Abstract

We present an experimental and numerical study of the wavelength dependence, near resonance, of the optical tweezer trap stiffness on three different dye-doped 1μm polystyrene spheres with peak absorptions at λ=625, 775, and 840 nm. Experimentally, an increase in the trap stiffness of 35% on the red side of resonance was observed for the dye-doped spheres relative to polystyrene spheres without dye. Numerical simulations for spheres of different sizes, between 20 nm and 1μm, and for absorption strengths corresponding to peak extinction coefficient values between 0.0027 and 0.081 were also conducted. Numerical results showed a maximum increase in the trap stiffness of 35%, which is consistent with experimental results.

© 2009 Optical Society of America

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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
  32. K. C. Toussaint, M. Liu, M. Pelton, J. Pesic, M. J. Guffey, P. Guyot-Sionnest, and N. F. Scherer, “Plasmon resonance-based optical trapping of single and multiple Au nanoparticles,” Opt. Express 15, 12017-12029 (2007).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  35. M. J. Lang, P. M. Fordyce, A. M. Engh, K. C. Neuman, and S. M. Block, “Simultaneous, coincident optical trapping and single-molecule fluorescence,” Nat. Methods 1, 133-139 (2004).
    [CrossRef]
  36. K. Svoboda and S. M. Block, “Biological applications of optical forces,” Annu. Rev. Biophys. Biomol. Struct. 23, 247-285 (1994).
    [CrossRef] [PubMed]
  37. K. Visscher, S. P. Gross, and S. M. Block, “Construction of multiple-beam optical traps with nanometer-resolution position sensing,” IEEE J. Sel. Top. Quantum Electron. 2, 1066-1076 (1996).
    [CrossRef]
  38. L. Oddershede, S. Grego, S. F. Nørrelykke, and K. Berg-Sørensen, “Optical tweezers: probing biological surfaces,” Probe Microsc. 2, 129-137 (2001).
  39. G. Knöner, S. Parkin, T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Measurement of the index of refraction of single microparticles,” Phys. Rev. Lett. 97, 157402 (2006).
    [CrossRef] [PubMed]

2008

C. Selhuber-Unkel, I. Zins, O. Schubert, C. Sonnichsen, and L. B. Oddershede, “Quantitative optical trapping of single gold nanorods,” Nano Lett. 8, 2998-3003 (2008).
[CrossRef] [PubMed]

2007

M. Z. Liu, P. Guyot-Sionnest, T. W. Lee, and S. K. Gray, “Optical properties of rodlike and bipyramidal gold nanoparticles from three-dimensional computations,” Phys. Rev. B 76, 235428 (2007).
[CrossRef]

T. A. Nieminen, V. L. Y. Loke, A. B. Stilgoe, G. Knöner, A. M. Branczyk, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Optical tweezers computational toolbox,” J. Opt. A, Pure Appl. Opt. 9, S196-S203 (2007).
[CrossRef]

K. C. Toussaint, M. Liu, M. Pelton, J. Pesic, M. J. Guffey, P. Guyot-Sionnest, and N. F. Scherer, “Plasmon resonance-based optical trapping of single and multiple Au nanoparticles,” Opt. Express 15, 12017-12029 (2007).
[CrossRef] [PubMed]

2006

G. Knöner, S. Parkin, T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Measurement of the index of refraction of single microparticles,” Phys. Rev. Lett. 97, 157402 (2006).
[CrossRef] [PubMed]

2005

P. M. Hansen, V. K. Bhatia, N. Harrit, and L. Oddershede, “Expanding the optical trapping range of gold nanoparticles,” Nano Lett. 5, 1937-1942 (2005).
[CrossRef] [PubMed]

2004

M. J. Lang, P. M. Fordyce, A. M. Engh, K. C. Neuman, and S. M. Block, “Simultaneous, coincident optical trapping and single-molecule fluorescence,” Nat. Methods 1, 133-139 (2004).
[CrossRef]

T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Computational modelling of optical tweezers,” Proc. SPIE 5514, 514-523 (2004).
[CrossRef]

K. C. Neuman and S. M. Block, “Optical trapping,” Rev. Sci. Instrum. 75, 2787-2809 (2004).
[CrossRef]

2003

T. A. Nieminen, H. Rubinsztein-Dunlop, and N. R. Heckenberg, “Multipole expansion of strongly focused laser beams,” J. Quant. Spectrosc. Radiat. Transf. 79-80, 1005-1017 (2003).
[CrossRef]

T. A. Nieminen, H. Rubinsztein-Dunlop, and N. R. Heckenberg, “Calculation of the T-matrix: general considerations and application of the point-matching method,” J. Quant. Spectrosc. Radiat. Transf. 79-80, 1019-1029 (2003).
[CrossRef]

2002

N. Malagnino, G. Pesce, A. Sasso, and E. Arimondo, “Measurements of trapping efficiency and stiffness in optical tweezers,” Opt. Commun. 214, 15-24 (2002).
[CrossRef]

R. R. Agayan, F. Gittes, R. Kopelman, and C. F. Schmidt, “Optical trapping near resonance absorption,” Appl. Opt. 41, 2318-2327 (2002).
[CrossRef] [PubMed]

2001

L. Oddershede, S. Grego, S. F. Nørrelykke, and K. Berg-Sørensen, “Optical tweezers: probing biological surfaces,” Probe Microsc. 2, 129-137 (2001).

E. R. Dufresne, G. C. Spalding, M. T. Dearing, S. A. Sheets, and D. G. Grier, “Computer-generated holographic optical tweezer arrays,” Rev. Sci. Instrum. 72, 1810-1816 (2001).
[CrossRef]

T. A. Nieminen, H. Rubinsztein-Dunlop, N. R. Heckenberg, and A. I. Bishop, “Numerical modelling of optical trapping,” Comput. Phys. Commun. 142, 468-471 (2001).
[CrossRef]

A. D. Yoffe, “Semiconductor quantum dots and related systems: electronic, optical, luminescence and related properties of low dimensional systems,” Adv. Phys. 50, 1-208 (2001).
[CrossRef]

2000

S. Schultz, D. R. Smith, J. J. Mock, and D. A. Schultz, “Single-target molecule detection with nonbleaching multicolor optical immunolabels,” Proc. Natl. Acad. Sci. U.S.A. 97, 996-1001 (2000).
[CrossRef] [PubMed]

A. Ashkin, “History of optical trapping and manipulation of small-neutral particle, atoms, and molecules,” IEEE J. Sel. Top. Quantum Electron. 6, 841-856 (2000).
[CrossRef]

1999

S. J. Oldenburg, J. B. Jackson, S. L. Westcott, and N. J. Halas, “Infrared extinction properties of gold nanoshells,” Appl. Phys. Lett. 75, 2897-2899 (1999).
[CrossRef]

H. Kataura, Y. Kumazawa, Y. Maniwa, I. Umezu, S. Suzuki, Y. Ohtsuka, and Y. Achiba, “Optical properties of single-wall carbon nanotubes,” Synth. Met. 103, 2555-2558 (1999).
[CrossRef]

