorta, and S. M. Block, “An optical apparatus for rotation and trapping,” Methods Enzymol. 475, 377–404 (2010).
[Crossref] [PubMed]

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Liška, M.

P. Zemánek, A. Jonáš, P. Jákl, M. Šerý, J. Ježek, and M. Liška, “Theoretical comparison of optical traps created by standing wave and single beam,” Opt. Commun. 220, 401–412 (2003).
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P. Zemánek, A. Jonáš, L. Šrámek, and M. Liška, “Optical trapping of Rayleigh particles using a Gaussian standing wave,” Opt. Commun. 151, 273–285 (1998).
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F. Xu, J. A. Lock, G. Gouesbet, and C. Tropea, “Radiation torque exerted on a spheroid: Analytical solution,” Phys. Rev. A 78, 013843 (2008).
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B. Mihiretie, P. Snabre, J.-C. Loudet, and B. Pouligny, “Optically driven oscillations of ellipsoidal particles. Part I: Experimental observations,” Eur. Phys. J. E 37, 124 (2014).
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Y. Han, A. Alsayed, M. Nobili, J. Zhang, T. Lubensky, and A. Yodh, “Brownian motion of an ellipsoid,” Science 314, 626–630 (2006).
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Mahmood, H.

J. Guck, R. Ananthakrishnan, H. Mahmood, T. Moon, C. Cunningham, and J. Kas, “The optical stretcher: A novel laser tool to micromanipulate cells,” Biophys. J. 1, 767–784 (2001).
[Crossref]

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Z. Cheng and T. Mason, “Rotational diffusion microrheology,” Phys. Rev. Lett. 90, 018304 (2003).
[Crossref] [PubMed]

Z. Cheng, P. Chaikin, and T. Mason, “Light streak tracking of optically trapped thin microdisks,” Phys. Rev. Lett. 89, 108303 (2002).
[Crossref] [PubMed]

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Mihiretie, B.

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B. M. Mihiretie, P. Snabre, J. C. Loudet, and B. Pouligny, “Radiation pressure makes ellipsoidal particles tumble,” Europhys. Lett. 100, 48005 (2012).
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D. Phillips, M. Padgett, S. Hanna, Y.-L. Ho, D. Carberry, M. Miles, and S. Simpson, “Shape-induced force fields in optical trapping,” Nature Photon. 8, 400–405 (2014).
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J. Millen, T. Deesuwan, P. Barker, and J. Anders, “Nanoscale temperature measurements using non-equilibrium Brownian dynamics of a levitated nanosphere,” Nature Nanotech. 9, 425–429 (2014).
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J. A. Champion, Y. K. Katare, and S. Mitragotri, “Making polymeric micro- and nanoparticles of complex shapes,” Proc. Natl. Acad. Sci. USA 104, 11901–11904 (2007).
[Crossref] [PubMed]

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S. Zwick, T. Haist, Y. Miyamoto, L. He, M. Warber, A. Hermerschmidt, and W. Osten, “Holographic twin traps,” J. Opt. A: Pure Appl. Opt. 11, 034011 (2009).
[Crossref]

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J. Guck, R. Ananthakrishnan, H. Mahmood, T. Moon, C. Cunningham, and J. Kas, “The optical stretcher: A novel laser tool to micromanipulate cells,” Biophys. J. 1, 767–784 (2001).
[Crossref]

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A. Bishop, T. Nieminen, N. Heckenberg, and H. Rubinsztein-Dunlop, “Optical microrheology using rotating laser-trapped particles,” Phys. Rev. Lett. 92, 198104 (2004).
[Crossref] [PubMed]

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[Crossref]

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S. Parkin, G. Knöner, W. Singer, T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Optical torque on microscopic objects,” Methods Cell. Biol. 82, 525–561 (2007).
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Y. Han, A. Alsayed, M. Nobili, J. Zhang, T. Lubensky, and A. Yodh, “Brownian motion of an ellipsoid,” Science 314, 626–630 (2006).
[Crossref] [PubMed]

Odell, J. A.

