Abstract

The polarizability of a nanostructure is an important parameter that determines the optical properties. An exact semi-analytical solution of the electrostatic polarizability of a general geometry consisting of two segments forming a cylinder that can be arbitrarily buried in a substrate is derived using bipolar coordinates, cosine-, and sine-transformations. Based on the presented expressions, we analyze the polarizability of several metal nanowire geometries that are important within plasmonics. Our results provide physical insight into the interplay between the multiple resonances found in the polarizability of metal nanowires at surfaces.

© 2012 OSA

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. S. A. Maier, Plasmonics: Fundamentals and Applications (Springer, 2007).
  2. L. Novotny and B. Hecht, Principles of Nano-optics (Cambridge2006).
  3. A. V. Zayats and I. I. Smolyaninov, “Near-field photonics: surface plasmon polaritons and localized surface plasmons,” J. Opt. A: Pure Appl. Opt. 5, S16–S50 (2003).
    [CrossRef]
  4. S. A. Maier and H. A. Atwater, “Plasmonics: localization and guiding of electromagnetic energy in metal/dielectric structures,” J. Appl. Phys. 98, 011101 (2005).
    [CrossRef]
  5. W. A. Murray and W. L. Barnes, “Plasmonic materials,” Adv. Mater. 19, 3771–3782 (2007).
    [CrossRef]
  6. S. Lal, S. Link, and N. J. Halas, “Nano-optics from sensing to waveguiding,” Nat. Photonics 1, 641–648 (2007).
    [CrossRef]
  7. M. Moskovits, “Surface-enhanced spectroscopy,” Rev. Mod. Phys. 57, 783–826 (1985).
    [CrossRef]
  8. Y. C. Coa, R. Jin, and C. A. Mirkin, “Nanoparticles with Raman spectroscopic fingerprints for DNA and RNA detection,” Science 297, 1536–1540 (2002).
    [CrossRef]
  9. A. J. Haes and R. P. V. Duyne, “A nanoscale optical biosensor: sensitivity and selectivity of an approach based on the localized surface plasmon resonance spectroscopy of triangular silver nanoparticles,” J. Am. Chem. Soc. 124, 10596–10604 (2002).
    [CrossRef] [PubMed]
  10. K. R. Catchpole and A. Polman, “Plasmonic solar cells,” Opt. Express 16, 21793–21800 (2008).
    [CrossRef] [PubMed]
  11. H. A. Atwater and A. Polman, “Plasmonics for improved photovoltaic devices,” Nat. Mater. 9, 205–213 (2010).
    [CrossRef] [PubMed]
  12. V. E. Ferry, J. N. Munday, and H. A. Atwater, “Design considerations for plasmonic photovoltaics,” Adv. Mater. 22, 4794–4808 (2010).
    [CrossRef] [PubMed]
  13. L. Lorenz, “Lysbevægelsen i og udenfor en af plane lysbølger belyst kugle,” K. Dan. Vidensk. Selsk. Skr. 6, 1–62 (1890).
  14. G. Mie, “Beitrage zur optik truber medien speziell kolloidaler metallosungen,” Ann. Physik. 330, 337–445 (1908).
    [CrossRef]
  15. C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1983).
  16. L. Rayleigh, “The dispersal of light by a dielectric cylinder,” Phil. Mag. 36, 365–376 (1918).
  17. J. R. Wait, “Scattering of a plane wave from a circular cylinder at oblique incidence,” Can. J. Phys. 33, 189–195 (1955).
    [CrossRef]
  18. A. Taflove and S. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method (Artech House, 2000).
  19. J. Jin, The Finite Element Method in Electrodynamics (Wiley, 2002).
  20. T. Søndergaard, “Modeling of plasmonic nanostructures: Green’s function integral equation methods,” Phys. Status Solidi B 244, 3448–3462 (2007).
    [CrossRef]
  21. O. J. F. Martin, C. Girard, and A. Dereux, “Generalized field propagator for electromagnetic scattering and light confinement,” Phys. Rev. Lett. 74, 526–529 (1995).
    [CrossRef] [PubMed]
  22. F. J. Garcia de Abajo and A. Howie, “Retarded field calculation of electron energy loss in inhomogenous dielectrics,” Phys. Rev. B 65, 115418 (2002).
    [CrossRef]
  23. J. Jung, T. G. Pedersen, T. Søndergaard, K. Pedersen, A. N. Larsen, and B. B. Nielsen, “Electrostatic plasmon resonances of metal nanospheres in layered geometries,” Phys. Rev. B 81, 125413 (2010).
    [CrossRef]
  24. F. Hallermann, C. Rockstuhl, S. Fahr, G. Seifert, S. Wackerow, H. Graener, G. V. Plessen, and F. Lederer, “On the use of localized plasmon polaritons in solar cells,” Phys. Status Solidi A 205, 2844–2861 (2008).
    [CrossRef]
  25. J. W. Yoon, W. J. Park, K. J. Lee, S. H. Song, and R. Magnusson, “Surface-plasmon mediated total absorption of light into silicon,” Opt. Express 19, 20673–20680 (2011).
    [CrossRef] [PubMed]
  26. P. C. Waterman, “Surface fields and the T matrix,” J. Opt. Soc. Am. A 16, 2968–2977 (1999).
    [CrossRef]
  27. 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]
  28. A. Salandrino, A. Alu, and N. Engheta, “Parallel, series, and intermediate interconnects of optical nanocircuit elements. 1. Analytical solution,” J. Opt. Soc. Am. B 24, 3007–3013 (2007).
    [CrossRef]
  29. M Pitkonen, “A closed-form solution for the polarizability of a dielectric double half-cylinder,” J. Electromagn. Waves Appl. 24, 1267–1277 (2010).
    [CrossRef]
  30. H. Kettunen, H. Wallen, and A. Sihvola, “Polarizability of a dielectic hemisphere,” J. Appl. Phys. 102, 044105 (2007).
    [CrossRef]
  31. Y. Luo, J. B. Pendry, and A. Aubry, “Surface plasmons and singularities,” Nano Lett. 10, 4186–4191 (2010).
    [CrossRef]
  32. Y. Luo, A. Aubry, and J. B. Pendry, “Electromagnetic contribution to surface-enhanced Raman scattering from rough metal surfaces: a transformation optics approach,” Phys. Rev. B 83, 155422 (2011).
    [CrossRef]
  33. J. Jung and T. G. Pedersen, “Exact polarizability and plasmon resonances of partly buried nanowires,” Opt. Express 19, 22775–22785 (2011).
    [CrossRef] [PubMed]
  34. P. M. Morse and H. Feshbach, Methods of Theoretical Physics, Part II (McGraw-Hill Book Company Inc., 1953).
  35. H. E. Lockwood, A Book of Curves (Cambridge University Press, 1963).
  36. A. Jonquiere, “Note sur la serie ∑n=1∞xnns,” Bulletin de la Socit Mathmatique de France 17, 142–152 (1889).
  37. P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6, 4370–4379 (1972).
    [CrossRef]
  38. J. R. Arias-Gonzalez and M. Nieto-Vesperinas, “Resonant near-field eigenmodes of nanocylinders on flat surfaces under both homogenous and inhomogenous lightwave excitation,” J. Opt. Soc. Am. A 18, 657–665 (2001).
    [CrossRef]
  39. A. Aubry, D. Y. Lei, S. A. Maier, and J. B. Pendry, “Plasmonic hybridization between nanowires and a metallic surface: a transformation optics approach,” ACS Nano 53293–3308 (2011).
    [CrossRef] [PubMed]