C. H. Choi, J. Ivanic, M. S. Gordon, and K. Ruedenberg, “Rapid and stable determination of rotation matrices between spherical harmonics by direct recursion,” J. Chem. Phys. 111, 8825-8831 (1999).
[CrossRef]

1997

M. D. Wang, H. Yin, R. Landick, J. Gelles, and S. M. Block, “Stretching DNA with optical tweezers,” Biophys. J. 72, 1335-1346 (1997).
[CrossRef] [PubMed]

1996

D. T. Chiu and R. N. Zare, “Biased diffusion, optical trapping, and manipulation of single molecules in solution,” J. Am. Chem. Soc. 118, 6512-6513 (1996).
[CrossRef]

K. Visscher, S. P. Gross, and S. M. Block, “Construction of multiple-beam optical traps with nanometer-resolution position sensing,” IEEE J. Sel. Top. Quantum Electron. 2, 1066-1076 (1996).
[CrossRef]

1994

K. Svoboda and S. M. Block, “Biological applications of optical forces,” Annu. Rev. Biophys. Biomol. Struct. 23, 247-285 (1994).
[CrossRef] [PubMed]

K. Svoboda and S. M. Block, “Optical trapping of metallic Rayleigh particles,” Opt. Lett. 19, 930-932 (1994).
[CrossRef] [PubMed]

K. F. Ren, G. Grehan, and G. Gouesbet, “Radiation pressure forces exerted on a particle arbitrarily located in a Gaussian-beam by using the generalized Lorenz-Mie theory, and associated resonance effects,” Opt. Commun. 108, 343-354 (1994).
[CrossRef]

1993

K. Svoboda, C. F. Schmidt, B. J. Schnapp, and S. M. Block, “Direct observation of kinesin stepping by optical trapping interferometry,” Nature 365, 721-727 (1993).
[CrossRef] [PubMed]

1992

A. Ashkin, “Forces of a single-beam gradient laser trap on a dielectric sphere in the ray optics regime,” Biophys. J. 61, 569-582 (1992).
[CrossRef] [PubMed]

1986

S. Chu, J. E. Bjorkholm, A. Ashkin, and A. Cable, “Experimental-observation of optically trapped atoms,” Phys. Rev. Lett. 57, 314-317 (1986).
[CrossRef] [PubMed]

A. Ashkin, J. M. Dziedzic, J. E. Bjorkholm, and S. Chu, “Observation of a single-beam gradient force optical trap for dielectric particles,” Opt. Lett. 11, 288-290 (1986).
[CrossRef] [PubMed]

1908

G. Mie, “Beiträge Zur Optik Trüber Medien, Speziell Kolloidaler Metallösungen,” Ann. Phys. (Leipzig) 25, 377-445 (1908).
[CrossRef]

Achiba, Y.

H. Kataura, Y. Kumazawa, Y. Maniwa, I. Umezu, S. Suzuki, Y. Ohtsuka, and Y. Achiba, “Optical properties of single-wall carbon nanotubes,” Synth. Met. 103, 2555-2558 (1999).
[CrossRef]

Agayan, R. R.

Arimondo, E.

N. Malagnino, G. Pesce, A. Sasso, and E. Arimondo, “Measurements of trapping efficiency and stiffness in optical tweezers,” Opt. Commun. 214, 15-24 (2002).
[CrossRef]

Ashkin, A.

A. Ashkin, “History of optical trapping and manipulation of small-neutral particle, atoms, and molecules,” IEEE J. Sel. Top. Quantum Electron. 6, 841-856 (2000).
[CrossRef]

A. Ashkin, “Forces of a single-beam gradient laser trap on a dielectric sphere in the ray optics regime,” Biophys. J. 61, 569-582 (1992).
[CrossRef] [PubMed]

S. Chu, J. E. Bjorkholm, A. Ashkin, and A. Cable, “Experimental-observation of optically trapped atoms,” Phys. Rev. Lett. 57, 314-317 (1986).
[CrossRef] [PubMed]

A. Ashkin, J. M. Dziedzic, J. E. Bjorkholm, and S. Chu, “Observation of a single-beam gradient force optical trap for dielectric particles,” Opt. Lett. 11, 288-290 (1986).
[CrossRef] [PubMed]

Berg-Sørensen, K.

L. Oddershede, S. Grego, S. F. Nørrelykke, and K. Berg-Sørensen, “Optical tweezers: probing biological surfaces,” Probe Microsc. 2, 129-137 (2001).

Bhatia, V. K.

P. M. Hansen, V. K. Bhatia, N. Harrit, and L. Oddershede, “Expanding the optical trapping range of gold nanoparticles,” Nano Lett. 5, 1937-1942 (2005).
[CrossRef] [PubMed]

Bishop, A. I.

T. A. Nieminen, H. Rubinsztein-Dunlop, N. R. Heckenberg, and A. I. Bishop, “Numerical modelling of optical trapping,” Comput. Phys. Commun. 142, 468-471 (2001).
[CrossRef]

Bjorkholm, J. E.

A. Ashkin, J. M. Dziedzic, J. E. Bjorkholm, and S. Chu, “Observation of a single-beam gradient force optical trap for dielectric particles,” Opt. Lett. 11, 288-290 (1986).
[CrossRef] [PubMed]

S. Chu, J. E. Bjorkholm, A. Ashkin, and A. Cable, “Experimental-observation of optically trapped atoms,” Phys. Rev. Lett. 57, 314-317 (1986).
[CrossRef] [PubMed]

Block, S. M.

M. J. Lang, P. M. Fordyce, A. M. Engh, K. C. Neuman, and S. M. Block, “Simultaneous, coincident optical trapping and single-molecule fluorescence,” Nat. Methods 1, 133-139 (2004).
[CrossRef]

K. C. Neuman and S. M. Block, “Optical trapping,” Rev. Sci. Instrum. 75, 2787-2809 (2004).
[CrossRef]

M. D. Wang, H. Yin, R. Landick, J. Gelles, and S. M. Block, “Stretching DNA with optical tweezers,” Biophys. J. 72, 1335-1346 (1997).
[CrossRef] [PubMed]

K. Visscher, S. P. Gross, and S. M. Block, “Construction of multiple-beam optical traps with nanometer-resolution position sensing,” IEEE J. Sel. Top. Quantum Electron. 2, 1066-1076 (1996).
[CrossRef]

K. Svoboda and S. M. Block, “Optical trapping of metallic Rayleigh particles,” Opt. Lett. 19, 930-932 (1994).
[CrossRef] [PubMed]

K. Svoboda and S. M. Block, “Biological applications of optical forces,” Annu. Rev. Biophys. Biomol. Struct. 23, 247-285 (1994).
[CrossRef] [PubMed]

K. Svoboda, C. F. Schmidt, B. J. Schnapp, and S. M. Block, “Direct observation of kinesin stepping by optical trapping interferometry,” Nature 365, 721-727 (1993).
[CrossRef] [PubMed]

Bohren, C. F.

