Abstract

A dual-beam optical trap is used to trap and manipulate dielectric particles. When the refractive index of these particles is comparable to that of the surrounding medium, equilibrium trapping locations within the system shift from stable to unstable depending on fiber separation and particle size. This is due to to the relationship between gradient and scattering forces. We experimentally and computationally study the transitions between stable and unstable trapping of poly(methyl methacrylate) beads for a range of parameters relevant to experimental setups involving giant unilamellar vesicles. We present stability maps for various fiber separations and particle sizes, and find that careful attention to particle size and configuration is necessary to obtain reproducible quantitative results for soft matter stretching experiments.

© 2015 Optical Society of America

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References

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  1. A. Ashkin, “Acceleration and trapping of particles by radiation pressure,” Phys. Rev. Lett. 24(4), 156–159 (1970).
    [Crossref]
  2. J. Jass, S. Schedin, J. Ohlsson, U. J. Nilsson, B. E. Uhlin, and O. Axner, “Physical properties of Escherichia coli P Pili measured by optical tweezers,” Biophys. J. 87(6), 4271–4283 (2004).
    [Crossref] [PubMed]
  3. K. Gibble and S. Chu, “Laser-cooled Cs frequency standard and a measurement of the frequency shift due to ultracold collisions,” Phys. Rev. Lett. 70(12), 1771–1774 (1993).
    [Crossref] [PubMed]
  4. M. E. Solmaz, R. Biswas, S. Sankhagowit, J. R. Thompson, C. A. Mejia, N. Malmstadt, and M. L. Povinelli, “Optical stretching of giant unilamellar vesicles with an integrated dual-beam optical trap,” Biomed. Opt. Express 3(10), 2419–2427 (2012).
    [Crossref] [PubMed]
  5. S. Sankhagowit, S. H. Wu, R. Biswas, C. T. Riche, M. L. Povinelli, and N. Malmstadt, “The dynamics of giant unilamellar vesicle oxidation probed by morphological transitions,” Biochim. Biophys. Acta 1838(10), 2615–2624 (2014).
    [Crossref] [PubMed]
  6. J. Guck, R. Ananthakrishnan, H. Mahmood, T. J. Moon, C. C. Cunningham, and J. Kãs, “The optical stretcher: a novel laser tool to micromanipulate cells,” Biophys. J. 81(2), 767–784 (2001).
    [Crossref] [PubMed]
  7. J. Guck, R. Ananthakrishnan, H. Mahmood, T. J. Moon, C. C. Cunningham, and J. Kãs, “Optical deformability of soft biological dielectrics,” Phys. Rev. Lett. 84(23), 5451–5454 (2000).
    [Crossref] [PubMed]
  8. P. B. Bareil, Y. Sheng, Y. Chen, and A. Chiou, “Calculation of spherical red blood cell deformation in a dual-beam optical stretcher,” Opt. Express 15(24), 16029–16034 (2007).
    [Crossref] [PubMed]
  9. E. A. Evans, “New membrane concept applied to the analysis of fluid shear-and micropipette-deformed red blood cells,” Biophys. J. 13(9), 941–954 (1973).
    [Crossref] [PubMed]
  10. T. M. Piñón, A. R. Castelli, L. S. Hirst, and J. E. Sharping, “Fiber-optic trap-on-a-chip platform for probing low refractive index contrast biomaterials,” Appl. Opt. 52(11), 2340–2345 (2013).
    [Crossref] [PubMed]
  11. E. Sidick, S. D. Collins, and A. Knoesen, “Trapping forces in a multiple-beam fiber-optic trap,” Appl. Opt. 36(25), 6423–6432 (1997).
    [Crossref]
  12. U. Delabre, K. Feld, E. Crespo, G. Whyte, C. Sykes, U. Seifert, and J. Guck, “Deformation of phospholipid vesicles in an optical stretcher,” Soft Matter 11(30), 6075–60882015
    [Crossref] [PubMed]
  13. E. J. G. Peterman, F. Gittes, and C. F. Schmidt, “Laser-induced heating in optical traps,” Biophys. J. 84(2), 1308–1316 (2003).
    [Crossref] [PubMed]

2015 (1)

