Abstract

We study the blueshift of the surface plasmon (SP) resonance energy of isolated Ag nanoparticles with decreasing particle diameter, which we recently measured using electron energy loss spectroscopy (EELS) [1]. As the particle diameter decreases from 26 down to 3.5 nm, a large blueshift of 0.5 eV of the SP resonance energy is observed. In this paper, we base our theoretical interpretation of our experimental findings on the nonlocal hydrodynamic model, and compare the effect of the substrate on the SP resonance energy to the approach of an effective homogeneous background permittivity. We derive the nonlocal polarizability of a small metal sphere embedded in a homogeneous dielectric environment, leading to the nonlocal generalization of the classical Clausius–Mossotti factor. We also present an exact formalism based on multipole expansions and scattering matrices to determine the optical response of a metal sphere on a dielectric substrate of finite thickness, taking into account retardation and nonlocal effects. We find that the substrate-based calculations show a similar-sized blueshift as calculations based on a sphere in a homogeneous environment, and that they both agree qualitatively with the EELS measurements.

© 2013 OSA

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  1. S. Raza, N. Stenger, S. Kadkhodazadeh, S. V. Fischer, N. Kostesha, A.-P. Jauho, A. Burrows, M. Wubs, and N. A. Mortensen, “Blueshift of the surface plasmon resonance in silver nanoparticles studied with EELS,” Nanophotonics2, 131–138 (2013).
    [CrossRef]
  2. G. Mie, “Beiträge zur Optik trüber Medien, speziell kolloidaler Metallösungen,” Ann. Phys.330, 377–445 (1908).
    [CrossRef]
  3. S. A. Maier, Plasmonics: Fundamentals and Applications (Springer, New York, 2007).
  4. N. D. Lang and W. Kohn, “Theory of metal surfaces: Charge density and surface energy,” Phys. Rev. B1, 4555–4568 (1970).
    [CrossRef]
  5. A. Boardman, B. Paranjape, and R. Teshima, “The effect of structure on surface plasmons,” Surf. Sci.49, 275–292 (1975).
    [CrossRef]
  6. A. J. Bennett, “Influence of the electron charge distribution on surface-plasmon dispersion,” Phys. Rev. B1, 203–207 (1970).
    [CrossRef]
  7. P. Apell, “A simple derivation of the surface contribution to the reflectivity of a metal, and its use in the Van der Waals interaction,” Phys. Scr.24, 795–806 (1981).
    [CrossRef]
  8. P. J. Feibelman, “Surface electromagnetic fields,” Prog. Surf. Sci.12, 287–407 (1982).
    [CrossRef]
  9. R. Ruppin, “Optical properties of a plasma sphere,” Phys. Rev. Lett.31, 1434–1437 (1973).
    [CrossRef]
  10. A. D. Boardman and B. V. Paranjape, “The optical surface modes of metal spheres,” J. Phys. F: Met. Phys.7, 1935–1945 (1977).
    [CrossRef]
  11. P. Apell and Å. Ljungbert, “A general non-local theory for the electromagnetic response of a small metal particle,” Phys. Scr.26, 113–118 (1982).
    [CrossRef]
  12. C. Schwartz and W. L. Schaich, “Hydrodynamic models of surface plasmons,” Phys. Rev. B26, 7008–7011 (1982).
    [CrossRef]
  13. A. I. Fernández-Domínguez, A. Wiener, F. J. García-Vidal, S. A. Maier, and J. B. Pendry, “Transformation-optics description of nonlocal effects in plasmonic nanostructures,” Phys. Rev. Lett.108, 106802 (2012).
    [CrossRef] [PubMed]
  14. C. David and F. J. García de Abajo, “Spatial nonlocality in the optical response of metal nanoparticles,” J. Phys. Chem. C115, 19470–19475 (2012).
    [CrossRef]
  15. G. Toscano, S. Raza, A.-P. Jauho, N. A. Mortensen, and M. Wubs, “Modified field enhancement and extinction in plasmonic nanowire dimers due to nonlocal response,” Opt. Express20, 4176–4188 (2012).
    [CrossRef] [PubMed]
  16. C. Ciracì, R. T. Hill, J. J. Mock, Y. Urzhumov, A. I. Fernández-Domínguez, S. A. Maier, J. B. Pendry, A. Chilkoti, and D. R. Smith, “Probing the ultimate limits of plasmonic enhancement,” Science337, 1072–1074 (2012).
    [CrossRef] [PubMed]
  17. U. Kreibig and C. Fragstein, “The limitation of electron mean free path in small silver particles,” Z. Physik224, 307–323 (1969).
    [CrossRef]
  18. L. Genzel, T. P. Martin, and U. Kreibig, “Dielectric function and plasma resonance of small metal particles,” Z. Phys. B21, 339–346 (1975).
    [CrossRef]
  19. P. Apell and D. R. Penn, “Optical properties of small metal spheres: Surface effects,” Phys. Rev. Lett.50, 1316–1319 (1983).
    [CrossRef]
  20. O. Keller, M. Xiao, and S. Bozhevolnyi, “Optical diamagnetic polarizability of a mesoscopic metallic sphere: transverse self-field approach,” Opt. Comm.102, 238–244 (1993).
    [CrossRef]
  21. U. Kreibig and L. Genzel, “Optical absorption of small metallic particles,” Surf. Sci.156, 678–700 (1985).
    [CrossRef]
  22. K.-P. Charlé, W. Schulze, and B. Winter, “The size dependent shift of the surface-plasmon absorption-band of small spherical metal particles,” Z. Phys. D12, 471–475 (1989).
    [CrossRef]
  23. H. Hövel, S. Fritz, A. Hilger, U. Kreibig, and M. Vollmer, “Width of cluster plasmon resonances: Bulk dielectric functions and chemical interface damping,” Phys. Rev. B48, 18178–18188 (1993).
    [CrossRef]
  24. J. Tiggesbäumker, L. Köller, K.-H. Meiwes-Broer, and A. Liebsch, “Blue shift of the Mie plasma frequency in Ag clusters and particles,” Phys. Rev. A48, R1749–R1752 (1993).
    [CrossRef] [PubMed]
  25. S. Berciaud, L. Cognet, P. Tamarat, and B. Lounis, “Observation of intrinsic size effects in the optical response of individual gold nanoparticles,” Nano Lett.5, 515–518 (2005).
    [CrossRef] [PubMed]
  26. F. Ouyang, P. Batson, and M. Isaacson, “Quantum size effects in the surface-plasmon excitation of small metallic particles by electron-energy-loss spectroscopy,” Phys. Rev. B46, 15421–15425 (1992).
    [CrossRef]
  27. J. A. Scholl, A. L. Koh, and J. A. Dionne, “Quantum plasmon resonances of individual metallic nanoparticles,” Nature483, 421–427 (2012).
    [CrossRef] [PubMed]
  28. A. Boardman, Electromagnetic Surface Modes. Hydrodynamic theory of plasmon-polaritons on plane surfaces. (John Wiley and Sons, Chichester, 1982).
  29. P. Apell, “The electromagnetic field near a metal surface in the semi-classical infinite barrier model,” Phys. Scr.17, 535–542 (1978).
    [CrossRef]
  30. L. Mulfinger, S. D. Solomon, M. Bahadory, A. Jeyarajasingam, S. A. Rutkowsky, and C. Boritz, “Synthesis and study of silver nanoparticles,” J. Chem. Educ.84, 322–325 (2007).
    [CrossRef]
  31. F. J. García de Abajo, “Optical excitations in electron microscopy,” Rev. Mod. Phys.82, 209–275 (2010).
    [CrossRef]
  32. J. Aizpurua, A. Rivacoba, and S. P. Apell, “Electron-energy losses in hemispherical targets,” Phys. Rev. B54, 2901–2909 (1996).
    [CrossRef]
  33. A. Boardman and R. Ruppin, “The boundary conditions between spatially dispersive media,” Surf. Sci.112, 153–167 (1981).
    [CrossRef]
  34. D. J. Griffiths, Introduction to Electrodynamics (Benjamin Cummings), 3rd ed.
  35. F. Bloch, “Bremsvermögen von Atomen mit mehreren Elektronen,” Z. Phys. A81, 363–376 (1933).
  36. S. Raza, G. Toscano, A.-P. Jauho, M. Wubs, and N. A. Mortensen, “Unusual resonances in nanoplasmonic structures due to nonlocal response,” Phys. Rev. B84, 121412(R) (2011).
    [CrossRef]
  37. G. Toscano, S. Raza, W. Yan, C. Jeppesen, S. Xiao, M. Wubs, A.-P. Jauho, S. I. Bozhevolnyi, and N. A. Mortensen, “Nonlocal response in plasmonic waveguiding with extreme light confinement,” Nanophotonics2, 161–166 (2013).
    [CrossRef]
  38. F. Sauter, “Der Einfiuß von Plasmawellen auf das Reflexionsvermögen von Metallen (I),” Z. Physik203, 488–494 (1967).
    [CrossRef]
  39. F. Forstmann and H. Stenschke, “Electrodynamics at metal boundaries with inclusion of plasma waves,” Phys. Rev. Lett.38, 1365–1368 (1977).
    [CrossRef]
  40. G. Barton, “Some surface effects in the hydrodynamic model of metals,” Rep. Prog. Phys.42, 963–1016 (1979).
    [CrossRef]
  41. J. D. Jackson, Classical electrodynamics, 3rd ed. (Wiley, 1998).
  42. I. Villo-Perez, Z. Mišković, and N. Arista, “Plasmon spectra of nano-structures: A hydrodynamic model,” in “Trends in Nanophysics,” V. Bârsan and A. Aldea, eds. (SpringerBerlin Heidelberg, 2010), Engineering Materials, pp. 217–254.
    [CrossRef]
  43. Y. Luo, A. I. Fernández-Domínguez, A. Wiener, S. A. Maier, and J. B. Pendry, “Surface plasmons and nonlocality: A simple model,” Phys. Rev. Lett.111, 093901 (2013).
    [CrossRef] [PubMed]
  44. I. Lindau and P. O. Nilsson, “Experimental evidence for excitation of longitudinal plasmons by photons,” Phys. Lett. A31, 352–353 (1970).
    [CrossRef]
  45. K.-P. Charlé, L. König, S. Nepijko, I. Rabin, and W. Schulze, “The surface plasmon resonance of free and embedded Ag-clusters in the size range 1,5 nm < D < 30 nm,” Cryst. Res. Technol.33, 1085–1096 (1998).
    [CrossRef]
  46. W. Yan and , in preparation (2013).
  47. C. Bohren and D. Huffman, Absorption and Scattering of Light by Small Particles (John Wiley & Sons, 1983).
  48. C. David, N. A. Mortensen, and J. Christensen, “Perfect imaging, epsilon-near zero phenomena and waveguiding in the scope of nonlocal effects,” Sci. Rep.3, 2526 (2013).
    [CrossRef] [PubMed]
  49. T. Bååk, “Silicon oxynitride; a material for GRIN optics,” Appl. Opt.21, 1069–1072 (1982).
    [CrossRef] [PubMed]
  50. A. D. Rakić, A. B. Djurišić, J. M. Elazar, and M. L. Majewski, “Optical properties of metallic films for vertical-cavity optoelectronic devices.” Appl. Opt.37, 5271–5283 (1998).
    [CrossRef]
  51. R. Ruppin, “Surface modes and optical absorption of a small sphere above a substrate,” Surf. Sci.127, 108–118 (1983).
    [CrossRef]
  52. A. Liebsch, “Surface-plasmon dispersion and size dependence of Mie resonance: silver versus simple metals,” Phys. Rev. B48, 11317–11328 (1993).
    [CrossRef]
  53. R. Carmina Monreal, T. J. Antosiewicz, and S. P. Apell, “Competition between surface screening and size quantization for surface plasmons in nanoparticles,” New J. Phys.15, 083044 (2013).
    [CrossRef]

