Abstract

We examine the size dependence of gradient and nongradient contributions to the optically induced force on single, isolated nanometer-sized silver particles in water under plane-wave illumination. Using a recently developed method based on discrete-dipole approximation (DDA), we find that all contributions scale linearly with volume in this regime. This dependence can be rationalized by using semiempirical considerations based on the Mie–Debye theory. We also comment on a common approach to determining conservative and nonconservative force contributions on a single particle in an externally applied field. Our analysis suggests that the Mie–Debye theory cross sections cannot be used to evaluate conservative and nonconservative contributions to the force. Finally, we comment on aspects of the relationship between DDA and continuum-based treatments of optical force phenomena and find that inclusion of multiple scattering effects are essential to an understanding of the size dependence of the forces on mesoscopic particles.

© 2006 Optical Society of America

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    [CrossRef]
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    [CrossRef] [PubMed]
  53. B. T. Draine and P. J. Flatau, "Discrete-dipole approximation for scattering calculations," J. Opt. Soc. Am. A 11, 1491-1499 (1994).
    [CrossRef]
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    [CrossRef]
  55. C. M. J. Wijers, "The local field and what it means," Phys. Status Solidi A 188, 1251-1260 (2001).
    [CrossRef]

2006

V. Wong and M. A. Ratner, "Explicit computation of gradient and non-gradient contributions to optical forces in the discrete-dipole approximation," J. Opt. Soc. Am. B 23, 1801-1814 (2006).
[CrossRef]

V. Wong and M. A. Ratner, "Gradient and non-gradient contributions to plasmon enhanced optical forces on silver nanoparticles," Phys. Rev. B 73, 075416 (2006).
[CrossRef]

V. Wong and M. A. Ratner, "Geometry dependent properties of optically induced forces between silver nanoparticles," J. Phys. Chem. B 110, 19243-19253 (2006).
[CrossRef] [PubMed]

2004

F. J. Garcia de Abajo, "Electromagnetic forces and torques in nanoparticles irradiated by plane waves," J. Quant. Spectrosc. Radiat. Transf. 89, 3-9 (2004).
[CrossRef]

M. Nieto-Vesperinas, P. C. Chaumet, and A. Rahmani, "Near-field photonic forces," Philos. Trans. R. Soc. London Ser. A 362, 719-737 (2004).
[CrossRef]

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

A. Rahmani, P. C. Chaumet, and G. W. Bryant, "On the importance of local-field corrections for polarizable particles on a finite lattice: application to the discrete dipole approximation," Astrophys. J. 607, 873-878 (2004).
[CrossRef]

M. J. Collinge and B. T. Draine, "Discrete-dipole approximation with polarizabilities that account for both finite wavelength and target geometry," J. Opt. Soc. Am. A 21, 2023-2028 (2004).
[CrossRef]

A. Rohrbach, H. Kress, and E. H. K. Stelzer, "Reply to comment on: 'Trapping force, force constant, and potential depths for dielectric spheres in the presence of spherical aberrations'," Appl. Opt. 43, 1827-1829 (2004).
[CrossRef]

2003

B. Onoa, S. Dumont, J. Liphardt, S. B. Smith, I. Tinoco, and C. Bustamante, "Identifying kinetic barriers to mechanical unfolding of the T. thermophila ribozyme," Science 299, 1892-1895 (2003).
[CrossRef] [PubMed]

M. P. MacDonald, G. C. Spalding, and K. Dholakia, "Microfluidic sorting in an optical lattice," Nature 426, 421-424 (2003).
[CrossRef] [PubMed]

J. R. Arias-Gonzalez and M. Nieto-Vesperinas, "Optical forces on small particles: attractive and repulsive nature and plasmon-resonance conditions," J. Opt. Soc. Am. A 20, 1201-1209 (2003).
[CrossRef]

2002

A. Ehrlicher, T. Betz, B. Stuhrmann, D. Koch, V. Milner, M. G. Raizen, and J. Kas, "Guiding neuronal growth with light," Proc. Natl. Acad. Sci. U.S.A. 99, 16024-16028 (2002).
[CrossRef] [PubMed]

2001

A. Rohrbach and E. H. K. Stelzer, "Optical trapping of dielectric particles in arbitrary fields," J. Opt. Soc. Am. A 18, 839-853 (2001).
[CrossRef]