U. Delabre, K. Feld, E. Crespo, G. Whyte, C. Sykes, U. Seifert, and J. Guck, “Deformation of phospholipid vesicles in an optical stretcher,” Soft Matter 11(30), 6075–60882015
[Crossref] [PubMed]

2014 (1)

S. Sankhagowit, S. H. Wu, R. Biswas, C. T. Riche, M. L. Povinelli, and N. Malmstadt, “The dynamics of giant unilamellar vesicle oxidation probed by morphological transitions,” Biochim. Biophys. Acta 1838(10), 2615–2624 (2014).
[Crossref] [PubMed]

2013 (1)

2012 (1)

2007 (1)

2004 (1)

J. Jass, S. Schedin, J. Ohlsson, U. J. Nilsson, B. E. Uhlin, and O. Axner, “Physical properties of Escherichia coli P Pili measured by optical tweezers,” Biophys. J. 87(6), 4271–4283 (2004).
[Crossref] [PubMed]

2003 (1)

E. J. G. Peterman, F. Gittes, and C. F. Schmidt, “Laser-induced heating in optical traps,” Biophys. J. 84(2), 1308–1316 (2003).
[Crossref] [PubMed]

2001 (1)

J. Guck, R. Ananthakrishnan, H. Mahmood, T. J. Moon, C. C. Cunningham, and J. Kãs, “The optical stretcher: a novel laser tool to micromanipulate cells,” Biophys. J. 81(2), 767–784 (2001).
[Crossref] [PubMed]

2000 (1)

J. Guck, R. Ananthakrishnan, H. Mahmood, T. J. Moon, C. C. Cunningham, and J. Kãs, “Optical deformability of soft biological dielectrics,” Phys. Rev. Lett. 84(23), 5451–5454 (2000).
[Crossref] [PubMed]

1997 (1)

1993 (1)

K. Gibble and S. Chu, “Laser-cooled Cs frequency standard and a measurement of the frequency shift due to ultracold collisions,” Phys. Rev. Lett. 70(12), 1771–1774 (1993).
[Crossref] [PubMed]

1973 (1)

E. A. Evans, “New membrane concept applied to the analysis of fluid shear-and micropipette-deformed red blood cells,” Biophys. J. 13(9), 941–954 (1973).
[Crossref] [PubMed]

1970 (1)

A. Ashkin, “Acceleration and trapping of particles by radiation pressure,” Phys. Rev. Lett. 24(4), 156–159 (1970).
[Crossref]

Ananthakrishnan, R.

J. Guck, R. Ananthakrishnan, H. Mahmood, T. J. Moon, C. C. Cunningham, and J. Kãs, “The optical stretcher: a novel laser tool to micromanipulate cells,” Biophys. J. 81(2), 767–784 (2001).
[Crossref] [PubMed]

J. Guck, R. Ananthakrishnan, H. Mahmood, T. J. Moon, C. C. Cunningham, and J. Kãs, “Optical deformability of soft biological dielectrics,” Phys. Rev. Lett. 84(23), 5451–5454 (2000).
[Crossref] [PubMed]

Ashkin, A.

A. Ashkin, “Acceleration and trapping of particles by radiation pressure,” Phys. Rev. Lett. 24(4), 156–159 (1970).
[Crossref]

Axner, O.

J. Jass, S. Schedin, J. Ohlsson, U. J. Nilsson, B. E. Uhlin, and O. Axner, “Physical properties of Escherichia coli P Pili measured by optical tweezers,” Biophys. J. 87(6), 4271–4283 (2004).
[Crossref] [PubMed]

Bareil, P. B.

Biswas, R.

S. Sankhagowit, S. H. Wu, R. Biswas, C. T. Riche, M. L. Povinelli, and N. Malmstadt, “The dynamics of giant unilamellar vesicle oxidation probed by morphological transitions,” Biochim. Biophys. Acta 1838(10), 2615–2624 (2014).
[Crossref] [PubMed]

M. E. Solmaz, R. Biswas, S. Sankhagowit, J. R. Thompson, C. A. Mejia, N. Malmstadt, and M. L. Povinelli, “Optical stretching of giant unilamellar vesicles with an integrated dual-beam optical trap,” Biomed. Opt. Express 3(10), 2419–2427 (2012).
[Crossref] [PubMed]

Castelli, A. R.

