Abstract

An optical bottle method is developed to determine the potential-energy profile of colloidal Rayleigh nanoparticles in an optical trap. The three-dimensional distribution of fluorescent particles in the trap is measured by laser scanning confocal fluorescence microscopy. At sufficiently low concentrations at which interactions between the particles are negligible, the single-particle trapping potential-energy profile is determined from the equilibrium number-density profile by use of the Boltzmann distribution. Fluorescence imaging as well as calculations based on a discrete dipole approximation show that effects due to scattering forces are negligible for polystyrene particles of size less than 10% of the wavelength of the trapping laser, thus justifying the assumption of conservative forces in the equilibrium potential-energy determinations. The new optical bottle method measures the entire two-dimensional trapping-potential profile for an individual nanoparticle without the restriction that only one particle be contained in the trap, thus obviating the need for high laser power.

© 2013 Optical Society of America

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2013 (1)

2011 (1)

2010 (3)

J. Ng, Z. Lin, and C. T. Chan, Phys. Rev. Lett. 104, 103601 (2010).
[CrossRef]

J. Junio, S. Park, M. W. Kim, and H. D. Ou-Yang, Solid State Commun. 150, 1003 (2010).
[CrossRef]

L. Ling, F. Zhou, L. Huang, and Z. Y. Li, J. Appl. Phys. 108, 073110 (2010).
[CrossRef]

2009 (2)

G. Pesce, G. Volpe, A. C. De Luca, G. Rusciano, and G. Volpe, Europhys. Lett. 86, 38002 (2009).
[CrossRef]

P. Wu, R. Huang, C. Tischer, A. Jonas, and E.-L. Florin, Phys. Rev. Lett 103, 108101 (2009).
[CrossRef]

2008 (2)

Y. Roichman, B. Sun, A. Stolarski, and D. G. Grier, Phys. Rev. Lett. 101, 128301 (2008).
[CrossRef]

A. N. Grigorenko, N. W. Roberts, M. R. Dickinson, and Y. Zhang, Nat. Photonics 2, 365 (2008).
[CrossRef]

2005 (2)

P. Y. Chiou, A. T. Ohta, and M. C. Wu, Nature 436, 370 (2005).
[CrossRef]

A. Rohrbach, Phys. Rev. Lett. 95, 168102 (2005).
[CrossRef]

2004 (1)

K. Berg-Sorensen and H. Flyvbjerg, Rev. Sci. Instrum. 75, 594 (2004).
[CrossRef]

2003 (2)

A. J. Wright, T. A. Wood, M. R. Dickinson, H. F. Gleeson, and T. Mullin, J. Mod. Opt. 50, 1521 (2003).

A. Mazolli, P. A. M. Neto, and H. M. Nussenzveig, Proc. R. Soc. London A 459, 3021 (2003).
[CrossRef]

1999 (1)

L. I. McCann, M. Dykman, and B. Golding, Nature 402, 785 (1999).
[CrossRef]

1998 (1)

E. L. Florin, A. Pralle, E. H. K. Stelzer, and J. K. H. Horber, Appl. Phys. A 66, S75 (1998).
[CrossRef]

1996 (2)

R. M. Simmons, J. T. Finer, S. Chu, and J. A. Spudich, Biophys. J. 70, 1813 (1996).
[CrossRef]

Y. Harada and T. Asakura, Opt. Commun. 124, 529 (1996).
[CrossRef]

1994 (1)

K. Svoboda, P. P. Mitra, and S. M. Block, Proc. Natl. Acad. Sci. USA 91, 11782 (1994).
[CrossRef]

1992 (1)

A. Ashkin, Biophys. J. 61, 569 (1992).
[CrossRef]

1989 (1)

J. P. Barton and D. R. Alexander, J. Appl. Phys. 66, 2800 (1989).
[CrossRef]

1986 (1)

Alexander, D. R.

J. P. Barton and D. R. Alexander, J. Appl. Phys. 66, 2800 (1989).
[CrossRef]

Asakura, T.

Y. Harada and T. Asakura, Opt. Commun. 124, 529 (1996).
[CrossRef]

Ashkin, A.

Barton, J. P.

J. P. Barton and D. R. Alexander, J. Appl. Phys. 66, 2800 (1989).
[CrossRef]

Berg-Sorensen, K.

K. Berg-Sorensen and H. Flyvbjerg, Rev. Sci. Instrum. 75, 594 (2004).
[CrossRef]

Bjorkholm, J. E.

Block, S. M.

K. Svoboda, P. P. Mitra, and S. M. Block, Proc. Natl. Acad. Sci. USA 91, 11782 (1994).
[CrossRef]

Chan, C. T.