C. C. Ho, A. Keller, J. A. Odell, and R. H. Ottewill, “Preparation of monodisperse ellipsoidal polystyrene particles,” Colloid Polym. Sci. 271, 469–479 (1993).
[Crossref]

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L. Oroszi, P. Galajda, H. Kirei, S. Bottka, and P. Ormos, “Direct measurement of torque in an optical trap and its application to double-strand DNA,” Phys. Rev. Lett. 97, 058301 (2006).
[Crossref] [PubMed]

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L. Oroszi, P. Galajda, H. Kirei, S. Bottka, and P. Ormos, “Direct measurement of torque in an optical trap and its application to double-strand DNA,” Phys. Rev. Lett. 97, 058301 (2006).
[Crossref] [PubMed]

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S. Zwick, T. Haist, Y. Miyamoto, L. He, M. Warber, A. Hermerschmidt, and W. Osten, “Holographic twin traps,” J. Opt. A: Pure Appl. Opt. 11, 034011 (2009).
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C. C. Ho, A. Keller, J. A. Odell, and R. H. Ottewill, “Preparation of monodisperse ellipsoidal polystyrene particles,” Colloid Polym. Sci. 271, 469–479 (1993).
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D. Phillips, M. Padgett, S. Hanna, Y.-L. Ho, D. Carberry, M. Miles, and S. Simpson, “Shape-induced force fields in optical trapping,” Nature Photon. 8, 400–405 (2014).
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S. Parkin, G. Knöner, W. Singer, T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Optical torque on microscopic objects,” Methods Cell. Biol. 82, 525–561 (2007).
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D. Phillips, M. Padgett, S. Hanna, Y.-L. Ho, D. Carberry, M. Miles, and S. Simpson, “Shape-induced force fields in optical trapping,” Nature Photon. 8, 400–405 (2014).
[Crossref]

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M. Aas, A. Jonáš, A. Kiraz, O. Brzobohatý, J. Ježek, Z. Pilát, and P. Zemánek, “Spectral tuning of lasing emission from optofluidic droplet microlasers using optical stretching,” Opt. Express 21, 21381–21394 (2013).
[Crossref]

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Pouligny, B.

B. Mihiretie, P. Snabre, J.-C. Loudet, and B. Pouligny, “Optically driven oscillations of ellipsoidal particles. Part I: Experimental observations,” Eur. Phys. J. E 37, 124 (2014).
[Crossref]

B. M. Mihiretie, P. Snabre, J. C. Loudet, and B. Pouligny, “Radiation pressure makes ellipsoidal particles tumble,” Europhys. Lett. 100, 48005 (2012).
[Crossref]

Ren, K.

F. Xu, K. Ren, G. Gouesbet, X. Cai, and G. Gréhan, “Theoretical prediction of radiation pressure force exerted on a spheroid by an arbitrarily shaped beam,” Phys. Rev. E 75, 026613 (2007).
[Crossref]

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Ritsch-Marte, M.

Rodrigo, P. J.

Rubinsztein-Dunlop, H.

S. Parkin, G. Knöner, W. Singer, T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Optical torque on microscopic objects,” Methods Cell. Biol. 82, 525–561 (2007).
[Crossref] [PubMed]

A. Bishop, T. Nieminen, N. Heckenberg, and H. Rubinsztein-Dunlop, “Optical microrheology using rotating laser-trapped particles,” Phys. Rev. Lett. 92, 198104 (2004).
[Crossref] [PubMed]

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

Šerý, M.

P. Zemánek, A. Jonáš, P. Jákl, M. Šerý, J. Ježek, and M. Liška, “Theoretical comparison of optical traps created by standing wave and single beam,” Opt. Commun. 220, 401–412 (2003).
[Crossref]

Sibbett, W.

Šiler, M.

O. Brzobohatý, V. Karásek, M. Šiler, J. Trojek, and P. Zemánek, “Static and dynamic behavior of two optically bound microparticles in a standing wave,” Opt. Express 19, 19613–19626 (2011).
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M. Šiler and P. Zemánek, “Parametric study of optical forces acting upon nanoparticles in a single, or a standing, evanescent wave,” J. Opt. 13, 044016 (2011).
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M. Šiler, T. Čižmár, A. Jonáš, and P. Zemánek, “Surface delivery of a single nanoparticle under moving evanescent standing-wave illumination,” New. J. Phys. 10, 113010 (2008).
[Crossref]

T. Čižmár, M. Šiler, and P. Zemánek, “An optical nanotrap array movable over a milimetre range,” Appl. Phys. B 84, 197–203 (2006).
[Crossref]

Simpson, S.