Chen, Y.

Chiou, A.

Chu, S.

K. Gibble and S. Chu, “Laser-cooled Cs frequency standard and a measurement of the frequency shift due to ultracold collisions,” Phys. Rev. Lett. 70(12), 1771–1774 (1993).
[Crossref] [PubMed]

Collins, S. D.

Crespo, E.

U. Delabre, K. Feld, E. Crespo, G. Whyte, C. Sykes, U. Seifert, and J. Guck, “Deformation of phospholipid vesicles in an optical stretcher,” Soft Matter 11(30), 6075–60882015
[Crossref] [PubMed]

Cunningham, C. C.

J. Guck, R. Ananthakrishnan, H. Mahmood, T. J. Moon, C. C. Cunningham, and J. Kãs, “The optical stretcher: a novel laser tool to micromanipulate cells,” Biophys. J. 81(2), 767–784 (2001).
[Crossref] [PubMed]

J. Guck, R. Ananthakrishnan, H. Mahmood, T. J. Moon, C. C. Cunningham, and J. Kãs, “Optical deformability of soft biological dielectrics,” Phys. Rev. Lett. 84(23), 5451–5454 (2000).
[Crossref] [PubMed]

Delabre, U.

U. Delabre, K. Feld, E. Crespo, G. Whyte, C. Sykes, U. Seifert, and J. Guck, “Deformation of phospholipid vesicles in an optical stretcher,” Soft Matter 11(30), 6075–60882015
[Crossref] [PubMed]

Evans, E. A.

E. A. Evans, “New membrane concept applied to the analysis of fluid shear-and micropipette-deformed red blood cells,” Biophys. J. 13(9), 941–954 (1973).
[Crossref] [PubMed]

Feld, K.

U. Delabre, K. Feld, E. Crespo, G. Whyte, C. Sykes, U. Seifert, and J. Guck, “Deformation of phospholipid vesicles in an optical stretcher,” Soft Matter 11(30), 6075–60882015
[Crossref] [PubMed]

Gibble, K.

K. Gibble and S. Chu, “Laser-cooled Cs frequency standard and a measurement of the frequency shift due to ultracold collisions,” Phys. Rev. Lett. 70(12), 1771–1774 (1993).
[Crossref] [PubMed]

Gittes, F.

E. J. G. Peterman, F. Gittes, and C. F. Schmidt, “Laser-induced heating in optical traps,” Biophys. J. 84(2), 1308–1316 (2003).
[Crossref] [PubMed]

Guck, J.

U. Delabre, K. Feld, E. Crespo, G. Whyte, C. Sykes, U. Seifert, and J. Guck, “Deformation of phospholipid vesicles in an optical stretcher,” Soft Matter 11(30), 6075–60882015
[Crossref] [PubMed]

J. Guck, R. Ananthakrishnan, H. Mahmood, T. J. Moon, C. C. Cunningham, and J. Kãs, “The optical stretcher: a novel laser tool to micromanipulate cells,” Biophys. J. 81(2), 767–784 (2001).
[Crossref] [PubMed]

J. Guck, R. Ananthakrishnan, H. Mahmood, T. J. Moon, C. C. Cunningham, and J. Kãs, “Optical deformability of soft biological dielectrics,” Phys. Rev. Lett. 84(23), 5451–5454 (2000).
[Crossref] [PubMed]

Hirst, L. S.

Jass, J.

J. Jass, S. Schedin, J. Ohlsson, U. J. Nilsson, B. E. Uhlin, and O. Axner, “Physical properties of Escherichia coli P Pili measured by optical tweezers,” Biophys. J. 87(6), 4271–4283 (2004).
[Crossref] [PubMed]

Kãs, J.

J. Guck, R. Ananthakrishnan, H. Mahmood, T. J. Moon, C. C. Cunningham, and J. Kãs, “The optical stretcher: a novel laser tool to micromanipulate cells,” Biophys. J. 81(2), 767–784 (2001).
[Crossref] [PubMed]

J. Guck, R. Ananthakrishnan, H. Mahmood, T. J. Moon, C. C. Cunningham, and J. Kãs, “Optical deformability of soft biological dielectrics,” Phys. Rev. Lett. 84(23), 5451–5454 (2000).
[Crossref] [PubMed]

Knoesen, A.