2013 (5)

S. Raza, N. Stenger, S. Kadkhodazadeh, S. V. Fischer, N. Kostesha, A.-P. Jauho, A. Burrows, M. Wubs, and N. A. Mortensen, “Blueshift of the surface plasmon resonance in silver nanoparticles studied with EELS,” Nanophotonics2, 131–138 (2013).
[CrossRef]

G. Toscano, S. Raza, W. Yan, C. Jeppesen, S. Xiao, M. Wubs, A.-P. Jauho, S. I. Bozhevolnyi, and N. A. Mortensen, “Nonlocal response in plasmonic waveguiding with extreme light confinement,” Nanophotonics2, 161–166 (2013).
[CrossRef]

Y. Luo, A. I. Fernández-Domínguez, A. Wiener, S. A. Maier, and J. B. Pendry, “Surface plasmons and nonlocality: A simple model,” Phys. Rev. Lett.111, 093901 (2013).
[CrossRef] [PubMed]

C. David, N. A. Mortensen, and J. Christensen, “Perfect imaging, epsilon-near zero phenomena and waveguiding in the scope of nonlocal effects,” Sci. Rep.3, 2526 (2013).
[CrossRef] [PubMed]

R. Carmina Monreal, T. J. Antosiewicz, and S. P. Apell, “Competition between surface screening and size quantization for surface plasmons in nanoparticles,” New J. Phys.15, 083044 (2013).
[CrossRef]

2012 (5)

A. I. Fernández-Domínguez, A. Wiener, F. J. García-Vidal, S. A. Maier, and J. B. Pendry, “Transformation-optics description of nonlocal effects in plasmonic nanostructures,” Phys. Rev. Lett.108, 106802 (2012).
[CrossRef] [PubMed]

C. David and F. J. García de Abajo, “Spatial nonlocality in the optical response of metal nanoparticles,” J. Phys. Chem. C115, 19470–19475 (2012).
[CrossRef]

G. Toscano, S. Raza, A.-P. Jauho, N. A. Mortensen, and M. Wubs, “Modified field enhancement and extinction in plasmonic nanowire dimers due to nonlocal response,” Opt. Express20, 4176–4188 (2012).
[CrossRef] [PubMed]

C. Ciracì, R. T. Hill, J. J. Mock, Y. Urzhumov, A. I. Fernández-Domínguez, S. A. Maier, J. B. Pendry, A. Chilkoti, and D. R. Smith, “Probing the ultimate limits of plasmonic enhancement,” Science337, 1072–1074 (2012).
[CrossRef] [PubMed]

J. A. Scholl, A. L. Koh, and J. A. Dionne, “Quantum plasmon resonances of individual metallic nanoparticles,” Nature483, 421–427 (2012).
[CrossRef] [PubMed]

2011 (1)

S. Raza, G. Toscano, A.-P. Jauho, M. Wubs, and N. A. Mortensen, “Unusual resonances in nanoplasmonic structures due to nonlocal response,” Phys. Rev. B84, 121412(R) (2011).
[CrossRef]

2010 (1)

F. J. García de Abajo, “Optical excitations in electron microscopy,” Rev. Mod. Phys.82, 209–275 (2010).
[CrossRef]

2007 (1)

L. Mulfinger, S. D. Solomon, M. Bahadory, A. Jeyarajasingam, S. A. Rutkowsky, and C. Boritz, “Synthesis and study of silver nanoparticles,” J. Chem. Educ.84, 322–325 (2007).
[CrossRef]

2005 (1)

S. Berciaud, L. Cognet, P. Tamarat, and B. Lounis, “Observation of intrinsic size effects in the optical response of individual gold nanoparticles,” Nano Lett.5, 515–518 (2005).
[CrossRef] [PubMed]

1998 (2)

A. D. Rakić, A. B. Djurišić, J. M. Elazar, and M. L. Majewski, “Optical properties of metallic films for vertical-cavity optoelectronic devices.” Appl. Opt.37, 5271–5283 (1998).
[CrossRef]

K.-P. Charlé, L. König, S. Nepijko, I. Rabin, and W. Schulze, “The surface plasmon resonance of free and embedded Ag-clusters in the size range 1,5 nm < D < 30 nm,” Cryst. Res. Technol.33, 1085–1096 (1998).
[CrossRef]

1996 (1)

J. Aizpurua, A. Rivacoba, and S. P. Apell, “Electron-energy losses in hemispherical targets,” Phys. Rev. B54, 2901–2909 (1996).
[CrossRef]

1993 (4)

H. Hövel, S. Fritz, A. Hilger, U. Kreibig, and M. Vollmer, “Width of cluster plasmon resonances: Bulk dielectric functions and chemical interface damping,” Phys. Rev. B48, 18178–18188 (1993).
[CrossRef]

J. Tiggesbäumker, L. Köller, K.-H. Meiwes-Broer, and A. Liebsch, “Blue shift of the Mie plasma frequency in Ag clusters and particles,” Phys. Rev. A48, R1749–R1752 (1993).
[CrossRef] [PubMed]

O. Keller, M. Xiao, and S. Bozhevolnyi, “Optical diamagnetic polarizability of a mesoscopic metallic sphere: transverse self-field approach,” Opt. Comm.102, 238–244 (1993).
[CrossRef]

A. Liebsch, “Surface-plasmon dispersion and size dependence of Mie resonance: silver versus simple metals,” Phys. Rev. B48, 11317–11328 (1993).
[CrossRef]

1992 (1)

F. Ouyang, P. Batson, and M. Isaacson, “Quantum size effects in the surface-plasmon excitation of small metallic particles by electron-energy-loss spectroscopy,” Phys. Rev. B46, 15421–15425 (1992).
[CrossRef]

1989 (1)

K.-P. Charlé, W. Schulze, and B. Winter, “The size dependent shift of the surface-plasmon absorption-band of small spherical metal particles,” Z. Phys. D12, 471–475 (1989).
[CrossRef]

1985 (1)

U. Kreibig and L. Genzel, “Optical absorption of small metallic particles,” Surf. Sci.156, 678–700 (1985).
[CrossRef]

1983 (2)

P. Apell and D. R. Penn, “Optical properties of small metal spheres: Surface effects,” Phys. Rev. Lett.50, 1316–1319 (1983).
[CrossRef]

R. Ruppin, “Surface modes and optical absorption of a small sphere above a substrate,” Surf. Sci.127, 108–118 (1983).
[CrossRef]