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles, 1st ed. (Wiley, 1998).
[CrossRef]

Born, M.

M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, 2005).

Branczyk, A. M.

T. A. Nieminen, V. L. Y. Loke, A. B. Stilgoe, G. Knöner, A. M. Branczyk, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Optical tweezers computational toolbox,” J. Opt. A, Pure Appl. Opt. 9, S196-S203 (2007).
[CrossRef]

Cable, A.

S. Chu, J. E. Bjorkholm, A. Ashkin, and A. Cable, “Experimental-observation of optically trapped atoms,” Phys. Rev. Lett. 57, 314-317 (1986).
[CrossRef] [PubMed]

Chiu, D. T.

D. T. Chiu and R. N. Zare, “Biased diffusion, optical trapping, and manipulation of single molecules in solution,” J. Am. Chem. Soc. 118, 6512-6513 (1996).
[CrossRef]

Choi, C. H.

C. H. Choi, J. Ivanic, M. S. Gordon, and K. Ruedenberg, “Rapid and stable determination of rotation matrices between spherical harmonics by direct recursion,” J. Chem. Phys. 111, 8825-8831 (1999).
[CrossRef]

Chu, S.

S. Chu, J. E. Bjorkholm, A. Ashkin, and A. Cable, “Experimental-observation of optically trapped atoms,” Phys. Rev. Lett. 57, 314-317 (1986).
[CrossRef] [PubMed]

A. Ashkin, J. M. Dziedzic, J. E. Bjorkholm, and S. Chu, “Observation of a single-beam gradient force optical trap for dielectric particles,” Opt. Lett. 11, 288-290 (1986).
[CrossRef] [PubMed]

Dearing, M. T.

E. R. Dufresne, G. C. Spalding, M. T. Dearing, S. A. Sheets, and D. G. Grier, “Computer-generated holographic optical tweezer arrays,” Rev. Sci. Instrum. 72, 1810-1816 (2001).
[CrossRef]

Dufresne, E. R.

E. R. Dufresne, G. C. Spalding, M. T. Dearing, S. A. Sheets, and D. G. Grier, “Computer-generated holographic optical tweezer arrays,” Rev. Sci. Instrum. 72, 1810-1816 (2001).
[CrossRef]

Dziedzic, J. M.

Engh, A. M.

M. J. Lang, P. M. Fordyce, A. M. Engh, K. C. Neuman, and S. M. Block, “Simultaneous, coincident optical trapping and single-molecule fluorescence,” Nat. Methods 1, 133-139 (2004).
[CrossRef]

Fordyce, P. M.

M. J. Lang, P. M. Fordyce, A. M. Engh, K. C. Neuman, and S. M. Block, “Simultaneous, coincident optical trapping and single-molecule fluorescence,” Nat. Methods 1, 133-139 (2004).
[CrossRef]

Gelles, J.

M. D. Wang, H. Yin, R. Landick, J. Gelles, and S. M. Block, “Stretching DNA with optical tweezers,” Biophys. J. 72, 1335-1346 (1997).
[CrossRef] [PubMed]

Gittes, F.

Gordon, M. S.

C. H. Choi, J. Ivanic, M. S. Gordon, and K. Ruedenberg, “Rapid and stable determination of rotation matrices between spherical harmonics by direct recursion,” J. Chem. Phys. 111, 8825-8831 (1999).
[CrossRef]

Gouesbet, G.

K. F. Ren, G. Grehan, and G. Gouesbet, “Radiation pressure forces exerted on a particle arbitrarily located in a Gaussian-beam by using the generalized Lorenz-Mie theory, and associated resonance effects,” Opt. Commun. 108, 343-354 (1994).
[CrossRef]

Gray, S. K.

M. Z. Liu, P. Guyot-Sionnest, T. W. Lee, and S. K. Gray, “Optical properties of rodlike and bipyramidal gold nanoparticles from three-dimensional computations,” Phys. Rev. B 76, 235428 (2007).
[CrossRef]

Grego, S.

L. Oddershede, S. Grego, S. F. Nørrelykke, and K. Berg-Sørensen, “Optical tweezers: probing biological surfaces,” Probe Microsc. 2, 129-137 (2001).

Grehan, G.

K. F. Ren, G. Grehan, and G. Gouesbet, “Radiation pressure forces exerted on a particle arbitrarily located in a Gaussian-beam by using the generalized Lorenz-Mie theory, and associated resonance effects,” Opt. Commun. 108, 343-354 (1994).
[CrossRef]

Grier, D. G.

E. R. Dufresne, G. C. Spalding, M. T. Dearing, S. A. Sheets, and D. G. Grier, “Computer-generated holographic optical tweezer arrays,” Rev. Sci. Instrum. 72, 1810-1816 (2001).
[CrossRef]

Gross, S. P.

K. Visscher, S. P. Gross, and S. M. Block, “Construction of multiple-beam optical traps with nanometer-resolution position sensing,” IEEE J. Sel. Top. Quantum Electron. 2, 1066-1076 (1996).
[CrossRef]

Guffey, M. J.

Guyot-Sionnest, P.

K. C. Toussaint, M. Liu, M. Pelton, J. Pesic, M. J. Guffey, P. Guyot-Sionnest, and N. F. Scherer, “Plasmon resonance-based optical trapping of single and multiple Au nanoparticles,” Opt. Express 15, 12017-12029 (2007).
[CrossRef] [PubMed]

M. Z. Liu, P. Guyot-Sionnest, T. W. Lee, and S. K. Gray, “Optical properties of rodlike and bipyramidal gold nanoparticles from three-dimensional computations,” Phys. Rev. B 76, 235428 (2007).
[CrossRef]

Halas, N. J.

S. J. Oldenburg, J. B. Jackson, S. L. Westcott, and N. J. Halas, “Infrared extinction properties of gold nanoshells,” Appl. Phys. Lett. 75, 2897-2899 (1999).
[CrossRef]

Hansen, P. M.

P. M. Hansen, V. K. Bhatia, N. Harrit, and L. Oddershede, “Expanding the optical trapping range of gold nanoparticles,” Nano Lett. 5, 1937-1942 (2005).
[CrossRef] [PubMed]

Harrit, N.

P. M. Hansen, V. K. Bhatia, N. Harrit, and L. Oddershede, “Expanding the optical trapping range of gold nanoparticles,” Nano Lett. 5, 1937-1942 (2005).
[CrossRef] [PubMed]

Heckenberg, N. R.

