Abstract

We theoretically analyze the optical forces between two nearby silver nanoparticles for the case when the wavelength of the incoming light is close to the localized surface plasmon resonance (LSPR). It is shown that the optical force between the nanoparticles is enhanced by the LSPR and that it changes from attractive to repulsive for wavelengths slightly shorter than the resonance when the polarization of the incident light is parallel to the axis of the dimer. This behavior can be utilized to generate a stable separation distance between the nanoparticles. In the Rayleigh limit, the equilibrium distance is uniquely determined by the real part of the particle polarizability and the wavelength of the incident light. The results suggest that near-field optical forces can be used to manipulate and organize plasmonic nanoparticles with a tunable spatial resolution in the nanometer regime.

© 2007 Optical Society of America

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References

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2007 (2)

M. Righini, A. S. Zelenina, C. Girard, and R. Quidant, "Parallel and selective trapping in a patterned plasmonic landscape " Nature Physics 3, 477-480 (2007).Q1
[CrossRef]

A. S. Zelenina, R. Quidant, and M. Nieto-Vesperinas, "Enhanced optical forces between coupled resonant metal nanoparticles," Opt. Lett. 32, 1156-1158 (2007).
[CrossRef] [PubMed]

2006 (3)

F. Svedberg and M. Kall, "On the importance of optical forces in surface-enhanced Raman scattering (SERS)," Faraday Discuss. 132, 35-44 (2006).
[CrossRef] [PubMed]

F. Svedberg, Z. P. Li, H. X. Xu, and M. Kall, "Creating hot nanoparticle pairs for surface-enhanced Raman spectroscopy through optical manipulation," Nano. Lett. 6, 2639-2641 (2006).
[CrossRef] [PubMed]

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

2005 (2)

A. J. Hallock, P. L. Redmond, and L. E. Brus, "Optical forces between metallic particles," Proc. Natl. Acad. Sci. U. S. A. 102, 1280-1284 (2005).
[CrossRef] [PubMed]

R. Quidant, D. Petrov, and G. Badenes, "Radiation forces on a Rayleigh dielectric sphere in a patterned optical near field," Opt. Lett. 30, 1009-1011 (2005).
[CrossRef] [PubMed]

2004 (1)

J. Prikulis, F. Svedberg, M. Kall, J. Enger, K. Ramser, M. Goksor, and D. Hanstorp, "Optical spectroscopy of single trapped metal nanoparticles in solution," Nano. Lett. 4, 115-118 (2004).
[CrossRef]

2003 (1)

2002 (2)

H. X. Xu and M. Kall, "Surface-plasmon-enhanced optical forces in silver nanoaggregates," Phys. Rev. Lett. 89, 246802 (2002).
[CrossRef] [PubMed]

P. C. Chaumet, A. Rahmani, and M. Nieto-Vesperinas, "Optical trapping and manipulation of nano-objects with an apertureless probe," Phys. Rev. Lett. 88, 123601 (2002).
[CrossRef] [PubMed]

2001 (1)

L. Paterson, M. P. MacDonald, J. Arlt, W. Sibbett, P. E. Bryant, and K. Dholakia, "Controlled rotation of optically trapped microscopic particles," Science 292, 912-914 (2001).
[CrossRef] [PubMed]

2000 (1)

1999 (1)

K. Okamoto and S. Kawata, "Radiation force exerted on subwavelength particles near a nanoaperture," Phys. Rev. Lett. 83, 4534-4537 (1999).
[CrossRef]

1998 (1)

M. E. J. Friese, T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, "Optical alignment and spinning of laser-trapped microscopic particles," Nature 394, 348-350 (1998).
[CrossRef]

1997 (2)

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

1996 (1)

S. B. Smith, Y. J. Cui, and C. Bustamante, "Overstretching B-DNA: The elastic response of individual double-stranded and single-stranded DNA molecules," Science 271, 795-799 (1996).
[CrossRef] [PubMed]

1994 (2)

J. C. Crocker and D. G. Grier, "Microscopic Measurement of the Pair Interaction Potential of Charge-Stabilized Colloid," Phys. Rev. Lett. 73, 352-355 (1994)
[CrossRef] [PubMed]

B. T. Draine and P. J. Flatau, "Discrete-Dipole Approximation for Scattering Calculations," J. Opt. Soc. Am. A 11, 1491-1499 (1994).
[CrossRef]

1986 (1)

Biophys. J. (1)

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]

Faraday Discuss. (1)

F. Svedberg and M. Kall, "On the importance of optical forces in surface-enhanced Raman scattering (SERS)," Faraday Discuss. 132, 35-44 (2006).
[CrossRef] [PubMed]

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

J. Phys. Chem. B (1)

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

Nano. Lett. (2)