2011 (4)

J. W. Yoon, W. J. Park, K. J. Lee, S. H. Song, and R. Magnusson, “Surface-plasmon mediated total absorption of light into silicon,” Opt. Express 19, 20673–20680 (2011).
[CrossRef] [PubMed]

Y. Luo, A. Aubry, and J. B. Pendry, “Electromagnetic contribution to surface-enhanced Raman scattering from rough metal surfaces: a transformation optics approach,” Phys. Rev. B 83, 155422 (2011).
[CrossRef]

J. Jung and T. G. Pedersen, “Exact polarizability and plasmon resonances of partly buried nanowires,” Opt. Express 19, 22775–22785 (2011).
[CrossRef] [PubMed]

A. Aubry, D. Y. Lei, S. A. Maier, and J. B. Pendry, “Plasmonic hybridization between nanowires and a metallic surface: a transformation optics approach,” ACS Nano 53293–3308 (2011).
[CrossRef] [PubMed]

2010 (5)

Y. Luo, J. B. Pendry, and A. Aubry, “Surface plasmons and singularities,” Nano Lett. 10, 4186–4191 (2010).
[CrossRef]

M Pitkonen, “A closed-form solution for the polarizability of a dielectric double half-cylinder,” J. Electromagn. Waves Appl. 24, 1267–1277 (2010).
[CrossRef]

H. A. Atwater and A. Polman, “Plasmonics for improved photovoltaic devices,” Nat. Mater. 9, 205–213 (2010).
[CrossRef] [PubMed]

V. E. Ferry, J. N. Munday, and H. A. Atwater, “Design considerations for plasmonic photovoltaics,” Adv. Mater. 22, 4794–4808 (2010).
[CrossRef] [PubMed]

J. Jung, T. G. Pedersen, T. Søndergaard, K. Pedersen, A. N. Larsen, and B. B. Nielsen, “Electrostatic plasmon resonances of metal nanospheres in layered geometries,” Phys. Rev. B 81, 125413 (2010).
[CrossRef]

2008 (2)

F. Hallermann, C. Rockstuhl, S. Fahr, G. Seifert, S. Wackerow, H. Graener, G. V. Plessen, and F. Lederer, “On the use of localized plasmon polaritons in solar cells,” Phys. Status Solidi A 205, 2844–2861 (2008).
[CrossRef]

K. R. Catchpole and A. Polman, “Plasmonic solar cells,” Opt. Express 16, 21793–21800 (2008).
[CrossRef] [PubMed]

2007 (5)

T. Søndergaard, “Modeling of plasmonic nanostructures: Green’s function integral equation methods,” Phys. Status Solidi B 244, 3448–3462 (2007).
[CrossRef]

W. A. Murray and W. L. Barnes, “Plasmonic materials,” Adv. Mater. 19, 3771–3782 (2007).
[CrossRef]

S. Lal, S. Link, and N. J. Halas, “Nano-optics from sensing to waveguiding,” Nat. Photonics 1, 641–648 (2007).
[CrossRef]

H. Kettunen, H. Wallen, and A. Sihvola, “Polarizability of a dielectic hemisphere,” J. Appl. Phys. 102, 044105 (2007).
[CrossRef]

A. Salandrino, A. Alu, and N. Engheta, “Parallel, series, and intermediate interconnects of optical nanocircuit elements. 1. Analytical solution,” J. Opt. Soc. Am. B 24, 3007–3013 (2007).
[CrossRef]

2005 (1)

S. A. Maier and H. A. Atwater, “Plasmonics: localization and guiding of electromagnetic energy in metal/dielectric structures,” J. Appl. Phys. 98, 011101 (2005).
[CrossRef]

2003 (1)

A. V. Zayats and I. I. Smolyaninov, “Near-field photonics: surface plasmon polaritons and localized surface plasmons,” J. Opt. A: Pure Appl. Opt. 5, S16–S50 (2003).
[CrossRef]