D. Phillips, M. Padgett, S. Hanna, Y.-L. Ho, D. Carberry, M. Miles, and S. Simpson, “Shape-induced force fields in optical trapping,” Nature Photon. 8, 400–405 (2014).
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S. H. Simpson, “Inhomogeneous and anisotropic particles in optical traps: Physical behaviour and applications,” J. Quant. Spectrosc. Radiat. Transf. 146, 81–99 (2014).
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S. H. Simpson and S. Hanna, “Computational study of the optical trapping of ellipsoidal particles,” Phys. Rev. A 84, 053808 (2011).
[Crossref]

S. H. Simpson and S. Hanna, “Optical angular momentum transfer by Laguerre-Gaussian beams,” J. Opt. Soc. Am. A 26, 625–638 (2009).
[Crossref]

S. H. Simpson and S. Hanna, “Optical trapping of spheroidal particles in Gaussian beams,” J. Opt. Soc. Am. A 24, 430 (2007).
[Crossref]

Singer, W.

S. Parkin, G. Knöner, W. Singer, T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Optical torque on microscopic objects,” Methods Cell. Biol. 82, 525–561 (2007).
[Crossref] [PubMed]

W. Singer, M. Frick, S. Bernet, and M. Ritsch-Marte, “Self-organized array of regularly spaced microbeads in a fiber-optical trap,” J. Opt. Soc. Am. B 20, 1568–1574 (2003).
[Crossref]

Sinton, D.

R. Gordon, M. Kawano, J. T. Blakely, and D. Sinton, “Optohydrodynamic theory of particles in a dual-beam optical trap,” Phys. Rev. B 77, 245125 (2008).
[Crossref]

Smith, D.

Snabre, P.

B. Mihiretie, P. Snabre, J.-C. Loudet, and B. Pouligny, “Optically driven oscillations of ellipsoidal particles. Part I: Experimental observations,” Eur. Phys. J. E 37, 124 (2014).
[Crossref]

B. M. Mihiretie, P. Snabre, J. C. Loudet, and B. Pouligny, “Radiation pressure makes ellipsoidal particles tumble,” Europhys. Lett. 100, 48005 (2012).
[Crossref]

Šrámek, L.

P. Zemánek, A. Jonáš, L. Šrámek, and M. Liška, “Optical trapping of Rayleigh particles using a Gaussian standing wave,” Opt. Commun. 151, 273–285 (1998).
[Crossref]

Steiger, R.

Tatarkova, S. A.

S. A. Tatarkova, A. E. Carruthers, and K. Dholakia, “One-Dimensional Optically Bound Arrays of Microscopic Particles,” Phys. Rev. Lett. 89, 283901 (2002).
[Crossref]

Thalhammer, G.

Trojek, J.

Tropea, C.

F. Xu, J. A. Lock, G. Gouesbet, and C. Tropea, “Radiation torque exerted on a spheroid: Analytical solution,” Phys. Rev. A 78, 013843 (2008).
[Crossref]

Tsang, L.

L. Tsang, Scattering of Electromagnetic Waves (Wiley, 2001).

Vitrant, G.

Warber, M.

S. Zwick, T. Haist, Y. Miyamoto, L. He, M. Warber, A. Hermerschmidt, and W. Osten, “Holographic twin traps,” J. Opt. A: Pure Appl. Opt. 11, 034011 (2009).
[Crossref]

Wright, E. M.

D. M. Gherardi, A. E. Carruthers, T. Čižmár, E. M. Wright, and K. Dholakia, “A dual beam photonic crystal fibre trap for microscopic particles,” Appl. Phys. Lett. 93, 041110 (2008).
[Crossref]

Xu, F.

F. Xu, J. A. Lock, G. Gouesbet, and C. Tropea, “Radiation torque exerted on a spheroid: Analytical solution,” Phys. Rev. A 78, 013843 (2008).
[Crossref]

F. Xu, K. Ren, G. Gouesbet, X. Cai, and G. Gréhan, “Theoretical prediction of radiation pressure force exerted on a spheroid by an arbitrarily shaped beam,” Phys. Rev. E 75, 026613 (2007).
[Crossref]

Yodh, A.

