Abstract

It is generally accepted that the interaction between particles mediated by the scattered light (called optical binding) is very weak. Therefore, the optical binding is usually neglected in a multi-particle trapping in distinct optical traps. Here we show that even the presence of only two dielectric particles confined in the standing wave leads to their significantly different behavior comparing to the case of a single trapped particle. We obtained persuading coincidence between our experimental records and the results of the deterministic and stochastic theoretical simulations based on the coupled dipole method.

© 2011 OSA

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    [CrossRef]
  37. 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]
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2011 (2)

T. Čižmár, D. I. C. Dalgarno, P. C. Ashok, F. J. Gunn-Moore, and K. Dholakia, “Interference-free superposition of nonzero order light modes: Functionalized optical landscapes,” Appl. Phys. Lett. 98, 081114 (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]

2010 (7)

Y. Liu and M. Yu, “Optical manipulation and binding of microrods with multiple traps enabled in an inclined dual-fiber system,” Biomicrofluidics 4, 043010 (2010).
[CrossRef]

K. Dholakia and P. Zemánek, “Gripped by light: optical binding,” Rev. Mod. Phys. 82, 1767–1791 (2010).
[CrossRef]

T. Čižmár, L. C. D. Romero, K. Dholakia, and D. L. Andrews, “Multiple optical trapping and binding: new routes to self-assembly,” J. Phys. B 43, 102001 (2010).
[CrossRef]

J. E. de Oliveira Rodrigues and R. Dickman, “Asymmetric exclusion process in a system of interacting Brownian particles,” Phys. Rev. E 81, 061108 (2010).
[CrossRef]

T. Čižmár, M. Mazilu, and K. Dholakia, “In situ wavefront correction and its application to micromanipulation,” Nat. Photonics 4, 388–394 (2010).
[CrossRef]

M. Šiler and P. Zemánek, “Particle jumps between optical traps in a one-dimensional optical lattice,” New. J. Phys. 12, 083001 (2010).
[CrossRef]

O. Brzobohatý, T. Čižmár, V. Karásek, M. Šiler, K. Dholakia, and P. Zemánek, “Experimental and theoretical determination of optical binding forces,” Opt. Express 18, 25389–25402 (2010).
[CrossRef] [PubMed]

2009 (1)

V. Karásek, O. Brzobohatý, and P. Zemánek, “Longitudinal optical binding of several spherical particles studied by the coupled dipole method,” J. Opt. A: Pure Appl. Opt. 11, 034009 (2009).
[CrossRef]

2008 (6)

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]

V. Karásek, T. Čižmár, O. Brzobohatý, P. Zemánek, V. Garcés-Chávez, and K. Dholakia, “Long-range one-dimensional longitudinal optical binding,” Phys. Rev. Lett. 101, 143601 (2008).
[CrossRef] [PubMed]

Z. H. Hang, J. Ng, and C. T. Chan, “Stability of extended structures stabilized by light as governed by the competition of two length scales,” Phys. Rev. A 77, 063838 (2008).
[CrossRef]

J. M. Taylor, L. Y. Wong, C. D. Bain, and G. D. Love, “Emergent properties in optically bound matter,” Opt. Express 16, 6921–6928 (2008).
[CrossRef] [PubMed]

O. Brzobohatý, T. Čižmár, and P. Zemánek, “High quality quasi-Bessel beam generated by round-tip axicon,” Opt. Express 16, 12688–12700 (2008).
[PubMed]

S. K. Mohanty, K. S. Mohanty, and M. W. Berns, “Organization of microscale objects using a microfabricated optical fiber,” Opt. Lett. 33, 2155–2157 (2008).
[CrossRef] [PubMed]

2007 (5)

F. J. G. de Abajo, “Collective oscillations in optical matter,” Opt. Express 15, 11082–11094 (2007).
[CrossRef]

N. K. Metzger, R. F. Marchington, M. Mazilu, R. L. Smith, K. Dholakia, and E. M. Wright, “Measurement of the restoring forces acting on two optically bound particles from normal mode correlations,” Phys. Rev. Lett. 98, 068102 (2007).
[CrossRef] [PubMed]

P. J. Reece, E. M. Wright, and K. Dholakia, “Experimental observation of modulation instability and optical spatial soliton arrays in soft condensed matter,” Phys. Rev. Lett. 98, 203902 (2007).
[CrossRef] [PubMed]

V. Karásek and P. Zemánek, “Analytical description of longitudinal optical binding of two spherical nanoparticles,” J. Opt. A: Pure Appl. Opt. 9, S215–S220 (2007).
[CrossRef]

X. Yu, T. Torisawa, and N. Umeda, “Manipulation of particles with counter-propagating evanescent waves,” Chin. Phys. Lett 24, 2833–2835 (2007).
[CrossRef]

2006 (7)

2005 (5)

E. Schonbrun, R. Pistun, P. Jordan, J. Cooper, K. D. Wulff, J. Courtial, and M. Padgett, “3D interferometric optical tweezers using a single spatial light modulator,” Opt. Express 13, 3777–3786 (2005).
[CrossRef] [PubMed]

A. Casaburi, G. Pesce, P. Zemánek, and A. Sasso, “Two-and three-beam interferometric optical tweezers,” Opt. Commun. 251, 393–404 (2005).
[CrossRef]