A. G. Hoekstra, M. Frijlink, L. B. F. M. Waters, and P. M. A. Sloot, "Radation forces in the discrete-dipole approximation," J. Opt. Soc. Am. A 18, 1944-1953 (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]

S. C. Grover, A. G. Skirtach, R. C. Gauthier, and C. P. Grover, "Automated single-cell sorting system based on optical trapping," J. Biomed. Opt. 6, 14-22 (2001).
[CrossRef] [PubMed]

A. Lachish-Zalait, D. Zbaida, E. Klein, and M. Elbaum, "Direct surface patterning from solutions: localized microchemistry using a focused laser," Adv. Funct. Mater. 11, 218-223 (2001).
[CrossRef]

T. Sugiura, "Laser trapping of a metallic probe for near field microscopy," Top. Appl. Phys. 81, 143-161 (2001).
[CrossRef]

L. Novotny, "Forces in optical near-fields," Top. Appl. Phys. 81, 123-141 (2001).
[CrossRef]

C. M. J. Wijers, "The local field and what it means," Phys. Status Solidi A 188, 1251-1260 (2001).
[CrossRef]

2000

P. C. Chaumet and M. Nieto-Vesperinas, "Coupled dipole method determination of the electromagnetic force on a particle over a flat dielectric substrate," Phys. Rev. B 61, 14119-14127 (2000).
[CrossRef]

P. C. Chaumet and M. Nieto-Vesperinas, "Time-averaged total force on a dipolar sphere in an electromagnetic field," Opt. Lett. 25, 1065-1067 (2000).
[CrossRef]

1999

1997

L. Novotny, X. Bian, and X. S. Xie, "Theory of nanometric optical tweezers," Phys. Rev. Lett. 79, 645-648 (1997).
[CrossRef]

T. T. Perkins, D. E. Smith, and S. Chu, "Single polymer dynamics in an elongational flow," Science 276, 2016-2021 (1997).
[CrossRef] [PubMed]

1996

B. T. Draine and J. C. Weingartner, "Radiative torques on interstellar grains. I. Superthermal spin-up," Astrophys. J. 470, 551-565 (1996).
[CrossRef]

Y. Harada and T. Asakura, "Radiation forces on a dielectric sphere in the Rayleigh scattering regime," Opt. Commun. 124, 529-541 (1996).
[CrossRef]

1994

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

K. Visscher and G. J. Brakenhoff, "Theoretical study of optically induced forces on spherical particles in a single beam trap I: Rayleigh scatters," Optik 89, 174-180 (1992).

1990

A. Lakhtakia, "Macroscopic theory of the coupled dipole approximation method," Opt. Commun. 79, 1-5 (1990).
[CrossRef]

1988

G. H. Goedecke and S. G. O'Brien, "Scattering by irregular inhomogeneous particles via the digitized Green's function algorithm," Appl. Opt. 27, 2431-2438 (1988).
[CrossRef] [PubMed]

B. T. Draine, "The discrete-dipole approximation and its application to interstellar graphite grains," Astrophys. J. 333, 848-872 (1988).
[CrossRef]

1987

R. Fuchs and F. Claro, "Multipolar response of small metallic spheres: nonlocal theory," Phys. Rev. B 35, 3722-3727 (1987).
[CrossRef]

1986

1983

W. A. Kraus and G. C. Schatz, "Plasmon resonance broadening in small metal particles," J. Chem. Phys. 79, 6130-6139 (1983).
[CrossRef]

A. Ashkin and J. P. Gordon, "Stability of radiation-pressure particle traps: an optical Earnshaw theorem," Opt. Lett. 8, 511-513 (1983).
[CrossRef] [PubMed]

1971

A. Ashkin and J. M. Dziedzic, "Optical levitation by radiation pressure," Appl. Phys. Lett. 19, 283-285 (1971).
[CrossRef]

1970

A. Ashkin, "Acceleration and trapping of particles by radiation pressure," Phys. Rev. Lett. 24, 156-159 (1970).
[CrossRef]

1909

P. Debye, "Lichtdruck auf Kugeln von bliebigem Material," Ann. Phys. 30, 57-136 (1909).
[CrossRef]

1908

G. Mie, "Beitrage zur Optik truber Medien speziell kolloidaler Metallosungen," Ann. Phys. 25, 377-455 (1908).
[CrossRef]

Arfken, G.