Y. Han, A. Alsayed, M. Nobili, J. Zhang, T. Lubensky, and A. Yodh, “Brownian motion of an ellipsoid,” Science 314, 626–630 (2006).
[Crossref] [PubMed]

Zemánek, P.

A. Arzola, P. Jákl, L. Chvátal, and P. Zemánek, “Rotation, oscillation and hydrodynamic synchronization of optically trapped oblate spheroidal microparticles,” Opt. Express 22, 16207–16221 (2014).
[Crossref] [PubMed]

M. Aas, A. Jonáš, A. Kiraz, O. Brzobohatý, J. Ježek, Z. Pilát, and P. Zemánek, “Spectral tuning of lasing emission from optofluidic droplet microlasers using optical stretching,” Opt. Express 21, 21381–21394 (2013).
[Crossref]

J. Trojek, L. Chvátal, and P. Zemánek, “Optical alignment and confinement of an ellipsoidal nanorod in optical tweezers: a theoretical study,” J. Opt. Soc. Am. A 29, 1224–1236 (2012).
[Crossref]

O. Brzobohatý, V. Karásek, M. Šiler, J. Trojek, and P. Zemánek, “Static and dynamic behavior of two optically bound microparticles in a standing wave,” Opt. Express 19, 19613–19626 (2011).
[Crossref] [PubMed]

O. Brzobohatý, V. Karásek, T. Čižmár, and P. Zemánek, “Dynamic size tuning of multidimensional optically bound matter,” Appl. Phys. Lett. 99, 101105 (2011).
[Crossref]

T. Čižmár, O. Brzobohatý, K. Dholakia, and P. Zemánek, “The holographic optical micro-manipulation system based on counter-propagating beams,” Laser Phys. Lett. 8, 50–56 (2011).
[Crossref]

M. Šiler and P. Zemánek, “Parametric study of optical forces acting upon nanoparticles in a single, or a standing, evanescent wave,” J. Opt. 13, 044016 (2011).
[Crossref]

M. Šiler, T. Čižmár, A. Jonáš, and P. Zemánek, “Surface delivery of a single nanoparticle under moving evanescent standing-wave illumination,” New. J. Phys. 10, 113010 (2008).
[Crossref]

T. Čižmár, M. Šiler, and P. Zemánek, “An optical nanotrap array movable over a milimetre range,” Appl. Phys. B 84, 197–203 (2006).
[Crossref]

T. Čižmár, V. Garcés-Chávez, K. Dholakia, and P. Zemánek, “Optical conveyor belt for delivery of submicron objects,” Appl. Phys. Lett. 86, 174101 (2005).
[Crossref]

P. Zemánek, A. Jonáš, P. Jákl, M. Šerý, J. Ježek, and M. Liška, “Theoretical comparison of optical traps created by standing wave and single beam,” Opt. Commun. 220, 401–412 (2003).
[Crossref]

P. Zemánek, A. Jonáš, L. Šrámek, and M. Liška, “Optical trapping of Rayleigh particles using a Gaussian standing wave,” Opt. Commun. 151, 273–285 (1998).
[Crossref]

Zhang, J.

Y. Han, A. Alsayed, M. Nobili, J. Zhang, T. Lubensky, and A. Yodh, “Brownian motion of an ellipsoid,” Science 314, 626–630 (2006).
[Crossref] [PubMed]

Zwick, S.

S. Zwick, T. Haist, Y. Miyamoto, L. He, M. Warber, A. Hermerschmidt, and W. Osten, “Holographic twin traps,” J. Opt. A: Pure Appl. Opt. 11, 034011 (2009).
[Crossref]

Appl. Phys. B (1)

T. Čižmár, M. Šiler, and P. Zemánek, “An optical nanotrap array movable over a milimetre range,” Appl. Phys. B 84, 197–203 (2006).
[Crossref]

Appl. Phys. Lett. (3)

D. M. Gherardi, A. E. Carruthers, T. Čižmár, E. M. Wright, and K. Dholakia, “A dual beam photonic crystal fibre trap for microscopic particles,” Appl. Phys. Lett. 93, 041110 (2008).
[Crossref]

T. Čižmár, V. Garcés-Chávez, K. Dholakia, and P. Zemánek, “Optical conveyor belt for delivery of submicron objects,” Appl. Phys. Lett. 86, 174101 (2005).
[Crossref]

