Abstract

We study an optical response of a system of two parallel close metallic cylinders having nanoscale dimensions. Surface plasmon excitation in the gap between the cylinders is specifically analyzed. In particular, resonance frequencies and field enhancement were investigated as functions of geometrical characteristics of the system and ohmic losses in the metal. The results of numerical simulations were systematically compared with the analytical theory, obtained in the quasi-static limit. The analytical method was generalized in order to take into account the retardation effects. We also present the physical qualitative picture of the plasmon modes, which is validated by numerical simulations and analytical theory.

© 2012 Optical Society of America

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  1. M. Suzuki, A. Takada, T. Yamada, T. Hayasaka, K. Sasaki, E. Takahashi, and S. Kumagai, “Low-reflective wire-grid polarizers with absorptive interference overlayers,” Nanotechnology 21, 175604 (2010).
    [CrossRef]
  2. Y. Ekinci, H. H. Solak, C. David, and H. Sigg, “Bilayer Al wire-grids as broadband and high-performance polarizers,” Opt. Express 14, 2323–2334 (2006).
    [CrossRef]
  3. R. M. Bakker, H-K. Yuan, Z. Liu, V. P. Drachev, A. V. Kildishev, V. M. Shalaev, R. H. Pedersen, S. Gresillon, and A. Boltasseva, “Enhanced localized fluorescence in plasmonic nanoantennae,” Appl. Phys. Lett. 92, 043101 (2008).
    [CrossRef]
  4. J. Zhang, Y. Fu, M. H. Chowdhury, and J. R. Lakowicz, “Metal-enhanced single-molecule fluorescence on silver particle monomer and dimer: coupling effect between metal particles,” Nano Lett. 7, 2101–2107 (2007).
    [CrossRef]
  5. D. Bloemendal, P. Ghenuche, R. Quidant, I. G. Cormack, P. Loza-Alvarez, and G. Badenes, “Local field spectroscopy of metal dimers by TPL microscopy,” Plasmonics 1, 41–44(2006).
    [CrossRef]
  6. P. K. Jain, W. Huang, and M. A. El-Sayed, “On the universal scaling behavior of the distance decay of plasmon coupling in metal nanoparticle pairs: a plasmon ruler equation,” Nano Lett. 7, 2080–2088 (2007).
    [CrossRef]
  7. J. Berthelot, A. Bouhelier, C. Huang, J. Margueritat, G. Colas-des-Francs, E. Finot, J-C. Weeber, A. Dereux, S. Kostcheev, H. I. E. Ahrach, A-L. Baudrion, J. Plain, R. Bachelot, P. Royer, and G. P. Wiederrecht, “Tuning of an optical dimer nanoantenna by electrically controlling its load impedance,” Nano Lett. 9, 3914–3921(2009).
    [CrossRef]
  8. Z.-K. Zhou, M. Li, Z.-J. Yang, X.-N. Peng, X.-R. Su, Z.-S. Zhang, J.-B. Li, N.-C. Kim, X.-F. Yu, L. Zhou, Z.-H. Hao, and Q.-Q. Wang, “Plasmon-mediated radiative energy transfer across a silver nanowire array via resonant transmission and subwavelength imaging,” ACS Nano 4, 5003–5010 (2010).
    [CrossRef]
  9. 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]
  10. A. W. Sanders, D. A. Routenberg, B. J. Wiley, Y. Xia, E. R. Dufresne, and M. A. Reed, “Observation of plasmon propagation, redirection and fan-out in silver nanowires,” Nano Lett. 6, 1822–1826 (2006).
    [CrossRef]
  11. J. Clarkson, J. Winans, and P. Facuhet, “On the scaling behavior of dipole and quadrupole modes in coupled plasmonic nanoparticle pairs,” Opt. Mater. Express 1, 970–979 (2011).
    [CrossRef]
  12. I. Romero, J. Aizpurua, G. W. Bryant, and F. J. Garcia De Abajo, “Plasmons in nearly touching metallic nanoparticles: singular response in the limit of touching dimers,” Opt. Express 14, 9988–9999 (2006).
    [CrossRef]
  13. V. Amendola, O. M. Bakr, and F. Stellacci, “A study of the surface plasmon resonance of silver nanoparticles by the discrete dipole approximation method: effect of shape, size, structure and assembly,” Plasmonics 585–97 (2010).