G. Arfken, Mathematical Methods for Physicists (Academic, 1970).

Arias-Gonzalez, J. R.

Asakura, T.

Y. Harada and T. Asakura, "Radiation forces on a dielectric sphere in the Rayleigh scattering regime," Opt. Commun. 124, 529-541 (1996).
[CrossRef]

Ashkin, A.

Betz, T.

A. Ehrlicher, T. Betz, B. Stuhrmann, D. Koch, V. Milner, M. G. Raizen, and J. Kas, "Guiding neuronal growth with light," Proc. Natl. Acad. Sci. U.S.A. 99, 16024-16028 (2002).
[CrossRef] [PubMed]

Bian, X.

L. Novotny, X. Bian, and X. S. Xie, "Theory of nanometric optical tweezers," Phys. Rev. Lett. 79, 645-648 (1997).
[CrossRef]

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.

Block, S. M.

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

K. Svoboda and S. M. Block, "Optical trapping of metallic Rayleigh particles," Opt. Lett. 19, 930-932 (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 (Wiley Inter-Science, 1983).

Bonin, K. D.

K. D. Bonin and V. V. Kresin, Electric-Dipole Polarizabilities of Atoms, Molecules and Clusters (World Scientific, 1997).
[CrossRef]

Borisenko, A. I.

A. I. Borisenko and I. E. Tarapov, Vector and Tensor Analysis (Dover, 1968).

Brakenhoff, G. J.

K. Visscher and G. J. Brakenhoff, "Theoretical study of optically induced forces on spherical particles in a single beam trap I: Rayleigh scatters," Optik 89, 174-180 (1992).

Bronk, B. V.

Bryant, G. W.

A. Rahmani, P. C. Chaumet, and G. W. Bryant, "On the importance of local-field corrections for polarizable particles on a finite lattice: application to the discrete dipole approximation," Astrophys. J. 607, 873-878 (2004).
[CrossRef]

Bustamante, C.

B. Onoa, S. Dumont, J. Liphardt, S. B. Smith, I. Tinoco, and C. Bustamante, "Identifying kinetic barriers to mechanical unfolding of the T. thermophila ribozyme," Science 299, 1892-1895 (2003).
[CrossRef] [PubMed]

Chaumet, P. C.

A. Rahmani, P. C. Chaumet, and G. W. Bryant, "On the importance of local-field corrections for polarizable particles on a finite lattice: application to the discrete dipole approximation," Astrophys. J. 607, 873-878 (2004).
[CrossRef]

M. Nieto-Vesperinas, P. C. Chaumet, and A. Rahmani, "Near-field photonic forces," Philos. Trans. R. Soc. London Ser. A 362, 719-737 (2004).
[CrossRef]

P. C. Chaumet and M. Nieto-Vesperinas, "Time-averaged total force on a dipolar sphere in an electromagnetic field," Opt. Lett. 25, 1065-1067 (2000).
[CrossRef]

P. C. Chaumet and M. Nieto-Vesperinas, "Coupled dipole method determination of the electromagnetic force on a particle over a flat dielectric substrate," Phys. Rev. B 61, 14119-14127 (2000).
[CrossRef]

Chu, S.

Claro, F.

R. Fuchs and F. Claro, "Multipolar response of small metallic spheres: nonlocal theory," Phys. Rev. B 35, 3722-3727 (1987).
[CrossRef]

Cohen-Tannoudji, C.

C. Cohen-Tannoudji, J. Dupont-Roc, and G. Grynberg, Atom-Photon Interactions (Wiley-Interscience, 1992).

Collinge, M. J.

Debye, P.

P. Debye, "Lichtdruck auf Kugeln von bliebigem Material," Ann. Phys. 30, 57-136 (1909).
[CrossRef]

Dholakia, K.

M. P. MacDonald, G. C. Spalding, and K. Dholakia, "Microfluidic sorting in an optical lattice," Nature 426, 421-424 (2003).
[CrossRef] [PubMed]

Draine, B. T.