T. A. Nieminen, V. L. Y. Loke, A. B. Stilgoe, G. Knöner, A. M. Branczyk, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Optical tweezers computational toolbox,” J. Opt. A, Pure Appl. Opt. 9, S196-S203 (2007).
[CrossRef]

G. Knöner, S. Parkin, T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Measurement of the index of refraction of single microparticles,” Phys. Rev. Lett. 97, 157402 (2006).
[CrossRef] [PubMed]

T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Computational modelling of optical tweezers,” Proc. SPIE 5514, 514-523 (2004).
[CrossRef]

T. A. Nieminen, H. Rubinsztein-Dunlop, and N. R. Heckenberg, “Calculation of the T-matrix: general considerations and application of the point-matching method,” J. Quant. Spectrosc. Radiat. Transf. 79-80, 1019-1029 (2003).
[CrossRef]

T. A. Nieminen, H. Rubinsztein-Dunlop, and N. R. Heckenberg, “Multipole expansion of strongly focused laser beams,” J. Quant. Spectrosc. Radiat. Transf. 79-80, 1005-1017 (2003).
[CrossRef]

T. A. Nieminen, H. Rubinsztein-Dunlop, N. R. Heckenberg, and A. I. Bishop, “Numerical modelling of optical trapping,” Comput. Phys. Commun. 142, 468-471 (2001).
[CrossRef]

Hect, B.

L. Novotny and B. Hect, Principles of Nano-Optics, 1st ed. (Cambridge U. Press, 2006).

Huffman, D. R.

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles, 1st ed. (Wiley, 1998).
[CrossRef]

Hulst, H. C. d.

H. C. d. Hulst, Light Scattering by Small Particles, 1st ed. (Dover, 1981).

Ivanic, J.

C. H. Choi, J. Ivanic, M. S. Gordon, and K. Ruedenberg, “Rapid and stable determination of rotation matrices between spherical harmonics by direct recursion,” J. Chem. Phys. 111, 8825-8831 (1999).
[CrossRef]

Jackson, J. B.

S. J. Oldenburg, J. B. Jackson, S. L. Westcott, and N. J. Halas, “Infrared extinction properties of gold nanoshells,” Appl. Phys. Lett. 75, 2897-2899 (1999).
[CrossRef]

Jackson, J. D.

J. D. Jackson, Classical Electrodynamics, 3rd ed. (Wiley, 1998).

Kataura, H.

H. Kataura, Y. Kumazawa, Y. Maniwa, I. Umezu, S. Suzuki, Y. Ohtsuka, and Y. Achiba, “Optical properties of single-wall carbon nanotubes,” Synth. Met. 103, 2555-2558 (1999).
[CrossRef]

Knöner, G.

T. A. Nieminen, V. L. Y. Loke, A. B. Stilgoe, G. Knöner, A. M. Branczyk, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Optical tweezers computational toolbox,” J. Opt. A, Pure Appl. Opt. 9, S196-S203 (2007).
[CrossRef]

G. Knöner, S. Parkin, T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Measurement of the index of refraction of single microparticles,” Phys. Rev. Lett. 97, 157402 (2006).
[CrossRef] [PubMed]

Kopelman, R.

Kumazawa, Y.

H. Kataura, Y. Kumazawa, Y. Maniwa, I. Umezu, S. Suzuki, Y. Ohtsuka, and Y. Achiba, “Optical properties of single-wall carbon nanotubes,” Synth. Met. 103, 2555-2558 (1999).
[CrossRef]

Lacis, A. A.

M. I. Mishchenko, L. D. Travis, and A. A. Lacis, Scattering, Absorption, and Emission of Light by Small Paticles, 1st ed. (Cambridge U. Press, 2002).

Landick, R.

M. D. Wang, H. Yin, R. Landick, J. Gelles, and S. M. Block, “Stretching DNA with optical tweezers,” Biophys. J. 72, 1335-1346 (1997).
[CrossRef] [PubMed]

Lang, M. J.

M. J. Lang, P. M. Fordyce, A. M. Engh, K. C. Neuman, and S. M. Block, “Simultaneous, coincident optical trapping and single-molecule fluorescence,” Nat. Methods 1, 133-139 (2004).
[CrossRef]

Lee, T. W.

M. Z. Liu, P. Guyot-Sionnest, T. W. Lee, and S. K. Gray, “Optical properties of rodlike and bipyramidal gold nanoparticles from three-dimensional computations,” Phys. Rev. B 76, 235428 (2007).
[CrossRef]

Liu, M.

Liu, M. Z.

M. Z. Liu, P. Guyot-Sionnest, T. W. Lee, and S. K. Gray, “Optical properties of rodlike and bipyramidal gold nanoparticles from three-dimensional computations,” Phys. Rev. B 76, 235428 (2007).
[CrossRef]

Loke, V. L. Y.

T. A. Nieminen, V. L. Y. Loke, A. B. Stilgoe, G. Knöner, A. M. Branczyk, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Optical tweezers computational toolbox,” J. Opt. A, Pure Appl. Opt. 9, S196-S203 (2007).
[CrossRef]

Malagnino, N.

N. Malagnino, G. Pesce, A. Sasso, and E. Arimondo, “Measurements of trapping efficiency and stiffness in optical tweezers,” Opt. Commun. 214, 15-24 (2002).
[CrossRef]

Maniwa, Y.

H. Kataura, Y. Kumazawa, Y. Maniwa, I. Umezu, S. Suzuki, Y. Ohtsuka, and Y. Achiba, “Optical properties of single-wall carbon nanotubes,” Synth. Met. 103, 2555-2558 (1999).
[CrossRef]

Mie, G.

G. Mie, “Beiträge Zur Optik Trüber Medien, Speziell Kolloidaler Metallösungen,” Ann. Phys. (Leipzig) 25, 377-445 (1908).
[CrossRef]

Mishchenko, M. I.

M. I. Mishchenko, L. D. Travis, and A. A. Lacis, Scattering, Absorption, and Emission of Light by Small Paticles, 1st ed. (Cambridge U. Press, 2002).

Mock, J. J.

S. Schultz, D. R. Smith, J. J. Mock, and D. A. Schultz, “Single-target molecule detection with nonbleaching multicolor optical immunolabels,” Proc. Natl. Acad. Sci. U.S.A. 97, 996-1001 (2000).
[CrossRef] [PubMed]

Neuman, K. C.

K. C. Neuman and S. M. Block, “Optical trapping,” Rev. Sci. Instrum. 75, 2787-2809 (2004).
[CrossRef]

M. J. Lang, P. M. Fordyce, A. M. Engh, K. C. Neuman, and S. M. Block, “Simultaneous, coincident optical trapping and single-molecule fluorescence,” Nat. Methods 1, 133-139 (2004).
[CrossRef]

Nieminen, T. A.