    [CrossRef]
  14. Y. Cheng, M. Wang, G. Borghs, and H. Chen, “Gold nanoparticle dimers for plasmon sensing,” Langmuir 27, 7884–7891 (2011).
    [CrossRef]
  15. G. Haran, “Single-molecule Raman spectroscopy: a probe of surface dynamics and plasmonic fields,” Acc. Chem. Res. 43, 1135–1143 (2010).
    [CrossRef]
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    [CrossRef]
  18. D. Y. Fedyanin, A. V. Arsenin, V. G. Leiman, and A. D. Gladun, “Backward waves in planar insulator-metal-insulator waveguide structures,” J. Opt. 12, 015002 (2010).
    [CrossRef]
  19. I. P. Kaminow, W. L. Mammel, and H. P. Weber, “Metal-clad optical waveguides: analytical and experimental study,” Appl. Opt. 13, 396–405 (1974).
    [CrossRef]
  20. C. A. Pfeiffer, E. N. Economou, and K. L. Ngai, “Surface polaritons in a circularly cylindrical interface: surface plasmons,” Phys. Rev. B 10, 3038–3051 (1974).
    [CrossRef]
  21. P. Nordlander, C. Oubre, E. Prodan, K. Li, and M. I. Stockman, “Plasmon hybridization in nanoparticle dimers,” Nano Letters 4, 899–903 (2004).
    [CrossRef]
  22. S. V. Zhukovsky, C. Kremers, and D. N. Chigrin, “Plasmonic rod dimers as elementary planar chiral meta-atoms,” Opt. Lett. 36, 2278–2280 (2011).
  23. M. Hentschel, D. Dregely, R. Vogelgesang, H. Giessen, and N. Liu, “Plasmonic oligomers: the role of individual particles in collective behavior,” ACS Nano 5, 2042–2050 (2011).
    [CrossRef]
  24. J. Petschulat, C. Menzel, A. Chipouline, C. Rockstuhl, A. Tünnermann, F. Lederer, and T. Pertsch, “Multipole approach to metamaterials,” Phys. Rev. A 78, 043811 (2008).
    [CrossRef]
  25. D. N. Chigrin, C. Kremers, and S. V. Zhukovsky, “Plasmonic nanoparticle monomers and dimers: from nano-antennas to chiral metamaterials,” Appl. Phys. B: Lasers Opt. 105, 81–97 (2011).
    [CrossRef]
  26. V. Lebedev, S. Vergeles, and P. Vorobev, “Giant enhancement of electric field between two close metallic grains due to plasmonic resonance,” Opt. Lett. 35, 640–642 (2010).
    [CrossRef]
  27. V. V. Klimov and D. V. Guzatov, “Strongly localized plasmon oscillations in a cluster of two metallic nanospheres and their influence on spontaneous emission of an atom,” Phys. Rev. B 75, 24303 (2007).
    [CrossRef]
  28. M. H. Davis, “Two charged spherical conductors in a uniform electric field: forces and field strength,” Q. J. Mech. Appl. Math. 17, 499–511 (1964).
    [CrossRef]
  29. P. E. Vorobev, “Electric field enhancement between two parallel cylinders due to plasmonic resonance,” J. Exp. Theor. Phys. 110, 193–198 (2010).
    [CrossRef]
  30. A. M. Michaels, J. Jiang, and L. Brus, “Ag nanocrystal junctions as the site for surface-enhanced Raman scattering of single rhodamine 6G molecules,” J. Phys. Chem. B 104, 11965(2000).
    [CrossRef]
  31. J. Pomplun, S. Burger, L. Zschiedrich, and F. Schmidt, “Adaptive finite element method for simulation of optical nano structures,” Phys. Status Solidi B 244, 3419–3434 (2007).
    [CrossRef]
  32. J. Hoffmann, C. Hafner, P. Leidenberger, J. Hesselbarth, and S. Burger, “Comparison of electromagnetic field solvers for the 3D analysis of plasmonic nanoantennas,” Proc. SPIE 7390, 73900J (2009).
    [CrossRef]
  33. S. Burger, R. Köhle, L. Zschiedrich, W. Gao, F. Schmidt, R. März, and C. Nölscher, “Benchmark of FEM, waveguide and FDTD algorithms for rigorous mask simulation,” Proc. SPIE 5992, 599216 (2005).
    [CrossRef]
  34. P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6, 4370–4379 (1972).
    [CrossRef]