M. J. Collinge and B. T. Draine, "Discrete-dipole approximation with polarizabilities that account for both finite wavelength and target geometry," J. Opt. Soc. Am. A 21, 2023-2028 (2004).
[CrossRef]

B. T. Draine and J. C. Weingartner, "Radiative torques on interstellar grains. I. Superthermal spin-up," Astrophys. J. 470, 551-565 (1996).
[CrossRef]

B. T. Draine and P. J. Flatau, "Discrete-dipole approximation for scattering calculations," J. Opt. Soc. Am. A 11, 1491-1499 (1994).
[CrossRef]

B. T. Draine, "The discrete-dipole approximation and its application to interstellar graphite grains," Astrophys. J. 333, 848-872 (1988).
[CrossRef]

B. T. Draine and P. J. Flatau, "User guide to the discrete dipole approximation code DDSCAT 6.0," arxiv.org e-print archive, astro-physics/0309069, 2 September 2003.

Druger, S. D.

Dumont, S.

B. Onoa, S. Dumont, J. Liphardt, S. B. Smith, I. Tinoco, and C. Bustamante, "Identifying kinetic barriers to mechanical unfolding of the T. thermophila ribozyme," Science 299, 1892-1895 (2003).
[CrossRef] [PubMed]

Dupont-Roc, J.

C. Cohen-Tannoudji, J. Dupont-Roc, and G. Grynberg, Atom-Photon Interactions (Wiley-Interscience, 1992).

Dziedzic, J. M.

Ehrlicher, A.

A. Ehrlicher, T. Betz, B. Stuhrmann, D. Koch, V. Milner, M. G. Raizen, and J. Kas, "Guiding neuronal growth with light," Proc. Natl. Acad. Sci. U.S.A. 99, 16024-16028 (2002).
[CrossRef] [PubMed]

Elbaum, M.

A. Lachish-Zalait, D. Zbaida, E. Klein, and M. Elbaum, "Direct surface patterning from solutions: localized microchemistry using a focused laser," Adv. Funct. Mater. 11, 218-223 (2001).
[CrossRef]

Flatau, P. J.

B. T. Draine and P. J. Flatau, "Discrete-dipole approximation for scattering calculations," J. Opt. Soc. Am. A 11, 1491-1499 (1994).
[CrossRef]

B. T. Draine and P. J. Flatau, "User guide to the discrete dipole approximation code DDSCAT 6.0," arxiv.org e-print archive, astro-physics/0309069, 2 September 2003.

Frijlink, M.

Fuchs, R.

R. Fuchs and F. Claro, "Multipolar response of small metallic spheres: nonlocal theory," Phys. Rev. B 35, 3722-3727 (1987).
[CrossRef]

Garcia de Abajo, F. J.

F. J. Garcia de Abajo, "Electromagnetic forces and torques in nanoparticles irradiated by plane waves," J. Quant. Spectrosc. Radiat. Transf. 89, 3-9 (2004).
[CrossRef]

Gauthier, R. C.

S. C. Grover, A. G. Skirtach, R. C. Gauthier, and C. P. Grover, "Automated single-cell sorting system based on optical trapping," J. Biomed. Opt. 6, 14-22 (2001).
[CrossRef] [PubMed]

Goedecke, G. H.

Gordon, J. P.

Grover, C. P.

S. C. Grover, A. G. Skirtach, R. C. Gauthier, and C. P. Grover, "Automated single-cell sorting system based on optical trapping," J. Biomed. Opt. 6, 14-22 (2001).
[CrossRef] [PubMed]

Grover, S. C.

S. C. Grover, A. G. Skirtach, R. C. Gauthier, and C. P. Grover, "Automated single-cell sorting system based on optical trapping," J. Biomed. Opt. 6, 14-22 (2001).
[CrossRef] [PubMed]

Grynberg, G.

C. Cohen-Tannoudji, J. Dupont-Roc, and G. Grynberg, Atom-Photon Interactions (Wiley-Interscience, 1992).

Harada, Y.

Y. Harada and T. Asakura, "Radiation forces on a dielectric sphere in the Rayleigh scattering regime," Opt. Commun. 124, 529-541 (1996).
[CrossRef]

Hay, G. E.

G. E. Hay, Vector and Tensor Analysis (Dover, 1953).

Heckenberg, N. R.

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]

Hoekstra, A. G.

Huffman, D. R.

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley Inter-Science, 1983).

Jackson, J. D.

J. D. Jackson, Classical Electrodynamics (Wiley, 1975).

Kas, J.

A. Ehrlicher, T. Betz, B. Stuhrmann, D. Koch, V. Milner, M. G. Raizen, and J. Kas, "Guiding neuronal growth with light," Proc. Natl. Acad. Sci. U.S.A. 99, 16024-16028 (2002).
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Koch, D.

