Abstract

The response of gold nanoparticle dimers is studied theoretically near and beyond the limit where the particles are touching. As the particles approach each other, a dominant dipole feature is observed that is pushed into the infrared due to interparticle coupling and that is associated with a large pileup of induced charge in the interparticle gap. The redshift becomes singular as the particle separation decreases. The response weakens for very small separation when the coupling across the interparticle gap becomes so strong that dipolar oscillations across the pair are inhibited. Lower-wavelength, higher-order modes show a similar separation dependence in nearly touching dimers. After touching, singular behavior is observed through the emergence of a new infrared absorption peak, also accompanied by huge charge pileup at the interparticle junction, if initial interparticle contact is made at a single point. This new mode is distinctly different from the lowest mode of the separated dimer. When the junction is made by contact between flat surfaces, charge at the junction is neutralized and mode evolution is continuous through contact. The calculated singular response explains recent experiments on metallic nanoparticle dimers and is relevant in the design of nanoparticle-based sensors and plasmon circuits.

© 2006 Optical Society of America

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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
  41. S. A. Maier, P. G. Kik, H. A. Atwater, S. Meltzer, E. Harel, B. E. Koel, and A. A. G. Requicha, "Local detection of electromagnetic energy transport below the diffraction limit in metal nanoparticle plasmon waveguides," Nat. Mater. 2, 229-232 (2003).
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  42. L. A. Sweatlock, S. A. Maier, H. A. Atwater, J. J. Penninkhof, and A. Polman, "Highly confined electromagnetic fields in arrays of strongly coupled Ag nanoparticles," Phys. Rev. B 71, 235408 (2005).
    [CrossRef]
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    [CrossRef]

2006 (1)

J. A. Dionne, L. A. Sweatlock, H. A. Atwater, and A. Polman, "Plasmon slot waveguides: towards chip-scale propagation with subwavelength-scale localization," Phys. Rev. B 73, 035407 (2006).
[CrossRef]

2005 (5)

L. A. Sweatlock, S. A. Maier, H. A. Atwater, J. J. Penninkhof, and A. Polman, "Highly confined electromagnetic fields in arrays of strongly coupled Ag nanoparticles," Phys. Rev. B 71, 235408 (2005).
[CrossRef]

L. Gunnarsson, T. Rindzevicius, J. Prikulis, B. Kasemo, M. Käll, S. Zou, and G. C. Schatz, "Confined plasmons in nanofabricated single silver particle pairs: experimental observations of strong interparticle interactions," J. Phys. Chem. B 109, 1079-1087 (2005).
[CrossRef]

C. E. Talley, J. B. Jackson, C. Oubre, N. K. Grady, C. W. Hollars, S. M. Lane, T. R. Huser, P. Nordlander, and N. J. Halas, "Surface-enhanced Raman scattering from individual Au nanoparticles and nanoparticle dimer substrates," Nano Lett. 5, 1569-1574 (2005).
[CrossRef] [PubMed]

J. J. Xiao, J. P. Huang, and K. W. Yu, "Optical response of strongly coupled metal nanoparticles in dimer arrays," Phys. Rev. B 71, 045404 (2005).
[CrossRef]

J. Aizpurua, G. W. Bryant, L. J. Richter, F. J. García de Abajo, B. K. Kelly, and T. Mallouk, "Optical properties of coupled metallic nanorods for field-enhanced spectroscopy," Phys. Rev. B 71, 235420 (2005).
[CrossRef]

2004 (5)

P. Nordlander and E. Prodan, "Plasmon hybridization in nanoparticles near metallic surfaces," Nano Lett. 4, 2209-2213 (2004).
[CrossRef]

D. A. Genov, A. K. Sarychev, V. M. Shalaev, and A. Wei, "Resonant field enhancements from metal nanoparticle arrays," Nano Lett. 4, 153-158 (2004).
[CrossRef]