2002 (3)

Y. C. Coa, R. Jin, and C. A. Mirkin, “Nanoparticles with Raman spectroscopic fingerprints for DNA and RNA detection,” Science 297, 1536–1540 (2002).
[CrossRef]

A. J. Haes and R. P. V. Duyne, “A nanoscale optical biosensor: sensitivity and selectivity of an approach based on the localized surface plasmon resonance spectroscopy of triangular silver nanoparticles,” J. Am. Chem. Soc. 124, 10596–10604 (2002).
[CrossRef] [PubMed]

F. J. Garcia de Abajo and A. Howie, “Retarded field calculation of electron energy loss in inhomogenous dielectrics,” Phys. Rev. B 65, 115418 (2002).
[CrossRef]

2001 (1)

1999 (1)

1995 (1)

O. J. F. Martin, C. Girard, and A. Dereux, “Generalized field propagator for electromagnetic scattering and light confinement,” Phys. Rev. Lett. 74, 526–529 (1995).
[CrossRef] [PubMed]

1994 (1)

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]

1985 (1)

M. Moskovits, “Surface-enhanced spectroscopy,” Rev. Mod. Phys. 57, 783–826 (1985).
[CrossRef]

1972 (1)

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

1955 (1)

J. R. Wait, “Scattering of a plane wave from a circular cylinder at oblique incidence,” Can. J. Phys. 33, 189–195 (1955).
[CrossRef]

1918 (1)

L. Rayleigh, “The dispersal of light by a dielectric cylinder,” Phil. Mag. 36, 365–376 (1918).

1908 (1)

G. Mie, “Beitrage zur optik truber medien speziell kolloidaler metallosungen,” Ann. Physik. 330, 337–445 (1908).
[CrossRef]

1890 (1)

L. Lorenz, “Lysbevægelsen i og udenfor en af plane lysbølger belyst kugle,” K. Dan. Vidensk. Selsk. Skr. 6, 1–62 (1890).

1889 (1)

A. Jonquiere, “Note sur la serie ∑n=1∞xnns,” Bulletin de la Socit Mathmatique de France 17, 142–152 (1889).

Alu, A.

Arias-Gonzalez, J. R.

Atwater, H. A.

H. A. Atwater and A. Polman, “Plasmonics for improved photovoltaic devices,” Nat. Mater. 9, 205–213 (2010).
[CrossRef] [PubMed]

V. E. Ferry, J. N. Munday, and H. A. Atwater, “Design considerations for plasmonic photovoltaics,” Adv. Mater. 22, 4794–4808 (2010).
[CrossRef] [PubMed]

S. A. Maier and H. A. Atwater, “Plasmonics: localization and guiding of electromagnetic energy in metal/dielectric structures,” J. Appl. Phys. 98, 011101 (2005).
[CrossRef]

Aubry, A.

Y. Luo, A. Aubry, and J. B. Pendry, “Electromagnetic contribution to surface-enhanced Raman scattering from rough metal surfaces: a transformation optics approach,” Phys. Rev. B 83, 155422 (2011).
[CrossRef]

A. Aubry, D. Y. Lei, S. A. Maier, and J. B. Pendry, “Plasmonic hybridization between nanowires and a metallic surface: a transformation optics approach,” ACS Nano 53293–3308 (2011).
[CrossRef] [PubMed]

Y. Luo, J. B. Pendry, and A. Aubry, “Surface plasmons and singularities,” Nano Lett. 10, 4186–4191 (2010).
[CrossRef]

Barnes, W. L.

W. A. Murray and W. L. Barnes, “Plasmonic materials,” Adv. Mater. 19, 3771–3782 (2007).
[CrossRef]

Bohren, C. F.

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

Catchpole, K. R.

Christy, R. W.

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

Coa, Y. C.

Y. C. Coa, R. Jin, and C. A. Mirkin, “Nanoparticles with Raman spectroscopic fingerprints for DNA and RNA detection,” Science 297, 1536–1540 (2002).
[CrossRef]

Dereux, A.

O. J. F. Martin, C. Girard, and A. Dereux, “Generalized field propagator for electromagnetic scattering and light confinement,” Phys. Rev. Lett. 74, 526–529 (1995).
[CrossRef] [PubMed]

Duyne, R. P. V.

A. J. Haes and R. P. V. Duyne, “A nanoscale optical biosensor: sensitivity and selectivity of an approach based on the localized surface plasmon resonance spectroscopy of triangular silver nanoparticles,” J. Am. Chem. Soc. 124, 10596–10604 (2002).
[CrossRef] [PubMed]

Engheta, N.

Fahr, S.

F. Hallermann, C. Rockstuhl, S. Fahr, G. Seifert, S. Wackerow, H. Graener, G. V. Plessen, and F. Lederer, “On the use of localized plasmon polaritons in solar cells,” Phys. Status Solidi A 205, 2844–2861 (2008).
[CrossRef]

Ferry, V. E.

V. E. Ferry, J. N. Munday, and H. A. Atwater, “Design considerations for plasmonic photovoltaics,” Adv. Mater. 22, 4794–4808 (2010).
[CrossRef] [PubMed]

Feshbach, H.

P. M. Morse and H. Feshbach, Methods of Theoretical Physics, Part II (McGraw-Hill Book Company Inc., 1953).

Garcia de Abajo, F. J.

F. J. Garcia de Abajo and A. Howie, “Retarded field calculation of electron energy loss in inhomogenous dielectrics,” Phys. Rev. B 65, 115418 (2002).
[CrossRef]

Girard, C.

O. J. F. Martin, C. Girard, and A. Dereux, “Generalized field propagator for electromagnetic scattering and light confinement,” Phys. Rev. Lett. 74, 526–529 (1995).
[CrossRef] [PubMed]

Graener, H.