A. Ehrlicher, T. Betz, B. Stuhrmann, D. Koch, V. Milner, M. G. Raizen, and J. Kas, "Guiding neuronal growth with light," Proc. Natl. Acad. Sci. U.S.A. 99, 16024-16028 (2002).
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Lachish-Zalait, A.

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G. Mie, "Beitrage zur Optik truber Medien speziell kolloidaler Metallosungen," Ann. Phys. 25, 377-455 (1908).
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A. Ehrlicher, T. Betz, B. Stuhrmann, D. Koch, V. Milner, M. G. Raizen, and J. Kas, "Guiding neuronal growth with light," Proc. Natl. Acad. Sci. U.S.A. 99, 16024-16028 (2002).
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K. C. Neuman and S. M. Block, "Optical trapping," Rev. Sci. Instrum. 75, 2787-2809 (2004).
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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]

Nieto-Vesperinas, M.

M. Nieto-Vesperinas, P. C. Chaumet, and A. Rahmani, "Near-field photonic forces," Philos. Trans. R. Soc. London Ser. A 362, 719-737 (2004).
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L. Novotny, "Forces in optical near-fields," Top. Appl. Phys. 81, 123-141 (2001).
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L. Novotny, X. Bian, and X. S. Xie, "Theory of nanometric optical tweezers," Phys. Rev. Lett. 79, 645-648 (1997).
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Onoa, B.

B. Onoa, S. Dumont, J. Liphardt, S. B. Smith, I. Tinoco, and C. Bustamante, "Identifying kinetic barriers to mechanical unfolding of the T. thermophila ribozyme," Science 299, 1892-1895 (2003).
[CrossRef] [PubMed]

Perkins, T. T.

T. T. Perkins, D. E. Smith, and S. Chu, "Single polymer dynamics in an elongational flow," Science 276, 2016-2021 (1997).
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Rahmani, A.

M. Nieto-Vesperinas, P. C. Chaumet, and A. Rahmani, "Near-field photonic forces," Philos. Trans. R. Soc. London Ser. A 362, 719-737 (2004).
[CrossRef]

A. Rahmani, P. C. Chaumet, and G. W. Bryant, "On the importance of local-field corrections for polarizable particles on a finite lattice: application to the discrete dipole approximation," Astrophys. J. 607, 873-878 (2004).
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Raizen, M. G.

A. Ehrlicher, T. Betz, B. Stuhrmann, D. Koch, V. Milner, M. G. Raizen, and J. Kas, "Guiding neuronal growth with light," Proc. Natl. Acad. Sci. U.S.A. 99, 16024-16028 (2002).
[CrossRef] [PubMed]

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V. Wong and M. A. Ratner, "Explicit computation of gradient and non-gradient contributions to optical forces in the discrete-dipole approximation," J. Opt. Soc. Am. B 23, 1801-1814 (2006).
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V. Wong and M. A. Ratner, "Geometry dependent properties of optically induced forces between silver nanoparticles," J. Phys. Chem. B 110, 19243-19253 (2006).
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V. Wong and M. A. Ratner, "Gradient and non-gradient contributions to plasmon enhanced optical forces on silver nanoparticles," Phys. Rev. B 73, 075416 (2006).
[CrossRef]

Rohrbach, A.

Rubinsztein-Dunlop, H.

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]

Schatz, G. C.

W. A. Kraus and G. C. Schatz, "Plasmon resonance broadening in small metal particles," J. Chem. Phys. 79, 6130-6139 (1983).
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Schmidt, C. F.

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).
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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).
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Skirtach, A. G.

S. C. Grover, A. G. Skirtach, R. C. Gauthier, and C. P. Grover, "Automated single-cell sorting system based on optical trapping," J. Biomed. Opt. 6, 14-22 (2001).
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Sloot, P. M. A.

Smith, D. E.

T. T. Perkins, D. E. Smith, and S. Chu, "Single polymer dynamics in an elongational flow," Science 276, 2016-2021 (1997).
[CrossRef] [PubMed]

Smith, S. B.

B. Onoa, S. Dumont, J. Liphardt, S. B. Smith, I. Tinoco, and C. Bustamante, "Identifying kinetic barriers to mechanical unfolding of the T. thermophila ribozyme," Science 299, 1892-1895 (2003).
[CrossRef] [PubMed]

Spalding, G. C.