T. A. Nieminen, V. L. Y. Loke, A. B. Stilgoe, G. Knöner, A. M. Branczyk, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Optical tweezers computational toolbox,” J. Opt. A, Pure Appl. Opt. 9, S196-S203 (2007).
[CrossRef]

G. Knöner, S. Parkin, T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Measurement of the index of refraction of single microparticles,” Phys. Rev. Lett. 97, 157402 (2006).
[CrossRef] [PubMed]

T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Computational modelling of optical tweezers,” Proc. SPIE 5514, 514-523 (2004).
[CrossRef]

T. A. Nieminen, H. Rubinsztein-Dunlop, and N. R. Heckenberg, “Calculation of the T-matrix: general considerations and application of the point-matching method,” J. Quant. Spectrosc. Radiat. Transf. 79-80, 1019-1029 (2003).
[CrossRef]

T. A. Nieminen, H. Rubinsztein-Dunlop, and N. R. Heckenberg, “Multipole expansion of strongly focused laser beams,” J. Quant. Spectrosc. Radiat. Transf. 79-80, 1005-1017 (2003).
[CrossRef]

T. A. Nieminen, H. Rubinsztein-Dunlop, N. R. Heckenberg, and A. I. Bishop, “Numerical modelling of optical trapping,” Comput. Phys. Commun. 142, 468-471 (2001).
[CrossRef]

Nørrelykke, S. F.

L. Oddershede, S. Grego, S. F. Nørrelykke, and K. Berg-Sørensen, “Optical tweezers: probing biological surfaces,” Probe Microsc. 2, 129-137 (2001).

Novotny, L.

L. Novotny and B. Hect, Principles of Nano-Optics, 1st ed. (Cambridge U. Press, 2006).

Oddershede, L.

P. M. Hansen, V. K. Bhatia, N. Harrit, and L. Oddershede, “Expanding the optical trapping range of gold nanoparticles,” Nano Lett. 5, 1937-1942 (2005).
[CrossRef] [PubMed]

L. Oddershede, S. Grego, S. F. Nørrelykke, and K. Berg-Sørensen, “Optical tweezers: probing biological surfaces,” Probe Microsc. 2, 129-137 (2001).

Oddershede, L. B.

C. Selhuber-Unkel, I. Zins, O. Schubert, C. Sonnichsen, and L. B. Oddershede, “Quantitative optical trapping of single gold nanorods,” Nano Lett. 8, 2998-3003 (2008).
[CrossRef] [PubMed]

Ohtsuka, Y.

H. Kataura, Y. Kumazawa, Y. Maniwa, I. Umezu, S. Suzuki, Y. Ohtsuka, and Y. Achiba, “Optical properties of single-wall carbon nanotubes,” Synth. Met. 103, 2555-2558 (1999).
[CrossRef]

Oldenburg, S. J.

S. J. Oldenburg, J. B. Jackson, S. L. Westcott, and N. J. Halas, “Infrared extinction properties of gold nanoshells,” Appl. Phys. Lett. 75, 2897-2899 (1999).
[CrossRef]

Parkin, S.

G. Knöner, S. Parkin, T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Measurement of the index of refraction of single microparticles,” Phys. Rev. Lett. 97, 157402 (2006).
[CrossRef] [PubMed]

Pelton, M.

Pesce, G.

N. Malagnino, G. Pesce, A. Sasso, and E. Arimondo, “Measurements of trapping efficiency and stiffness in optical tweezers,” Opt. Commun. 214, 15-24 (2002).
[CrossRef]

Pesic, J.

Ren, K. F.

K. F. Ren, G. Grehan, and G. Gouesbet, “Radiation pressure forces exerted on a particle arbitrarily located in a Gaussian-beam by using the generalized Lorenz-Mie theory, and associated resonance effects,” Opt. Commun. 108, 343-354 (1994).
[CrossRef]

Rubinsztein-Dunlop, H.

T. A. Nieminen, V. L. Y. Loke, A. B. Stilgoe, G. Knöner, A. M. Branczyk, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Optical tweezers computational toolbox,” J. Opt. A, Pure Appl. Opt. 9, S196-S203 (2007).
[CrossRef]

G. Knöner, S. Parkin, T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Measurement of the index of refraction of single microparticles,” Phys. Rev. Lett. 97, 157402 (2006).
[CrossRef] [PubMed]

T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Computational modelling of optical tweezers,” Proc. SPIE 5514, 514-523 (2004).
[CrossRef]

T. A. Nieminen, H. Rubinsztein-Dunlop, and N. R. Heckenberg, “Calculation of the T-matrix: general considerations and application of the point-matching method,” J. Quant. Spectrosc. Radiat. Transf. 79-80, 1019-1029 (2003).
[CrossRef]

T. A. Nieminen, H. Rubinsztein-Dunlop, and N. R. Heckenberg, “Multipole expansion of strongly focused laser beams,” J. Quant. Spectrosc. Radiat. Transf. 79-80, 1005-1017 (2003).
[CrossRef]

T. A. Nieminen, H. Rubinsztein-Dunlop, N. R. Heckenberg, and A. I. Bishop, “Numerical modelling of optical trapping,” Comput. Phys. Commun. 142, 468-471 (2001).
[CrossRef]

Ruedenberg, K.

C. H. Choi, J. Ivanic, M. S. Gordon, and K. Ruedenberg, “Rapid and stable determination of rotation matrices between spherical harmonics by direct recursion,” J. Chem. Phys. 111, 8825-8831 (1999).
[CrossRef]

Sasso, A.

N. Malagnino, G. Pesce, A. Sasso, and E. Arimondo, “Measurements of trapping efficiency and stiffness in optical tweezers,” Opt. Commun. 214, 15-24 (2002).
[CrossRef]

Scherer, N. F.

Schmidt, C. F.

R. R. Agayan, F. Gittes, R. Kopelman, and C. F. Schmidt, “Optical trapping near resonance absorption,” Appl. Opt. 41, 2318-2327 (2002).
[CrossRef] [PubMed]

K. Svoboda, C. F. Schmidt, B. J. Schnapp, and S. M. Block, “Direct observation of kinesin stepping by optical trapping interferometry,” Nature 365, 721-727 (1993).
[CrossRef] [PubMed]

Schnapp, B. J.

K. Svoboda, C. F. Schmidt, B. J. Schnapp, and S. M. Block, “Direct observation of kinesin stepping by optical trapping interferometry,” Nature 365, 721-727 (1993).
[CrossRef] [PubMed]

Schubert, O.

C. Selhuber-Unkel, I. Zins, O. Schubert, C. Sonnichsen, and L. B. Oddershede, “Quantitative optical trapping of single gold nanorods,” Nano Lett. 8, 2998-3003 (2008).
[CrossRef] [PubMed]

Schultz, D. A.

S. Schultz, D. R. Smith, J. J. Mock, and D. A. Schultz, “Single-target molecule detection with nonbleaching multicolor optical immunolabels,” Proc. Natl. Acad. Sci. U.S.A. 97, 996-1001 (2000).
[CrossRef] [PubMed]

Schultz, S.

S. Schultz, D. R. Smith, J. J. Mock, and D. A. Schultz, “Single-target molecule detection with nonbleaching multicolor optical immunolabels,” Proc. Natl. Acad. Sci. U.S.A. 97, 996-1001 (2000).
[CrossRef] [PubMed]

Selhuber-Unkel, C.