Mahmood, H.

J. Guck, R. Ananthakrishnan, H. Mahmood, T. J. Moon, C. C. Cunningham, and J. Kãs, “The optical stretcher: a novel laser tool to micromanipulate cells,” Biophys. J. 81(2), 767–784 (2001).
[Crossref] [PubMed]

J. Guck, R. Ananthakrishnan, H. Mahmood, T. J. Moon, C. C. Cunningham, and J. Kãs, “Optical deformability of soft biological dielectrics,” Phys. Rev. Lett. 84(23), 5451–5454 (2000).
[Crossref] [PubMed]

Malmstadt, N.

S. Sankhagowit, S. H. Wu, R. Biswas, C. T. Riche, M. L. Povinelli, and N. Malmstadt, “The dynamics of giant unilamellar vesicle oxidation probed by morphological transitions,” Biochim. Biophys. Acta 1838(10), 2615–2624 (2014).
[Crossref] [PubMed]

M. E. Solmaz, R. Biswas, S. Sankhagowit, J. R. Thompson, C. A. Mejia, N. Malmstadt, and M. L. Povinelli, “Optical stretching of giant unilamellar vesicles with an integrated dual-beam optical trap,” Biomed. Opt. Express 3(10), 2419–2427 (2012).
[Crossref] [PubMed]

Mejia, C. A.

Moon, T. J.

J. Guck, R. Ananthakrishnan, H. Mahmood, T. J. Moon, C. C. Cunningham, and J. Kãs, “The optical stretcher: a novel laser tool to micromanipulate cells,” Biophys. J. 81(2), 767–784 (2001).
[Crossref] [PubMed]

J. Guck, R. Ananthakrishnan, H. Mahmood, T. J. Moon, C. C. Cunningham, and J. Kãs, “Optical deformability of soft biological dielectrics,” Phys. Rev. Lett. 84(23), 5451–5454 (2000).
[Crossref] [PubMed]

Nilsson, U. J.

J. Jass, S. Schedin, J. Ohlsson, U. J. Nilsson, B. E. Uhlin, and O. Axner, “Physical properties of Escherichia coli P Pili measured by optical tweezers,” Biophys. J. 87(6), 4271–4283 (2004).
[Crossref] [PubMed]

Ohlsson, J.

J. Jass, S. Schedin, J. Ohlsson, U. J. Nilsson, B. E. Uhlin, and O. Axner, “Physical properties of Escherichia coli P Pili measured by optical tweezers,” Biophys. J. 87(6), 4271–4283 (2004).
[Crossref] [PubMed]

Peterman, E. J. G.

E. J. G. Peterman, F. Gittes, and C. F. Schmidt, “Laser-induced heating in optical traps,” Biophys. J. 84(2), 1308–1316 (2003).
[Crossref] [PubMed]

Piñón, T. M.

Povinelli, M. L.

S. Sankhagowit, S. H. Wu, R. Biswas, C. T. Riche, M. L. Povinelli, and N. Malmstadt, “The dynamics of giant unilamellar vesicle oxidation probed by morphological transitions,” Biochim. Biophys. Acta 1838(10), 2615–2624 (2014).
[Crossref] [PubMed]

M. E. Solmaz, R. Biswas, S. Sankhagowit, J. R. Thompson, C. A. Mejia, N. Malmstadt, and M. L. Povinelli, “Optical stretching of giant unilamellar vesicles with an integrated dual-beam optical trap,” Biomed. Opt. Express 3(10), 2419–2427 (2012).
[Crossref] [PubMed]

Riche, C. T.

S. Sankhagowit, S. H. Wu, R. Biswas, C. T. Riche, M. L. Povinelli, and N. Malmstadt, “The dynamics of giant unilamellar vesicle oxidation probed by morphological transitions,” Biochim. Biophys. Acta 1838(10), 2615–2624 (2014).
[Crossref] [PubMed]

Sankhagowit, S.