M. P. MacDonald, G. C. Spalding, and K. Dholakia, "Microfluidic sorting in an optical lattice," Nature 426, 421-424 (2003).
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J. A. Stratton, Electromagnetic Theory (McGraw-Hill, 1941).

Stuhrmann, B.

A. Ehrlicher, T. Betz, B. Stuhrmann, D. Koch, V. Milner, M. G. Raizen, and J. Kas, "Guiding neuronal growth with light," Proc. Natl. Acad. Sci. U.S.A. 99, 16024-16028 (2002).
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Sugiura, T.

T. Sugiura, "Laser trapping of a metallic probe for near field microscopy," Top. Appl. Phys. 81, 143-161 (2001).
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K. Svoboda and S. M. Block, "Optical trapping of metallic Rayleigh particles," Opt. Lett. 19, 930-932 (1994).
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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).
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K. Visscher and G. J. Brakenhoff, "Theoretical study of optically induced forces on spherical particles in a single beam trap I: Rayleigh scatters," Optik 89, 174-180 (1992).

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U. Kreibig and M. Vollmer, Optical Properties of Metal Clusters (Springer, 1995).

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C. M. J. Wijers, "The local field and what it means," Phys. Status Solidi A 188, 1251-1260 (2001).
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V. Wong and M. A. Ratner, "Explicit computation of gradient and non-gradient contributions to optical forces in the discrete-dipole approximation," J. Opt. Soc. Am. B 23, 1801-1814 (2006).
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V. Wong and M. A. Ratner, "Geometry dependent properties of optically induced forces between silver nanoparticles," J. Phys. Chem. B 110, 19243-19253 (2006).
[CrossRef] [PubMed]

V. Wong and M. A. Ratner, "Gradient and non-gradient contributions to plasmon enhanced optical forces on silver nanoparticles," Phys. Rev. B 73, 075416 (2006).
[CrossRef]

Xie, X. S.

L. Novotny, X. Bian, and X. S. Xie, "Theory of nanometric optical tweezers," Phys. Rev. Lett. 79, 645-648 (1997).
[CrossRef]

Zbaida, D.

A. Lachish-Zalait, D. Zbaida, E. Klein, and M. Elbaum, "Direct surface patterning from solutions: localized microchemistry using a focused laser," Adv. Funct. Mater. 11, 218-223 (2001).
[CrossRef]

Adv. Funct. Mater.

A. Lachish-Zalait, D. Zbaida, E. Klein, and M. Elbaum, "Direct surface patterning from solutions: localized microchemistry using a focused laser," Adv. Funct. Mater. 11, 218-223 (2001).
[CrossRef]

Ann. Phys.

G. Mie, "Beitrage zur Optik truber Medien speziell kolloidaler Metallosungen," Ann. Phys. 25, 377-455 (1908).
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A. Rahmani, P. C. Chaumet, and G. W. Bryant, "On the importance of local-field corrections for polarizable particles on a finite lattice: application to the discrete dipole approximation," Astrophys. J. 607, 873-878 (2004).
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[CrossRef]

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]

J. Biomed. Opt.

S. C. Grover, A. G. Skirtach, R. C. Gauthier, and C. P. Grover, "Automated single-cell sorting system based on optical trapping," J. Biomed. Opt. 6, 14-22 (2001).
[CrossRef] [PubMed]

J. Chem. Phys.

W. A. Kraus and G. C. Schatz, "Plasmon resonance broadening in small metal particles," J. Chem. Phys. 79, 6130-6139 (1983).
[CrossRef]

J. Opt. Soc. Am. A

J. Opt. Soc. Am. B

J. Phys. Chem. B

V. Wong and M. A. Ratner, "Geometry dependent properties of optically induced forces between silver nanoparticles," J. Phys. Chem. B 110, 19243-19253 (2006).
[CrossRef] [PubMed]

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F. J. Garcia de Abajo, "Electromagnetic forces and torques in nanoparticles irradiated by plane waves," J. Quant. Spectrosc. Radiat. Transf. 89, 3-9 (2004).
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Nature

M. P. MacDonald, G. C. Spalding, and K. Dholakia, "Microfluidic sorting in an optical lattice," Nature 426, 421-424 (2003).
[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]

Opt. Commun.