P. Nordlander, C. Oubre, E. Prodan, K. Li, and M. I. Stockman, "Plasmon hybridization in nanoparticle dimers," Nano Lett. 4, 899-903 (2004).
[CrossRef]

T. Atay, J. H. Song, and A. V. Nurmikko, "Strongly interacting plasmon nanoparticle pairs: from dipole-dipole interaction to conductively coupled regime," Nano Lett. 4, 1627-1631 (2004).
[CrossRef]

K. G. Thomas, S. Barazzouk, B. I. Ipe, S. T. S. Joseph, and P. V. Kamat, "Uniaxial plasmon coupling through longitudinal self-assembly of gold nanorods," J. Phys. Chem. B,  108, 13066-13068 (2004).
[CrossRef]

2003 (4)

E. Prodan, C. Radloff, N. J. Halas, and P. Nordlander, "A hybridization model for the plasmon response of complex nanostructures," Science,  302, 419-422 (2003).
[CrossRef] [PubMed]

J. Aizpurua, P. Hanarp, D. S. Sutherland, M. Käll, G. W. Bryant, and F. J. García de Abajo, "Optical properties of gold nanorings," Phys. Rev. Lett. 90, 057401 (2003).
[CrossRef] [PubMed]

W. Rechberger, A. Hohenau, A. Leitner, J. R. Krenn, B. Lamprecht, and F. R. Aussenegg, "Optical properties of two interacting gold nanoparticles," Opt. Commun. 220, 137-141 (2003).
[CrossRef]

S. A. Maier, P. G. Kik, H. A. Atwater, S. Meltzer, E. Harel, B. E. Koel, and A. A. G. Requicha, "Local detection of electromagnetic energy transport below the diffraction limit in metal nanoparticle plasmon waveguides," Nat. Mater. 2, 229-232 (2003).
[CrossRef]

2002 (4)

H. Tamaru, H. Kuwata, H. T. Miyazaki, and K. Miyano, "Resonant light scattering from individual Ag nanoparticles and particle pairs," Appl. Phys. Lett. 80, 1826-1828 (2002).
[CrossRef]

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

A. A. Lalayan, K. S. Bagdasaryan, P. G. Petrosyan, Kh. V. Nerkararyan, and J. B. Ketterson, "Anomalous field enhancement from the superfocusing of surface plasmons at contacting silver surfaces," J. Appl. Phys. 91, 2965-2968 (2002).
[CrossRef]

F. J. García de Abajo and A. Howie, "Relativistic electron energy loss and electron-induced photon emission in inhomogeneous dielectrics," Phys. Rev. Lett., 80, 5180-5183 (1998); "Retarded field calculation of electron energy loss in inhomogeneous dielectrics," Phys. Rev. B 75, 115418 (2002).
[CrossRef]

2001 (3)

A. Pack, M. Hietschold, and R. Wannemacher, "Failure of local mie theory: optical spectra of colloidal aggregates," Opt. Commun. 194, 277-287 (2001).
[CrossRef]

T. Ung, L. M. Liz-Marzán, and P. Mulvaney, "Optical properties of thin films of Au@SiO2 particles," J. Phys. Chem. B 105, 3441-3452 (2001).
[CrossRef]

C. Pecharromán, F. Esteban-Betegón, J. F. Bartolomé, S. López-Esteban, and J. S. Moya, "New percolative BaTiO3-Ni composites with a high and frequency-independent dielectric constant (εr≈80 000)," Adv. Mater. 13, 1541-1544 (2001).
[CrossRef]

2000 (3)

M. El-Kouedi and C. A. Foss, "Optical properties of gold-silver iodide nanoparticle pair structures," J. Phys. Chem. B 104, 4031-4037 (2000).
[CrossRef]

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. 97, 996-1001 (2000).
[CrossRef] [PubMed]

C. Pecharromán and J. S. Moya, "Experimental evidence of a giant capacitance in insulator-conductor composites at the percolation threshold," Adv. Mater. 12, 294-297 (2000).
[CrossRef]