S. Sankhagowit, S. H. Wu, R. Biswas, C. T. Riche, M. L. Povinelli, and N. Malmstadt, “The dynamics of giant unilamellar vesicle oxidation probed by morphological transitions,” Biochim. Biophys. Acta 1838(10), 2615–2624 (2014).
[Crossref] [PubMed]

M. E. Solmaz, R. Biswas, S. Sankhagowit, J. R. Thompson, C. A. Mejia, N. Malmstadt, and M. L. Povinelli, “Optical stretching of giant unilamellar vesicles with an integrated dual-beam optical trap,” Biomed. Opt. Express 3(10), 2419–2427 (2012).
[Crossref] [PubMed]

Schedin, S.

J. Jass, S. Schedin, J. Ohlsson, U. J. Nilsson, B. E. Uhlin, and O. Axner, “Physical properties of Escherichia coli P Pili measured by optical tweezers,” Biophys. J. 87(6), 4271–4283 (2004).
[Crossref] [PubMed]

Schmidt, C. F.

E. J. G. Peterman, F. Gittes, and C. F. Schmidt, “Laser-induced heating in optical traps,” Biophys. J. 84(2), 1308–1316 (2003).
[Crossref] [PubMed]

Seifert, U.

U. Delabre, K. Feld, E. Crespo, G. Whyte, C. Sykes, U. Seifert, and J. Guck, “Deformation of phospholipid vesicles in an optical stretcher,” Soft Matter 11(30), 6075–60882015
[Crossref] [PubMed]

Sharping, J. E.

Sheng, Y.

Sidick, E.

Solmaz, M. E.

Sykes, C.

U. Delabre, K. Feld, E. Crespo, G. Whyte, C. Sykes, U. Seifert, and J. Guck, “Deformation of phospholipid vesicles in an optical stretcher,” Soft Matter 11(30), 6075–60882015
[Crossref] [PubMed]

Thompson, J. R.

Uhlin, B. E.

J. Jass, S. Schedin, J. Ohlsson, U. J. Nilsson, B. E. Uhlin, and O. Axner, “Physical properties of Escherichia coli P Pili measured by optical tweezers,” Biophys. J. 87(6), 4271–4283 (2004).
[Crossref] [PubMed]

Whyte, G.

U. Delabre, K. Feld, E. Crespo, G. Whyte, C. Sykes, U. Seifert, and J. Guck, “Deformation of phospholipid vesicles in an optical stretcher,” Soft Matter 11(30), 6075–60882015
[Crossref] [PubMed]

Wu, S. H.

S. Sankhagowit, S. H. Wu, R. Biswas, C. T. Riche, M. L. Povinelli, and N. Malmstadt, “The dynamics of giant unilamellar vesicle oxidation probed by morphological transitions,” Biochim. Biophys. Acta 1838(10), 2615–2624 (2014).
[Crossref] [PubMed]

Appl. Opt. (2)

Biochim. Biophys. Acta (1)

S. Sankhagowit, S. H. Wu, R. Biswas, C. T. Riche, M. L. Povinelli, and N. Malmstadt, “The dynamics of giant unilamellar vesicle oxidation probed by morphological transitions,” Biochim. Biophys. Acta 1838(10), 2615–2624 (2014).
[Crossref] [PubMed]

Biomed. Opt. Express (1)

Biophys. J. (4)

J. Guck, R. Ananthakrishnan, H. Mahmood, T. J. Moon, C. C. Cunningham, and J. Kãs, “The optical stretcher: a novel laser tool to micromanipulate cells,” Biophys. J. 81(2), 767–784 (2001).
[Crossref] [PubMed]

J. Jass, S. Schedin, J. Ohlsson, U. J. Nilsson, B. E. Uhlin, and O. Axner, “Physical properties of Escherichia coli P Pili measured by optical tweezers,” Biophys. J. 87(6), 4271–4283 (2004).
[Crossref] [PubMed]

E. A. Evans, “New membrane concept applied to the analysis of fluid shear-and micropipette-deformed red blood cells,” Biophys. J. 13(9), 941–954 (1973).
[Crossref] [PubMed]