C. Selhuber-Unkel, I. Zins, O. Schubert, C. Sonnichsen, and L. B. Oddershede, “Quantitative optical trapping of single gold nanorods,” Nano Lett. 8, 2998-3003 (2008).
[CrossRef] [PubMed]

Sheets, S. A.

E. R. Dufresne, G. C. Spalding, M. T. Dearing, S. A. Sheets, and D. G. Grier, “Computer-generated holographic optical tweezer arrays,” Rev. Sci. Instrum. 72, 1810-1816 (2001).
[CrossRef]

Smith, D. R.

S. Schultz, D. R. Smith, J. J. Mock, and D. A. Schultz, “Single-target molecule detection with nonbleaching multicolor optical immunolabels,” Proc. Natl. Acad. Sci. U.S.A. 97, 996-1001 (2000).
[CrossRef] [PubMed]

Sonnichsen, C.

C. Selhuber-Unkel, I. Zins, O. Schubert, C. Sonnichsen, and L. B. Oddershede, “Quantitative optical trapping of single gold nanorods,” Nano Lett. 8, 2998-3003 (2008).
[CrossRef] [PubMed]

Spalding, G. C.

E. R. Dufresne, G. C. Spalding, M. T. Dearing, S. A. Sheets, and D. G. Grier, “Computer-generated holographic optical tweezer arrays,” Rev. Sci. Instrum. 72, 1810-1816 (2001).
[CrossRef]

Stilgoe, A. B.

T. A. Nieminen, V. L. Y. Loke, A. B. Stilgoe, G. Knöner, A. M. Branczyk, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Optical tweezers computational toolbox,” J. Opt. A, Pure Appl. Opt. 9, S196-S203 (2007).
[CrossRef]

Suzuki, S.

H. Kataura, Y. Kumazawa, Y. Maniwa, I. Umezu, S. Suzuki, Y. Ohtsuka, and Y. Achiba, “Optical properties of single-wall carbon nanotubes,” Synth. Met. 103, 2555-2558 (1999).
[CrossRef]

Svoboda, K.

K. Svoboda and S. M. Block, “Optical trapping of metallic Rayleigh particles,” Opt. Lett. 19, 930-932 (1994).
[CrossRef] [PubMed]

K. Svoboda and S. M. Block, “Biological applications of optical forces,” Annu. Rev. Biophys. Biomol. Struct. 23, 247-285 (1994).
[CrossRef] [PubMed]

K. Svoboda, C. F. Schmidt, B. J. Schnapp, and S. M. Block, “Direct observation of kinesin stepping by optical trapping interferometry,” Nature 365, 721-727 (1993).
[CrossRef] [PubMed]

Toussaint, K. C.

Travis, L. D.

M. I. Mishchenko, L. D. Travis, and A. A. Lacis, Scattering, Absorption, and Emission of Light by Small Paticles, 1st ed. (Cambridge U. Press, 2002).

Umezu, I.

H. Kataura, Y. Kumazawa, Y. Maniwa, I. Umezu, S. Suzuki, Y. Ohtsuka, and Y. Achiba, “Optical properties of single-wall carbon nanotubes,” Synth. Met. 103, 2555-2558 (1999).
[CrossRef]

Visscher, K.

K. Visscher, S. P. Gross, and S. M. Block, “Construction of multiple-beam optical traps with nanometer-resolution position sensing,” IEEE J. Sel. Top. Quantum Electron. 2, 1066-1076 (1996).
[CrossRef]

Wang, M. D.

M. D. Wang, H. Yin, R. Landick, J. Gelles, and S. M. Block, “Stretching DNA with optical tweezers,” Biophys. J. 72, 1335-1346 (1997).
[CrossRef] [PubMed]

Westcott, S. L.

S. J. Oldenburg, J. B. Jackson, S. L. Westcott, and N. J. Halas, “Infrared extinction properties of gold nanoshells,” Appl. Phys. Lett. 75, 2897-2899 (1999).
[CrossRef]

Wolf, E.

M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, 2005).

Yin, H.

M. D. Wang, H. Yin, R. Landick, J. Gelles, and S. M. Block, “Stretching DNA with optical tweezers,” Biophys. J. 72, 1335-1346 (1997).
[CrossRef] [PubMed]

Yoffe, A. D.

A. D. Yoffe, “Semiconductor quantum dots and related systems: electronic, optical, luminescence and related properties of low dimensional systems,” Adv. Phys. 50, 1-208 (2001).
[CrossRef]

Zare, R. N.

D. T. Chiu and R. N. Zare, “Biased diffusion, optical trapping, and manipulation of single molecules in solution,” J. Am. Chem. Soc. 118, 6512-6513 (1996).
[CrossRef]

Zins, I.

C. Selhuber-Unkel, I. Zins, O. Schubert, C. Sonnichsen, and L. B. Oddershede, “Quantitative optical trapping of single gold nanorods,” Nano Lett. 8, 2998-3003 (2008).
[CrossRef] [PubMed]

Adv. Phys.

A. D. Yoffe, “Semiconductor quantum dots and related systems: electronic, optical, luminescence and related properties of low dimensional systems,” Adv. Phys. 50, 1-208 (2001).
[CrossRef]

Ann. Phys. (Leipzig)

G. Mie, “Beiträge Zur Optik Trüber Medien, Speziell Kolloidaler Metallösungen,” Ann. Phys. (Leipzig) 25, 377-445 (1908).
[CrossRef]

Annu. Rev. Biophys. Biomol. Struct.

K. Svoboda and S. M. Block, “Biological applications of optical forces,” Annu. Rev. Biophys. Biomol. Struct. 23, 247-285 (1994).
[CrossRef] [PubMed]

Appl. Opt.

Appl. Phys. Lett.

S. J. Oldenburg, J. B. Jackson, S. L. Westcott, and N. J. Halas, “Infrared extinction properties of gold nanoshells,” Appl. Phys. Lett. 75, 2897-2899 (1999).
[CrossRef]

Biophys. J.

M. D. Wang, H. Yin, R. Landick, J. Gelles, and S. M. Block, “Stretching DNA with optical tweezers,” Biophys. J. 72, 1335-1346 (1997).
[CrossRef] [PubMed]

A. Ashkin, “Forces of a single-beam gradient laser trap on a dielectric sphere in the ray optics regime,” Biophys. J. 61, 569-582 (1992).
[CrossRef] [PubMed]

Comput. Phys. Commun.

T. A. Nieminen, H. Rubinsztein-Dunlop, N. R. Heckenberg, and A. I. Bishop, “Numerical modelling of optical trapping,” Comput. Phys. Commun. 142, 468-471 (2001).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron.