F. Hallermann, C. Rockstuhl, S. Fahr, G. Seifert, S. Wackerow, H. Graener, G. V. Plessen, and F. Lederer, “On the use of localized plasmon polaritons in solar cells,” Phys. Status Solidi A 205, 2844–2861 (2008).
[CrossRef]

Haes, A. J.

A. J. Haes and R. P. V. Duyne, “A nanoscale optical biosensor: sensitivity and selectivity of an approach based on the localized surface plasmon resonance spectroscopy of triangular silver nanoparticles,” J. Am. Chem. Soc. 124, 10596–10604 (2002).
[CrossRef] [PubMed]

Hagness, S.

A. Taflove and S. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method (Artech House, 2000).

Halas, N. J.

S. Lal, S. Link, and N. J. Halas, “Nano-optics from sensing to waveguiding,” Nat. Photonics 1, 641–648 (2007).
[CrossRef]

Hallermann, F.

F. Hallermann, C. Rockstuhl, S. Fahr, G. Seifert, S. Wackerow, H. Graener, G. V. Plessen, and F. Lederer, “On the use of localized plasmon polaritons in solar cells,” Phys. Status Solidi A 205, 2844–2861 (2008).
[CrossRef]

Hecht, B.

L. Novotny and B. Hecht, Principles of Nano-optics (Cambridge2006).

Howie, A.

F. J. Garcia de Abajo and A. Howie, “Retarded field calculation of electron energy loss in inhomogenous dielectrics,” Phys. Rev. B 65, 115418 (2002).
[CrossRef]

Huffman, D. R.

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

Jin, J.

J. Jin, The Finite Element Method in Electrodynamics (Wiley, 2002).

Jin, R.

Y. C. Coa, R. Jin, and C. A. Mirkin, “Nanoparticles with Raman spectroscopic fingerprints for DNA and RNA detection,” Science 297, 1536–1540 (2002).
[CrossRef]

Johnson, P. B.

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

Jonquiere, A.

A. Jonquiere, “Note sur la serie ∑n=1∞xnns,” Bulletin de la Socit Mathmatique de France 17, 142–152 (1889).

Jung, J.

J. Jung and T. G. Pedersen, “Exact polarizability and plasmon resonances of partly buried nanowires,” Opt. Express 19, 22775–22785 (2011).
[CrossRef] [PubMed]

J. Jung, T. G. Pedersen, T. Søndergaard, K. Pedersen, A. N. Larsen, and B. B. Nielsen, “Electrostatic plasmon resonances of metal nanospheres in layered geometries,” Phys. Rev. B 81, 125413 (2010).
[CrossRef]

Kettunen, H.

H. Kettunen, H. Wallen, and A. Sihvola, “Polarizability of a dielectic hemisphere,” J. Appl. Phys. 102, 044105 (2007).
[CrossRef]

Lal, S.

S. Lal, S. Link, and N. J. Halas, “Nano-optics from sensing to waveguiding,” Nat. Photonics 1, 641–648 (2007).
[CrossRef]

Larsen, A. N.

J. Jung, T. G. Pedersen, T. Søndergaard, K. Pedersen, A. N. Larsen, and B. B. Nielsen, “Electrostatic plasmon resonances of metal nanospheres in layered geometries,” Phys. Rev. B 81, 125413 (2010).
[CrossRef]

Lederer, F.

F. Hallermann, C. Rockstuhl, S. Fahr, G. Seifert, S. Wackerow, H. Graener, G. V. Plessen, and F. Lederer, “On the use of localized plasmon polaritons in solar cells,” Phys. Status Solidi A 205, 2844–2861 (2008).
[CrossRef]

Lee, K. J.

Lei, D. Y.

A. Aubry, D. Y. Lei, S. A. Maier, and J. B. Pendry, “Plasmonic hybridization between nanowires and a metallic surface: a transformation optics approach,” ACS Nano 53293–3308 (2011).
[CrossRef] [PubMed]

Link, S.

S. Lal, S. Link, and N. J. Halas, “Nano-optics from sensing to waveguiding,” Nat. Photonics 1, 641–648 (2007).
[CrossRef]

Lockwood, H. E.

H. E. Lockwood, A Book of Curves (Cambridge University Press, 1963).

Lorenz, L.

L. Lorenz, “Lysbevægelsen i og udenfor en af plane lysbølger belyst kugle,” K. Dan. Vidensk. Selsk. Skr. 6, 1–62 (1890).

Luo, Y.

Y. Luo, A. Aubry, and J. B. Pendry, “Electromagnetic contribution to surface-enhanced Raman scattering from rough metal surfaces: a transformation optics approach,” Phys. Rev. B 83, 155422 (2011).
[CrossRef]

Y. Luo, J. B. Pendry, and A. Aubry, “Surface plasmons and singularities,” Nano Lett. 10, 4186–4191 (2010).
[CrossRef]

Magnusson, R.

Maier, S. A.

A. Aubry, D. Y. Lei, S. A. Maier, and J. B. Pendry, “Plasmonic hybridization between nanowires and a metallic surface: a transformation optics approach,” ACS Nano 53293–3308 (2011).
[CrossRef] [PubMed]

S. A. Maier and H. A. Atwater, “Plasmonics: localization and guiding of electromagnetic energy in metal/dielectric structures,” J. Appl. Phys. 98, 011101 (2005).
[CrossRef]

S. A. Maier, Plasmonics: Fundamentals and Applications (Springer, 2007).

Martin, O. J. F.

O. J. F. Martin, C. Girard, and A. Dereux, “Generalized field propagator for electromagnetic scattering and light confinement,” Phys. Rev. Lett. 74, 526–529 (1995).
[CrossRef] [PubMed]

Mie, G.