1982 (4)

T. Bååk, “Silicon oxynitride; a material for GRIN optics,” Appl. Opt.21, 1069–1072 (1982).
[CrossRef] [PubMed]

P. Apell and Å. Ljungbert, “A general non-local theory for the electromagnetic response of a small metal particle,” Phys. Scr.26, 113–118 (1982).
[CrossRef]

C. Schwartz and W. L. Schaich, “Hydrodynamic models of surface plasmons,” Phys. Rev. B26, 7008–7011 (1982).
[CrossRef]

P. J. Feibelman, “Surface electromagnetic fields,” Prog. Surf. Sci.12, 287–407 (1982).
[CrossRef]

1981 (2)

P. Apell, “A simple derivation of the surface contribution to the reflectivity of a metal, and its use in the Van der Waals interaction,” Phys. Scr.24, 795–806 (1981).
[CrossRef]

A. Boardman and R. Ruppin, “The boundary conditions between spatially dispersive media,” Surf. Sci.112, 153–167 (1981).
[CrossRef]

1979 (1)

G. Barton, “Some surface effects in the hydrodynamic model of metals,” Rep. Prog. Phys.42, 963–1016 (1979).
[CrossRef]

1978 (1)

P. Apell, “The electromagnetic field near a metal surface in the semi-classical infinite barrier model,” Phys. Scr.17, 535–542 (1978).
[CrossRef]

1977 (2)

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

F. Forstmann and H. Stenschke, “Electrodynamics at metal boundaries with inclusion of plasma waves,” Phys. Rev. Lett.38, 1365–1368 (1977).
[CrossRef]

1975 (2)

L. Genzel, T. P. Martin, and U. Kreibig, “Dielectric function and plasma resonance of small metal particles,” Z. Phys. B21, 339–346 (1975).
[CrossRef]

A. Boardman, B. Paranjape, and R. Teshima, “The effect of structure on surface plasmons,” Surf. Sci.49, 275–292 (1975).
[CrossRef]

1973 (1)

R. Ruppin, “Optical properties of a plasma sphere,” Phys. Rev. Lett.31, 1434–1437 (1973).
[CrossRef]

1970 (3)

N. D. Lang and W. Kohn, “Theory of metal surfaces: Charge density and surface energy,” Phys. Rev. B1, 4555–4568 (1970).
[CrossRef]

A. J. Bennett, “Influence of the electron charge distribution on surface-plasmon dispersion,” Phys. Rev. B1, 203–207 (1970).
[CrossRef]

I. Lindau and P. O. Nilsson, “Experimental evidence for excitation of longitudinal plasmons by photons,” Phys. Lett. A31, 352–353 (1970).
[CrossRef]

1969 (1)

U. Kreibig and C. Fragstein, “The limitation of electron mean free path in small silver particles,” Z. Physik224, 307–323 (1969).
[CrossRef]

1967 (1)

F. Sauter, “Der Einfiuß von Plasmawellen auf das Reflexionsvermögen von Metallen (I),” Z. Physik203, 488–494 (1967).
[CrossRef]

1933 (1)

F. Bloch, “Bremsvermögen von Atomen mit mehreren Elektronen,” Z. Phys. A81, 363–376 (1933).

1908 (1)

G. Mie, “Beiträge zur Optik trüber Medien, speziell kolloidaler Metallösungen,” Ann. Phys.330, 377–445 (1908).
[CrossRef]

Aizpurua, J.

J. Aizpurua, A. Rivacoba, and S. P. Apell, “Electron-energy losses in hemispherical targets,” Phys. Rev. B54, 2901–2909 (1996).
[CrossRef]

Antosiewicz, T. J.

R. Carmina Monreal, T. J. Antosiewicz, and S. P. Apell, “Competition between surface screening and size quantization for surface plasmons in nanoparticles,” New J. Phys.15, 083044 (2013).
[CrossRef]

Apell, P.

P. Apell and D. R. Penn, “Optical properties of small metal spheres: Surface effects,” Phys. Rev. Lett.50, 1316–1319 (1983).
[CrossRef]

P. Apell and Å. Ljungbert, “A general non-local theory for the electromagnetic response of a small metal particle,” Phys. Scr.26, 113–118 (1982).
[CrossRef]

P. Apell, “A simple derivation of the surface contribution to the reflectivity of a metal, and its use in the Van der Waals interaction,” Phys. Scr.24, 795–806 (1981).
[CrossRef]

P. Apell, “The electromagnetic field near a metal surface in the semi-classical infinite barrier model,” Phys. Scr.17, 535–542 (1978).
[CrossRef]

Apell, S. P.

R. Carmina Monreal, T. J. Antosiewicz, and S. P. Apell, “Competition between surface screening and size quantization for surface plasmons in nanoparticles,” New J. Phys.15, 083044 (2013).
[CrossRef]

J. Aizpurua, A. Rivacoba, and S. P. Apell, “Electron-energy losses in hemispherical targets,” Phys. Rev. B54, 2901–2909 (1996).
[CrossRef]

Arista, N.

I. Villo-Perez, Z. Mišković, and N. Arista, “Plasmon spectra of nano-structures: A hydrodynamic model,” in “Trends in Nanophysics,” V. Bârsan and A. Aldea, eds. (SpringerBerlin Heidelberg, 2010), Engineering Materials, pp. 217–254.
[CrossRef]

Bååk, T.

Bahadory, M.

L. Mulfinger, S. D. Solomon, M. Bahadory, A. Jeyarajasingam, S. A. Rutkowsky, and C. Boritz, “Synthesis and study of silver nanoparticles,” J. Chem. Educ.84, 322–325 (2007).
[CrossRef]

Barton, G.

G. Barton, “Some surface effects in the hydrodynamic model of metals,” Rep. Prog. Phys.42, 963–1016 (1979).
[CrossRef]

Batson, P.

F. Ouyang, P. Batson, and M. Isaacson, “Quantum size effects in the surface-plasmon excitation of small metallic particles by electron-energy-loss spectroscopy,” Phys. Rev. B46, 15421–15425 (1992).
[CrossRef]

Bennett, A. J.

A. J. Bennett, “Influence of the electron charge distribution on surface-plasmon dispersion,” Phys. Rev. B1, 203–207 (1970).
[CrossRef]

Berciaud, S.

S. Berciaud, L. Cognet, P. Tamarat, and B. Lounis, “Observation of intrinsic size effects in the optical response of individual gold nanoparticles,” Nano Lett.5, 515–518 (2005).
[CrossRef] [PubMed]

Bloch, F.

F. Bloch, “Bremsvermögen von Atomen mit mehreren Elektronen,” Z. Phys. A81, 363–376 (1933).

Boardman, A.

A. Boardman and R. Ruppin, “The boundary conditions between spatially dispersive media,” Surf. Sci.112, 153–167 (1981).
[CrossRef]

A. Boardman, B. Paranjape, and R. Teshima, “The effect of structure on surface plasmons,” Surf. Sci.49, 275–292 (1975).
[CrossRef]

A. Boardman, Electromagnetic Surface Modes. Hydrodynamic theory of plasmon-polaritons on plane surfaces. (John Wiley and Sons, Chichester, 1982).

Boardman, A. D.

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

Bohren, C.

C. Bohren and D. Huffman, Absorption and Scattering of Light by Small Particles (John Wiley & Sons, 1983).

Boritz, C.

L. Mulfinger, S. D. Solomon, M. Bahadory, A. Jeyarajasingam, S. A. Rutkowsky, and C. Boritz, “Synthesis and study of silver nanoparticles,” J. Chem. Educ.84, 322–325 (2007).
[CrossRef]

Bozhevolnyi, S.

O. Keller, M. Xiao, and S. Bozhevolnyi, “Optical diamagnetic polarizability of a mesoscopic metallic sphere: transverse self-field approach,” Opt. Comm.102, 238–244 (1993).
[CrossRef]

Bozhevolnyi, S. I.

G. Toscano, S. Raza, W. Yan, C. Jeppesen, S. Xiao, M. Wubs, A.-P. Jauho, S. I. Bozhevolnyi, and N. A. Mortensen, “Nonlocal response in plasmonic waveguiding with extreme light confinement,” Nanophotonics2, 161–166 (2013).
[CrossRef]

Burrows, A.

S. Raza, N. Stenger, S. Kadkhodazadeh, S. V. Fischer, N. Kostesha, A.-P. Jauho, A. Burrows, M. Wubs, and N. A. Mortensen, “Blueshift of the surface plasmon resonance in silver nanoparticles studied with EELS,” Nanophotonics2, 131–138 (2013).
[CrossRef]

Carmina Monreal, R.

R. Carmina Monreal, T. J. Antosiewicz, and S. P. Apell, “Competition between surface screening and size quantization for surface plasmons in nanoparticles,” New J. Phys.15, 083044 (2013).
[CrossRef]

Charlé, K.-P.