J.-M. Fournier, J. Rohner, P. Jacquot, R. Johann, S. Mieas, and R.-P. Salathé, “Assembling mesoscopic partices by various optical schemes,” Proc. SPIE 14, 59300Y (2005).
[CrossRef]

D. McGloin and K. Dholakia, “Bessel beams: diffraction in a new light,” Contemp. Phys. 46, 15–28 (2005).
[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]

2004 (1)

R. Gómez-Medina and J. J. Sáenz, “Usually strong optical interaction between particles in quasi-one-dimensional geometries,” Phys. Rev. Lett. 93, 243602 (2004).
[CrossRef]

2003 (2)

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]

2002 (2)

P. Zemánek, A. Jonáš, and M. Liška, “Simplified description of optical forces acting on a nanoparticle in the Gaussian standing wave,” J. Opt. Soc. Am. A 19, 1025–1034 (2002).
[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]

2001 (1)

M. K. Cheezum, W. F. Walker, and W. H. Guilford, “Quantitative comparison of algorithms for tracking single fluorescent particles,” Biophys. J. 81, 2378–2388 (2001).
[CrossRef] [PubMed]

1999 (1)

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]

1997 (1)

A. E. Chiou, W. Wang, G. J. Sonek, J. Hong, and M. W. Berns, “Interferometric optical tweezers,” Opt. Commun. 133, 7–10 (1997).
[CrossRef]

1991 (1)

1990 (1)

M. M. Burns, J.-M. Fournier, and J. A. Golovchenko, “Optical matter: crystallization and binding in intense optical fields,” Science 249, 749–754 (1990).
[CrossRef] [PubMed]

1989 (1)

M. M. Burns, J.-M. Fournier, and J. A. Golovchenko, “Optical binding,” Phys. Rev. Lett. 63, 1233–1236 (1989).
[CrossRef] [PubMed]

1986 (1)

1940 (1)

H. A. Kramers, “Brownian motion in the field of force and the diffusion model of chemical reactions,” Physica 7, 284–304 (1940).
[CrossRef]

Andrews, D. L.

T. Čižmár, L. C. D. Romero, K. Dholakia, and D. L. Andrews, “Multiple optical trapping and binding: new routes to self-assembly,” J. Phys. B 43, 102001 (2010).
[CrossRef]

Ashkin, A.

Ashok, P. C.

T. Čižmár, D. I. C. Dalgarno, P. C. Ashok, F. J. Gunn-Moore, and K. Dholakia, “Interference-free superposition of nonzero order light modes: Functionalized optical landscapes,” Appl. Phys. Lett. 98, 081114 (2011).
[CrossRef]

Bain, C. D.

Bernet, S.

Berns, M. W.

S. K. Mohanty, K. S. Mohanty, and M. W. Berns, “Organization of microscale objects using a microfabricated optical fiber,” Opt. Lett. 33, 2155–2157 (2008).
[CrossRef] [PubMed]

A. E. Chiou, W. Wang, G. J. Sonek, J. Hong, and M. W. Berns, “Interferometric optical tweezers,” Opt. Commun. 133, 7–10 (1997).
[CrossRef]

Bjorkholm, J. E.

Brzobohatý, O.

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, T. Čižmár, V. Karásek, M. Šiler, K. Dholakia, and P. Zemánek, “Experimental and theoretical determination of optical binding forces,” Opt. Express 18, 25389–25402 (2010).
[CrossRef] [PubMed]

V. Karásek, O. Brzobohatý, and P. Zemánek, “Longitudinal optical binding of several spherical particles studied by the coupled dipole method,” J. Opt. A: Pure Appl. Opt. 11, 034009 (2009).
[CrossRef]

V. Karásek, T. Čižmár, O. Brzobohatý, P. Zemánek, V. Garcés-Chávez, and K. Dholakia, “Long-range one-dimensional longitudinal optical binding,” Phys. Rev. Lett. 101, 143601 (2008).
[CrossRef] [PubMed]

O. Brzobohatý, T. Čižmár, and P. Zemánek, “High quality quasi-Bessel beam generated by round-tip axicon,” Opt. Express 16, 12688–12700 (2008).
[PubMed]

Burns, M. M.

M. M. Burns, J.-M. Fournier, and J. A. Golovchenko, “Optical matter: crystallization and binding in intense optical fields,” Science 249, 749–754 (1990).
[CrossRef] [PubMed]

M. M. Burns, J.-M. Fournier, and J. A. Golovchenko, “Optical binding,” Phys. Rev. Lett. 63, 1233–1236 (1989).
[CrossRef] [PubMed]

Carpenter, A. E.

Carruthers, A. E.

S. A. Tatarkova, A. E. Carruthers, and K. Dholakia, “One-dimensional optically bound arrays of microscopic particles,” Phys. Rev. Lett. 89, 283901 (2002).
[CrossRef]

Casaburi, A.

A. Casaburi, G. Pesce, P. Zemánek, and A. Sasso, “Two-and three-beam interferometric optical tweezers,” Opt. Commun. 251, 393–404 (2005).
[CrossRef]

Chan, C. T.