G. Mie, “Beitrage zur optik truber medien speziell kolloidaler metallosungen,” Ann. Physik. 330, 337–445 (1908).
[CrossRef]

Mirkin, C. A.

Y. C. Coa, R. Jin, and C. A. Mirkin, “Nanoparticles with Raman spectroscopic fingerprints for DNA and RNA detection,” Science 297, 1536–1540 (2002).
[CrossRef]

Morse, P. M.

P. M. Morse and H. Feshbach, Methods of Theoretical Physics, Part II (McGraw-Hill Book Company Inc., 1953).

Moskovits, M.

M. Moskovits, “Surface-enhanced spectroscopy,” Rev. Mod. Phys. 57, 783–826 (1985).
[CrossRef]

Munday, J. N.

V. E. Ferry, J. N. Munday, and H. A. Atwater, “Design considerations for plasmonic photovoltaics,” Adv. Mater. 22, 4794–4808 (2010).
[CrossRef] [PubMed]

Murray, W. A.

W. A. Murray and W. L. Barnes, “Plasmonic materials,” Adv. Mater. 19, 3771–3782 (2007).
[CrossRef]

Nielsen, B. B.

J. Jung, T. G. Pedersen, T. Søndergaard, K. Pedersen, A. N. Larsen, and B. B. Nielsen, “Electrostatic plasmon resonances of metal nanospheres in layered geometries,” Phys. Rev. B 81, 125413 (2010).
[CrossRef]

Nieto-Vesperinas, M.

Novotny, L.

L. Novotny and B. Hecht, Principles of Nano-optics (Cambridge2006).

Paley, A. V.

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]

Park, W. J.

Pedersen, K.

J. Jung, T. G. Pedersen, T. Søndergaard, K. Pedersen, A. N. Larsen, and B. B. Nielsen, “Electrostatic plasmon resonances of metal nanospheres in layered geometries,” Phys. Rev. B 81, 125413 (2010).
[CrossRef]

Pedersen, T. G.

J. Jung and T. G. Pedersen, “Exact polarizability and plasmon resonances of partly buried nanowires,” Opt. Express 19, 22775–22785 (2011).
[CrossRef] [PubMed]

J. Jung, T. G. Pedersen, T. Søndergaard, K. Pedersen, A. N. Larsen, and B. B. Nielsen, “Electrostatic plasmon resonances of metal nanospheres in layered geometries,” Phys. Rev. B 81, 125413 (2010).
[CrossRef]

Pendry, J. B.

Y. Luo, A. Aubry, and J. B. Pendry, “Electromagnetic contribution to surface-enhanced Raman scattering from rough metal surfaces: a transformation optics approach,” Phys. Rev. B 83, 155422 (2011).
[CrossRef]

A. Aubry, D. Y. Lei, S. A. Maier, and J. B. Pendry, “Plasmonic hybridization between nanowires and a metallic surface: a transformation optics approach,” ACS Nano 53293–3308 (2011).
[CrossRef] [PubMed]

Y. Luo, J. B. Pendry, and A. Aubry, “Surface plasmons and singularities,” Nano Lett. 10, 4186–4191 (2010).
[CrossRef]

Pitkonen, M

M Pitkonen, “A closed-form solution for the polarizability of a dielectric double half-cylinder,” J. Electromagn. Waves Appl. 24, 1267–1277 (2010).
[CrossRef]

Plessen, G. V.

F. Hallermann, C. Rockstuhl, S. Fahr, G. Seifert, S. Wackerow, H. Graener, G. V. Plessen, and F. Lederer, “On the use of localized plasmon polaritons in solar cells,” Phys. Status Solidi A 205, 2844–2861 (2008).
[CrossRef]

Polman, A.

H. A. Atwater and A. Polman, “Plasmonics for improved photovoltaic devices,” Nat. Mater. 9, 205–213 (2010).
[CrossRef] [PubMed]

K. R. Catchpole and A. Polman, “Plasmonic solar cells,” Opt. Express 16, 21793–21800 (2008).
[CrossRef] [PubMed]

Radchik, A. V.

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]

Rayleigh, L.

L. Rayleigh, “The dispersal of light by a dielectric cylinder,” Phil. Mag. 36, 365–376 (1918).

Rockstuhl, C.

F. Hallermann, C. Rockstuhl, S. Fahr, G. Seifert, S. Wackerow, H. Graener, G. V. Plessen, and F. Lederer, “On the use of localized plasmon polaritons in solar cells,” Phys. Status Solidi A 205, 2844–2861 (2008).
[CrossRef]

Salandrino, A.

Seifert, G.

F. Hallermann, C. Rockstuhl, S. Fahr, G. Seifert, S. Wackerow, H. Graener, G. V. Plessen, and F. Lederer, “On the use of localized plasmon polaritons in solar cells,” Phys. Status Solidi A 205, 2844–2861 (2008).
[CrossRef]

Sihvola, A.

H. Kettunen, H. Wallen, and A. Sihvola, “Polarizability of a dielectic hemisphere,” J. Appl. Phys. 102, 044105 (2007).
[CrossRef]

Smith, G. B.

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]

Smolyaninov, I. I.

A. V. Zayats and I. I. Smolyaninov, “Near-field photonics: surface plasmon polaritons and localized surface plasmons,” J. Opt. A: Pure Appl. Opt. 5, S16–S50 (2003).
[CrossRef]

Søndergaard, T.