O. Brzobohatý, V. Karásek, T. Čižmár, and P. Zemánek, “Dynamic size tuning of multidimensional optically bound matter,” Appl. Phys. Lett. 99, 101105 (2011).
[Crossref]

Biophys. J. (1)

J. Guck, R. Ananthakrishnan, H. Mahmood, T. Moon, C. Cunningham, and J. Kas, “The optical stretcher: A novel laser tool to micromanipulate cells,” Biophys. J. 1, 767–784 (2001).
[Crossref]

Colloid Polym. Sci. (1)

C. C. Ho, A. Keller, J. A. Odell, and R. H. Ottewill, “Preparation of monodisperse ellipsoidal polystyrene particles,” Colloid Polym. Sci. 271, 469–479 (1993).
[Crossref]

Eur. Phys. J. E (1)

B. Mihiretie, P. Snabre, J.-C. Loudet, and B. Pouligny, “Optically driven oscillations of ellipsoidal particles. Part I: Experimental observations,” Eur. Phys. J. E 37, 124 (2014).
[Crossref]

Europhys. Lett. (1)

B. M. Mihiretie, P. Snabre, J. C. Loudet, and B. Pouligny, “Radiation pressure makes ellipsoidal particles tumble,” Europhys. Lett. 100, 48005 (2012).
[Crossref]

J. Opt. (1)

M. Šiler and P. Zemánek, “Parametric study of optical forces acting upon nanoparticles in a single, or a standing, evanescent wave,” J. Opt. 13, 044016 (2011).
[Crossref]

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

S. Zwick, T. Haist, Y. Miyamoto, L. He, M. Warber, A. Hermerschmidt, and W. Osten, “Holographic twin traps,” J. Opt. A: Pure Appl. Opt. 11, 034011 (2009).
[Crossref]

J. Opt. Soc. Am. A (4)

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

J. Phys. Radium (2)

F. Perrin, “Mouvement brownien d’un ellipsoide - i. dispersion dielectrique pour des molecules ellipsoidales,” J. Phys. Radium 5, 497–511 (1934).
[Crossref]

F. Perrin, “Mouvement brownien d’un ellipsoide (II). rotation libre et d’polarisation des fluorescences. translation et diffusion de molecules ellipsoidales,” J. Phys. Radium 7, 1–11 (1936).
[Crossref]

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

S. H. Simpson, “Inhomogeneous and anisotropic particles in optical traps: Physical behaviour and applications,” J. Quant. Spectrosc. Radiat. Transf. 146, 81–99 (2014).
[Crossref]

Laser Photon. Rev. (1)

D. Palima and J. Glückstad, “Generalized phase contrast matched to Gaussian illumination,” Laser Photon. Rev. 7, 478–494 (2013).
[Crossref]

Laser Phys. Lett. (1)

T. Čižmár, O. Brzobohatý, K. Dholakia, and P. Zemánek, “The holographic optical micro-manipulation system based on counter-propagating beams,” Laser Phys. Lett. 8, 50–56 (2011).
[Crossref]

Methods Cell. Biol. (1)

S. Parkin, G. Knöner, W. Singer, T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Optical torque on microscopic objects,” Methods Cell. Biol. 82, 525–561 (2007).
[Crossref] [PubMed]

Methods Enzymol. (1)

B. Gutierrez-Medina, J. O. Andreasson, W. J. Greenleaf, A. LaPorta, and S. M. Block, “An optical apparatus for rotation and trapping,” Methods Enzymol. 475, 377–404 (2010).
[Crossref] [PubMed]

Nature Commun. (1)

Y. Arita, M. Mazilu, and K. Dholakia, “Laser-induced rotation and cooling of a trapped microgyroscope in vacuum,” Nature Commun. 4, 2374 (2013).
[Crossref]

Nature Nanotech. (1)

J. Millen, T. Deesuwan, P. Barker, and J. Anders, “Nanoscale temperature measurements using non-equilibrium Brownian dynamics of a levitated nanosphere,” Nature Nanotech. 9, 425–429 (2014).
[Crossref]

Nature Photon. (2)