K.-P. Charlé, L. König, S. Nepijko, I. Rabin, and W. Schulze, “The surface plasmon resonance of free and embedded Ag-clusters in the size range 1,5 nm < D < 30 nm,” Cryst. Res. Technol.33, 1085–1096 (1998).
[CrossRef]

K.-P. Charlé, W. Schulze, and B. Winter, “The size dependent shift of the surface-plasmon absorption-band of small spherical metal particles,” Z. Phys. D12, 471–475 (1989).
[CrossRef]

Chilkoti, A.

C. Ciracì, R. T. Hill, J. J. Mock, Y. Urzhumov, A. I. Fernández-Domínguez, S. A. Maier, J. B. Pendry, A. Chilkoti, and D. R. Smith, “Probing the ultimate limits of plasmonic enhancement,” Science337, 1072–1074 (2012).
[CrossRef] [PubMed]

Christensen, J.

C. David, N. A. Mortensen, and J. Christensen, “Perfect imaging, epsilon-near zero phenomena and waveguiding in the scope of nonlocal effects,” Sci. Rep.3, 2526 (2013).
[CrossRef] [PubMed]

Ciracì, C.

C. Ciracì, R. T. Hill, J. J. Mock, Y. Urzhumov, A. I. Fernández-Domínguez, S. A. Maier, J. B. Pendry, A. Chilkoti, and D. R. Smith, “Probing the ultimate limits of plasmonic enhancement,” Science337, 1072–1074 (2012).
[CrossRef] [PubMed]

Cognet, L.

S. Berciaud, L. Cognet, P. Tamarat, and B. Lounis, “Observation of intrinsic size effects in the optical response of individual gold nanoparticles,” Nano Lett.5, 515–518 (2005).
[CrossRef] [PubMed]

David, C.

C. David, N. A. Mortensen, and J. Christensen, “Perfect imaging, epsilon-near zero phenomena and waveguiding in the scope of nonlocal effects,” Sci. Rep.3, 2526 (2013).
[CrossRef] [PubMed]

C. David and F. J. García de Abajo, “Spatial nonlocality in the optical response of metal nanoparticles,” J. Phys. Chem. C115, 19470–19475 (2012).
[CrossRef]

Dionne, J. A.

J. A. Scholl, A. L. Koh, and J. A. Dionne, “Quantum plasmon resonances of individual metallic nanoparticles,” Nature483, 421–427 (2012).
[CrossRef] [PubMed]

Djurišic, A. B.

Elazar, J. M.

Feibelman, P. J.

P. J. Feibelman, “Surface electromagnetic fields,” Prog. Surf. Sci.12, 287–407 (1982).
[CrossRef]

Fernández-Domínguez, A. I.

Y. Luo, A. I. Fernández-Domínguez, A. Wiener, S. A. Maier, and J. B. Pendry, “Surface plasmons and nonlocality: A simple model,” Phys. Rev. Lett.111, 093901 (2013).
[CrossRef] [PubMed]

A. I. Fernández-Domínguez, A. Wiener, F. J. García-Vidal, S. A. Maier, and J. B. Pendry, “Transformation-optics description of nonlocal effects in plasmonic nanostructures,” Phys. Rev. Lett.108, 106802 (2012).
[CrossRef] [PubMed]

C. Ciracì, R. T. Hill, J. J. Mock, Y. Urzhumov, A. I. Fernández-Domínguez, S. A. Maier, J. B. Pendry, A. Chilkoti, and D. R. Smith, “Probing the ultimate limits of plasmonic enhancement,” Science337, 1072–1074 (2012).
[CrossRef] [PubMed]

Fischer, S. V.

S. Raza, N. Stenger, S. Kadkhodazadeh, S. V. Fischer, N. Kostesha, A.-P. Jauho, A. Burrows, M. Wubs, and N. A. Mortensen, “Blueshift of the surface plasmon resonance in silver nanoparticles studied with EELS,” Nanophotonics2, 131–138 (2013).
[CrossRef]

Forstmann, F.

F. Forstmann and H. Stenschke, “Electrodynamics at metal boundaries with inclusion of plasma waves,” Phys. Rev. Lett.38, 1365–1368 (1977).
[CrossRef]

Fragstein, C.

U. Kreibig and C. Fragstein, “The limitation of electron mean free path in small silver particles,” Z. Physik224, 307–323 (1969).
[CrossRef]

Fritz, S.

H. Hövel, S. Fritz, A. Hilger, U. Kreibig, and M. Vollmer, “Width of cluster plasmon resonances: Bulk dielectric functions and chemical interface damping,” Phys. Rev. B48, 18178–18188 (1993).
[CrossRef]

García de Abajo, F. J.

C. David and F. J. García de Abajo, “Spatial nonlocality in the optical response of metal nanoparticles,” J. Phys. Chem. C115, 19470–19475 (2012).
[CrossRef]

F. J. García de Abajo, “Optical excitations in electron microscopy,” Rev. Mod. Phys.82, 209–275 (2010).
[CrossRef]

García-Vidal, F. J.

A. I. Fernández-Domínguez, A. Wiener, F. J. García-Vidal, S. A. Maier, and J. B. Pendry, “Transformation-optics description of nonlocal effects in plasmonic nanostructures,” Phys. Rev. Lett.108, 106802 (2012).
[CrossRef] [PubMed]

Genzel, L.

U. Kreibig and L. Genzel, “Optical absorption of small metallic particles,” Surf. Sci.156, 678–700 (1985).
[CrossRef]

L. Genzel, T. P. Martin, and U. Kreibig, “Dielectric function and plasma resonance of small metal particles,” Z. Phys. B21, 339–346 (1975).
[CrossRef]

Griffiths, D. J.

D. J. Griffiths, Introduction to Electrodynamics (Benjamin Cummings), 3rd ed.

Hilger, A.

H. Hövel, S. Fritz, A. Hilger, U. Kreibig, and M. Vollmer, “Width of cluster plasmon resonances: Bulk dielectric functions and chemical interface damping,” Phys. Rev. B48, 18178–18188 (1993).
[CrossRef]

Hill, R. T.

C. Ciracì, R. T. Hill, J. J. Mock, Y. Urzhumov, A. I. Fernández-Domínguez, S. A. Maier, J. B. Pendry, A. Chilkoti, and D. R. Smith, “Probing the ultimate limits of plasmonic enhancement,” Science337, 1072–1074 (2012).
[CrossRef] [PubMed]

Hövel, H.

H. Hövel, S. Fritz, A. Hilger, U. Kreibig, and M. Vollmer, “Width of cluster plasmon resonances: Bulk dielectric functions and chemical interface damping,” Phys. Rev. B48, 18178–18188 (1993).
[CrossRef]

Huffman, D.

C. Bohren and D. Huffman, Absorption and Scattering of Light by Small Particles (John Wiley & Sons, 1983).

Isaacson, M.

F. Ouyang, P. Batson, and M. Isaacson, “Quantum size effects in the surface-plasmon excitation of small metallic particles by electron-energy-loss spectroscopy,” Phys. Rev. B46, 15421–15425 (1992).
[CrossRef]

Jackson, J. D.

J. D. Jackson, Classical electrodynamics, 3rd ed. (Wiley, 1998).

Jauho, A.-P.

G. Toscano, S. Raza, W. Yan, C. Jeppesen, S. Xiao, M. Wubs, A.-P. Jauho, S. I. Bozhevolnyi, and N. A. Mortensen, “Nonlocal response in plasmonic waveguiding with extreme light confinement,” Nanophotonics2, 161–166 (2013).
[CrossRef]

S. Raza, N. Stenger, S. Kadkhodazadeh, S. V. Fischer, N. Kostesha, A.-P. Jauho, A. Burrows, M. Wubs, and N. A. Mortensen, “Blueshift of the surface plasmon resonance in silver nanoparticles studied with EELS,” Nanophotonics2, 131–138 (2013).
[CrossRef]

G. Toscano, S. Raza, A.-P. Jauho, N. A. Mortensen, and M. Wubs, “Modified field enhancement and extinction in plasmonic nanowire dimers due to nonlocal response,” Opt. Express20, 4176–4188 (2012).
[CrossRef] [PubMed]

S. Raza, G. Toscano, A.-P. Jauho, M. Wubs, and N. A. Mortensen, “Unusual resonances in nanoplasmonic structures due to nonlocal response,” Phys. Rev. B84, 121412(R) (2011).
[CrossRef]

Jeppesen, C.

G. Toscano, S. Raza, W. Yan, C. Jeppesen, S. Xiao, M. Wubs, A.-P. Jauho, S. I. Bozhevolnyi, and N. A. Mortensen, “Nonlocal response in plasmonic waveguiding with extreme light confinement,” Nanophotonics2, 161–166 (2013).
[CrossRef]

Jeyarajasingam, A.

L. Mulfinger, S. D. Solomon, M. Bahadory, A. Jeyarajasingam, S. A. Rutkowsky, and C. Boritz, “Synthesis and study of silver nanoparticles,” J. Chem. Educ.84, 322–325 (2007).
[CrossRef]

Kadkhodazadeh, S.

S. Raza, N. Stenger, S. Kadkhodazadeh, S. V. Fischer, N. Kostesha, A.-P. Jauho, A. Burrows, M. Wubs, and N. A. Mortensen, “Blueshift of the surface plasmon resonance in silver nanoparticles studied with EELS,” Nanophotonics2, 131–138 (2013).
[CrossRef]

Keller, O.