2011 (5)

Y. Cheng, M. Wang, G. Borghs, and H. Chen, “Gold nanoparticle dimers for plasmon sensing,” Langmuir 27, 7884–7891 (2011).
[CrossRef]

M. Hentschel, D. Dregely, R. Vogelgesang, H. Giessen, and N. Liu, “Plasmonic oligomers: the role of individual particles in collective behavior,” ACS Nano 5, 2042–2050 (2011).
[CrossRef]

D. N. Chigrin, C. Kremers, and S. V. Zhukovsky, “Plasmonic nanoparticle monomers and dimers: from nano-antennas to chiral metamaterials,” Appl. Phys. B: Lasers Opt. 105, 81–97 (2011).
[CrossRef]

S. V. Zhukovsky, C. Kremers, and D. N. Chigrin, “Plasmonic rod dimers as elementary planar chiral meta-atoms,” Opt. Lett. 36, 2278–2280 (2011).

J. Clarkson, J. Winans, and P. Facuhet, “On the scaling behavior of dipole and quadrupole modes in coupled plasmonic nanoparticle pairs,” Opt. Mater. Express 1, 970–979 (2011).
[CrossRef]

2010 (7)

V. Lebedev, S. Vergeles, and P. Vorobev, “Giant enhancement of electric field between two close metallic grains due to plasmonic resonance,” Opt. Lett. 35, 640–642 (2010).
[CrossRef]

G. Haran, “Single-molecule Raman spectroscopy: a probe of surface dynamics and plasmonic fields,” Acc. Chem. Res. 43, 1135–1143 (2010).
[CrossRef]

D. Y. Fedyanin, A. V. Arsenin, V. G. Leiman, and A. D. Gladun, “Backward waves in planar insulator-metal-insulator waveguide structures,” J. Opt. 12, 015002 (2010).
[CrossRef]

M. Suzuki, A. Takada, T. Yamada, T. Hayasaka, K. Sasaki, E. Takahashi, and S. Kumagai, “Low-reflective wire-grid polarizers with absorptive interference overlayers,” Nanotechnology 21, 175604 (2010).
[CrossRef]

P. E. Vorobev, “Electric field enhancement between two parallel cylinders due to plasmonic resonance,” J. Exp. Theor. Phys. 110, 193–198 (2010).
[CrossRef]

Z.-K. Zhou, M. Li, Z.-J. Yang, X.-N. Peng, X.-R. Su, Z.-S. Zhang, J.-B. Li, N.-C. Kim, X.-F. Yu, L. Zhou, Z.-H. Hao, and Q.-Q. Wang, “Plasmon-mediated radiative energy transfer across a silver nanowire array via resonant transmission and subwavelength imaging,” ACS Nano 4, 5003–5010 (2010).
[CrossRef]

V. Amendola, O. M. Bakr, and F. Stellacci, “A study of the surface plasmon resonance of silver nanoparticles by the discrete dipole approximation method: effect of shape, size, structure and assembly,” Plasmonics 585–97 (2010).
[CrossRef]