Z. H. Hang, J. Ng, and C. T. Chan, “Stability of extended structures stabilized by light as governed by the competition of two length scales,” Phys. Rev. A 77, 063838 (2008).
[CrossRef]

J. Ng and C. T. Chan, “Localized vibrational modes in optically bound structures,” Opt. Lett. 31, 2583–2585 (2006).
[CrossRef] [PubMed]

Cheezum, M. K.

M. K. Cheezum, W. F. Walker, and W. H. Guilford, “Quantitative comparison of algorithms for tracking single fluorescent particles,” Biophys. J. 81, 2378–2388 (2001).
[CrossRef] [PubMed]

Chiou, A. E.

A. E. Chiou, W. Wang, G. J. Sonek, J. Hong, and M. W. Berns, “Interferometric optical tweezers,” Opt. Commun. 133, 7–10 (1997).
[CrossRef]

Chu, S.

Cižmár, T.

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]

T. Čižmár, D. I. C. Dalgarno, P. C. Ashok, F. J. Gunn-Moore, and K. Dholakia, “Interference-free superposition of nonzero order light modes: Functionalized optical landscapes,” Appl. Phys. Lett. 98, 081114 (2011).
[CrossRef]

O. Brzobohatý, T. Čižmár, V. Karásek, M. Šiler, K. Dholakia, and P. Zemánek, “Experimental and theoretical determination of optical binding forces,” Opt. Express 18, 25389–25402 (2010).
[CrossRef] [PubMed]

T. Čižmár, L. C. D. Romero, K. Dholakia, and D. L. Andrews, “Multiple optical trapping and binding: new routes to self-assembly,” J. Phys. B 43, 102001 (2010).
[CrossRef]

T. Čižmár, M. Mazilu, and K. Dholakia, “In situ wavefront correction and its application to micromanipulation,” Nat. Photonics 4, 388–394 (2010).
[CrossRef]

V. Karásek, T. Čižmár, O. Brzobohatý, P. Zemánek, V. Garcés-Chávez, and K. Dholakia, “Long-range one-dimensional longitudinal optical binding,” Phys. Rev. Lett. 101, 143601 (2008).
[CrossRef] [PubMed]

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]

O. Brzobohatý, T. Čižmár, and P. Zemánek, “High quality quasi-Bessel beam generated by round-tip axicon,” Opt. Express 16, 12688–12700 (2008).
[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]

M. Šiler, T. Čižmár, M. Šerý, and P. Zemánek, “Optical forces generated by evanescent standing waves and their usage for sub-micron particle delivery,” Appl. Phys. B 84, 157–165 (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]

Cooper, J.

Courtial, J.

E. Schonbrun, R. Pistun, P. Jordan, J. Cooper, K. D. Wulff, J. Courtial, and M. Padgett, “3D interferometric optical tweezers using a single spatial light modulator,” Opt. Express 13, 3777–3786 (2005).
[CrossRef] [PubMed]

G. Spalding, J. Courtial, and R. D. Leonardo, “Holographic optical trapping,” in Structured Light and Its Applications: An Introduction to Phase-Structured Beams and Nanoscale Optical Forces (Elsevier, Academic Press, 2008).
[PubMed]

Dalgarno, D. I. C.

T. Čižmár, D. I. C. Dalgarno, P. C. Ashok, F. J. Gunn-Moore, and K. Dholakia, “Interference-free superposition of nonzero order light modes: Functionalized optical landscapes,” Appl. Phys. Lett. 98, 081114 (2011).
[CrossRef]

de Abajo, F. J. G.

de Oliveira Rodrigues, J. E.

J. E. de Oliveira Rodrigues and R. Dickman, “Asymmetric exclusion process in a system of interacting Brownian particles,” Phys. Rev. E 81, 061108 (2010).
[CrossRef]

Dholakia, K.

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]

T. Čižmár, D. I. C. Dalgarno, P. C. Ashok, F. J. Gunn-Moore, and K. Dholakia, “Interference-free superposition of nonzero order light modes: Functionalized optical landscapes,” Appl. Phys. Lett. 98, 081114 (2011).
[CrossRef]

K. Dholakia and P. Zemánek, “Gripped by light: optical binding,” Rev. Mod. Phys. 82, 1767–1791 (2010).
[CrossRef]

T. Čižmár, L. C. D. Romero, K. Dholakia, and D. L. Andrews, “Multiple optical trapping and binding: new routes to self-assembly,” J. Phys. B 43, 102001 (2010).
[CrossRef]

T. Čižmár, M. Mazilu, and K. Dholakia, “In situ wavefront correction and its application to micromanipulation,” Nat. Photonics 4, 388–394 (2010).
[CrossRef]

O. Brzobohatý, T. Čižmár, V. Karásek, M. Šiler, K. Dholakia, and P. Zemánek, “Experimental and theoretical determination of optical binding forces,” Opt. Express 18, 25389–25402 (2010).
[CrossRef] [PubMed]

V. Karásek, T. Čižmár, O. Brzobohatý, P. Zemánek, V. Garcés-Chávez, and K. Dholakia, “Long-range one-dimensional longitudinal optical binding,” Phys. Rev. Lett. 101, 143601 (2008).
[CrossRef] [PubMed]