M. Padgett and R. Bowman, “Tweezers with a twist,” Nature Photon. 5, 343–348 (2011).
[Crossref]

D. Phillips, M. Padgett, S. Hanna, Y.-L. Ho, D. Carberry, M. Miles, and S. Simpson, “Shape-induced force fields in optical trapping,” Nature Photon. 8, 400–405 (2014).
[Crossref]

New. J. Phys. (1)

M. Šiler, T. Čižmár, A. Jonáš, and P. Zemánek, “Surface delivery of a single nanoparticle under moving evanescent standing-wave illumination,” New. J. Phys. 10, 113010 (2008).
[Crossref]

Opt. Commun. (2)

P. Zemánek, A. Jonáš, L. Šrámek, and M. Liška, “Optical trapping of Rayleigh particles using a Gaussian standing wave,” Opt. Commun. 151, 273–285 (1998).
[Crossref]

P. Zemánek, A. Jonáš, P. Jákl, M. Šerý, J. Ježek, and M. Liška, “Theoretical comparison of optical traps created by standing wave and single beam,” Opt. Commun. 220, 401–412 (2003).
[Crossref]

Opt. Express (7)

P. J. Rodrigo, I. R. Perch-Nielsen, C. A. Alonzo, and J. Glueckstad, “GPC-based optical micromanipulation in 3D real-time using a single spatial light modulator,” Opt. Express 14, 13107–13112 (2006).
[Crossref] [PubMed]

M. Pitzek, R. Steiger, G. Thalhammer, S. Bernet, and M. Ritsch-Marte, “Optical mirror trap with a large field of view,” Opt. Express 17, 19414–19423 (2009).
[Crossref] [PubMed]

P. Jess, V. Garcés-Chávez, D. Smith, M. Mazilu, L. Paterson, A. Riches, C. Herrington, W. Sibbett, and K. Dholakia, “Dual beam fibre trap for Raman microspectroscopy of single cells,” Opt. Express 14, 5779–5791 (2006).
[Crossref] [PubMed]

M. Aas, A. Jonáš, A. Kiraz, O. Brzobohatý, J. Ježek, Z. Pilát, and P. Zemánek, “Spectral tuning of lasing emission from optofluidic droplet microlasers using optical stretching,” Opt. Express 21, 21381–21394 (2013).
[Crossref]

A. Arzola, P. Jákl, L. Chvátal, and P. Zemánek, “Rotation, oscillation and hydrodynamic synchronization of optically trapped oblate spheroidal microparticles,” Opt. Express 22, 16207–16221 (2014).
[Crossref] [PubMed]

C.-L. Lin, G. Vitrant, M. Bouriau, R. Casalegno, and P. L. Baldeck, “Optically driven Archimedes micro-screws for micropump application,” Opt. Express 19, 8267–8276 (2011).
[Crossref] [PubMed]

O. Brzobohatý, V. Karásek, M. Šiler, J. Trojek, and P. Zemánek, “Static and dynamic behavior of two optically bound microparticles in a standing wave,” Opt. Express 19, 19613–19626 (2011).
[Crossref] [PubMed]

Opt. Lett. (1)

Phys. Rev. A (3)

F. Xu, J. A. Lock, G. Gouesbet, and C. Tropea, “Radiation torque exerted on a spheroid: Analytical solution,” Phys. Rev. A 78, 013843 (2008).
[Crossref]

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

S. H. Simpson and S. Hanna, “Computational study of the optical trapping of ellipsoidal particles,” Phys. Rev. A 84, 053808 (2011).
[Crossref]

Phys. Rev. B (1)

R. Gordon, M. Kawano, J. T. Blakely, and D. Sinton, “Optohydrodynamic theory of particles in a dual-beam optical trap,” Phys. Rev. B 77, 245125 (2008).
[Crossref]

Phys. Rev. E (1)

F. Xu, K. Ren, G. Gouesbet, X. Cai, and G. Gréhan, “Theoretical prediction of radiation pressure force exerted on a spheroid by an arbitrarily shaped beam,” Phys. Rev. E 75, 026613 (2007).
[Crossref]

Phys. Rev. Lett. (6)

L. Oroszi, P. Galajda, H. Kirei, S. Bottka, and P. Ormos, “Direct measurement of torque in an optical trap and its application to double-strand DNA,” Phys. Rev. Lett. 97, 058301 (2006).
[Crossref] [PubMed]