2009 (2)

J. Berthelot, A. Bouhelier, C. Huang, J. Margueritat, G. Colas-des-Francs, E. Finot, J-C. Weeber, A. Dereux, S. Kostcheev, H. I. E. Ahrach, A-L. Baudrion, J. Plain, R. Bachelot, P. Royer, and G. P. Wiederrecht, “Tuning of an optical dimer nanoantenna by electrically controlling its load impedance,” Nano Lett. 9, 3914–3921(2009).
[CrossRef]

J. Hoffmann, C. Hafner, P. Leidenberger, J. Hesselbarth, and S. Burger, “Comparison of electromagnetic field solvers for the 3D analysis of plasmonic nanoantennas,” Proc. SPIE 7390, 73900J (2009).
[CrossRef]

2008 (2)

J. Petschulat, C. Menzel, A. Chipouline, C. Rockstuhl, A. Tünnermann, F. Lederer, and T. Pertsch, “Multipole approach to metamaterials,” Phys. Rev. A 78, 043811 (2008).
[CrossRef]

R. M. Bakker, H-K. Yuan, Z. Liu, V. P. Drachev, A. V. Kildishev, V. M. Shalaev, R. H. Pedersen, S. Gresillon, and A. Boltasseva, “Enhanced localized fluorescence in plasmonic nanoantennae,” Appl. Phys. Lett. 92, 043101 (2008).
[CrossRef]

2007 (4)

J. Zhang, Y. Fu, M. H. Chowdhury, and J. R. Lakowicz, “Metal-enhanced single-molecule fluorescence on silver particle monomer and dimer: coupling effect between metal particles,” Nano Lett. 7, 2101–2107 (2007).
[CrossRef]

P. K. Jain, W. Huang, and M. A. El-Sayed, “On the universal scaling behavior of the distance decay of plasmon coupling in metal nanoparticle pairs: a plasmon ruler equation,” Nano Lett. 7, 2080–2088 (2007).
[CrossRef]

V. V. Klimov and D. V. Guzatov, “Strongly localized plasmon oscillations in a cluster of two metallic nanospheres and their influence on spontaneous emission of an atom,” Phys. Rev. B 75, 24303 (2007).
[CrossRef]

J. Pomplun, S. Burger, L. Zschiedrich, and F. Schmidt, “Adaptive finite element method for simulation of optical nano structures,” Phys. Status Solidi B 244, 3419–3434 (2007).
[CrossRef]

2006 (4)

Y. Ekinci, H. H. Solak, C. David, and H. Sigg, “Bilayer Al wire-grids as broadband and high-performance polarizers,” Opt. Express 14, 2323–2334 (2006).
[CrossRef]

I. Romero, J. Aizpurua, G. W. Bryant, and F. J. Garcia De Abajo, “Plasmons in nearly touching metallic nanoparticles: singular response in the limit of touching dimers,” Opt. Express 14, 9988–9999 (2006).
[CrossRef]

D. Bloemendal, P. Ghenuche, R. Quidant, I. G. Cormack, P. Loza-Alvarez, and G. Badenes, “Local field spectroscopy of metal dimers by TPL microscopy,” Plasmonics 1, 41–44(2006).
[CrossRef]

A. W. Sanders, D. A. Routenberg, B. J. Wiley, Y. Xia, E. R. Dufresne, and M. A. Reed, “Observation of plasmon propagation, redirection and fan-out in silver nanowires,” Nano Lett. 6, 1822–1826 (2006).
[CrossRef]

2005 (1)

S. Burger, R. Köhle, L. Zschiedrich, W. Gao, F. Schmidt, R. März, and C. Nölscher, “Benchmark of FEM, waveguide and FDTD algorithms for rigorous mask simulation,” Proc. SPIE 5992, 599216 (2005).
[CrossRef]

2004 (1)

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

2003 (1)

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]

2000 (1)