P. J. Reece, E. M. Wright, and K. Dholakia, “Experimental observation of modulation instability and optical spatial soliton arrays in soft condensed matter,” Phys. Rev. Lett. 98, 203902 (2007).
[CrossRef] [PubMed]

N. K. Metzger, R. F. Marchington, M. Mazilu, R. L. Smith, K. Dholakia, and E. M. Wright, “Measurement of the restoring forces acting on two optically bound particles from normal mode correlations,” Phys. Rev. Lett. 98, 068102 (2007).
[CrossRef] [PubMed]

V. Karásek, K. Dholakia, and P. Zemánek, “Analysis of optical binding in one dimension,” Appl. Phys. B 84, 149–156 (2006).
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T. Čižmár, V. Garcés-Chávez, K. Dholakia, and P. Zemánek, “Optical conveyor belt for delivery of submicron objects,” Appl. Phys. Lett. 86, 174101 (2005).
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D. McGloin and K. Dholakia, “Bessel beams: diffraction in a new light,” Contemp. Phys. 46, 15–28 (2005).
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S. A. Tatarkova, A. E. Carruthers, and K. Dholakia, “One-dimensional optically bound arrays of microscopic particles,” Phys. Rev. Lett. 89, 283901 (2002).
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V. Karásek, T. Čižmár, O. Brzobohatý, P. Zemánek, V. Garcés-Chávez, and K. Dholakia, “Long-range one-dimensional longitudinal optical binding,” Phys. Rev. Lett. 101, 143601 (2008).
[CrossRef] [PubMed]

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

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M. M. Burns, J.-M. Fournier, and J. A. Golovchenko, “Optical binding,” Phys. Rev. Lett. 63, 1233–1236 (1989).
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Guilford, W. H.

M. K. Cheezum, W. F. Walker, and W. H. Guilford, “Quantitative comparison of algorithms for tracking single fluorescent particles,” Biophys. J. 81, 2378–2388 (2001).
[CrossRef] [PubMed]

Gunn-Moore, F. J.

T. Čižmár, D. I. C. Dalgarno, P. C. Ashok, F. J. Gunn-Moore, and K. Dholakia, “Interference-free superposition of nonzero order light modes: Functionalized optical landscapes,” Appl. Phys. Lett. 98, 081114 (2011).
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Hang, Z. H.

Z. H. Hang, J. Ng, and C. T. Chan, “Stability of extended structures stabilized by light as governed by the competition of two length scales,” Phys. Rev. A 77, 063838 (2008).
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Hong, J.

A. E. Chiou, W. Wang, G. J. Sonek, J. Hong, and M. W. Berns, “Interferometric optical tweezers,” Opt. Commun. 133, 7–10 (1997).
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Jacquot, P.

J.-M. Fournier, J. Rohner, P. Jacquot, R. Johann, S. Mieas, and R.-P. Salathé, “Assembling mesoscopic partices by various optical schemes,” Proc. SPIE 14, 59300Y (2005).
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Jákl, P.

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, 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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J.-M. Fournier, J. Rohner, P. Jacquot, R. Johann, S. Mieas, and R.-P. Salathé, “Assembling mesoscopic partices by various optical schemes,” Proc. SPIE 14, 59300Y (2005).
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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).
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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, and M. Liška, “Simplified description of optical forces acting on a nanoparticle in the Gaussian standing wave,” J. Opt. Soc. Am. A 19, 1025–1034 (2002).
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P. Zemánek, A. Jonáš, L. Šrámek, and M. Liška, “Optical trapping of nanoparticles and microparticles using Gaussian standing wave.” Opt. Lett. 24, 1448–1450 (1999).
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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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Karásek, V.

O. Brzobohatý, T. Čižmár, V. Karásek, M. Šiler, K. Dholakia, and P. Zemánek, “Experimental and theoretical determination of optical binding forces,” Opt. Express 18, 25389–25402 (2010).
[CrossRef] [PubMed]

V. Karásek, O. Brzobohatý, and P. Zemánek, “Longitudinal optical binding of several spherical particles studied by the coupled dipole method,” J. Opt. A: Pure Appl. Opt. 11, 034009 (2009).
[CrossRef]

V. Karásek, T. Čižmár, O. Brzobohatý, P. Zemánek, V. Garcés-Chávez, and K. Dholakia, “Long-range one-dimensional longitudinal optical binding,” Phys. Rev. Lett. 101, 143601 (2008).
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V. Karásek and P. Zemánek, “Analytical description of longitudinal optical binding of two spherical nanoparticles,” J. Opt. A: Pure Appl. Opt. 9, S215–S220 (2007).
[CrossRef]

V. Karásek, K. Dholakia, and P. Zemánek, “Analysis of optical binding in one dimension,” Appl. Phys. B 84, 149–156 (2006).
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G. Spalding, J. Courtial, and R. D. Leonardo, “Holographic optical trapping,” in Structured Light and Its Applications: An Introduction to Phase-Structured Beams and Nanoscale Optical Forces (Elsevier, Academic Press, 2008).
[PubMed]

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).
[CrossRef]

P. Zemánek, A. Jonáš, and M. Liška, “Simplified description of optical forces acting on a nanoparticle in the Gaussian standing wave,” J. Opt. Soc. Am. A 19, 1025–1034 (2002).
[CrossRef]

P. Zemánek, A. Jonáš, L. Šrámek, and M. Liška, “Optical trapping of nanoparticles and microparticles using Gaussian standing wave.” Opt. Lett. 24, 1448–1450 (1999).
[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]

Liu, Y.