O. Keller, M. Xiao, and S. Bozhevolnyi, “Optical diamagnetic polarizability of a mesoscopic metallic sphere: transverse self-field approach,” Opt. Comm.102, 238–244 (1993).
[CrossRef]

Koh, A. L.

J. A. Scholl, A. L. Koh, and J. A. Dionne, “Quantum plasmon resonances of individual metallic nanoparticles,” Nature483, 421–427 (2012).
[CrossRef] [PubMed]

Kohn, W.

N. D. Lang and W. Kohn, “Theory of metal surfaces: Charge density and surface energy,” Phys. Rev. B1, 4555–4568 (1970).
[CrossRef]

Köller, L.

J. Tiggesbäumker, L. Köller, K.-H. Meiwes-Broer, and A. Liebsch, “Blue shift of the Mie plasma frequency in Ag clusters and particles,” Phys. Rev. A48, R1749–R1752 (1993).
[CrossRef] [PubMed]

König, L.

K.-P. Charlé, L. König, S. Nepijko, I. Rabin, and W. Schulze, “The surface plasmon resonance of free and embedded Ag-clusters in the size range 1,5 nm < D < 30 nm,” Cryst. Res. Technol.33, 1085–1096 (1998).
[CrossRef]

Kostesha, N.

S. Raza, N. Stenger, S. Kadkhodazadeh, S. V. Fischer, N. Kostesha, A.-P. Jauho, A. Burrows, M. Wubs, and N. A. Mortensen, “Blueshift of the surface plasmon resonance in silver nanoparticles studied with EELS,” Nanophotonics2, 131–138 (2013).
[CrossRef]

Kreibig, U.

H. Hövel, S. Fritz, A. Hilger, U. Kreibig, and M. Vollmer, “Width of cluster plasmon resonances: Bulk dielectric functions and chemical interface damping,” Phys. Rev. B48, 18178–18188 (1993).
[CrossRef]

U. Kreibig and L. Genzel, “Optical absorption of small metallic particles,” Surf. Sci.156, 678–700 (1985).
[CrossRef]

L. Genzel, T. P. Martin, and U. Kreibig, “Dielectric function and plasma resonance of small metal particles,” Z. Phys. B21, 339–346 (1975).
[CrossRef]

U. Kreibig and C. Fragstein, “The limitation of electron mean free path in small silver particles,” Z. Physik224, 307–323 (1969).
[CrossRef]

Lang, N. D.

N. D. Lang and W. Kohn, “Theory of metal surfaces: Charge density and surface energy,” Phys. Rev. B1, 4555–4568 (1970).
[CrossRef]

Liebsch, A.

J. Tiggesbäumker, L. Köller, K.-H. Meiwes-Broer, and A. Liebsch, “Blue shift of the Mie plasma frequency in Ag clusters and particles,” Phys. Rev. A48, R1749–R1752 (1993).
[CrossRef] [PubMed]

A. Liebsch, “Surface-plasmon dispersion and size dependence of Mie resonance: silver versus simple metals,” Phys. Rev. B48, 11317–11328 (1993).
[CrossRef]

Lindau, I.

I. Lindau and P. O. Nilsson, “Experimental evidence for excitation of longitudinal plasmons by photons,” Phys. Lett. A31, 352–353 (1970).
[CrossRef]

Ljungbert, Å.

P. Apell and Å. Ljungbert, “A general non-local theory for the electromagnetic response of a small metal particle,” Phys. Scr.26, 113–118 (1982).
[CrossRef]

Lounis, B.

S. Berciaud, L. Cognet, P. Tamarat, and B. Lounis, “Observation of intrinsic size effects in the optical response of individual gold nanoparticles,” Nano Lett.5, 515–518 (2005).
[CrossRef] [PubMed]

Luo, Y.

Y. Luo, A. I. Fernández-Domínguez, A. Wiener, S. A. Maier, and J. B. Pendry, “Surface plasmons and nonlocality: A simple model,” Phys. Rev. Lett.111, 093901 (2013).
[CrossRef] [PubMed]

Maier, S. A.

Y. Luo, A. I. Fernández-Domínguez, A. Wiener, S. A. Maier, and J. B. Pendry, “Surface plasmons and nonlocality: A simple model,” Phys. Rev. Lett.111, 093901 (2013).
[CrossRef] [PubMed]

A. I. Fernández-Domínguez, A. Wiener, F. J. García-Vidal, S. A. Maier, and J. B. Pendry, “Transformation-optics description of nonlocal effects in plasmonic nanostructures,” Phys. Rev. Lett.108, 106802 (2012).
[CrossRef] [PubMed]

C. Ciracì, R. T. Hill, J. J. Mock, Y. Urzhumov, A. I. Fernández-Domínguez, S. A. Maier, J. B. Pendry, A. Chilkoti, and D. R. Smith, “Probing the ultimate limits of plasmonic enhancement,” Science337, 1072–1074 (2012).
[CrossRef] [PubMed]

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

Majewski, M. L.

Martin, T. P.

L. Genzel, T. P. Martin, and U. Kreibig, “Dielectric function and plasma resonance of small metal particles,” Z. Phys. B21, 339–346 (1975).
[CrossRef]

Meiwes-Broer, K.-H.

J. Tiggesbäumker, L. Köller, K.-H. Meiwes-Broer, and A. Liebsch, “Blue shift of the Mie plasma frequency in Ag clusters and particles,” Phys. Rev. A48, R1749–R1752 (1993).
[CrossRef] [PubMed]

Mie, G.

G. Mie, “Beiträge zur Optik trüber Medien, speziell kolloidaler Metallösungen,” Ann. Phys.330, 377–445 (1908).
[CrossRef]

Miškovic, Z.

I. Villo-Perez, Z. Mišković, and N. Arista, “Plasmon spectra of nano-structures: A hydrodynamic model,” in “Trends in Nanophysics,” V. Bârsan and A. Aldea, eds. (SpringerBerlin Heidelberg, 2010), Engineering Materials, pp. 217–254.
[CrossRef]

Mock, J. J.

C. Ciracì, R. T. Hill, J. J. Mock, Y. Urzhumov, A. I. Fernández-Domínguez, S. A. Maier, J. B. Pendry, A. Chilkoti, and D. R. Smith, “Probing the ultimate limits of plasmonic enhancement,” Science337, 1072–1074 (2012).
[CrossRef] [PubMed]

Mortensen, N. A.

S. Raza, N. Stenger, S. Kadkhodazadeh, S. V. Fischer, N. Kostesha, A.-P. Jauho, A. Burrows, M. Wubs, and N. A. Mortensen, “Blueshift of the surface plasmon resonance in silver nanoparticles studied with EELS,” Nanophotonics2, 131–138 (2013).
[CrossRef]

C. David, N. A. Mortensen, and J. Christensen, “Perfect imaging, epsilon-near zero phenomena and waveguiding in the scope of nonlocal effects,” Sci. Rep.3, 2526 (2013).
[CrossRef] [PubMed]

G. Toscano, S. Raza, W. Yan, C. Jeppesen, S. Xiao, M. Wubs, A.-P. Jauho, S. I. Bozhevolnyi, and N. A. Mortensen, “Nonlocal response in plasmonic waveguiding with extreme light confinement,” Nanophotonics2, 161–166 (2013).
[CrossRef]

G. Toscano, S. Raza, A.-P. Jauho, N. A. Mortensen, and M. Wubs, “Modified field enhancement and extinction in plasmonic nanowire dimers due to nonlocal response,” Opt. Express20, 4176–4188 (2012).
[CrossRef] [PubMed]

S. Raza, G. Toscano, A.-P. Jauho, M. Wubs, and N. A. Mortensen, “Unusual resonances in nanoplasmonic structures due to nonlocal response,” Phys. Rev. B84, 121412(R) (2011).
[CrossRef]

Mulfinger, L.

L. Mulfinger, S. D. Solomon, M. Bahadory, A. Jeyarajasingam, S. A. Rutkowsky, and C. Boritz, “Synthesis and study of silver nanoparticles,” J. Chem. Educ.84, 322–325 (2007).
[CrossRef]

Nepijko, S.

K.-P. Charlé, L. König, S. Nepijko, I. Rabin, and W. Schulze, “The surface plasmon resonance of free and embedded Ag-clusters in the size range 1,5 nm < D < 30 nm,” Cryst. Res. Technol.33, 1085–1096 (1998).
[CrossRef]

Nilsson, P. O.

I. Lindau and P. O. Nilsson, “Experimental evidence for excitation of longitudinal plasmons by photons,” Phys. Lett. A31, 352–353 (1970).
[CrossRef]

Ouyang, F.

F. Ouyang, P. Batson, and M. Isaacson, “Quantum size effects in the surface-plasmon excitation of small metallic particles by electron-energy-loss spectroscopy,” Phys. Rev. B46, 15421–15425 (1992).
[CrossRef]

Paranjape, B.

A. Boardman, B. Paranjape, and R. Teshima, “The effect of structure on surface plasmons,” Surf. Sci.49, 275–292 (1975).
[CrossRef]

Paranjape, B. V.