J. Ng, Z. Lin, and C. T. Chan, Phys. Rev. Lett. 104, 103601 (2010).
[CrossRef]

Chiou, P. Y.

P. Y. Chiou, A. T. Ohta, and M. C. Wu, Nature 436, 370 (2005).
[CrossRef]

Chu, S.

R. M. Simmons, J. T. Finer, S. Chu, and J. A. Spudich, Biophys. J. 70, 1813 (1996).
[CrossRef]

A. Ashkin, J. M. Dziedzic, J. E. Bjorkholm, and S. Chu, Opt. Lett. 11, 288 (1986).
[CrossRef]

Cohen, J. A.

De Luca, A. C.

G. Pesce, G. Volpe, A. C. De Luca, G. Rusciano, and G. Volpe, Europhys. Lett. 86, 38002 (2009).
[CrossRef]

Dickinson, M. R.

A. N. Grigorenko, N. W. Roberts, M. R. Dickinson, and Y. Zhang, Nat. Photonics 2, 365 (2008).
[CrossRef]

A. J. Wright, T. A. Wood, M. R. Dickinson, H. F. Gleeson, and T. Mullin, J. Mod. Opt. 50, 1521 (2003).

Dykman, M.

L. I. McCann, M. Dykman, and B. Golding, Nature 402, 785 (1999).
[CrossRef]

Dziedzic, J. M.

Finer, J. T.

R. M. Simmons, J. T. Finer, S. Chu, and J. A. Spudich, Biophys. J. 70, 1813 (1996).
[CrossRef]

Florin, E. L.

E. L. Florin, A. Pralle, E. H. K. Stelzer, and J. K. H. Horber, Appl. Phys. A 66, S75 (1998).
[CrossRef]

Florin, E.-L.

P. Wu, R. Huang, C. Tischer, A. Jonas, and E.-L. Florin, Phys. Rev. Lett 103, 108101 (2009).
[CrossRef]

Flyvbjerg, H.

K. Berg-Sorensen and H. Flyvbjerg, Rev. Sci. Instrum. 75, 594 (2004).
[CrossRef]

Fu, J.

Gleeson, H. F.

A. J. Wright, T. A. Wood, M. R. Dickinson, H. F. Gleeson, and T. Mullin, J. Mod. Opt. 50, 1521 (2003).

Golding, B.

L. I. McCann, M. Dykman, and B. Golding, Nature 402, 785 (1999).
[CrossRef]

Grier, D. G.

Y. Roichman, B. Sun, A. Stolarski, and D. G. Grier, Phys. Rev. Lett. 101, 128301 (2008).
[CrossRef]

Grigorenko, A. N.

A. N. Grigorenko, N. W. Roberts, M. R. Dickinson, and Y. Zhang, Nat. Photonics 2, 365 (2008).
[CrossRef]

Guo, H.

Harada, Y.

Y. Harada and T. Asakura, Opt. Commun. 124, 529 (1996).
[CrossRef]

Horber, J. K. H.

E. L. Florin, A. Pralle, E. H. K. Stelzer, and J. K. H. Horber, Appl. Phys. A 66, S75 (1998).
[CrossRef]

Huang, L.

Huang, R.

P. Wu, R. Huang, C. Tischer, A. Jonas, and E.-L. Florin, Phys. Rev. Lett 103, 108101 (2009).
[CrossRef]

Jonas, A.

P. Wu, R. Huang, C. Tischer, A. Jonas, and E.-L. Florin, Phys. Rev. Lett 103, 108101 (2009).
[CrossRef]

Junio, J.

J. Junio, J. Ng, J. A. Cohen, Z. F. Lin, and H. D. Ou-Yang, Opt. Lett. 36, 1497 (2011).
[CrossRef]

J. Junio, S. Park, M. W. Kim, and H. D. Ou-Yang, Solid State Commun. 150, 1003 (2010).
[CrossRef]

Kim, M. W.

J. Junio, S. Park, M. W. Kim, and H. D. Ou-Yang, Solid State Commun. 150, 1003 (2010).
[CrossRef]

Li, J.

Li, Z. Y.

L. Ling, F. Zhou, L. Huang, and Z. Y. Li, J. Appl. Phys. 108, 073110 (2010).
[CrossRef]

Li, Z.-Y.

Lin, Z.

J. Ng, Z. Lin, and C. T. Chan, Phys. Rev. Lett. 104, 103601 (2010).
[CrossRef]

Lin, Z. F.

Ling, L.

Mazolli, A.

A. Mazolli, P. A. M. Neto, and H. M. Nussenzveig, Proc. R. Soc. London A 459, 3021 (2003).
[CrossRef]

McCann, L. I.

L. I. McCann, M. Dykman, and B. Golding, Nature 402, 785 (1999).
[CrossRef]

Mitra, P. P.