Y. Liu and M. Yu, “Optical manipulation and binding of microrods with multiple traps enabled in an inclined dual-fiber system,” Biomicrofluidics 4, 043010 (2010).
[CrossRef]

Love, G. D.

Marchington, R. F.

N. K. Metzger, R. F. Marchington, M. Mazilu, R. L. Smith, K. Dholakia, and E. M. Wright, “Measurement of the restoring forces acting on two optically bound particles from normal mode correlations,” Phys. Rev. Lett. 98, 068102 (2007).
[CrossRef] [PubMed]

Masuhara, H.

Mazilu, M.

T. Čižmár, M. Mazilu, and K. Dholakia, “In situ wavefront correction and its application to micromanipulation,” Nat. Photonics 4, 388–394 (2010).
[CrossRef]

N. K. Metzger, R. F. Marchington, M. Mazilu, R. L. Smith, K. Dholakia, and E. M. Wright, “Measurement of the restoring forces acting on two optically bound particles from normal mode correlations,” Phys. Rev. Lett. 98, 068102 (2007).
[CrossRef] [PubMed]

McGloin, D.

D. McGloin and K. Dholakia, “Bessel beams: diffraction in a new light,” Contemp. Phys. 46, 15–28 (2005).
[CrossRef]

Mellor, C. D.

Metzger, N. K.

N. K. Metzger, R. F. Marchington, M. Mazilu, R. L. Smith, K. Dholakia, and E. M. Wright, “Measurement of the restoring forces acting on two optically bound particles from normal mode correlations,” Phys. Rev. Lett. 98, 068102 (2007).
[CrossRef] [PubMed]

Mieas, S.

J.-M. Fournier, J. Rohner, P. Jacquot, R. Johann, S. Mieas, and R.-P. Salathé, “Assembling mesoscopic partices by various optical schemes,” Proc. SPIE 14, 59300Y (2005).
[CrossRef]

Misawa, H.

Mohanty, K. S.

Mohanty, S. K.

Ng, J.

Z. H. Hang, J. Ng, and C. T. Chan, “Stability of extended structures stabilized by light as governed by the competition of two length scales,” Phys. Rev. A 77, 063838 (2008).
[CrossRef]

J. Ng and C. T. Chan, “Localized vibrational modes in optically bound structures,” Opt. Lett. 31, 2583–2585 (2006).
[CrossRef] [PubMed]

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Perkins, T. T.

Pesce, G.

A. Casaburi, G. Pesce, P. Zemánek, and A. Sasso, “Two-and three-beam interferometric optical tweezers,” Opt. Commun. 251, 393–404 (2005).
[CrossRef]

Pistun, R.

Reece, P. J.

P. J. Reece, E. M. Wright, and K. Dholakia, “Experimental observation of modulation instability and optical spatial soliton arrays in soft condensed matter,” Phys. Rev. Lett. 98, 203902 (2007).
[CrossRef] [PubMed]

Ritsch-Marte, M.

Rohner, J.

J.-M. Fournier, J. Rohner, P. Jacquot, R. Johann, S. Mieas, and R.-P. Salathé, “Assembling mesoscopic partices by various optical schemes,” Proc. SPIE 14, 59300Y (2005).
[CrossRef]

Romero, L. C. D.

T. Čižmár, L. C. D. Romero, K. Dholakia, and D. L. Andrews, “Multiple optical trapping and binding: new routes to self-assembly,” J. Phys. B 43, 102001 (2010).
[CrossRef]

Sáenz, J. J.

R. Gómez-Medina and J. J. Sáenz, “Usually strong optical interaction between particles in quasi-one-dimensional geometries,” Phys. Rev. Lett. 93, 243602 (2004).
[CrossRef]

Salathé, R.-P.

J.-M. Fournier, J. Rohner, P. Jacquot, R. Johann, S. Mieas, and R.-P. Salathé, “Assembling mesoscopic partices by various optical schemes,” Proc. SPIE 14, 59300Y (2005).
[CrossRef]

Sasaki, K.

Sasso, A.

A. Casaburi, G. Pesce, P. Zemánek, and A. Sasso, “Two-and three-beam interferometric optical tweezers,” Opt. Commun. 251, 393–404 (2005).
[CrossRef]

Schonbrun, E.

Seol, Y.

Šerý, M.

M. Šiler, T. Čižmár, M. Šerý, and P. Zemánek, “Optical forces generated by evanescent standing waves and their usage for sub-micron particle delivery,” Appl. Phys. B 84, 157–165 (2006).
[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]

Šiler, M.