Y. Harada and T. Asakura, "Radiation forces on a dielectric sphere in the Rayleigh scattering regime," Opt. Commun. 124, 529-541 (1996).
[CrossRef]

A. Lakhtakia, "Macroscopic theory of the coupled dipole approximation method," Opt. Commun. 79, 1-5 (1990).
[CrossRef]

Opt. Lett.

Optik

K. Visscher and G. J. Brakenhoff, "Theoretical study of optically induced forces on spherical particles in a single beam trap I: Rayleigh scatters," Optik 89, 174-180 (1992).

Philos. Trans. R. Soc. London Ser. A

M. Nieto-Vesperinas, P. C. Chaumet, and A. Rahmani, "Near-field photonic forces," Philos. Trans. R. Soc. London Ser. A 362, 719-737 (2004).
[CrossRef]

Phys. Rev. B

P. C. Chaumet and M. Nieto-Vesperinas, "Coupled dipole method determination of the electromagnetic force on a particle over a flat dielectric substrate," Phys. Rev. B 61, 14119-14127 (2000).
[CrossRef]

V. Wong and M. A. Ratner, "Gradient and non-gradient contributions to plasmon enhanced optical forces on silver nanoparticles," Phys. Rev. B 73, 075416 (2006).
[CrossRef]

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A. Ashkin, "Acceleration and trapping of particles by radiation pressure," Phys. Rev. Lett. 24, 156-159 (1970).
[CrossRef]

L. Novotny, X. Bian, and X. S. Xie, "Theory of nanometric optical tweezers," Phys. Rev. Lett. 79, 645-648 (1997).
[CrossRef]

Phys. Status Solidi A

C. M. J. Wijers, "The local field and what it means," Phys. Status Solidi A 188, 1251-1260 (2001).
[CrossRef]

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

A. Ehrlicher, T. Betz, B. Stuhrmann, D. Koch, V. Milner, M. G. Raizen, and J. Kas, "Guiding neuronal growth with light," Proc. Natl. Acad. Sci. U.S.A. 99, 16024-16028 (2002).
[CrossRef] [PubMed]

Rev. Sci. Instrum.

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

Science

B. Onoa, S. Dumont, J. Liphardt, S. B. Smith, I. Tinoco, and C. Bustamante, "Identifying kinetic barriers to mechanical unfolding of the T. thermophila ribozyme," Science 299, 1892-1895 (2003).
[CrossRef] [PubMed]

T. T. Perkins, D. E. Smith, and S. Chu, "Single polymer dynamics in an elongational flow," Science 276, 2016-2021 (1997).
[CrossRef] [PubMed]

Top. Appl. Phys.

T. Sugiura, "Laser trapping of a metallic probe for near field microscopy," Top. Appl. Phys. 81, 143-161 (2001).
[CrossRef]

L. Novotny, "Forces in optical near-fields," Top. Appl. Phys. 81, 123-141 (2001).
[CrossRef]

Other

A. I. Borisenko and I. E. Tarapov, Vector and Tensor Analysis (Dover, 1968).

G. E. Hay, Vector and Tensor Analysis (Dover, 1953).

G. Arfken, Mathematical Methods for Physicists (Academic, 1970).

U. Kreibig and M. Vollmer, Optical Properties of Metal Clusters (Springer, 1995).

M. Kerker, The Scattering of Light and Other Electromagnetic Radiation (Academic, 1969).

H. C. van de Hulst, Light Scattering by Small Particles (Dover, 1981).

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley Inter-Science, 1983).

J. A. Stratton, Electromagnetic Theory (McGraw-Hill, 1941).

J. D. Jackson, Classical Electrodynamics (Wiley, 1975).

B. T. Draine and P. J. Flatau, "User guide to the discrete dipole approximation code DDSCAT 6.0," arxiv.org e-print archive, astro-physics/0309069, 2 September 2003.

C. Cohen-Tannoudji, J. Dupont-Roc, and G. Grynberg, Atom-Photon Interactions (Wiley-Interscience, 1992).

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[CrossRef]

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Figures (3)

Fig. 1
Fig. 1

Contributions to the total force in Eq. (1), and their sum, as a function of effective radius, a, for three wavelengths. Both (a) and (b) show results for a silver particle in water under plane-wave illumination. (a) Force contributions along k for the sphere. At 335 nm , gradient forces were multiplied by 1 before computing the logarithm. At 402 and 469 nm , ( E * ) E forces were multiplied by 1 before computing the logarithm. All contributions exhibit proportional-to-volume scaling for small radius a. (b) Force contributions and sum along k for the prolate. The prolate major-to-minor axis ratio is R = 3.2 , and the incident polarization lies along the major axis. At 603 nm , the radiation-pressure force was multiplied by 1 before computing the logarithm. All contributions exhibit proportional-to-volume scaling for small radius a.