J. Jung, T. G. Pedersen, T. Søndergaard, K. Pedersen, A. N. Larsen, and B. B. Nielsen, “Electrostatic plasmon resonances of metal nanospheres in layered geometries,” Phys. Rev. B 81, 125413 (2010).
[CrossRef]

T. Søndergaard, “Modeling of plasmonic nanostructures: Green’s function integral equation methods,” Phys. Status Solidi B 244, 3448–3462 (2007).
[CrossRef]

Song, S. H.

Taflove, A.

A. Taflove and S. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method (Artech House, 2000).

Vagov, A. V.

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]

Wackerow, S.

F. Hallermann, C. Rockstuhl, S. Fahr, G. Seifert, S. Wackerow, H. Graener, G. V. Plessen, and F. Lederer, “On the use of localized plasmon polaritons in solar cells,” Phys. Status Solidi A 205, 2844–2861 (2008).
[CrossRef]

Wait, J. R.

J. R. Wait, “Scattering of a plane wave from a circular cylinder at oblique incidence,” Can. J. Phys. 33, 189–195 (1955).
[CrossRef]

Wallen, H.

H. Kettunen, H. Wallen, and A. Sihvola, “Polarizability of a dielectic hemisphere,” J. Appl. Phys. 102, 044105 (2007).
[CrossRef]

Waterman, P. C.

Yoon, J. W.

Zayats, A. V.

A. V. Zayats and I. I. Smolyaninov, “Near-field photonics: surface plasmon polaritons and localized surface plasmons,” J. Opt. A: Pure Appl. Opt. 5, S16–S50 (2003).
[CrossRef]

ACS Nano (1)

A. Aubry, D. Y. Lei, S. A. Maier, and J. B. Pendry, “Plasmonic hybridization between nanowires and a metallic surface: a transformation optics approach,” ACS Nano 53293–3308 (2011).
[CrossRef] [PubMed]

Adv. Mater. (2)

W. A. Murray and W. L. Barnes, “Plasmonic materials,” Adv. Mater. 19, 3771–3782 (2007).
[CrossRef]

V. E. Ferry, J. N. Munday, and H. A. Atwater, “Design considerations for plasmonic photovoltaics,” Adv. Mater. 22, 4794–4808 (2010).
[CrossRef] [PubMed]

Ann. Physik. (1)

G. Mie, “Beitrage zur optik truber medien speziell kolloidaler metallosungen,” Ann. Physik. 330, 337–445 (1908).
[CrossRef]

Bulletin de la Socit Mathmatique de France (1)

A. Jonquiere, “Note sur la serie ∑n=1∞xnns,” Bulletin de la Socit Mathmatique de France 17, 142–152 (1889).

Can. J. Phys. (1)

J. R. Wait, “Scattering of a plane wave from a circular cylinder at oblique incidence,” Can. J. Phys. 33, 189–195 (1955).
[CrossRef]

J. Am. Chem. Soc. (1)

A. J. Haes and R. P. V. Duyne, “A nanoscale optical biosensor: sensitivity and selectivity of an approach based on the localized surface plasmon resonance spectroscopy of triangular silver nanoparticles,” J. Am. Chem. Soc. 124, 10596–10604 (2002).
[CrossRef] [PubMed]

J. Appl. Phys. (3)

S. A. Maier and H. A. Atwater, “Plasmonics: localization and guiding of electromagnetic energy in metal/dielectric structures,” J. Appl. Phys. 98, 011101 (2005).
[CrossRef]

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]

H. Kettunen, H. Wallen, and A. Sihvola, “Polarizability of a dielectic hemisphere,” J. Appl. Phys. 102, 044105 (2007).
[CrossRef]

J. Electromagn. Waves Appl. (1)

M Pitkonen, “A closed-form solution for the polarizability of a dielectric double half-cylinder,” J. Electromagn. Waves Appl. 24, 1267–1277 (2010).
[CrossRef]

J. Opt. A: Pure Appl. Opt. (1)

A. V. Zayats and I. I. Smolyaninov, “Near-field photonics: surface plasmon polaritons and localized surface plasmons,” J. Opt. A: Pure Appl. Opt. 5, S16–S50 (2003).
[CrossRef]

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

J. Opt. Soc. Am. B (1)

K. Dan. Vidensk. Selsk. Skr. (1)

L. Lorenz, “Lysbevægelsen i og udenfor en af plane lysbølger belyst kugle,” K. Dan. Vidensk. Selsk. Skr. 6, 1–62 (1890).

Nano Lett. (1)

Y. Luo, J. B. Pendry, and A. Aubry, “Surface plasmons and singularities,” Nano Lett. 10, 4186–4191 (2010).
[CrossRef]

Nat. Mater. (1)

H. A. Atwater and A. Polman, “Plasmonics for improved photovoltaic devices,” Nat. Mater. 9, 205–213 (2010).
[CrossRef] [PubMed]

Nat. Photonics (1)

S. Lal, S. Link, and N. J. Halas, “Nano-optics from sensing to waveguiding,” Nat. Photonics 1, 641–648 (2007).
[CrossRef]

Opt. Express (3)

Phil. Mag. (1)

L. Rayleigh, “The dispersal of light by a dielectric cylinder,” Phil. Mag. 36, 365–376 (1918).

Phys. Rev. B (4)

F. J. Garcia de Abajo and A. Howie, “Retarded field calculation of electron energy loss in inhomogenous dielectrics,” Phys. Rev. B 65, 115418 (2002).
[CrossRef]

J. Jung, T. G. Pedersen, T. Søndergaard, K. Pedersen, A. N. Larsen, and B. B. Nielsen, “Electrostatic plasmon resonances of metal nanospheres in layered geometries,” Phys. Rev. B 81, 125413 (2010).
[CrossRef]

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

Y. Luo, A. Aubry, and J. B. Pendry, “Electromagnetic contribution to surface-enhanced Raman scattering from rough metal surfaces: a transformation optics approach,” Phys. Rev. B 83, 155422 (2011).
[CrossRef]