O. Brzobohatý, T. Čižmár, V. Karásek, M. Šiler, K. Dholakia, and P. Zemánek, “Experimental and theoretical determination of optical binding forces,” Opt. Express 18, 25389–25402 (2010).
[CrossRef] [PubMed]

M. Šiler and P. Zemánek, “Particle jumps between optical traps in a one-dimensional optical lattice,” New. J. Phys. 12, 083001 (2010).
[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]

M. Šiler, T. Čižmár, M. Šerý, and P. Zemánek, “Optical forces generated by evanescent standing waves and their usage for sub-micron particle delivery,” Appl. Phys. B 84, 157–165 (2006).
[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]

Singer, W.

Smith, R. L.

N. K. Metzger, R. F. Marchington, M. Mazilu, R. L. Smith, K. Dholakia, and E. M. Wright, “Measurement of the restoring forces acting on two optically bound particles from normal mode correlations,” Phys. Rev. Lett. 98, 068102 (2007).
[CrossRef] [PubMed]

Sonek, G. J.

A. E. Chiou, W. Wang, G. J. Sonek, J. Hong, and M. W. Berns, “Interferometric optical tweezers,” Opt. Commun. 133, 7–10 (1997).
[CrossRef]

Spalding, G.

G. Spalding, J. Courtial, and R. D. Leonardo, “Holographic optical trapping,” in Structured Light and Its Applications: An Introduction to Phase-Structured Beams and Nanoscale Optical Forces (Elsevier, Academic Press, 2008).
[PubMed]

Šrámek, L.

P. Zemánek, A. Jonáš, L. Šrámek, and M. Liška, “Optical trapping of nanoparticles and microparticles using Gaussian standing wave.” Opt. Lett. 24, 1448–1450 (1999).
[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]

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]

Taylor, J. M.

Torisawa, T.

X. Yu, T. Torisawa, and N. Umeda, “Manipulation of particles with counter-propagating evanescent waves,” Chin. Phys. Lett 24, 2833–2835 (2007).
[CrossRef]

Umeda, N.

X. Yu, T. Torisawa, and N. Umeda, “Manipulation of particles with counter-propagating evanescent waves,” Chin. Phys. Lett 24, 2833–2835 (2007).
[CrossRef]

Walker, W. F.

M. K. Cheezum, W. F. Walker, and W. H. Guilford, “Quantitative comparison of algorithms for tracking single fluorescent particles,” Biophys. J. 81, 2378–2388 (2001).
[CrossRef] [PubMed]

Wang, W.

A. E. Chiou, W. Wang, G. J. Sonek, J. Hong, and M. W. Berns, “Interferometric optical tweezers,” Opt. Commun. 133, 7–10 (1997).
[CrossRef]

Wong, L. Y.

Wright, E. M.

N. K. Metzger, R. F. Marchington, M. Mazilu, R. L. Smith, K. Dholakia, and E. M. Wright, “Measurement of the restoring forces acting on two optically bound particles from normal mode correlations,” Phys. Rev. Lett. 98, 068102 (2007).
[CrossRef] [PubMed]

P. J. Reece, E. M. Wright, and K. Dholakia, “Experimental observation of modulation instability and optical spatial soliton arrays in soft condensed matter,” Phys. Rev. Lett. 98, 203902 (2007).
[CrossRef] [PubMed]

Wulff, K. D.

Yu, M.

Y. Liu and M. Yu, “Optical manipulation and binding of microrods with multiple traps enabled in an inclined dual-fiber system,” Biomicrofluidics 4, 043010 (2010).
[CrossRef]

Yu, X.

X. Yu, T. Torisawa, and N. Umeda, “Manipulation of particles with counter-propagating evanescent waves,” Chin. Phys. Lett 24, 2833–2835 (2007).
[CrossRef]

Zemánek, P.

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]

K. Dholakia and P. Zemánek, “Gripped by light: optical binding,” Rev. Mod. Phys. 82, 1767–1791 (2010).
[CrossRef]

M. Šiler and P. Zemánek, “Particle jumps between optical traps in a one-dimensional optical lattice,” New. J. Phys. 12, 083001 (2010).
[CrossRef]

O. Brzobohatý, T. Čižmár, V. Karásek, M. Šiler, K. Dholakia, and P. Zemánek, “Experimental and theoretical determination of optical binding forces,” Opt. Express 18, 25389–25402 (2010).
[CrossRef] [PubMed]

V. Karásek, O. Brzobohatý, and P. Zemánek, “Longitudinal optical binding of several spherical particles studied by the coupled dipole method,” J. Opt. A: Pure Appl. Opt. 11, 034009 (2009).
[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]

V. Karásek, T. Čižmár, O. Brzobohatý, P. Zemánek, V. Garcés-Chávez, and K. Dholakia, “Long-range one-dimensional longitudinal optical binding,” Phys. Rev. Lett. 101, 143601 (2008).
[CrossRef] [PubMed]

O. Brzobohatý, T. Čižmár, and P. Zemánek, “High quality quasi-Bessel beam generated by round-tip axicon,” Opt. Express 16, 12688–12700 (2008).
[PubMed]

V. Karásek and P. Zemánek, “Analytical description of longitudinal optical binding of two spherical nanoparticles,” J. Opt. A: Pure Appl. Opt. 9, S215–S220 (2007).
[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]

V. Karásek, K. Dholakia, and P. Zemánek, “Analysis of optical binding in one dimension,” Appl. Phys. B 84, 149–156 (2006).
[CrossRef]