K. Svoboda, P. P. Mitra, and S. M. Block, Proc. Natl. Acad. Sci. USA 91, 11782 (1994).
[CrossRef]

Mullin, T.

A. J. Wright, T. A. Wood, M. R. Dickinson, H. F. Gleeson, and T. Mullin, J. Mod. Opt. 50, 1521 (2003).

Neto, P. A. M.

A. Mazolli, P. A. M. Neto, and H. M. Nussenzveig, Proc. R. Soc. London A 459, 3021 (2003).
[CrossRef]

Ng, J.

Nussenzveig, H. M.

A. Mazolli, P. A. M. Neto, and H. M. Nussenzveig, Proc. R. Soc. London A 459, 3021 (2003).
[CrossRef]

Ohta, A. T.

P. Y. Chiou, A. T. Ohta, and M. C. Wu, Nature 436, 370 (2005).
[CrossRef]

Ou-Yang, H. D.

Park, S.

J. Junio, S. Park, M. W. Kim, and H. D. Ou-Yang, Solid State Commun. 150, 1003 (2010).
[CrossRef]

Pesce, G.

G. Pesce, G. Volpe, A. C. De Luca, G. Rusciano, and G. Volpe, Europhys. Lett. 86, 38002 (2009).
[CrossRef]

Pralle, A.

E. L. Florin, A. Pralle, E. H. K. Stelzer, and J. K. H. Horber, Appl. Phys. A 66, S75 (1998).
[CrossRef]

Roberts, N. W.

A. N. Grigorenko, N. W. Roberts, M. R. Dickinson, and Y. Zhang, Nat. Photonics 2, 365 (2008).
[CrossRef]

Rohrbach, A.

A. Rohrbach, Phys. Rev. Lett. 95, 168102 (2005).
[CrossRef]

Roichman, Y.

Y. Roichman, B. Sun, A. Stolarski, and D. G. Grier, Phys. Rev. Lett. 101, 128301 (2008).
[CrossRef]

Rusciano, G.

G. Pesce, G. Volpe, A. C. De Luca, G. Rusciano, and G. Volpe, Europhys. Lett. 86, 38002 (2009).
[CrossRef]

Simmons, R. M.

R. M. Simmons, J. T. Finer, S. Chu, and J. A. Spudich, Biophys. J. 70, 1813 (1996).
[CrossRef]

Spudich, J. A.

R. M. Simmons, J. T. Finer, S. Chu, and J. A. Spudich, Biophys. J. 70, 1813 (1996).
[CrossRef]

Stelzer, E. H. K.

E. L. Florin, A. Pralle, E. H. K. Stelzer, and J. K. H. Horber, Appl. Phys. A 66, S75 (1998).
[CrossRef]

Stolarski, A.

Y. Roichman, B. Sun, A. Stolarski, and D. G. Grier, Phys. Rev. Lett. 101, 128301 (2008).
[CrossRef]

Sun, B.

Y. Roichman, B. Sun, A. Stolarski, and D. G. Grier, Phys. Rev. Lett. 101, 128301 (2008).
[CrossRef]

Svoboda, K.

K. Svoboda, P. P. Mitra, and S. M. Block, Proc. Natl. Acad. Sci. USA 91, 11782 (1994).
[CrossRef]

Tischer, C.

P. Wu, R. Huang, C. Tischer, A. Jonas, and E.-L. Florin, Phys. Rev. Lett 103, 108101 (2009).
[CrossRef]

Volpe, G.

G. Pesce, G. Volpe, A. C. De Luca, G. Rusciano, and G. Volpe, Europhys. Lett. 86, 38002 (2009).
[CrossRef]

G. Pesce, G. Volpe, A. C. De Luca, G. Rusciano, and G. Volpe, Europhys. Lett. 86, 38002 (2009).
[CrossRef]

Wood, T. A.

A. J. Wright, T. A. Wood, M. R. Dickinson, H. F. Gleeson, and T. Mullin, J. Mod. Opt. 50, 1521 (2003).

Wright, A. J.

A. J. Wright, T. A. Wood, M. R. Dickinson, H. F. Gleeson, and T. Mullin, J. Mod. Opt. 50, 1521 (2003).

Wu, M. C.

P. Y. Chiou, A. T. Ohta, and M. C. Wu, Nature 436, 370 (2005).
[CrossRef]

Wu, P.

P. Wu, R. Huang, C. Tischer, A. Jonas, and E.-L. Florin, Phys. Rev. Lett 103, 108101 (2009).
[CrossRef]

Zhang, Y.

A. N. Grigorenko, N. W. Roberts, M. R. Dickinson, and Y. Zhang, Nat. Photonics 2, 365 (2008).
[CrossRef]

Zhou, F.