K. Visscher, S. P. Gross, and S. M. Block, “Construction of multiple-beam optical traps with nanometer-resolution position sensing,” IEEE J. Sel. Top. Quantum Electron. 2, 1066-1076 (1996).
[CrossRef]

A. Ashkin, “History of optical trapping and manipulation of small-neutral particle, atoms, and molecules,” IEEE J. Sel. Top. Quantum Electron. 6, 841-856 (2000).
[CrossRef]

J. Am. Chem. Soc.

D. T. Chiu and R. N. Zare, “Biased diffusion, optical trapping, and manipulation of single molecules in solution,” J. Am. Chem. Soc. 118, 6512-6513 (1996).
[CrossRef]

J. Chem. Phys.

C. H. Choi, J. Ivanic, M. S. Gordon, and K. Ruedenberg, “Rapid and stable determination of rotation matrices between spherical harmonics by direct recursion,” J. Chem. Phys. 111, 8825-8831 (1999).
[CrossRef]

J. Opt. A, Pure Appl. Opt.

T. A. Nieminen, V. L. Y. Loke, A. B. Stilgoe, G. Knöner, A. M. Branczyk, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Optical tweezers computational toolbox,” J. Opt. A, Pure Appl. Opt. 9, S196-S203 (2007).
[CrossRef]

J. Quant. Spectrosc. Radiat. Transf.

T. A. Nieminen, H. Rubinsztein-Dunlop, and N. R. Heckenberg, “Multipole expansion of strongly focused laser beams,” J. Quant. Spectrosc. Radiat. Transf. 79-80, 1005-1017 (2003).
[CrossRef]

T. A. Nieminen, H. Rubinsztein-Dunlop, and N. R. Heckenberg, “Calculation of the T-matrix: general considerations and application of the point-matching method,” J. Quant. Spectrosc. Radiat. Transf. 79-80, 1019-1029 (2003).
[CrossRef]

Nano Lett.

C. Selhuber-Unkel, I. Zins, O. Schubert, C. Sonnichsen, and L. B. Oddershede, “Quantitative optical trapping of single gold nanorods,” Nano Lett. 8, 2998-3003 (2008).
[CrossRef] [PubMed]

P. M. Hansen, V. K. Bhatia, N. Harrit, and L. Oddershede, “Expanding the optical trapping range of gold nanoparticles,” Nano Lett. 5, 1937-1942 (2005).
[CrossRef] [PubMed]

Nat. Methods

M. J. Lang, P. M. Fordyce, A. M. Engh, K. C. Neuman, and S. M. Block, “Simultaneous, coincident optical trapping and single-molecule fluorescence,” Nat. Methods 1, 133-139 (2004).
[CrossRef]

Nature

K. Svoboda, C. F. Schmidt, B. J. Schnapp, and S. M. Block, “Direct observation of kinesin stepping by optical trapping interferometry,” Nature 365, 721-727 (1993).
[CrossRef] [PubMed]

Opt. Commun.

K. F. Ren, G. Grehan, and G. Gouesbet, “Radiation pressure forces exerted on a particle arbitrarily located in a Gaussian-beam by using the generalized Lorenz-Mie theory, and associated resonance effects,” Opt. Commun. 108, 343-354 (1994).
[CrossRef]

N. Malagnino, G. Pesce, A. Sasso, and E. Arimondo, “Measurements of trapping efficiency and stiffness in optical tweezers,” Opt. Commun. 214, 15-24 (2002).
[CrossRef]

Opt. Express

Opt. Lett.

Phys. Rev. B

M. Z. Liu, P. Guyot-Sionnest, T. W. Lee, and S. K. Gray, “Optical properties of rodlike and bipyramidal gold nanoparticles from three-dimensional computations,” Phys. Rev. B 76, 235428 (2007).
[CrossRef]

Phys. Rev. Lett.

S. Chu, J. E. Bjorkholm, A. Ashkin, and A. Cable, “Experimental-observation of optically trapped atoms,” Phys. Rev. Lett. 57, 314-317 (1986).
[CrossRef] [PubMed]

G. Knöner, S. Parkin, T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Measurement of the index of refraction of single microparticles,” Phys. Rev. Lett. 97, 157402 (2006).
[CrossRef] [PubMed]

Probe Microsc.

L. Oddershede, S. Grego, S. F. Nørrelykke, and K. Berg-Sørensen, “Optical tweezers: probing biological surfaces,” Probe Microsc. 2, 129-137 (2001).

Proc. Natl. Acad. Sci. U.S.A.

S. Schultz, D. R. Smith, J. J. Mock, and D. A. Schultz, “Single-target molecule detection with nonbleaching multicolor optical immunolabels,” Proc. Natl. Acad. Sci. U.S.A. 97, 996-1001 (2000).
[CrossRef] [PubMed]

Proc. SPIE

T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Computational modelling of optical tweezers,” Proc. SPIE 5514, 514-523 (2004).
[CrossRef]

Rev. Sci. Instrum.

E. R. Dufresne, G. C. Spalding, M. T. Dearing, S. A. Sheets, and D. G. Grier, “Computer-generated holographic optical tweezer arrays,” Rev. Sci. Instrum. 72, 1810-1816 (2001).
[CrossRef]

K. C. Neuman and S. M. Block, “Optical trapping,” Rev. Sci. Instrum. 75, 2787-2809 (2004).
[CrossRef]

Synth. Met.

H. Kataura, Y. Kumazawa, Y. Maniwa, I. Umezu, S. Suzuki, Y. Ohtsuka, and Y. Achiba, “Optical properties of single-wall carbon nanotubes,” Synth. Met. 103, 2555-2558 (1999).
[CrossRef]

Other

H. C. d. Hulst, Light Scattering by Small Particles, 1st ed. (Dover, 1981).

M. I. Mishchenko, L. D. Travis, and A. A. Lacis, Scattering, Absorption, and Emission of Light by Small Paticles, 1st ed. (Cambridge U. Press, 2002).

M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, 2005).

L. Novotny and B. Hect, Principles of Nano-Optics, 1st ed. (Cambridge U. Press, 2006).

J. D. Jackson, Classical Electrodynamics, 3rd ed. (Wiley, 1998).

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles, 1st ed. (Wiley, 1998).
[CrossRef]

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Figures (11)

Fig. 1
Fig. 1

(a) Real and imaginary parts (n and κ, respectively) of the complex index of refraction near resonance, obtained from the classic electron oscillator model of the dielectric constant. (b) The real and imaginary parts of the polarizability, α in units of meters cubed near resonance, calculated using the complex index of refraction in (a), and the Clausius–Mossotti equation [Eq. (6)]. Both (a) and (b) show that there is an increase in either the real part of the index of refraction (i.e., in the refractive index n) or the real part of the polarizability on the red side of the resonance, which can be related to the forces acting on a particle in an optical trap.

Fig. 2
Fig. 2

Extinction spectra of the dyes used in the 775 and 840 nm spheres in a dilute acetone solution, with peak absorption at 760 and 825 nm, respectively. The inset shows the spectrum of a Di H 2 O suspension of the 840 nm spheres, which has a broadened peak that is redshifted by 15   nm , as compared with the same dye in the acetone solution.