Phys. Rev. Lett. (1)

O. J. F. Martin, C. Girard, and A. Dereux, “Generalized field propagator for electromagnetic scattering and light confinement,” Phys. Rev. Lett. 74, 526–529 (1995).
[CrossRef] [PubMed]

Phys. Status Solidi A (1)

F. Hallermann, C. Rockstuhl, S. Fahr, G. Seifert, S. Wackerow, H. Graener, G. V. Plessen, and F. Lederer, “On the use of localized plasmon polaritons in solar cells,” Phys. Status Solidi A 205, 2844–2861 (2008).
[CrossRef]

Phys. Status Solidi B (1)

T. Søndergaard, “Modeling of plasmonic nanostructures: Green’s function integral equation methods,” Phys. Status Solidi B 244, 3448–3462 (2007).
[CrossRef]

Rev. Mod. Phys. (1)

M. Moskovits, “Surface-enhanced spectroscopy,” Rev. Mod. Phys. 57, 783–826 (1985).
[CrossRef]

Science (1)

Y. C. Coa, R. Jin, and C. A. Mirkin, “Nanoparticles with Raman spectroscopic fingerprints for DNA and RNA detection,” Science 297, 1536–1540 (2002).
[CrossRef]

Other (7)

S. A. Maier, Plasmonics: Fundamentals and Applications (Springer, 2007).

L. Novotny and B. Hecht, Principles of Nano-optics (Cambridge2006).

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

A. Taflove and S. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method (Artech House, 2000).

J. Jin, The Finite Element Method in Electrodynamics (Wiley, 2002).

P. M. Morse and H. Feshbach, Methods of Theoretical Physics, Part II (McGraw-Hill Book Company Inc., 1953).

H. E. Lockwood, A Book of Curves (Cambridge University Press, 1963).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (6)

Fig. 1
Fig. 1

(a) cross section of the geometry under consideration. The optical properties are described by the four dielectric constants ε1 to ε4. (b) and (c) two examples of geometries that can be analyzed using the approach.

Fig. 2
Fig. 2

Cross section of the geometry analyzed. In bipolar coordinates (u and v), the four different regions in the xy plane are given as ε1 : {−∞ < u < ∞ and w < v < π}, ε2 : {−∞ < u < ∞ and −π < v < wπ}, ε3 : {−∞ < u < ∞ and 0 < v < w}, and ε4 : {−∞ < u < ∞ and wπ < v < 0}.

Fig. 3
Fig. 3

Polarizability as a function of εr for three differently cut cylinders.

Fig. 4
Fig. 4

Polarizability as a function of εr for three differently cut cylinders on a quartz surface.

Fig. 5
Fig. 5

Polarizability as a function of εr for three cylinders differently buried in a quartz surface.

Fig. 6
Fig. 6

Imaginary part of the horizontal polarizability for a full cylinder lying on three different surfaces. (a) versus εr and (b) versus the photon energy. In (a), we use ε = εr + 0.01i and in (b) we use a dielectric constant for silver taken from the experiments of Ref. [37].

Tables (1)

Tables Icon

Table 1 Summary of the resonance conditions for the nanowire dielectric constant of the three configurations (a), (b), and (c) investigated.

Equations (26)