A. M. Michaels, J. Jiang, and L. Brus, “Ag nanocrystal junctions as the site for surface-enhanced Raman scattering of single rhodamine 6G molecules,” J. Phys. Chem. B 104, 11965(2000).
[CrossRef]

1977 (1)

A. D. Boardman and B. V. Paranjape, “The optical surface modes of metal spheres,” J. Phys. F 7, 1935–1945 (1977).
[CrossRef]

1974 (2)

C. A. Pfeiffer, E. N. Economou, and K. L. Ngai, “Surface polaritons in a circularly cylindrical interface: surface plasmons,” Phys. Rev. B 10, 3038–3051 (1974).
[CrossRef]

I. P. Kaminow, W. L. Mammel, and H. P. Weber, “Metal-clad optical waveguides: analytical and experimental study,” Appl. Opt. 13, 396–405 (1974).
[CrossRef]

1972 (1)

P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6, 4370–4379 (1972).
[CrossRef]

1964 (1)

M. H. Davis, “Two charged spherical conductors in a uniform electric field: forces and field strength,” Q. J. Mech. Appl. Math. 17, 499–511 (1964).
[CrossRef]

Ahrach, H. I. E.

J. Berthelot, A. Bouhelier, C. Huang, J. Margueritat, G. Colas-des-Francs, E. Finot, J-C. Weeber, A. Dereux, S. Kostcheev, H. I. E. Ahrach, A-L. Baudrion, J. Plain, R. Bachelot, P. Royer, and G. P. Wiederrecht, “Tuning of an optical dimer nanoantenna by electrically controlling its load impedance,” Nano Lett. 9, 3914–3921(2009).
[CrossRef]

Aizpurua, J.

Amendola, V.

V. Amendola, O. M. Bakr, and F. Stellacci, “A study of the surface plasmon resonance of silver nanoparticles by the discrete dipole approximation method: effect of shape, size, structure and assembly,” Plasmonics 585–97 (2010).
[CrossRef]

Arsenin, A. V.

D. Y. Fedyanin, A. V. Arsenin, V. G. Leiman, and A. D. Gladun, “Backward waves in planar insulator-metal-insulator waveguide structures,” J. Opt. 12, 015002 (2010).
[CrossRef]

Atwater, H. A.

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]

Bachelot, R.

J. Berthelot, A. Bouhelier, C. Huang, J. Margueritat, G. Colas-des-Francs, E. Finot, J-C. Weeber, A. Dereux, S. Kostcheev, H. I. E. Ahrach, A-L. Baudrion, J. Plain, R. Bachelot, P. Royer, and G. P. Wiederrecht, “Tuning of an optical dimer nanoantenna by electrically controlling its load impedance,” Nano Lett. 9, 3914–3921(2009).
[CrossRef]

Badenes, G.

D. Bloemendal, P. Ghenuche, R. Quidant, I. G. Cormack, P. Loza-Alvarez, and G. Badenes, “Local field spectroscopy of metal dimers by TPL microscopy,” Plasmonics 1, 41–44(2006).
[CrossRef]

Bakker, R. M.

R. M. Bakker, H-K. Yuan, Z. Liu, V. P. Drachev, A. V. Kildishev, V. M. Shalaev, R. H. Pedersen, S. Gresillon, and A. Boltasseva, “Enhanced localized fluorescence in plasmonic nanoantennae,” Appl. Phys. Lett. 92, 043101 (2008).
[CrossRef]

Bakr, O. M.

V. Amendola, O. M. Bakr, and F. Stellacci, “A study of the surface plasmon resonance of silver nanoparticles by the discrete dipole approximation method: effect of shape, size, structure and assembly,” Plasmonics 585–97 (2010).
[CrossRef]

Baudrion, A-L.