M. Šiler, T. Čižmár, M. Šerý, and P. Zemánek, “Optical forces generated by evanescent standing waves and their usage for sub-micron particle delivery,” Appl. Phys. B 84, 157–165 (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]

A. Casaburi, G. Pesce, P. Zemánek, and A. Sasso, “Two-and three-beam interferometric optical tweezers,” Opt. Commun. 251, 393–404 (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, and M. Liška, “Simplified description of optical forces acting on a nanoparticle in the Gaussian standing wave,” J. Opt. Soc. Am. A 19, 1025–1034 (2002).
[CrossRef]

P. Zemánek, A. Jonáš, L. Šrámek, and M. Liška, “Optical trapping of nanoparticles and microparticles using Gaussian standing wave.” Opt. Lett. 24, 1448–1450 (1999).
[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]

Appl. Phys. B (3)

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

M. Šiler, T. Čižmár, M. Šerý, and P. Zemánek, “Optical forces generated by evanescent standing waves and their usage for sub-micron particle delivery,” Appl. Phys. B 84, 157–165 (2006).
[CrossRef]

V. Karásek, K. Dholakia, and P. Zemánek, “Analysis of optical binding in one dimension,” Appl. Phys. B 84, 149–156 (2006).
[CrossRef]

Appl. Phys. Lett. (2)

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]

T. Čižmár, D. I. C. Dalgarno, P. C. Ashok, F. J. Gunn-Moore, and K. Dholakia, “Interference-free superposition of nonzero order light modes: Functionalized optical landscapes,” Appl. Phys. Lett. 98, 081114 (2011).
[CrossRef]

Biomicrofluidics (1)

Y. Liu and M. Yu, “Optical manipulation and binding of microrods with multiple traps enabled in an inclined dual-fiber system,” Biomicrofluidics 4, 043010 (2010).
[CrossRef]

Biophys. J. (1)

M. K. Cheezum, W. F. Walker, and W. H. Guilford, “Quantitative comparison of algorithms for tracking single fluorescent particles,” Biophys. J. 81, 2378–2388 (2001).
[CrossRef] [PubMed]

Chin. Phys. Lett (1)

X. Yu, T. Torisawa, and N. Umeda, “Manipulation of particles with counter-propagating evanescent waves,” Chin. Phys. Lett 24, 2833–2835 (2007).
[CrossRef]

Contemp. Phys. (1)

D. McGloin and K. Dholakia, “Bessel beams: diffraction in a new light,” Contemp. Phys. 46, 15–28 (2005).
[CrossRef]

J. Opt. A: Pure Appl. Opt. (2)

V. Karásek and P. Zemánek, “Analytical description of longitudinal optical binding of two spherical nanoparticles,” J. Opt. A: Pure Appl. Opt. 9, S215–S220 (2007).
[CrossRef]

V. Karásek, O. Brzobohatý, and P. Zemánek, “Longitudinal optical binding of several spherical particles studied by the coupled dipole method,” J. Opt. A: Pure Appl. Opt. 11, 034009 (2009).
[CrossRef]

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

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

J. Phys. B (1)

T. Čižmár, L. C. D. Romero, K. Dholakia, and D. L. Andrews, “Multiple optical trapping and binding: new routes to self-assembly,” J. Phys. B 43, 102001 (2010).
[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]

Nat. Photonics (1)

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[CrossRef]

New J. Phys. (1)

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[CrossRef]

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Figures (10)

Fig. 1
Fig. 1

Single particle optically trapped in two counter-propagating interfering Bessel beams. (a) Calculated force F(z) acting on the particle and optical potential U(z) for the symmetrical case (both laser beams have identical optical intensities 1.82 mW/μm2 on the beam axis). (b) Calculated force F(z) acting on the particle and optical potential U(z) for the asymmetrical case. In this case the optical intensity of the beam propagating along positive direction of z is higher by 5% relatively to the counter-propagating beam. The following parameters were used in the calculations: the Bessel beam core radii were equal to 2.15 μm, laser wavelength in vacuum 1064 nm, refractive index of the polystyrene particle 1.59 and water 1.32.

Fig. 2
Fig. 2

Two particles optically trapped in two counter-propagating interfering/non-interfering Bessel beams, respectively. (a) Behavior of two particles trapped in non-interfering beams depending on theirs separation. In this case the particles are stably optically bound at the mutual distance close to 10 μm. (b) Particles behavior in interfering beams. All dependencies are calculated for three slightly different positions zL (−121 nm (blue), 0 nm (green), 121 nm (red)) of the left-hand particle with respect to an intensity maximum of the standing wave. In the second row the calculated force acting on each particle (F L(z L, z′) and F R(z L, z′)) is shown. The third and fourth rows show the binding force (F bind(z L, z′) = F R(z L, z′) – F L(z L, z′)) and the optical potential U(z L, z′) (see Eq. (1)) related to the force F bind.The input parameters for the calculation were the same as in Fig. 1.