1999 (1)

F. J. García de Abajo, "Interaction of raidation and fast electrons with clusters of dielectrics: a multiple scattering approach," Phys. Rev. Lett. 82, 2776-2779 (1999).
[CrossRef]

1998 (2)

J. Aizpurua, A. Rivacoba, N. Zabala, and F. J. García de Abajo, "Collective excitations in an infinite set of aligned spheres," Surf. Sci. 402-404, 418-423 (1998).
[CrossRef]

A. O. Govorov, S. A. Studenikin, and W. R. Frank, "Low-frequency plasmons in coupled electronic microstructures," Phys. Solid State 40, 499-502 (1998).
[CrossRef]

1997 (1)

F. J. García de Abajo and J. Aizpurua, "Numerical simulation of electron energy loss near inhomogeneous dielectrics," Phys. Rev. B 56, 15873-15884 (1997).
[CrossRef]

1995 (1)

G. B. Smith, W. E. Vargas, G. A. Niklasson, J. A. Sotelo, A. V. Paley, and A. V. Radchik, "Optical properties of a pair of spheres: comparison of different theories," Opt. Commun. 15, 8-12 (1995).
[CrossRef]

1994 (2)

A. V. Vagov, A. Radchik, and G. B. Smith, "Optical response of arrays of spheres from the theory of hypercomplex variables," Phys. Rev. Lett. 73, 1035-1038 (1994).
[CrossRef] [PubMed]

A. V. Radchik, A. V. Paley, G. B. Smith, and A. V. Vagov, "Polarization and resonant absorption in intersecting cylinders and spheres," J. Appl. Phys. 76, 4827-4835 (1994).
[CrossRef]

1991 (1)

M. Schmeits and L. Dambly, "Fast-electron scattering by bispherical surface-plasmon modes," Phys. Rev. B 44, 12706-12712 (1991).
[CrossRef]

1987 (1)

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

1985 (1)

C. C. Chen and Y. C. Chou, "Electrical-conductivity fluctuations near the percolation threshold," Phys. Rev. Lett. 54, 2529-2532 (1985).
[CrossRef] [PubMed]

1984 (1)

F. Claro, "Multipolar effects in particulate matter," Solid State Commun. 49, 229-232 (1984).
[CrossRef]

1982 (2)

F. Claro, "Absorption spectrum of neighboring dielectric grains," Phys. Rev. B 25, 7875-7876 (1982).
[CrossRef]

R. Rupin, "Surface modes of two spheres," Phys. Rev. B 26, 3440-3444 (1982).
[CrossRef]

1977 (1)

D. R. McKenzie and R. C. McPhedran, "Exact modelling of cubic lattice permittivity and conductivity," Nature 265, 128-129 (1977).
[CrossRef]

1976 (1)

L. C. Davis, "Electrostatic edge modes of a dielectric wedge," Phys. Rev. B 14, 5523-5525 (1976).
[CrossRef]

1857 (1)

M. Faraday, "Experimental relations of gold (and other metals) to light," Philos. Trans. R. Soc. London 147, 145-181 (1857).
[CrossRef]

Aizpurua, J.

J. Aizpurua, G. W. Bryant, L. J. Richter, F. J. García de Abajo, B. K. Kelly, and T. Mallouk, "Optical properties of coupled metallic nanorods for field-enhanced spectroscopy," Phys. Rev. B 71, 235420 (2005).
[CrossRef]

J. Aizpurua, P. Hanarp, D. S. Sutherland, M. Käll, G. W. Bryant, and F. J. García de Abajo, "Optical properties of gold nanorings," Phys. Rev. Lett. 90, 057401 (2003).
[CrossRef] [PubMed]

J. Aizpurua, A. Rivacoba, N. Zabala, and F. J. García de Abajo, "Collective excitations in an infinite set of aligned spheres," Surf. Sci. 402-404, 418-423 (1998).
[CrossRef]

F. J. García de Abajo and J. Aizpurua, "Numerical simulation of electron energy loss near inhomogeneous dielectrics," Phys. Rev. B 56, 15873-15884 (1997).
[CrossRef]

Atay, T.