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

Pendry, J. B.

Y. Luo, A. I. Fernández-Domínguez, A. Wiener, S. A. Maier, and J. B. Pendry, “Surface plasmons and nonlocality: A simple model,” Phys. Rev. Lett.111, 093901 (2013).
[CrossRef] [PubMed]

A. I. Fernández-Domínguez, A. Wiener, F. J. García-Vidal, S. A. Maier, and J. B. Pendry, “Transformation-optics description of nonlocal effects in plasmonic nanostructures,” Phys. Rev. Lett.108, 106802 (2012).
[CrossRef] [PubMed]

C. Ciracì, R. T. Hill, J. J. Mock, Y. Urzhumov, A. I. Fernández-Domínguez, S. A. Maier, J. B. Pendry, A. Chilkoti, and D. R. Smith, “Probing the ultimate limits of plasmonic enhancement,” Science337, 1072–1074 (2012).
[CrossRef] [PubMed]

Penn, D. R.

P. Apell and D. R. Penn, “Optical properties of small metal spheres: Surface effects,” Phys. Rev. Lett.50, 1316–1319 (1983).
[CrossRef]

Rabin, I.

K.-P. Charlé, L. König, S. Nepijko, I. Rabin, and W. Schulze, “The surface plasmon resonance of free and embedded Ag-clusters in the size range 1,5 nm < D < 30 nm,” Cryst. Res. Technol.33, 1085–1096 (1998).
[CrossRef]

Rakic, A. D.

Raza, S.

G. Toscano, S. Raza, W. Yan, C. Jeppesen, S. Xiao, M. Wubs, A.-P. Jauho, S. I. Bozhevolnyi, and N. A. Mortensen, “Nonlocal response in plasmonic waveguiding with extreme light confinement,” Nanophotonics2, 161–166 (2013).
[CrossRef]

S. Raza, N. Stenger, S. Kadkhodazadeh, S. V. Fischer, N. Kostesha, A.-P. Jauho, A. Burrows, M. Wubs, and N. A. Mortensen, “Blueshift of the surface plasmon resonance in silver nanoparticles studied with EELS,” Nanophotonics2, 131–138 (2013).
[CrossRef]

G. Toscano, S. Raza, A.-P. Jauho, N. A. Mortensen, and M. Wubs, “Modified field enhancement and extinction in plasmonic nanowire dimers due to nonlocal response,” Opt. Express20, 4176–4188 (2012).
[CrossRef] [PubMed]

S. Raza, G. Toscano, A.-P. Jauho, M. Wubs, and N. A. Mortensen, “Unusual resonances in nanoplasmonic structures due to nonlocal response,” Phys. Rev. B84, 121412(R) (2011).
[CrossRef]

Rivacoba, A.

J. Aizpurua, A. Rivacoba, and S. P. Apell, “Electron-energy losses in hemispherical targets,” Phys. Rev. B54, 2901–2909 (1996).
[CrossRef]

Ruppin, R.

R. Ruppin, “Surface modes and optical absorption of a small sphere above a substrate,” Surf. Sci.127, 108–118 (1983).
[CrossRef]

A. Boardman and R. Ruppin, “The boundary conditions between spatially dispersive media,” Surf. Sci.112, 153–167 (1981).
[CrossRef]

R. Ruppin, “Optical properties of a plasma sphere,” Phys. Rev. Lett.31, 1434–1437 (1973).
[CrossRef]

Rutkowsky, S. A.

L. Mulfinger, S. D. Solomon, M. Bahadory, A. Jeyarajasingam, S. A. Rutkowsky, and C. Boritz, “Synthesis and study of silver nanoparticles,” J. Chem. Educ.84, 322–325 (2007).
[CrossRef]

Sauter, F.

F. Sauter, “Der Einfiuß von Plasmawellen auf das Reflexionsvermögen von Metallen (I),” Z. Physik203, 488–494 (1967).
[CrossRef]

Schaich, W. L.

C. Schwartz and W. L. Schaich, “Hydrodynamic models of surface plasmons,” Phys. Rev. B26, 7008–7011 (1982).
[CrossRef]

Scholl, J. A.

J. A. Scholl, A. L. Koh, and J. A. Dionne, “Quantum plasmon resonances of individual metallic nanoparticles,” Nature483, 421–427 (2012).
[CrossRef] [PubMed]

Schulze, W.

K.-P. Charlé, L. König, S. Nepijko, I. Rabin, and W. Schulze, “The surface plasmon resonance of free and embedded Ag-clusters in the size range 1,5 nm < D < 30 nm,” Cryst. Res. Technol.33, 1085–1096 (1998).
[CrossRef]

K.-P. Charlé, W. Schulze, and B. Winter, “The size dependent shift of the surface-plasmon absorption-band of small spherical metal particles,” Z. Phys. D12, 471–475 (1989).
[CrossRef]

Schwartz, C.

C. Schwartz and W. L. Schaich, “Hydrodynamic models of surface plasmons,” Phys. Rev. B26, 7008–7011 (1982).
[CrossRef]

Smith, D. R.

C. Ciracì, R. T. Hill, J. J. Mock, Y. Urzhumov, A. I. Fernández-Domínguez, S. A. Maier, J. B. Pendry, A. Chilkoti, and D. R. Smith, “Probing the ultimate limits of plasmonic enhancement,” Science337, 1072–1074 (2012).
[CrossRef] [PubMed]

Solomon, S. D.

L. Mulfinger, S. D. Solomon, M. Bahadory, A. Jeyarajasingam, S. A. Rutkowsky, and C. Boritz, “Synthesis and study of silver nanoparticles,” J. Chem. Educ.84, 322–325 (2007).
[CrossRef]

Stenger, N.

S. Raza, N. Stenger, S. Kadkhodazadeh, S. V. Fischer, N. Kostesha, A.-P. Jauho, A. Burrows, M. Wubs, and N. A. Mortensen, “Blueshift of the surface plasmon resonance in silver nanoparticles studied with EELS,” Nanophotonics2, 131–138 (2013).
[CrossRef]

Stenschke, H.

F. Forstmann and H. Stenschke, “Electrodynamics at metal boundaries with inclusion of plasma waves,” Phys. Rev. Lett.38, 1365–1368 (1977).
[CrossRef]

Tamarat, P.

S. Berciaud, L. Cognet, P. Tamarat, and B. Lounis, “Observation of intrinsic size effects in the optical response of individual gold nanoparticles,” Nano Lett.5, 515–518 (2005).
[CrossRef] [PubMed]

Teshima, R.

A. Boardman, B. Paranjape, and R. Teshima, “The effect of structure on surface plasmons,” Surf. Sci.49, 275–292 (1975).
[CrossRef]

Tiggesbäumker, J.

J. Tiggesbäumker, L. Köller, K.-H. Meiwes-Broer, and A. Liebsch, “Blue shift of the Mie plasma frequency in Ag clusters and particles,” Phys. Rev. A48, R1749–R1752 (1993).
[CrossRef] [PubMed]

Toscano, G.

G. Toscano, S. Raza, W. Yan, C. Jeppesen, S. Xiao, M. Wubs, A.-P. Jauho, S. I. Bozhevolnyi, and N. A. Mortensen, “Nonlocal response in plasmonic waveguiding with extreme light confinement,” Nanophotonics2, 161–166 (2013).
[CrossRef]

G. Toscano, S. Raza, A.-P. Jauho, N. A. Mortensen, and M. Wubs, “Modified field enhancement and extinction in plasmonic nanowire dimers due to nonlocal response,” Opt. Express20, 4176–4188 (2012).
[CrossRef] [PubMed]

S. Raza, G. Toscano, A.-P. Jauho, M. Wubs, and N. A. Mortensen, “Unusual resonances in nanoplasmonic structures due to nonlocal response,” Phys. Rev. B84, 121412(R) (2011).
[CrossRef]

Urzhumov, Y.

C. Ciracì, R. T. Hill, J. J. Mock, Y. Urzhumov, A. I. Fernández-Domínguez, S. A. Maier, J. B. Pendry, A. Chilkoti, and D. R. Smith, “Probing the ultimate limits of plasmonic enhancement,” Science337, 1072–1074 (2012).
[CrossRef] [PubMed]

Villo-Perez, I.

I. Villo-Perez, Z. Mišković, and N. Arista, “Plasmon spectra of nano-structures: A hydrodynamic model,” in “Trends in Nanophysics,” V. Bârsan and A. Aldea, eds. (SpringerBerlin Heidelberg, 2010), Engineering Materials, pp. 217–254.
[CrossRef]

Vollmer, M.

H. Hövel, S. Fritz, A. Hilger, U. Kreibig, and M. Vollmer, “Width of cluster plasmon resonances: Bulk dielectric functions and chemical interface damping,” Phys. Rev. B48, 18178–18188 (1993).
[CrossRef]

Wiener, A.

Y. Luo, A. I. Fernández-Domínguez, A. Wiener, S. A. Maier, and J. B. Pendry, “Surface plasmons and nonlocality: A simple model,” Phys. Rev. Lett.111, 093901 (2013).
[CrossRef] [PubMed]

A. I. Fernández-Domínguez, A. Wiener, F. J. García-Vidal, S. A. Maier, and J. B. Pendry, “Transformation-optics description of nonlocal effects in plasmonic nanostructures,” Phys. Rev. Lett.108, 106802 (2012).
[CrossRef] [PubMed]

Winter, B.