E. J. G. Peterman, F. Gittes, and C. F. Schmidt, “Laser-induced heating in optical traps,” Biophys. J. 84(2), 1308–1316 (2003).
[Crossref] [PubMed]

Opt. Express (1)

Phys. Rev. Lett. (3)

A. Ashkin, “Acceleration and trapping of particles by radiation pressure,” Phys. Rev. Lett. 24(4), 156–159 (1970).
[Crossref]

K. Gibble and S. Chu, “Laser-cooled Cs frequency standard and a measurement of the frequency shift due to ultracold collisions,” Phys. Rev. Lett. 70(12), 1771–1774 (1993).
[Crossref] [PubMed]

J. Guck, R. Ananthakrishnan, H. Mahmood, T. J. Moon, C. C. Cunningham, and J. Kãs, “Optical deformability of soft biological dielectrics,” Phys. Rev. Lett. 84(23), 5451–5454 (2000).
[Crossref] [PubMed]

Soft Matter (1)

U. Delabre, K. Feld, E. Crespo, G. Whyte, C. Sykes, U. Seifert, and J. Guck, “Deformation of phospholipid vesicles in an optical stretcher,” Soft Matter 11(30), 6075–60882015
[Crossref] [PubMed]

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Figures (6)

Fig. 1
Fig. 1

Schematic of the trapping forces [11]. An incoming ray strikes a particle, applying a force that can be split into a scattering and gradient force Fs and Fg. The particle traps if it has a larger refractive index than the surrounding medium.

Fig. 2
Fig. 2

Schematic of the experimental setup. The single-mode fibers are secured in place with drops of wax. A cover slip fastened with epoxy aligns the fibers in the trapping space and provides a flat field of view. The trapping space is expanded to show the relative sizes of the particles, beam and fibers. The fiber separation is fixed during chip assembly. A microscope is used to observe trapped particles and a computer controls the laser power from two separate 980 nm laser diodes.

Fig. 3
Fig. 3

(a) Simulations of the dimensionless trapping efficiency Qz along the beam axis z when the particle radius is 3.15 μm and the fiber separation are 23 μm, 75 μm, and 149 μm. The trap center is located at z = 0. (b) Pictures of experimentally trapped particles at a fiber separation of 129.1 μm. The contrast and brightness were adjusted to better view the particle and fibers.

Fig. 4
Fig. 4

Contour plot describing the expected stability at the center of the trap. The warmer colors indicate an unstable trapping regime, while the cooler colors indicate a stable trapping regime. The thick black zero line indicates location where the center is neither stable nor unstable. The contours are obtained from the simulations. Experimental data is given by markers. Open circles represent the particles observed to be trapped at z = 0 (indicating a stable equilibrium point at z = 0), while the crosses represent particles which drift away from z = 0 (indicating an unstable equilibrium point at z = 0.)

Fig. 5
Fig. 5

Bifurcation plots showing the axial stability locations vs. particle radius for three different traps with fiber separations of (a) 45 μm, (b) 92.9 μm, and (c) 129.1 μm. The red dots represent the simulated stable trapping location, and the symbols represent experimentally observed stably trapped particles. The trap center is located at z=0. Trapping locations are shown schematically within (c). The error bars were determined empirically through measurements of the inner and outer edges of both the fiber and beads.

Fig. 6
Fig. 6

Bifurcation plots of the axial stability locations as a function of fiber separation for particles of radius: (a) 3.15 μm and (b) 5.05 μm. The red dots indicate the simulated stable trapping location, the black lines show the location of the fiber ends, and the blue data points represent the observed stably trapped particles. The trap center is located at z = 0.

Equations (4)

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

F = n medium P 0 c Q ,
Q z = 2 r 0 2 0 θ max d θ sin 2 θ exp ( 2 r 2 / w 2 ) w 2 q z .
q z = cos ( α i θ ) + R cos ( α i + θ ) T 2 cos ( α i + θ 2 α r ) + R cos ( α i + θ ) 1 + R 2 + 2 R cos 2 α r ,
F z , tot = n 1 ( P 1 + P 2 ) c ( P 1 Q z 1 P 1 + P 2 P 1 Q z 2 P 1 + P 2 ) ,

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