J. Berthelot, A. Bouhelier, C. Huang, J. Margueritat, G. Colas-des-Francs, E. Finot, J-C. Weeber, A. Dereux, S. Kostcheev, H. I. E. Ahrach, A-L. Baudrion, J. Plain, R. Bachelot, P. Royer, and G. P. Wiederrecht, “Tuning of an optical dimer nanoantenna by electrically controlling its load impedance,” Nano Lett. 9, 3914–3921(2009).
[CrossRef]

Berthelot, J.

J. Berthelot, A. Bouhelier, C. Huang, J. Margueritat, G. Colas-des-Francs, E. Finot, J-C. Weeber, A. Dereux, S. Kostcheev, H. I. E. Ahrach, A-L. Baudrion, J. Plain, R. Bachelot, P. Royer, and G. P. Wiederrecht, “Tuning of an optical dimer nanoantenna by electrically controlling its load impedance,” Nano Lett. 9, 3914–3921(2009).
[CrossRef]

Bloemendal, D.

D. Bloemendal, P. Ghenuche, R. Quidant, I. G. Cormack, P. Loza-Alvarez, and G. Badenes, “Local field spectroscopy of metal dimers by TPL microscopy,” Plasmonics 1, 41–44(2006).
[CrossRef]

Boardman, A. D.

A. D. Boardman and B. V. Paranjape, “The optical surface modes of metal spheres,” J. Phys. F 7, 1935–1945 (1977).
[CrossRef]

Boltasseva, A.

R. M. Bakker, H-K. Yuan, Z. Liu, V. P. Drachev, A. V. Kildishev, V. M. Shalaev, R. H. Pedersen, S. Gresillon, and A. Boltasseva, “Enhanced localized fluorescence in plasmonic nanoantennae,” Appl. Phys. Lett. 92, 043101 (2008).
[CrossRef]

Borghs, G.

Y. Cheng, M. Wang, G. Borghs, and H. Chen, “Gold nanoparticle dimers for plasmon sensing,” Langmuir 27, 7884–7891 (2011).
[CrossRef]

Bouhelier, A.

J. Berthelot, A. Bouhelier, C. Huang, J. Margueritat, G. Colas-des-Francs, E. Finot, J-C. Weeber, A. Dereux, S. Kostcheev, H. I. E. Ahrach, A-L. Baudrion, J. Plain, R. Bachelot, P. Royer, and G. P. Wiederrecht, “Tuning of an optical dimer nanoantenna by electrically controlling its load impedance,” Nano Lett. 9, 3914–3921(2009).
[CrossRef]

Brus, L.

A. M. Michaels, J. Jiang, and L. Brus, “Ag nanocrystal junctions as the site for surface-enhanced Raman scattering of single rhodamine 6G molecules,” J. Phys. Chem. B 104, 11965(2000).
[CrossRef]

Bryant, G. W.

Burger, S.

J. Hoffmann, C. Hafner, P. Leidenberger, J. Hesselbarth, and S. Burger, “Comparison of electromagnetic field solvers for the 3D analysis of plasmonic nanoantennas,” Proc. SPIE 7390, 73900J (2009).
[CrossRef]

J. Pomplun, S. Burger, L. Zschiedrich, and F. Schmidt, “Adaptive finite element method for simulation of optical nano structures,” Phys. Status Solidi B 244, 3419–3434 (2007).
[CrossRef]

S. Burger, R. Köhle, L. Zschiedrich, W. Gao, F. Schmidt, R. März, and C. Nölscher, “Benchmark of FEM, waveguide and FDTD algorithms for rigorous mask simulation,” Proc. SPIE 5992, 599216 (2005).
[CrossRef]

Chen, H.

Y. Cheng, M. Wang, G. Borghs, and H. Chen, “Gold nanoparticle dimers for plasmon sensing,” Langmuir 27, 7884–7891 (2011).
[CrossRef]

Cheng, Y.

Y. Cheng, M. Wang, G. Borghs, and H. Chen, “Gold nanoparticle dimers for plasmon sensing,” Langmuir 27, 7884–7891 (2011).
[CrossRef]

Chigrin, D. N.