Z. Cheng, P. Chaikin, and T. Mason, “Light streak tracking of optically trapped thin microdisks,” Phys. Rev. Lett. 89, 108303 (2002).
[Crossref] [PubMed]

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

S. A. Tatarkova, A. E. Carruthers, and K. Dholakia, “One-Dimensional Optically Bound Arrays of Microscopic Particles,” Phys. Rev. Lett. 89, 283901 (2002).
[Crossref]

Z. Cheng and T. Mason, “Rotational diffusion microrheology,” Phys. Rev. Lett. 90, 018304 (2003).
[Crossref] [PubMed]

A. Bishop, T. Nieminen, N. Heckenberg, and H. Rubinsztein-Dunlop, “Optical microrheology using rotating laser-trapped particles,” Phys. Rev. Lett. 92, 198104 (2004).
[Crossref] [PubMed]

Proc. Natl. Acad. Sci. USA (1)

J. A. Champion, Y. K. Katare, and S. Mitragotri, “Making polymeric micro- and nanoparticles of complex shapes,” Proc. Natl. Acad. Sci. USA 104, 11901–11904 (2007).
[Crossref] [PubMed]

Science (1)

Y. Han, A. Alsayed, M. Nobili, J. Zhang, T. Lubensky, and A. Yodh, “Brownian motion of an ellipsoid,” Science 314, 626–630 (2006).
[Crossref] [PubMed]

Other (2)

L. Tsang, Scattering of Electromagnetic Waves (Wiley, 2001).

J. Happel and H. Brenner, Low Reynolds number hydrodynamics (Prentice–Hall, 1965).

Supplementary Material (8)

» Media 1: MP4 (81 KB)     
» Media 2: MP4 (1071 KB)     
» Media 3: MP4 (682 KB)     
» Media 4: MP4 (908 KB)     
» Media 5: MP4 (532 KB)     
» Media 6: MP4 (667 KB)     
» Media 7: MP4 (294 KB)     
» Media 8: MP4 (168 KB)     

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Figures (10)

Fig. 1
Fig. 1

Spheroid is optically trapped on the axis of two overlapping counter-propagating beams. The motion of the particle was observed by a CCD camera from a direction perpendicular to the axis of the laser beams. The orientation of the electric field on the beam axis of both counter-propagating beams according to Eqs. (1) and (2) and the final field formed by their interference following Eq. (3) is visualized.

Fig. 2
Fig. 2

Two stable orientations of the same oblate spheroid were observed in two counter-propagating Gaussian beam with opposite circular polarizations. a) Non-rotating spheroid, oriented with its symmetry axis parallel to the direction of the beam propagation. b) The same spheroid, oriented with its symmetry axis perpendicular to the direction of beam propagation, rotating around the horizontal beam axis (see Media 1). The original diameter of the sphere before deformation into the spheroid was 2μm and the spheroid aspect ratio is equal to 0.46 ± 0.02. The beam waists of counter-propagating beams were the same and equal to w0 = 4.36μm, total laser power incident on the sample plane was P = 85 mW.

Fig. 3
Fig. 3

Comparison of experimentally and theoretically obtained frequencies (normalized to 1W) of spheroid rotation for different aspect ratios a/a. Magenta and blue circles denote experimental data with standard deviations in the form of error bars. Red/dark red and grey/black lines correspond to the theoretical results obtained from the T-matrix and Comsol calculations respectively. Calculations were performed in equilibria associated with both intensity maxima and minima, the stable equilibrium being indicated by thick lines. Experimental parameters were the following: beam waists of the counter-propagating Gaussian beams w0 = 4.36μm, depending on the experiment the total power P at the sample plane was in the range (85 – 220) mW, polystyrene spheroids were obtained from spheres of original diameter 2μm. Spheroids denoted by magenta circles were prepared by the thermal method while those in blue color were carried out by the cold one.

Fig. 4
Fig. 4

a) Several images of the behavior of two equal spheroids from the same record. Left (right) column shows rotation of two longitudinally self-arranged spheroids starting at time t0 = 8 s (t0 = 95.9 s) from the beginning of the experiment. Within 0.9 s the spheroids rotated by about one half of the period (see Media 2 for the whole record, recorded with the frame rate 50 Hz). The parameters of the experiment were the following: horizontally counter-propagating Gaussian beams with w0 = 4.36μm, total power at the sample plane P = 85 mW, spheroids of equal aspect ratio 0.65 ± 0.02 were obtained by the high temperature method from polystyrene spheres of original diameter 2 μm. b) Minor axis of the rotating spheroids obtained from their pictures on the CCD camera. Blue or red curves denote the left or right spheroid.