Fig. 3
Fig. 3

A collimated Gaussian beam coming from the fiber laser IPG ILM-10-1070-LP (wavelength 1064 nm) is expanded on the telescope made of lenses L1 (f 1 = 150 mm) and L2 (f 2 = 300 mm) and projected on the SLM (Hamamatsu LCOS X10468-07). Encoded phase at the SLM produces two BBs in the focal plane of the lens L3 (f 3 = 400 mm) above the undiffracted zero-order beam. Unwanted higher diffraction orders and the zero-order are blocked by a dual aperture spatial filter placed into a focal plane of L3. The passed beams are separated by prisms P1 and P2, sent in opposite directions and collimated by lenses L4 and L7 (both with f 4 = 200 mm), respectively. Each of the lenses L4 and L7 forms a telescope with L3 projecting the SLM plane on mirrors M2 and M4, respectively. The SLM plane is imaged onto the back focal plane of aspherical lenses AS1 (AS2) (both f = 8 mm) by a telescope consisting of lenses L5 (L8) (f 5 = 100 mm) and L6 (L9) (f 6 = 150 mm). AS1 and AS2 focuses both beams into a capillary (Vitrocells 8510) containing the sample (SC). A half-wave plate is inserted into one of the arms to control the polarization of the beam and thereby to switch between the cases of interfering or non-interfering counter-propagating beams (not shown). To reach sub-micron alignment precision and stability of the system we omitted translational stages and properly placed the mirrors M2 and M4 to ensure lateral positioning of the focal points along the sample plane and the mirrors M3 and M5 to center the beams at the back aperture of the aspherical lenses. The right-hand side inset shows the spatial BB optical intensity between AS1 and AS2.

Fig. 4
Fig. 4

(a) Time record of the formation of an optically bound structure in two counter-propagating interfering BBs. A single isolated polystyrene particle of diameter 1070 nm is stably trapped in the interfering structure and afterwards (30 sec) the second polystyrene particle of the same size is trapped at the distance of about 25 μm apart from the first particle. Both particles start to move over the interfering structure to their new equilibrium positions and after about 50 s they are stably bound. (b) Experimental investigation of the dynamics of two optically bound particles forming the stable optically bound structure in two counter-propagating interfering BBs. Three different observations of two particles approaching their stationary inter-particle separation in the optically bound structure are presented. These experimental data were fitted using an exponential decay function (see Eq. (2)) where τ is the time constant of the structure formation.

Fig. 5
Fig. 5

Comparison of the optical potential (separation work) and theoretical probability density of two identical polystyrene particles placed on the optical axis at different inter-particle distances if particles of different diameters are considered. The red (resp. green) curves correspond to the left particle placed at the intensity maximum (resp. minimum). The blue curves show the results for non-interfering beams and lay in between the cases mentioned above. The radius of the BB used in the simulations was ρ 0 = 2.15nm. The motion of 1150 nm sized particles is minimally influenced by the standing wave and therefore its behavior is nearly identical to the case of two non-interfering beams.

Fig. 6
Fig. 6

A particle moving in a tilted periodic potential having several local energy minima - optical traps (black line). The particle located at the point z can reach the left trap edge (a) after the average time T while it is reflected back into the trap on its right edge (b). Similarly, T + is the average time needed to leave the trap over the right edge (b) while the particle is reflected back on the left edge (a). The average time needed to leave the well over any of its edges is denoted as T ±. Note, that the trap edges may be moved into any other points (e.g. a′ or b′).

Fig. 7
Fig. 7

(a) The average time that the right particle spends in a certain local potential energy minimum before it jumps to the neighboring potential minimum. We assume that the left particle is fixed in the intensity maximum of the standing wave and the dependence on the inter-particle separation is shown. We consider, that the particle starts its motion in one of the minimum of the potential energy profile shown by the green curve on the third line of Fig. 5. The blue, green, and red curves consider particles jumps over the local potential maximum located to the left, right, and both boundaries, respectively. (b) The average time required by the particle to reach the global minimum of the potential energy profile for various temperatures of water.

Fig. 8
Fig. 8

(a) Probability density of the pair of polystyrene particles of diameter 1070 nm being separated by a given distance at different times. (b)The time evolution of the mean inter-particle separation.

Fig. 9
Fig. 9

The influence of the laser beam optical intensity on the characteristic time τ needed to settle the particles into the stable optically bound structure.

Fig. 10
Fig. 10

The comparison of experimentally obtained distributions of particles separations with results of the Monte-Carlo simulations. The radius of BB used in the simulations was ρ 0 = 2.150nm.

Equations (6)

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U ( z L , z ) = 0 z F bind ( z L , z ) d z + U 0 .
f ( t ) = C 1 exp ( t / τ ) + C 2 ,
T ( z ) = γ k B T a z d x ψ ( x ) x b d x ψ ( x ) , where ψ ( z ) = exp [ U ( z ) k B T ]
T + ( z ) = γ k B T z b d x ψ ( x ) a x d x ψ ( x ) .
T ± ( z ) = γ k B T a b d y ψ ( y ) [ ( a z d y ψ ( y ) ) z b d x ψ ( x ) a x d x ψ ( x ) ( z b d y ψ ( y ) ) a z d x ψ ( x ) a x d x ψ ( x ) ] .
γ z ˙ L = F ( z L , z R ) + ξ ( t ) , γ z ˙ R = F ( z R , z L ) + ζ ( t ) ,

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