Fig. 3
Fig. 3

Experimental setup used to measure optical tweezer trap strength. Optical tweezer trapping was achieved by focusing either cw Ti:sapphire laser light (tunable between 750 and 840 nm) or diode laser light (980 nm) with a high NA objective. A detection laser (He–Ne) and a quadrant photodetector were used to measure the suppressed Brownian motion of a particle in the trap, from which the trap strength can be obtained. Notations: L, lenses; D, dichroic mirrors; and M, mirrors.

Fig. 4
Fig. 4

Example of the experimental data used for trap stiffness measurements. (a) Time series data of suppressed Brownian motion of a 1 μ m dye-doped polystyrene sphere in the optical trap at the wavelength of 810 nm at 28 mW. The trap stiffness is obtained using the standard deviation of the data and equipartition theorem. (b) The power spectrum of the Brownian motion data in (a). The trap stiffness is obtained from the corner frequency, f c , of the spectrum, which in this case is f c = 136.0   Hz .

Fig. 5
Fig. 5

Experimental results for the measurements of the trap stiffness near resonance. The wavelength dependence of the trap stiffness values (k dyed) is shown for 625, 775, and 840 nm dye-doped polystyrene spheres, all normalized by those measured on transparent spheres (k transparent) under the same conditions. An enhancement in the trap stiffness is a value greater than 1. For the 625 and 775 nm spheres, variations of the trap stiffness were within 10 % near resonance, which was within our experimental uncertainty. For the 840 nm spheres, a large effect due to the dye was observed, as no stable trapping could be achieved at 750–840 nm, but at 980 nm stable trapping was observed with a trap stiffness enhancement of 35 % .

Fig. 6
Fig. 6

Wavelength dependence of the (a) imaginary and (b) real parts of the complex index of refraction, calculated by applying the classic electron oscillator model to the case of the 775 nm spheres used in our experiments. (a) Values for the imaginary part of the index of refraction, κ, obtained from the manufacturer of the dye in the 775 nm spheres (diamonds), fit using the classic electron oscillator model of the dielectric constant (curve). (b) The corresponding refractive index values n calculated using the parameters extracted from the fit of the κ values in (a) and Eqs. (10, 12).

Fig. 7
Fig. 7

Numerically calculated trap efficiency Q in the (a) z direction ( Q z ) and the (b) x direction ( Q x ) as a function of position (z and x respectively) for the 775 nm spheres with κ peak = 0.054 and a diameter of 1 μ m . The laser beam propagation is along the z axis, as indicated in the inset of (a). The trap stiffness k z is determined from the slope of the Q z ( z ) at z = z e q , as illustrated in (a) for the case of λ = 596   nm . At λ = 641   nm , stable trapping is not possible (i.e., z e q is not achieved), and therefore in (b) the Q x data are shown only for λ = 596   nm . The trap stiffness k x is calculated from the slope of Q x ( x ) at x = 0 (i.e., in the center of the beam).

Fig. 8
Fig. 8

Numerically calculated wavelength dependence of the trap stiffness k x and k z for the 775 nm spheres with κ peak = 0.054 and a diameter of 1 μ m (k-dyed), normalized by the corresponding values calculated for the 1 μ m transparent polystyrene spheres (k-transparent). Stable trapping was not possible near resonance, which corresponds to zero values for k x and k z .

Fig. 9
Fig. 9

Numerically calculated dependence of the trap stiffness k x and k z , on the relative refractive index m for nonabsorbing (transparent) spheres with diameters of (a) 1 μ m and (b) 20 nm, trapped at λ = 780   nm . At m > 1.39 , stable trapping is not possible at this wavelength for 1 μ m spheres ( k z = 0 ) in (a), but is possible for 20 nm spheres in (b). Structure seen in (a) is due to Mie resonances.

Fig. 10
Fig. 10

(a) Numerically calculated sphere diameter dependence of the trap stiffness k x for the 775 nm spheres ( κ peak = 0.054 ). Results are shown for several wavelengths near the resonance. At small sphere sizes, the trap stiffness increases with the diameter ( d ) as k x d 3 , as expected for Rayleigh particles. At λ = 775   nm (692 nm), stable trapping cannot be achieved for spheres larger than 60 nm (300 nm). (b) Numerically calculated wavelength dependence of the trap stiffness for the 775 nm spheres with κ peak = 0.054 ( k x -dyed), normalized by the corresponding values calculated for transparent polystyrene spheres ( k x -transparent). Results are shown for various sphere diameters. At the diameter of 20 nm, stable trapping is possible at all wavelengths near the resonance, which is not the case for larger spheres. The largest enhancement of 35 % is achieved in 1 μ m spheres at λ = 836   nm .

Fig. 11
Fig. 11

Numerically calculated wavelength dependence of the trap stiffness for the 775 nm spheres with a diameter of 1 μ m ( k x -dyed), normalized by the corresponding values calculated for 1 μ m transparent polystyrene spheres ( k x -transparent). Results are shown for different peak values of the extinction coefficient ( κ peak ) . Stable trapping is not possible for the larger values of the extinction coefficient. The largest enhancement of 35 % on the red side of the resonance occurs for κ peak = 0.054 .

Equations (12)

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E in = i = 1 j = i i a i j M i j ( 2 ) ( k m r ) + b i j N i j ( 2 ) ( k m r ) ,
E out = i = 1 j = i i p i j M i j ( 1 ) ( k m r ) + q i j N i j ( 1 ) ( k m r ) ,
F z = 2 n m c i = 1 j = i i j i ( i + 1 ) Re ( a i j b i j p i j q i j ) 1 i + 1 [ i ( i + 2 ) ( i j 1 ) ( i + j + 1 ) ( 2 i + 1 ) ( 2 i + 3 ) ] 1 / 2 Re ( a i j a i + 1 , j + b i j b i + 1 , j p i j p i + 1 , j + q i j q i + 1 , j ) ,
F scat = k ̂ ( n m c ) C s c a t I = k ̂ 4 π 3 n m c ε o 2 λ 4 | α | 2 I ,
F abs = k ̂ ( n m c ) C a b s I = k ̂ 2 π c ε o λ [ Im ( α ) ] I ,
α = 4 π ε m ( d 2 ) 3 ( m 2 1 m 2 + 1 ) ,
F grad = Re ( α ) c n m ε o I .
1 2 k x σ 2 = 1 2 k B T ,
| x ̃ ( f ) 2 | = k B T π 2 β ( f c 2 + f 2 ) ,
Re [ ε ̃ ( ω ) / ε o ] = ε b + i f i ω i 2 ω 2 ( ω i 2 ω 2 ) 2 + ( γ i ω ) 2 ,
Im [ ε ̃ ( ω ) / ε o ] = i f i γ i ω ( ω i 2 ω 2 ) 2 + ( γ i ω ) 2 ,
n ̃ ( ω ) = n ( ω ) + i κ ( ω ) = ε ̃ ( ω ) / ε o ,

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