L. Ling, F. Zhou, L. Huang, and Z. Y. Li, J. Appl. Phys. 108, 073110 (2010).
[CrossRef]

Appl. Phys. A (1)

E. L. Florin, A. Pralle, E. H. K. Stelzer, and J. K. H. Horber, Appl. Phys. A 66, S75 (1998).
[CrossRef]

Biophys. J. (2)

A. Ashkin, Biophys. J. 61, 569 (1992).
[CrossRef]

R. M. Simmons, J. T. Finer, S. Chu, and J. A. Spudich, Biophys. J. 70, 1813 (1996).
[CrossRef]

Europhys. Lett. (1)

G. Pesce, G. Volpe, A. C. De Luca, G. Rusciano, and G. Volpe, Europhys. Lett. 86, 38002 (2009).
[CrossRef]

J. Appl. Phys. (2)

J. P. Barton and D. R. Alexander, J. Appl. Phys. 66, 2800 (1989).
[CrossRef]

L. Ling, F. Zhou, L. Huang, and Z. Y. Li, J. Appl. Phys. 108, 073110 (2010).
[CrossRef]

J. Mod. Opt. (1)

A. J. Wright, T. A. Wood, M. R. Dickinson, H. F. Gleeson, and T. Mullin, J. Mod. Opt. 50, 1521 (2003).

Nat. Photonics (1)

A. N. Grigorenko, N. W. Roberts, M. R. Dickinson, and Y. Zhang, Nat. Photonics 2, 365 (2008).
[CrossRef]

Nature (2)

P. Y. Chiou, A. T. Ohta, and M. C. Wu, Nature 436, 370 (2005).
[CrossRef]

L. I. McCann, M. Dykman, and B. Golding, Nature 402, 785 (1999).
[CrossRef]

Opt. Commun. (1)

Y. Harada and T. Asakura, Opt. Commun. 124, 529 (1996).
[CrossRef]

Opt. Express (1)

Opt. Lett. (2)

Phys. Rev. Lett (1)

P. Wu, R. Huang, C. Tischer, A. Jonas, and E.-L. Florin, Phys. Rev. Lett 103, 108101 (2009).
[CrossRef]

Phys. Rev. Lett. (3)

A. Rohrbach, Phys. Rev. Lett. 95, 168102 (2005).
[CrossRef]

J. Ng, Z. Lin, and C. T. Chan, Phys. Rev. Lett. 104, 103601 (2010).
[CrossRef]

Y. Roichman, B. Sun, A. Stolarski, and D. G. Grier, Phys. Rev. Lett. 101, 128301 (2008).
[CrossRef]

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

K. Svoboda, P. P. Mitra, and S. M. Block, Proc. Natl. Acad. Sci. USA 91, 11782 (1994).
[CrossRef]

Proc. R. Soc. London A (1)

A. Mazolli, P. A. M. Neto, and H. M. Nussenzveig, Proc. R. Soc. London A 459, 3021 (2003).
[CrossRef]

Rev. Sci. Instrum. (1)

K. Berg-Sorensen and H. Flyvbjerg, Rev. Sci. Instrum. 75, 594 (2004).
[CrossRef]

Solid State Commun. (1)

J. Junio, S. Park, M. W. Kim, and H. D. Ou-Yang, Solid State Commun. 150, 1003 (2010).
[CrossRef]

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Figures (3)

Fig. 1.
Fig. 1.

Schematic of the optical bottle setup (left) and a 3D confocal image (right) of nanoparticles in the vicinity of the focal point produced by the IR laser. DM, dichroic mirror; M, mirror; BE, beam expander; NA, numerical aperture; PMT, photon multiplier tube.

Fig. 2.
Fig. 2.

(a)–(c) XZ cross section fluorescence images for trapped PS particles of different sizes (images for 48 and 63 nm particles are not shown because they are similar to that for 100 nm particles). (d) XZ cross section for 200 nm PS in a low NA trap. (e) Normalized fluorescence intensity distributions along the Z axis. The particle number density is proportional to the fluorescence intensity at each location.

Fig. 3.
Fig. 3.

(a) Deconvoluted trapping potential-energy profile U(x,y,0) for 48 nm PS particles near the focal point of a 60 mW IR laser. (b) Trapping energies U(0) for PS spheres of sizes 48, 63, 100, 160, and 200 nm versus trapping power. (c) Calculated trapping energies per milliwatt of laser power using DDA along the X axis (solid squares), and the corresponding experimental results (empty circles). (d) Widths of trapping-potential profiles in the X (solid square) and Y (solid circle) directions fitted by a 2D Gaussian function for five differently sized PS particles. The two dashed lines are the DDA simulation results.

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