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

x = sinh u cosh u cos v and y = sin v cosh u cos v .
2 ϕ ( r ) = 0 r ,
ϕ i ( u , v ) = 0 ϕ i ¯ ( λ , v ) cos ( λ u ) d λ , ϕ i ¯ ( λ , v ) = 2 π 0 ϕ i ( u , v ) cos ( λ u ) d u ,
ϕ i ( u , v ) = 0 ϕ i ¯ ( λ , v ) sin ( λ u ) d λ , ϕ i ¯ ( λ , v ) = 2 π 0 ϕ i ( u , v ) sin ( λ u ) d u .
φ i ¯ ( λ , v ) = c i ( λ ) cosh ( λ v ) + s i ( λ ) sinh ( λ v ) .
ϕ 0 ( v ) ( u , v ) = sin v cosh u cos v { 1 for v > 0 ε 3 ε 4 for v < 0 and ϕ 0 ( h ) ( u , v ) = sinh u cosh u cos v ,
α ( v ) = 4 π 0 λ s 3 ( λ ) d λ and α ( h ) = 4 π 0 λ c 3 ( λ ) d λ .
v ϕ ¯ 0 ( v ) ( λ , v ) = 2 λ cosh [ λ ( π | v | ) ] sinh [ λ π ] and v ϕ ¯ 0 ( h ) ( λ , v ) = 2 λ sinh [ λ ( π | v | ) ] sinh ( λ π ) sgn ( v ) .
c 1 ( λ ) C 01 s 1 ( λ ) S 01 = c 3 ( λ ) C 01 s 3 ( λ ) S 01 , c 2 ( λ ) C 11 s 2 ( λ ) S 11 = c 4 ( λ ) C 11 s 4 ( λ ) S 11 , c 1 ( λ ) C 10 + s 1 ( λ ) S 10 = c 2 ( λ ) C 10 s 2 ( λ ) S 10 , c 3 ( λ ) = c 4 ( λ ) .
ε 1 [ c 1 ( λ ) S 01 + s 1 ( λ ) C 01 + 2 C 11 S 10 ] = ε 3 [ c 3 ( λ ) S 01 + s 3 ( λ ) C 01 + 2 C 11 S 10 ] , ε 2 [ c 2 ( λ ) S 11 + s 2 ( λ ) C 11 + ε 3 ε 4 2 C 01 S 10 ] = ε 4 [ c 4 ( λ ) S 11 + s 4 ( λ ) C 11 + ε 3 ε 4 2 C 01 S 10 ] , ε 1 [ c 1 ( λ ) S 10 + s 1 ( λ ) C 10 + 2 S 10 ] = ε 2 [ c 2 ( λ ) S 10 + s 2 ( λ ) C 10 + ε 3 ε 4 2 S 10 ] , ε 3 s 3 ( λ ) = ε 4 s 4 ( λ ) ,
ε 1 [ c 1 ( λ ) S 01 + s 1 ( λ ) C 01 + 2 S 11 S 10 ] = ε 3 [ c 3 ( λ ) S 01 + s 3 ( λ ) C 01 + 2 S 11 S 10 ] , ε 2 [ c 2 ( λ ) S 11 + s 2 ( λ ) C 11 + 2 S 01 S 10 ] = ε 4 [ c 4 ( λ ) S 11 + s 4 ( λ ) C 11 + 2 S 01 S 10 ] , ε 1 [ c 1 ( λ ) S 10 + s 1 ( λ ) C 10 ] = ε 2 [ c 2 ( λ ) S 10 + s 2 ( λ ) C 10 ] , ε 3 s 3 ( λ ) = ε 4 s 4 ( λ ) .
D = p , q D p q C p q and N = p , q N p q { C p q C 10 }
D 20 = ( ε 1 + ε 2 ) ( ε 1 + ε 3 ) ( ε 2 + ε 4 ) ( ε 3 + ε 4 ) , D 24 = ( ε 1 ε 2 ) ( ε 1 ε 3 ) ( ε 2 ε 4 ) ( ε 3 ε 4 ) , D 22 = 2 ( ε 1 2 ε 2 ε 3 ) ( ε 2 ε 3 ε 4 2 ) 2 ε 1 ( ε 2 ε 3 ) 2 ε 4 , D 02 = 2 ( ε 1 2 + ε 2 ε 3 ) ( ε 2 ε 3 + ε 4 2 ) + 2 ε 1 ( ε 2 + ε 3 ) 2 ε 4 , D 00 = 2 ( ε 1 2 ε 2 ε 3 ) ( ε 2 ε 3 ε 4 2 ) 2 ε 1 ( ε 2 + ε 3 ) 2 ε 4 8 ε 1 ε 2 ε 3 ε 4 .
N 14 = ( ε 1 ε 2 ) ( ε 1 ε 3 ) ( ε 2 ε 4 ) ε 3 , N 34 = ( ε 1 ε 2 ) ( ε 1 ε 3 ) ( ε 2 ε 4 ) ε 4 , N 32 = ( ε 1 + ε 2 ) ( ε 1 ε 3 ) ( ε 2 + ε 4 ) ε 4 , N 1 2 = ( ε 1 + ε 2 ) ( ε 1 + ε 3 ) ( ε 2 ε 4 ) ε 3 , N 12 = 2 ( ε 1 2 ε 4 2 + ε 2 2 ε 3 2 ) + ( ε 3 + ε 4 ) [ ε 1 2 ( ε 4 ε 2 ) + ε 2 2 ( ε 3 ε 1 ) + ( ε 1 + ε 2 ) ε 3 ε 4 ] ε 1 ε 2 ( ε 3 2 + 6 ε 3 ε 4 + ε 4 2 ) .
s 3 ( λ ) = N 12 ( C 12 C 10 ) + N 32 ( C 32 C 10 ) D 00 + D 20 C 20 + D 02 C 02 2 S 10 ,
s 3 ( λ ) 2 ( ε 1 ε 3 ) ε 4 e λ ( 2 π + w ) [ e 2 λ π ( ε 1 + ε 4 ) 2 ( e 2 λ w 1 ) ( ε 1 ε 3 ) ] ( ε 1 + ε 4 ) [ ε 3 ( ε 1 + ε 4 ) cosh ( λ w ) + ( ε 3 2 + ε 1 ε 4 ) sinh ( λ w ) ] ,
s 3 ( λ ) 2 ( ε 1 ε 3 ) ε 4 e λ w ε 3 ( ε 1 + ε 4 ) cosh ( λ w ) + ( ε 3 2 + ε 1 ε 4 ) sinh ( λ w ) .
α ( v ) = 4 π ε 4 w 2 ( ε 4 ε 3 ) Li 2 [ ( ε 3 ε 1 ) ( ε 3 ε 4 ) ( ε 3 + ε 1 ) ( ε 3 + ε 4 ) ] ,
c 3 ( λ ) 2 ( ε 1 ε 3 ) ε 3 exp ( λ w ) ( ε 1 + ε 4 ) ε 3 cosh ( λ w ) + ( ε 3 2 + ε 1 ε 4 ) sinh ( λ w ) ,
α ( h ) = 4 π ε 3 w 2 ( ε 4 ε 3 ) Li 2 [ ( ε 3 ε 1 ) ( ε 3 ε 4 ) ( ε 3 + ε 1 ) ( ε 3 + ε 4 ) ] .
s 3 ( λ ) 2 λ [ 1 π + ε 3 1 + ε 4 1 ( ε 1 1 + ε 4 1 ) ( π w ) + ( ε 2 1 + ε 3 1 ) w ] .
( ε 1 1 + ε 4 1 ) ( π w ) + ( ε 2 1 + ε 3 1 ) w = 0.
( ε 1 + ε 4 ) ( π w ) + ( ε 2 + ε 3 ) w = 0.
ε = ε h π w π + w and ε = ε h π + w π w .
ε = ε h ε 3 π w ε 3 π + ε h w and ε = ε h π + ε 3 w π w .
ε = π ε 3 ε 4 ε 3 ( π w ) + ε 4 w and ε = ε 4 ( π w ) + ε 3 w π .

Metrics