T. Atay, J. H. Song, and A. V. Nurmikko, "Strongly interacting plasmon nanoparticle pairs: from dipole-dipole interaction to conductively coupled regime," Nano Lett. 4, 1627-1631 (2004).
[CrossRef]

Atwater, H. A.

J. A. Dionne, L. A. Sweatlock, H. A. Atwater, and A. Polman, "Plasmon slot waveguides: towards chip-scale propagation with subwavelength-scale localization," Phys. Rev. B 73, 035407 (2006).
[CrossRef]

L. A. Sweatlock, S. A. Maier, H. A. Atwater, J. J. Penninkhof, and A. Polman, "Highly confined electromagnetic fields in arrays of strongly coupled Ag nanoparticles," Phys. Rev. B 71, 235408 (2005).
[CrossRef]

S. A. Maier, P. G. Kik, H. A. Atwater, S. Meltzer, E. Harel, B. E. Koel, and A. A. G. Requicha, "Local detection of electromagnetic energy transport below the diffraction limit in metal nanoparticle plasmon waveguides," Nat. Mater. 2, 229-232 (2003).
[CrossRef]

Aussenegg, F. R.

W. Rechberger, A. Hohenau, A. Leitner, J. R. Krenn, B. Lamprecht, and F. R. Aussenegg, "Optical properties of two interacting gold nanoparticles," Opt. Commun. 220, 137-141 (2003).
[CrossRef]

Bagdasaryan, K. S.

A. A. Lalayan, K. S. Bagdasaryan, P. G. Petrosyan, Kh. V. Nerkararyan, and J. B. Ketterson, "Anomalous field enhancement from the superfocusing of surface plasmons at contacting silver surfaces," J. Appl. Phys. 91, 2965-2968 (2002).
[CrossRef]

Barazzouk, S.

K. G. Thomas, S. Barazzouk, B. I. Ipe, S. T. S. Joseph, and P. V. Kamat, "Uniaxial plasmon coupling through longitudinal self-assembly of gold nanorods," J. Phys. Chem. B,  108, 13066-13068 (2004).
[CrossRef]

Bartolomé, J. F.

C. Pecharromán, F. Esteban-Betegón, J. F. Bartolomé, S. López-Esteban, and J. S. Moya, "New percolative BaTiO3-Ni composites with a high and frequency-independent dielectric constant (εr≈80 000)," Adv. Mater. 13, 1541-1544 (2001).
[CrossRef]

Bryant, G. W.

J. Aizpurua, G. W. Bryant, L. J. Richter, F. J. García de Abajo, B. K. Kelly, and T. Mallouk, "Optical properties of coupled metallic nanorods for field-enhanced spectroscopy," Phys. Rev. B 71, 235420 (2005).
[CrossRef]

J. Aizpurua, P. Hanarp, D. S. Sutherland, M. Käll, G. W. Bryant, and F. J. García de Abajo, "Optical properties of gold nanorings," Phys. Rev. Lett. 90, 057401 (2003).
[CrossRef] [PubMed]

Chen, C. C.

C. C. Chen and Y. C. Chou, "Electrical-conductivity fluctuations near the percolation threshold," Phys. Rev. Lett. 54, 2529-2532 (1985).
[CrossRef] [PubMed]

Chou, Y. C.

C. C. Chen and Y. C. Chou, "Electrical-conductivity fluctuations near the percolation threshold," Phys. Rev. Lett. 54, 2529-2532 (1985).
[CrossRef] [PubMed]

Claro, F.