S. V. Zhukovsky, C. Kremers, and D. N. Chigrin, “Plasmonic rod dimers as elementary planar chiral meta-atoms,” Opt. Lett. 36, 2278–2280 (2011).

D. N. Chigrin, C. Kremers, and S. V. Zhukovsky, “Plasmonic nanoparticle monomers and dimers: from nano-antennas to chiral metamaterials,” Appl. Phys. B: Lasers Opt. 105, 81–97 (2011).
[CrossRef]

Chipouline, A.

J. Petschulat, C. Menzel, A. Chipouline, C. Rockstuhl, A. Tünnermann, F. Lederer, and T. Pertsch, “Multipole approach to metamaterials,” Phys. Rev. A 78, 043811 (2008).
[CrossRef]

Chowdhury, M. H.

J. Zhang, Y. Fu, M. H. Chowdhury, and J. R. Lakowicz, “Metal-enhanced single-molecule fluorescence on silver particle monomer and dimer: coupling effect between metal particles,” Nano Lett. 7, 2101–2107 (2007).
[CrossRef]

Christy, R. W.

P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6, 4370–4379 (1972).
[CrossRef]

Clarkson, J.

Colas-des-Francs, G.

J. Berthelot, A. Bouhelier, C. Huang, J. Margueritat, G. Colas-des-Francs, E. Finot, J-C. Weeber, A. Dereux, S. Kostcheev, H. I. E. Ahrach, A-L. Baudrion, J. Plain, R. Bachelot, P. Royer, and G. P. Wiederrecht, “Tuning of an optical dimer nanoantenna by electrically controlling its load impedance,” Nano Lett. 9, 3914–3921(2009).
[CrossRef]

Cormack, I. G.

D. Bloemendal, P. Ghenuche, R. Quidant, I. G. Cormack, P. Loza-Alvarez, and G. Badenes, “Local field spectroscopy of metal dimers by TPL microscopy,” Plasmonics 1, 41–44(2006).
[CrossRef]

David, C.

Davis, M. H.

M. H. Davis, “Two charged spherical conductors in a uniform electric field: forces and field strength,” Q. J. Mech. Appl. Math. 17, 499–511 (1964).
[CrossRef]

De Abajo, F. J. Garcia

Dereux, A.

J. Berthelot, A. Bouhelier, C. Huang, J. Margueritat, G. Colas-des-Francs, E. Finot, J-C. Weeber, A. Dereux, S. Kostcheev, H. I. E. Ahrach, A-L. Baudrion, J. Plain, R. Bachelot, P. Royer, and G. P. Wiederrecht, “Tuning of an optical dimer nanoantenna by electrically controlling its load impedance,” Nano Lett. 9, 3914–3921(2009).
[CrossRef]

Drachev, V. P.

R. M. Bakker, H-K. Yuan, Z. Liu, V. P. Drachev, A. V. Kildishev, V. M. Shalaev, R. H. Pedersen, S. Gresillon, and A. Boltasseva, “Enhanced localized fluorescence in plasmonic nanoantennae,” Appl. Phys. Lett. 92, 043101 (2008).
[CrossRef]

Dregely, D.

M. Hentschel, D. Dregely, R. Vogelgesang, H. Giessen, and N. Liu, “Plasmonic oligomers: the role of individual particles in collective behavior,” ACS Nano 5, 2042–2050 (2011).
[CrossRef]

Dufresne, E. R.

A. W. Sanders, D. A. Routenberg, B. J. Wiley, Y. Xia, E. R. Dufresne, and M. A. Reed, “Observation of plasmon propagation, redirection and fan-out in silver nanowires,” Nano Lett. 6, 1822–1826 (2006).
[CrossRef]

Economou, E. N.

C. A. Pfeiffer, E. N. Economou, and K. L. Ngai, “Surface polaritons in a circularly cylindrical interface: surface plasmons,” Phys. Rev. B 10, 3038–3051 (1974).
[CrossRef]

Ekinci, Y.