K.-P. Charlé, W. Schulze, and B. Winter, “The size dependent shift of the surface-plasmon absorption-band of small spherical metal particles,” Z. Phys. D12, 471–475 (1989).
[CrossRef]

Wubs, M.

S. Raza, N. Stenger, S. Kadkhodazadeh, S. V. Fischer, N. Kostesha, A.-P. Jauho, A. Burrows, M. Wubs, and N. A. Mortensen, “Blueshift of the surface plasmon resonance in silver nanoparticles studied with EELS,” Nanophotonics2, 131–138 (2013).
[CrossRef]

G. Toscano, S. Raza, W. Yan, C. Jeppesen, S. Xiao, M. Wubs, A.-P. Jauho, S. I. Bozhevolnyi, and N. A. Mortensen, “Nonlocal response in plasmonic waveguiding with extreme light confinement,” Nanophotonics2, 161–166 (2013).
[CrossRef]

G. Toscano, S. Raza, A.-P. Jauho, N. A. Mortensen, and M. Wubs, “Modified field enhancement and extinction in plasmonic nanowire dimers due to nonlocal response,” Opt. Express20, 4176–4188 (2012).
[CrossRef] [PubMed]

S. Raza, G. Toscano, A.-P. Jauho, M. Wubs, and N. A. Mortensen, “Unusual resonances in nanoplasmonic structures due to nonlocal response,” Phys. Rev. B84, 121412(R) (2011).
[CrossRef]

Xiao, M.

O. Keller, M. Xiao, and S. Bozhevolnyi, “Optical diamagnetic polarizability of a mesoscopic metallic sphere: transverse self-field approach,” Opt. Comm.102, 238–244 (1993).
[CrossRef]

Xiao, S.

G. Toscano, S. Raza, W. Yan, C. Jeppesen, S. Xiao, M. Wubs, A.-P. Jauho, S. I. Bozhevolnyi, and N. A. Mortensen, “Nonlocal response in plasmonic waveguiding with extreme light confinement,” Nanophotonics2, 161–166 (2013).
[CrossRef]

Yan, W.

G. Toscano, S. Raza, W. Yan, C. Jeppesen, S. Xiao, M. Wubs, A.-P. Jauho, S. I. Bozhevolnyi, and N. A. Mortensen, “Nonlocal response in plasmonic waveguiding with extreme light confinement,” Nanophotonics2, 161–166 (2013).
[CrossRef]

W. Yan and , in preparation (2013).

Ann. Phys. (1)

G. Mie, “Beiträge zur Optik trüber Medien, speziell kolloidaler Metallösungen,” Ann. Phys.330, 377–445 (1908).
[CrossRef]

Appl. Opt. (2)

Cryst. Res. Technol. (1)

K.-P. Charlé, L. König, S. Nepijko, I. Rabin, and W. Schulze, “The surface plasmon resonance of free and embedded Ag-clusters in the size range 1,5 nm < D < 30 nm,” Cryst. Res. Technol.33, 1085–1096 (1998).
[CrossRef]

J. Chem. Educ. (1)

L. Mulfinger, S. D. Solomon, M. Bahadory, A. Jeyarajasingam, S. A. Rutkowsky, and C. Boritz, “Synthesis and study of silver nanoparticles,” J. Chem. Educ.84, 322–325 (2007).
[CrossRef]

J. Phys. Chem. C (1)

C. David and F. J. García de Abajo, “Spatial nonlocality in the optical response of metal nanoparticles,” J. Phys. Chem. C115, 19470–19475 (2012).
[CrossRef]

J. Phys. F: Met. Phys. (1)

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

Nano Lett. (1)

S. Berciaud, L. Cognet, P. Tamarat, and B. Lounis, “Observation of intrinsic size effects in the optical response of individual gold nanoparticles,” Nano Lett.5, 515–518 (2005).
[CrossRef] [PubMed]

Nanophotonics (2)

S. Raza, N. Stenger, S. Kadkhodazadeh, S. V. Fischer, N. Kostesha, A.-P. Jauho, A. Burrows, M. Wubs, and N. A. Mortensen, “Blueshift of the surface plasmon resonance in silver nanoparticles studied with EELS,” Nanophotonics2, 131–138 (2013).
[CrossRef]

G. Toscano, S. Raza, W. Yan, C. Jeppesen, S. Xiao, M. Wubs, A.-P. Jauho, S. I. Bozhevolnyi, and N. A. Mortensen, “Nonlocal response in plasmonic waveguiding with extreme light confinement,” Nanophotonics2, 161–166 (2013).
[CrossRef]

Nature (1)

J. A. Scholl, A. L. Koh, and J. A. Dionne, “Quantum plasmon resonances of individual metallic nanoparticles,” Nature483, 421–427 (2012).
[CrossRef] [PubMed]

New J. Phys. (1)

R. Carmina Monreal, T. J. Antosiewicz, and S. P. Apell, “Competition between surface screening and size quantization for surface plasmons in nanoparticles,” New J. Phys.15, 083044 (2013).
[CrossRef]

Opt. Comm. (1)

O. Keller, M. Xiao, and S. Bozhevolnyi, “Optical diamagnetic polarizability of a mesoscopic metallic sphere: transverse self-field approach,” Opt. Comm.102, 238–244 (1993).
[CrossRef]

Opt. Express (1)

Phys. Lett. A (1)

I. Lindau and P. O. Nilsson, “Experimental evidence for excitation of longitudinal plasmons by photons,” Phys. Lett. A31, 352–353 (1970).
[CrossRef]

Phys. Rev. A (1)

J. Tiggesbäumker, L. Köller, K.-H. Meiwes-Broer, and A. Liebsch, “Blue shift of the Mie plasma frequency in Ag clusters and particles,” Phys. Rev. A48, R1749–R1752 (1993).
[CrossRef] [PubMed]

Phys. Rev. B (8)

H. Hövel, S. Fritz, A. Hilger, U. Kreibig, and M. Vollmer, “Width of cluster plasmon resonances: Bulk dielectric functions and chemical interface damping,” Phys. Rev. B48, 18178–18188 (1993).
[CrossRef]

F. Ouyang, P. Batson, and M. Isaacson, “Quantum size effects in the surface-plasmon excitation of small metallic particles by electron-energy-loss spectroscopy,” Phys. Rev. B46, 15421–15425 (1992).
[CrossRef]

J. Aizpurua, A. Rivacoba, and S. P. Apell, “Electron-energy losses in hemispherical targets,” Phys. Rev. B54, 2901–2909 (1996).
[CrossRef]

C. Schwartz and W. L. Schaich, “Hydrodynamic models of surface plasmons,” Phys. Rev. B26, 7008–7011 (1982).
[CrossRef]

A. J. Bennett, “Influence of the electron charge distribution on surface-plasmon dispersion,” Phys. Rev. B1, 203–207 (1970).
[CrossRef]

N. D. Lang and W. Kohn, “Theory of metal surfaces: Charge density and surface energy,” Phys. Rev. B1, 4555–4568 (1970).
[CrossRef]

A. Liebsch, “Surface-plasmon dispersion and size dependence of Mie resonance: silver versus simple metals,” Phys. Rev. B48, 11317–11328 (1993).
[CrossRef]

S. Raza, G. Toscano, A.-P. Jauho, M. Wubs, and N. A. Mortensen, “Unusual resonances in nanoplasmonic structures due to nonlocal response,” Phys. Rev. B84, 121412(R) (2011).
[CrossRef]

Phys. Rev. Lett. (5)

Y. Luo, A. I. Fernández-Domínguez, A. Wiener, S. A. Maier, and J. B. Pendry, “Surface plasmons and nonlocality: A simple model,” Phys. Rev. Lett.111, 093901 (2013).
[CrossRef] [PubMed]

F. Forstmann and H. Stenschke, “Electrodynamics at metal boundaries with inclusion of plasma waves,” Phys. Rev. Lett.38, 1365–1368 (1977).
[CrossRef]

R. Ruppin, “Optical properties of a plasma sphere,” Phys. Rev. Lett.31, 1434–1437 (1973).
[CrossRef]

A. I. Fernández-Domínguez, A. Wiener, F. J. García-Vidal, S. A. Maier, and J. B. Pendry, “Transformation-optics description of nonlocal effects in plasmonic nanostructures,” Phys. Rev. Lett.108, 106802 (2012).
[CrossRef] [PubMed]

P. Apell and D. R. Penn, “Optical properties of small metal spheres: Surface effects,” Phys. Rev. Lett.50, 1316–1319 (1983).
[CrossRef]

Phys. Scr. (3)

P. Apell, “The electromagnetic field near a metal surface in the semi-classical infinite barrier model,” Phys. Scr.17, 535–542 (1978).
[CrossRef]

P. Apell and Å. Ljungbert, “A general non-local theory for the electromagnetic response of a small metal particle,” Phys. Scr.26, 113–118 (1982).
[CrossRef]