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

F. Claro, "Multipolar effects in particulate matter," Solid State Commun. 49, 229-232 (1984).
[CrossRef]

F. Claro, "Absorption spectrum of neighboring dielectric grains," Phys. Rev. B 25, 7875-7876 (1982).
[CrossRef]

Dambly, L.

M. Schmeits and L. Dambly, "Fast-electron scattering by bispherical surface-plasmon modes," Phys. Rev. B 44, 12706-12712 (1991).
[CrossRef]

Davis, L. C.

L. C. Davis, "Electrostatic edge modes of a dielectric wedge," Phys. Rev. B 14, 5523-5525 (1976).
[CrossRef]

Dionne, J. A.

J. A. Dionne, L. A. Sweatlock, H. A. Atwater, and A. Polman, "Plasmon slot waveguides: towards chip-scale propagation with subwavelength-scale localization," Phys. Rev. B 73, 035407 (2006).
[CrossRef]

El-Kouedi, M.

M. El-Kouedi and C. A. Foss, "Optical properties of gold-silver iodide nanoparticle pair structures," J. Phys. Chem. B 104, 4031-4037 (2000).
[CrossRef]

Esteban-Betegón, F.

C. Pecharromán, F. Esteban-Betegón, J. F. Bartolomé, S. López-Esteban, and J. S. Moya, "New percolative BaTiO3-Ni composites with a high and frequency-independent dielectric constant (εr≈80 000)," Adv. Mater. 13, 1541-1544 (2001).
[CrossRef]

Faraday, M.

M. Faraday, "Experimental relations of gold (and other metals) to light," Philos. Trans. R. Soc. London 147, 145-181 (1857).
[CrossRef]

Foss, C. A.