J. Prikulis, F. Svedberg, M. Kall, J. Enger, K. Ramser, M. Goksor, and D. Hanstorp, "Optical spectroscopy of single trapped metal nanoparticles in solution," Nano. Lett. 4, 115-118 (2004).
[CrossRef]

F. Svedberg, Z. P. Li, H. X. Xu, and M. Kall, "Creating hot nanoparticle pairs for surface-enhanced Raman spectroscopy through optical manipulation," Nano. Lett. 6, 2639-2641 (2006).
[CrossRef] [PubMed]

Nature (1)

M. E. J. Friese, T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, "Optical alignment and spinning of laser-trapped microscopic particles," Nature 394, 348-350 (1998).
[CrossRef]

Nature Physics (1)

M. Righini, A. S. Zelenina, C. Girard, and R. Quidant, "Parallel and selective trapping in a patterned plasmonic landscape " Nature Physics 3, 477-480 (2007).Q1
[CrossRef]

Opt. Lett. (4)

Phys. Rev. Lett. (5)

J. C. Crocker and D. G. Grier, "Microscopic Measurement of the Pair Interaction Potential of Charge-Stabilized Colloid," Phys. Rev. Lett. 73, 352-355 (1994)
[CrossRef] [PubMed]

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

P. C. Chaumet, A. Rahmani, and M. Nieto-Vesperinas, "Optical trapping and manipulation of nano-objects with an apertureless probe," Phys. Rev. Lett. 88, 123601 (2002).
[CrossRef] [PubMed]

K. Okamoto and S. Kawata, "Radiation force exerted on subwavelength particles near a nanoaperture," Phys. Rev. Lett. 83, 4534-4537 (1999).
[CrossRef]

H. X. Xu and M. Kall, "Surface-plasmon-enhanced optical forces in silver nanoaggregates," Phys. Rev. Lett. 89, 246802 (2002).
[CrossRef] [PubMed]

Proc. Natl. Acad. Sci. U. S. A. (1)

A. J. Hallock, P. L. Redmond, and L. E. Brus, "Optical forces between metallic particles," Proc. Natl. Acad. Sci. U. S. A. 102, 1280-1284 (2005).
[CrossRef] [PubMed]

Science (2)

S. B. Smith, Y. J. Cui, and C. Bustamante, "Overstretching B-DNA: The elastic response of individual double-stranded and single-stranded DNA molecules," Science 271, 795-799 (1996).
[CrossRef] [PubMed]

L. Paterson, M. P. MacDonald, J. Arlt, W. Sibbett, P. E. Bryant, and K. Dholakia, "Controlled rotation of optically trapped microscopic particles," Science 292, 912-914 (2001).
[CrossRef] [PubMed]

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Figures (4)

Fig. 1.
Fig. 1.

(a).Schematic of the interacting metal nanoparticles in the presence of a plane wave with polarization parallel to the axis of the dimer. (b) Polarizability of 5 nm radius silver nanoparticles.

Fig. 2.
Fig. 2.

Spectra of the optical force in the y direction between two silver nanoparticles, assuming a = 5 nm and intensity of the incident light of 1W/μm2, for various separation distances, using the CDA approximation. (a) Polarization of the incoming light parallel to the dimer. Inset: Same as Fig. 2(a) using the DDA approximation. (b) Polarization perpendicular to the dimer.

Fig. 3.
Fig. 3.

(a).Optical force in the y direction as a function of the separation distance between nanoparticles for different light wavelengths, and comparison with the Van der Waals force. The intensity of the incoming plane-wave is 1W/μm2. Inset: Wavelength dependence of the equilibrium distance between particles. (b) Potential energy in the y direction connected to the FVsW and optical force as a function of the separation distance of the nanoparticles.

Fig. 4.
Fig. 4.

(a). Potential energy in the y direction associated to the Van der Waals and optical force as a function of the separation distance of the nanoparticles, for nanoparticles of a = 15 nm and intensity of the incoming light of 200 mW/μn2 (b) Potential energies in x and (c) z directions when y=d eq .

Equations (6)

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

E 1 y = E 2 y = E y inc / ( 1 + α A yy )
F 1 = ( 1 4 Re [ α ] E 1 y 2 y 1 2 Im [ α ] Im [ E 1 y E 1 y * y ] ) u y + 1 2 Im [ α ] k E 1 y 2 u z
F 1 y = E y inc 2 2 α ˜ 4 α 2 Re [ A yy * y ( 1 + A yy α ) ]
F 1 y E y inc 2 3 y 4 α ˜ 4 α 2 ( 1 2 Re [ α ] y 3 )
d eq ( 2 Re [ α ] ) 1 / 3
d eq a ( ω 0 2 ( ω 0 2 ω 2 ) ( ω 0 2 ω 2 ) 2 + ω 2 Γ 2 ) 1 / 3 2 a

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