Fig. 5
Fig. 5

An example of different behavior of the same two spheroids (aspect ratio about 0.65 0.02) if they are separated (a) or in contact (b). If they are separated, the spheroids rotate with minor axes oriented perpendicularly. However, if they are in contact, the orientation of axes remains also perpendicular but they stop rotation. c) The periodic variations in the size of the minor ellipse axis bs indicate rotation around z axis, which continues until the particles make contact. Transversal xs and longitudinal zs time records of particle position are plotted in part d) and e), respectively. First frame in a) and b) corresponds to time t0 = 52.12 s and t0 = 55.34 s, respectively in parts c)–e). See Media 3 for the whole record, recorded with the frame rate 50 Hz. The parameters of the experiment were the same as in Fig. 4.

Fig. 6
Fig. 6

Snapshots of every second frame from Media 4 for two spheroids of larger aspect ratio 0.3 in contact. The left (right) record starts at time t0 = 0 (t0 = 22.76 s) from the beginning of the experiment. The parameters of the experiment were the following: horizontally counter-propagating Gaussian beams with w0 = 4.36μm, and the total power at the sample plane P = 240 mW, polystyrene spheroids were obtained by the low temperature method, described above, from spheres of original diameter 2μm.

Fig. 7
Fig. 7

a) Axial force on a single spheroid, as a function of the distance from a second, symmetrically displaced particle. b) Calculations of relative torque of two axially trapped spheroids as a function of the angle between their symmetry axes.

Fig. 8
Fig. 8

Another stable configuration for two spheroids. Left: The right particle spins horizontally while the left one does not rotate, but oscillates vertically depending on the orientation of the one on the right (see attached Media 5 starting at t = 8.12 s). The parameters of the experiment were the following: horizontally counter-propagating Gaussian beams with w0 = 4.36μm, and total power at the sample plane P = 240 mW, polystyrene spheroids of aspect ratio 0.25 were obtained by the low temperature method described above from spheres of original diameter 2μm. Right: Two spheroids of aspect ratio close to 0.65 arranged vertically and rotating horizontally around z axis (see attached Media 6 starting at t = 1.66 s). The parameters of the experiment were the following: horizontally counter-propagating Gaussian beams with w0 = 4.36μm, and the total power at the sample plane P = 240 mW, polystyrene spheroids were obtained by the low temperature method described above from spheres of original diameter 2μm.

Fig. 9
Fig. 9

Complex behavior of three and four optically bound spheroids. Left: Depending on the orientation of the spheroids, their axial and lateral positions are changed (see Media 7). The parameters of the experiment were the following: horizontally counter-propagating Gaussian beams with w0 = 4.36μm, and the total power at the sample plane P = 240 mW, polystyrene spheroids of aspect ratio 0.5 were obtained by the high temperature method from spheres of original diameter 2 μm. Right: Optically self-arranged spheroid dimers ( Media 8 from t = 5.2 s) changing their vertical position depending on angle of rotation of each couple. Parameters are the same as in the right record in Fig. 8.

Fig. 10
Fig. 10

Elements K y y r r and K z z t t of the stiffness matrix. The left column corresponds to the non-rotating orientation when the spheroid minor axis (SMA) points along the z-axis. The right column corresponds to the rotating one (the stiffness is evaluated when the SMA points along the x - axis). The blue and orange curves are drawn thick in intervals of aspect ratio, that allow for the stable equilibria. The gray curves show the incoherent parts of K y y r r, in graphs of K z z t t is zero.

Equations (3)

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

E + = [ E x , E y , 0 ] [ E G cos ( ω t k z ) , E G cos ( ω t k z π / 2 ) , 0 ] ,
E = [ E x , E y , 0 ] [ E G cos ( ω t + k z ) , E G cos ( ω t + k z π / 2 ) , 0 ] .
E = [ E x , E y , 0 ] = [ 2 E G cos ( ω t ) cos ( k z ) , 2 E G sin ( ω t ) cos ( k z ) , 0 ] .

Metrics