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L. A. Sweatlock, S. A. Maier, H. A. Atwater, J. J. Penninkhof, and A. Polman, "Highly confined electromagnetic fields in arrays of strongly coupled Ag nanoparticles," Phys. Rev. B 71, 235408 (2005).
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L. Gunnarsson, T. Rindzevicius, J. Prikulis, B. Kasemo, M. Käll, S. Zou, and G. C. Schatz, "Confined plasmons in nanofabricated single silver particle pairs: experimental observations of strong interparticle interactions," J. Phys. Chem. B 109, 1079-1087 (2005).
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P. Nordlander and E. Prodan, "Plasmon hybridization in nanoparticles near metallic surfaces," Nano Lett. 4, 2209-2213 (2004).
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S. A. Maier, P. G. Kik, H. A. Atwater, S. Meltzer, E. Harel, B. E. Koel, and A. A. G. Requicha, "Local detection of electromagnetic energy transport below the diffraction limit in metal nanoparticle plasmon waveguides," Nat. Mater. 2, 229-232 (2003).
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J. Aizpurua, G. W. Bryant, L. J. Richter, F. J. García de Abajo, B. K. Kelly, and T. Mallouk, "Optical properties of coupled metallic nanorods for field-enhanced spectroscopy," Phys. Rev. B 71, 235420 (2005).
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L. Gunnarsson, T. Rindzevicius, J. Prikulis, B. Kasemo, M. Käll, S. Zou, and G. C. Schatz, "Confined plasmons in nanofabricated single silver particle pairs: experimental observations of strong interparticle interactions," J. Phys. Chem. B 109, 1079-1087 (2005).
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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. 97, 996-1001 (2000).
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G. B. Smith, W. E. Vargas, G. A. Niklasson, J. A. Sotelo, A. V. Paley, and A. V. Radchik, "Optical properties of a pair of spheres: comparison of different theories," Opt. Commun. 15, 8-12 (1995).
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A. V. Radchik, A. V. Paley, G. B. Smith, and A. V. Vagov, "Polarization and resonant absorption in intersecting cylinders and spheres," J. Appl. Phys. 76, 4827-4835 (1994).
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A. V. Vagov, A. Radchik, and G. B. Smith, "Optical response of arrays of spheres from the theory of hypercomplex variables," Phys. Rev. Lett. 73, 1035-1038 (1994).
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G. B. Smith, W. E. Vargas, G. A. Niklasson, J. A. Sotelo, A. V. Paley, and A. V. Radchik, "Optical properties of a pair of spheres: comparison of different theories," Opt. Commun. 15, 8-12 (1995).
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P. Nordlander, C. Oubre, E. Prodan, K. Li, and M. I. Stockman, "Plasmon hybridization in nanoparticle dimers," Nano Lett. 4, 899-903 (2004).
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J. Aizpurua, P. Hanarp, D. S. Sutherland, M. Käll, G. W. Bryant, and F. J. García de Abajo, "Optical properties of gold nanorings," Phys. Rev. Lett. 90, 057401 (2003).
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J. A. Dionne, L. A. Sweatlock, H. A. Atwater, and A. Polman, "Plasmon slot waveguides: towards chip-scale propagation with subwavelength-scale localization," Phys. Rev. B 73, 035407 (2006).
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L. A. Sweatlock, S. A. Maier, H. A. Atwater, J. J. Penninkhof, and A. Polman, "Highly confined electromagnetic fields in arrays of strongly coupled Ag nanoparticles," Phys. Rev. B 71, 235408 (2005).
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C. E. Talley, J. B. Jackson, C. Oubre, N. K. Grady, C. W. Hollars, S. M. Lane, T. R. Huser, P. Nordlander, and N. J. Halas, "Surface-enhanced Raman scattering from individual Au nanoparticles and nanoparticle dimer substrates," Nano Lett. 5, 1569-1574 (2005).
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A. V. Radchik, A. V. Paley, G. B. Smith, and A. V. Vagov, "Polarization and resonant absorption in intersecting cylinders and spheres," J. Appl. Phys. 76, 4827-4835 (1994).
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G. B. Smith, W. E. Vargas, G. A. Niklasson, J. A. Sotelo, A. V. Paley, and A. V. Radchik, "Optical properties of a pair of spheres: comparison of different theories," Opt. Commun. 15, 8-12 (1995).
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H. Xu and M. Käll, "Surface-plasmon-enhanced optical forces in silver nanoaggregates," Phys.Rev. Lett. 89, 246802 (2002).
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J. J. Xiao, J. P. Huang, and K. W. Yu, "Optical response of strongly coupled metal nanoparticles in dimer arrays," Phys. Rev. B 71, 045404 (2005).
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H. Tamaru, H. Kuwata, H. T. Miyazaki, and K. Miyano, "Resonant light scattering from individual Ag nanoparticles and particle pairs," Appl. Phys. Lett. 80, 1826-1828 (2002).
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A. V. Radchik, A. V. Paley, G. B. Smith, and A. V. Vagov, "Polarization and resonant absorption in intersecting cylinders and spheres," J. Appl. Phys. 76, 4827-4835 (1994).
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C. E. Talley, J. B. Jackson, C. Oubre, N. K. Grady, C. W. Hollars, S. M. Lane, T. R. Huser, P. Nordlander, and N. J. Halas, "Surface-enhanced Raman scattering from individual Au nanoparticles and nanoparticle dimer substrates," Nano Lett. 5, 1569-1574 (2005).
[CrossRef] [PubMed]

T. Atay, J. H. Song, and A. V. Nurmikko, "Strongly interacting plasmon nanoparticle pairs: from dipole-dipole interaction to conductively coupled regime," Nano Lett. 4, 1627-1631 (2004).
[CrossRef]

P. Nordlander, C. Oubre, E. Prodan, K. Li, and M. I. Stockman, "Plasmon hybridization in nanoparticle dimers," Nano Lett. 4, 899-903 (2004).
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P. Nordlander and E. Prodan, "Plasmon hybridization in nanoparticles near metallic surfaces," Nano Lett. 4, 2209-2213 (2004).
[CrossRef]