El-Sayed, M. A.

P. K. Jain, W. Huang, and M. A. El-Sayed, “On the universal scaling behavior of the distance decay of plasmon coupling in metal nanoparticle pairs: a plasmon ruler equation,” Nano Lett. 7, 2080–2088 (2007).
[CrossRef]

Facuhet, P.

Fedyanin, D. Y.

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Figures (9)

Fig. 1.
Fig. 1.

Two close cylinders, coordinate system and field polarization.

Fig. 2.
Fig. 2.

Numerical simulation results for electric field enhancement in the center of the gap between the cylinders as a function of real part ε of model metal permittivity. The wavelength is λ=2μm, the radius of the cylinders is a=50nm, and the gap width is δ=2nm.

Fig. 3.
Fig. 3.

Value of real part of permittivity ε as a function of affinity of the cylinders for main resonance, n=1. It was taken a=50nm, ε=0.6, and λ=2μm in numerical simulations for model metal. For silver, a=15nm was taken.

Fig. 4.
Fig. 4.

Numerical simulation results for electric field enhancement in the center of the gap for silver cylinders as a function of wavelength for constant width gap δ=3nm. Compare with Fig. 2.

Fig. 5.
Fig. 5.

Numerical simulations results for electric field enhancement in the center of the gap for silver cylinders as a function of wavelength for constant ratio a/δ=10 (solid lines). Dashed line is given for comparison and corresponds to different ratio a/δ=15. Compare with Fig. 2.

Fig. 6.
Fig. 6.

Dependence of mode size on geometrical parameters, for λ=2μm, ε=0.6, a=30nm. Deviation from the dashed line corresponding to law (16) at large δ is due to contribution from nonresonance harmonics in expansion (12).

Fig. 7.
Fig. 7.

Dependence of electric field enhancement on imaginary part ε of model metal permittivity in the first resonance. The wavelength is λ=2μm, the radius of the cylinders is a=50nm, and the gap width is δ=1nm. The dotted line corresponds to law (17) at resonance in the pure quasi-static limit, and the dashed line accounts for radiative losses, which are given by Eq. (17).

Fig. 8.
Fig. 8.

Dependence of field enhancement factor in resonance on geometrical parameters. It was taken a=30nm, ε=0.6, and λ=2μm in numerical simulations for model metal. For silver, a=15nm was taken. Dashed lines correspond to theory prediction (17) without taking into consideration radiation losses; the solid line takes the losses into account [see Eq. (17)].

Fig. 9.
Fig. 9.

Field spatial dependence on the middle line between the cylinders. Parameters are a=30nm, δ=0.1nm, ε=17.4, ε=0.6, λ=2μm. Dashed line is asymptotics E1/x2; see Eq. (16).

Equations (17)

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

div1ε(r)gradH+ω2c2H=0,
div(ε(r)gradΦ)=0
x=asinhξ0sinηcoshξcosη;y=asinhξ0sinhξcoshξcosη.
21h2(ξ,η)(2ξ2+2η2),
Φin=E0a0Anenξcosnη;ξ>0,
Φout,ind=E0a1Bnsinhnξcosnη,
Φ0=signξE0asinhξ0(n=1+2en|ξ|cosnη+1).
Bn=2sinhξ0(1ε)enξ0sinhnξ0(ε+cothnξ0),An=2sinhξ0enξ0sinhnξ0(ε+cothnξ0).
εn=cothnξ0.
Exind=(sinhξsinηξ(1coshξcosη)η)Φind,outasinhξ0,
Eyind=((1coshξcosη)ξ+sinhξsinηη)Φind,outasinhξ0.
εres=1na/δ
Ey=4(a/δ)E0εε1x2/aδ1((x2/aδ)2+1)2,
l=aδ,
Ec=4sinh2ξ0Ecεε1=4aδE0εε1.
Ey=aδx2Ec.
ε1=πk2a2,

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