P. Apell, “A simple derivation of the surface contribution to the reflectivity of a metal, and its use in the Van der Waals interaction,” Phys. Scr.24, 795–806 (1981).
[CrossRef]

Prog. Surf. Sci. (1)

P. J. Feibelman, “Surface electromagnetic fields,” Prog. Surf. Sci.12, 287–407 (1982).
[CrossRef]

Rep. Prog. Phys. (1)

G. Barton, “Some surface effects in the hydrodynamic model of metals,” Rep. Prog. Phys.42, 963–1016 (1979).
[CrossRef]

Rev. Mod. Phys. (1)

F. J. García de Abajo, “Optical excitations in electron microscopy,” Rev. Mod. Phys.82, 209–275 (2010).
[CrossRef]

Sci. Rep. (1)

C. David, N. A. Mortensen, and J. Christensen, “Perfect imaging, epsilon-near zero phenomena and waveguiding in the scope of nonlocal effects,” Sci. Rep.3, 2526 (2013).
[CrossRef] [PubMed]

Science (1)

C. Ciracì, R. T. Hill, J. J. Mock, Y. Urzhumov, A. I. Fernández-Domínguez, S. A. Maier, J. B. Pendry, A. Chilkoti, and D. R. Smith, “Probing the ultimate limits of plasmonic enhancement,” Science337, 1072–1074 (2012).
[CrossRef] [PubMed]

Surf. Sci. (4)

A. Boardman, B. Paranjape, and R. Teshima, “The effect of structure on surface plasmons,” Surf. Sci.49, 275–292 (1975).
[CrossRef]

A. Boardman and R. Ruppin, “The boundary conditions between spatially dispersive media,” Surf. Sci.112, 153–167 (1981).
[CrossRef]

U. Kreibig and L. Genzel, “Optical absorption of small metallic particles,” Surf. Sci.156, 678–700 (1985).
[CrossRef]

R. Ruppin, “Surface modes and optical absorption of a small sphere above a substrate,” Surf. Sci.127, 108–118 (1983).
[CrossRef]

Z. Phys. A (1)

F. Bloch, “Bremsvermögen von Atomen mit mehreren Elektronen,” Z. Phys. A81, 363–376 (1933).

Z. Phys. B (1)

L. Genzel, T. P. Martin, and U. Kreibig, “Dielectric function and plasma resonance of small metal particles,” Z. Phys. B21, 339–346 (1975).
[CrossRef]

Z. Phys. D (1)

K.-P. Charlé, W. Schulze, and B. Winter, “The size dependent shift of the surface-plasmon absorption-band of small spherical metal particles,” Z. Phys. D12, 471–475 (1989).
[CrossRef]

Z. Physik (2)

U. Kreibig and C. Fragstein, “The limitation of electron mean free path in small silver particles,” Z. Physik224, 307–323 (1969).
[CrossRef]

F. Sauter, “Der Einfiuß von Plasmawellen auf das Reflexionsvermögen von Metallen (I),” Z. Physik203, 488–494 (1967).
[CrossRef]

Other (7)

J. D. Jackson, Classical electrodynamics, 3rd ed. (Wiley, 1998).

I. Villo-Perez, Z. Mišković, and N. Arista, “Plasmon spectra of nano-structures: A hydrodynamic model,” in “Trends in Nanophysics,” V. Bârsan and A. Aldea, eds. (SpringerBerlin Heidelberg, 2010), Engineering Materials, pp. 217–254.
[CrossRef]

W. Yan and , in preparation (2013).

C. Bohren and D. Huffman, Absorption and Scattering of Light by Small Particles (John Wiley & Sons, 1983).

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

D. J. Griffiths, Introduction to Electrodynamics (Benjamin Cummings), 3rd ed.

A. Boardman, Electromagnetic Surface Modes. Hydrodynamic theory of plasmon-polaritons on plane surfaces. (John Wiley and Sons, Chichester, 1982).

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Figures (3)

Fig. 1
Fig. 1

(a) Schematic image of the Ag nanoparticles deposited on 10 nm thick Si3N4 substrate. (b) Bright-field TEM image of sample. (c–f) Bright-field TEM images of single nanoparticles with diameters 3, 6, 10 and 13 nm, respectively. All scale bars are 10 nm long.

Fig. 2
Fig. 2

(a) Extinction cross section based on the nonlocal Clausius–Mossotti factor, Eq. (9), as a function of diameter 2R and normalized frequency ω/ωP. The real and imaginary parts of the normalized rescaled background permittivity ε̃B/εB as a function of normalized frequency are shown in (b) and (c), respectively, for three different sphere radii: 2 nm (red), 4 nm (green) and 8 nm (blue). Free-electron gas parameters used for the calculations: γ/ωP = 0.05, β/c = 5 × 10−3, ε = 1 and εB = 1.

Fig. 3
Fig. 3

EELS measurements of the SP resonance energy E plotted as a function of (a) diameter 2R and (b) inverse diameter 1/(2R). In (b), the black solid line is a linear fit to the experimental data and serves as a guide to the eye, while the blue dashed line represents calculations of a nonlocal sphere in a homogeneous environment [nonlocal Clausius–Mossotti factor, Eq. (9)]. From the average large-particle (2R > 20 nm) resonances we fit εB = 1.53. The red solid line represents calculations of a nonlocal sphere in vacuum situated on a 10 nm thick Si3N4 substrate with permittivity εS = 4.4 [49]. Material parameters for Ag are taken from Ref. [50] and the Fermi velocity is vF = 1.39 × 106 m/s.

Equations (31)

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D = en ,
H = 0 ,
× E = i ω μ 0 H ,
× H = i ω D + J ,
J = i ω en .
β 2 ω ( ω + i γ ) ( J ) + J = ε 0 σ E ,
α = 4 π R 3 ε D ε B ε D + 2 ε B ,
E = ϕ , J = ψ .
( 2 + k NL 2 ) n = 0 ,
2 ϕ = e ε 0 ε n ,
ψ = 1 i ω γ ( ε 0 ω P 2 ϕ e β 2 n ) ,
ϕ in = ϕ out , ε ϕ in r = ε B ϕ out r , ψ in r = 0 ,
n in = l , m A l j l ( k NL r ) Y l m ( θ , ϕ ) , n out = 0 ,
ϕ in = l , m [ D l r l A l e ε 0 ε k NL 2 j l ( k NL r ) ] Y l m ( θ , ϕ ) ,
ϕ out = l , m [ B l r l + C l r ( l + 1 ) ] Y l m ( θ , ϕ ) .
α NL = 4 π R 3 ε D ε B ( 1 + δ NL ) ε D + 2 ε B ( 1 + δ NL ) , δ NL = ε D ε ε j 1 ( k NL R ) k NL R j 1 ( k NL R ) ,
σ ext = 1 π R 2 [ ( ω / c ) 4 6 π | α NL | 2 + ( ω / c ) Im ( α NL ) ] .
ω 2 ω P 2 ε + β 2 π 2 R 2 n 2 ,
T l m σ l m σ = t l ( σ ) δ l l δ m m δ σ σ ,
t l ( 1 ) = j l ( x D ) j l ( x B ) j l ( x B ) j l ( x D ) j l ( x D ) h l ( 1 ) ( x B ) h l ( 1 ) ( x B ) j l ( x D ) ,
t l ( 2 ) = [ c l + j l ( x D ) ] ε B j l ( x B ) ε D j l ( x D ) j l ( x B ) [ c l + j l ( x D ) ] ε B h l ( 1 ) ( x B ) ε D j l ( x D ) h l ( 1 ) ( x B ) ,
c l = l ( l + 1 ) j l ( x NL ) j l ( x D ) x NL j l ( x NL ) ε D ε ε ,
M = ( I T S ) 1 T .
S l m 1 l m 1 = s l l m m d k x d k y f 1 y l m ( 1 ) y l m ( 1 ) + f 2 y l m ( 2 ) y l m ( 2 ) k B z ,
S l m 2 l m 2 = s l l m m d k x d k y f 2 y l m ( 1 ) y l m ( 1 ) + f 1 y l m ( 2 ) y l m ( 2 ) k B z ,
S l m 1 l m 2 = s l l m m d k x d k y f 2 y l m ( 1 ) y l m ( 2 ) + f 1 y l m ( 2 ) y l m ( 1 ) k B z ,
S l m 2 l m 1 = s l l m m d k x d k y f 1 y l m ( 1 ) y l m ( 2 ) + f 2 y l m ( 2 ) y l m ( 1 ) k B z ,
s l l m m = 2 i l l ( 1 ) l + m + m + 1 k B l ( l + 1 ) l ( l + 1 ) , y l m ( 1 ) = Y l m ( Ω k B ) θ k B , y l m ( 2 ) = m Y l m ( Ω k B ) sin θ k B ,
f σ = r σ [ 1 exp ( i k S z 2 t ) ] 1 r σ 2 exp ( i k S z 2 t ) exp ( i k B z 2 R ) ,
r 1 = k B z k S z k B z + k S z , r 2 = ε S k B z ε B k S z ε S k B z + ε B k S z .
σ ext = 1 k B 2 | E 0 | 2 Re ( a T Ma * ) ,

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