D. A. Genov, A. K. Sarychev, V. M. Shalaev, and A. Wei, "Resonant field enhancements from metal nanoparticle arrays," Nano Lett. 4, 153-158 (2004).
[CrossRef]

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S. A. Maier, P. G. Kik, H. A. Atwater, S. Meltzer, E. Harel, B. E. Koel, and A. A. G. Requicha, "Local detection of electromagnetic energy transport below the diffraction limit in metal nanoparticle plasmon waveguides," Nat. Mater. 2, 229-232 (2003).
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[CrossRef]

J. A. Dionne, L. A. Sweatlock, H. A. Atwater, and A. Polman, "Plasmon slot waveguides: towards chip-scale propagation with subwavelength-scale localization," Phys. Rev. B 73, 035407 (2006).
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[CrossRef] [PubMed]

J. Aizpurua, P. Hanarp, D. S. Sutherland, M. Käll, G. W. Bryant, and F. J. García de Abajo, "Optical properties of gold nanorings," Phys. Rev. Lett. 90, 057401 (2003).
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Phys. Solid State (1)

A. O. Govorov, S. A. Studenikin, and W. R. Frank, "Low-frequency plasmons in coupled electronic microstructures," Phys. Solid State 40, 499-502 (1998).
[CrossRef]

Phys.Rev. Lett. (1)

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

Proc. Natl. Acad. Sci. (1)

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. 97, 996-1001 (2000).
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Figures (6)

Fig. 1.
Fig. 1.

(a) Wavelength dependence of the imaginary part of the polarizability of the dimer formed by two spherical gold particles (a=60 nm) for different distances between their surfaces d. The applied electric field is polarized along the interparticle axis. (b) Same as (a) for a gold particle consisting of two overlapping spheres (d<0). Dashed curves have been added to guide the eye through the evolution of spectral features with varying d.

Fig. 2.
Fig. 2.

Contour plot showing the scattering cross section for two spherical gold particles as a function of the separation between their surfaces d (horizontal axis) and the light wavelength (vertical axis). Negative values of d correspond to overlapping spheres. The incoming electric field is polarized parallel to the line connecting the particle centers. The particle radius is a=60 nm. The cross section has been normalized to the projected area of one particle, πa 2. Solid curves are intended to guide the eye through the cross section maxima. The lower inset illustrates how unphysical modes become physical and dominant after touching (A-B-C curve).

Fig. 3.
Fig. 3.

Near-field maps and the corresponding induced surface charge distributions for two neighboring gold spheres as a function of their separation d and wavelength λ corresponding to selected points of Fig. 2, as indicated by labels A-H for overlapping spheres and I-L for separated spherical particles. The sphere radius is a=60 nm. The contour plots show the squared electric field in a plane that contains both sphere centers and that is parallel to the incident light direction (the light is coming from the left) and to the incident electric field polarization. The induced surface charge distribution corresponding to the excited modes under consideration is represented in the accompanying 3D plots.

Fig. 4.
Fig. 4.

Resonant wavelengths of standing and localized modes in gold dumbbell particles as a function of the length L of the central rod for two different values of the overlap distance d at L=0. All geometrical parameters are given in the insets.

Fig. 5.
Fig. 5.

Wavelength dependence of the imaginary part of the polarizability of an overlapping dimer with a smooth junction for sphere radii a=60 nm and overlap parameter d=-5 nm. The junction is smoothed by a toroidal surface of inner radius s as shown in the inset. Various values of s have been considered.

Fig. 6.
Fig. 6.

Wavelength dependence of the imaginary part of the polarizability of the dimer formed by two spherical KCl particles of radius a=2 µm for different distances between their surfaces d. The applied electric field is polarized along the interparticle axis. d<0 stands for overlapping particles. Dashed curves have been added to guide the eye through the evolution of spectral features with varying d.

Equations (1)

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Λ = ε Au + 1 ε Au 1 .

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