Fig. 2
Fig. 2

Real and imaginary parts of first-degree Mie–Debye coefficients as a function of sphere radius, a, at three wavelengths. Results are for a silver sphere in water. (a) Internal coefficients eventually become constant as a function of size for small sizes. (b) External coefficients eventually exhibit power-law decay as a function of a for small sizes. At 402 and 469 nm , Im ( A 1 ) was multiplied by 1 before computing the logarithm.

Fig. 3
Fig. 3

Real and imaginary parts of Mie–Debye coefficients as a function of degree, N, for different radii, a, at 402 nm . Results are for a silver sphere in water. (a) Internal coefficients decay slowly as a function of N. (b) External coefficients exhibit approximate power-law decay as a function of N for small sizes. Im ( A N ) were multiplied by 1 before computing the logarithm.

Equations (25)

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

F = 1 4 Re ( α ) E 2 + k 2 Im ( α ) Re ( E × H * ) 1 2 Im ( α ) Im [ ( E ) E * ] .
F = 1 2 Re d V ( ρ E * + J c × H * ) .
F = 1 2 Re d V ( E * ( P ) + P ̇ c × H * ) .
i x i ( a i b ) = b ( a ) + ( a ) b ,
d V E * ( P ) = d V ( P ) E * d V i x i ( P i E * ) .
V d V i x i ( P i E * ) = S d S ( P n ) E * .
F = 1 2 Re d V ( ( P ) E * + P ̇ c × H * ) .
F = 1 2 Re d V [ ( P ) E * i k P × H * ]
= 1 2 Re d V [ χ ( E ) E * i k χ ( E × H * ) ]
= 1 2 d V { Re ( χ ) Re [ ( E ) E * ] Im ( χ ) Im [ ( E ) E * ] + k Im ( χ ) Re ( E × H * ) + k Re ( χ ) Im ( E × H * ) } .
( a b ) = ( a ) b + ( b ) a + a × ( × b ) + b × ( × a ) ,
Re [ ( E ) E * ] = 1 2 E 2 k Im ( E × H * ) .
F = d V { Re ( χ ) 4 E 2 + k 2 Im ( χ ) Re ( E × H * ) Im ( χ ) 2 Im [ ( E ) E * ] } .
E int = n = 1 E n ( C n M o 1 n ( 1 ) i D n N e 1 n ( 1 ) ) ,
H int = k int θ μ int n = 1 E n ( D n M e 1 n ( 1 ) + i C n N o 1 n ( 1 ) ) .
E scat = n = 1 E n ( i A n N e 1 n ( 3 ) B n M o 1 n ( 3 ) ) .
H scat = k ω μ n = 1 E n ( i B n N o 1 n ( 3 ) + A n M e 1 n ( 3 ) ) .
Im [ ( E * ) E ] = Im ( n m E n * E m { C n * C m ( M o 1 n ( 1 ) * ) M o 1 m ( 1 ) + D n * D m ( N e 1 n ( 1 ) * ) N e 1 m ( 1 ) + i [ D n * C m ( N e 1 n ( 1 ) * ) M o 1 m ( 1 ) C n * D m ( M o 1 n ( 1 ) * ) N e 1 m ( 1 ) ] } ) .
F abs = n m c S C abs .
C pr = C ext cos θ C scat
= C abs + ( 1 cos θ ) C scat .
E ( r ) ( 1 + 4 π χ ( r ) 3 ) = E inc ( r ) + d V χ ( r ) G ( r r ) E ( r ) .
G ( r ) = exp ( i k r ) r ( k 2 ( n n 1 ) + i k r 1 r 2 ( 3 n n 1 ) ) .
E ( r i ) = E inc ( r i ) + j i E scat , j ( r i ) ,
E ( r i ) 2 = E inc ( r i ) 2 + ( j i E scat , j ( r i ) 2 ) + 2 Re [ ( j i E inc * ( r i ) E scat , j ( r i ) ) ] + 2 Re [ ( j , k i j < k E scat , j * ( r i ) E scat , k ( r i ) ) ] .

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