Abstract

Nanometer-sized metal particles exhibit broadening of the localized surface plasmon resonance (LSPR) in comparison to its value predicted by the classical Mie theory. Using our model for the LSPR dependence on non-local surface screening and size quantization, we quantitatively relate the observed plasmon width to the nanoparticle radius R and the permittivity of the surrounding medium εm. For Ag nanospheres larger than 8 nm only the non-local dynamical effects occurring at the surface are important and, up to a diameter of 25 nm, dominate over the bulk scattering mechanism. Qualitatively, the LSPR width is inversely proportional to the particle size and has a nonmonotonic dependence on the permittivity of the host medium, exhibiting for Ag a maximum at εm ≈ 2.5. Our calculated LSPR width is compared with recent experimental data.

© 2014 Optical Society of America

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    [Crossref]
  2. Y. Borensztein, P. De Andrès, R. Monreal, T. Lopez-Rios, and F. Flores, “Blue shift of the dipolar plasma resonance in small silver particles on an alumina surface,” Phys. Rev. B 33, 2828–2830 (1986).
    [Crossref]
  3. 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. A 48, R1749–R1752 (1993).
    [Crossref] [PubMed]
  4. C. Yannouleas, “Microscopic description of the surface dipole plasmon in large NaN clusters (950 ≲ N ≲ 12050),” Phys. Rev. B 58, 6748–6751 (1998).
    [Crossref]
  5. S. Fedrigo, W. Harbich, and J. Buttet, “Collective dipole oscillations in small silver clusters embedded in rare-gas matrices,” Phys. Rev. B 47, 10706–10715 (1993).
    [Crossref]
  6. E. Townsend and G. W. Bryant, “Plasmonic properties of metallic nanoparticles: The effects of size quantization,” Nano Letters 12, 429–434 (2012).
    [Crossref]
  7. C. Sönnichsen, T. Franzl, T. Wilk, G. von Plessen, J. Feldmann, O. Wilson, and P. Mulvaney, “Drastic reduction of plasmon damping in gold nanorods,” Phys. Rev. Lett. 88, 077402 (2002).
    [Crossref] [PubMed]
  8. C. Sönnichsen, T. Franzl, T. Wilk, G. von Plessen, and J. Feldmann, “Plasmon resonances in large noble-metal clusters,” New J. Phys. 4, 93 (2002).
    [Crossref]
  9. T. Klar, M. Perner, S. Grosse, G. von Plessen, W. Spirkl, and J. Feldmann, “Surface-plasmon resonances in single metallic nanoparticles,” Phys. Rev. Lett. 80, 4249–4252 (1998).
    [Crossref]
  10. S. Peng, J. M. McMahon, G. C. Schatz, S. K. Gray, and Y. Sun, “Reversing the size-dependence of surface plasmon resonances,” Proc. Natl. Acad. Sci. U.S.A. 107, 14530–14534 (2010).
    [Crossref] [PubMed]
  11. 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,” Science 337, 1072–1074 (2012).
    [Crossref] [PubMed]
  12. 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]
  13. T. V. Teperik, P. Nordlander, J. Aizpurua, and A. G. Borisov, “Robust subnanometric plasmon ruler by rescaling of the nonlocal optical response,” Phys. Rev. Lett. 110, 263901 (2013).
    [Crossref] [PubMed]
  14. A. Garcia-Etxarri, P. Apell, M. Käll, and J. Aizpurua, “A combination of concave/convex surfaces for field-enhancement optimization: the indented nanocone,” Opt. Express 20, 25201–25212 (2012).
    [Crossref] [PubMed]
  15. R. C. 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]
  16. Y. Fan, J. Li, H. Chen, X. Lu, and X. Liu, “Size-dependence of the effective electron-phonon energy relaxation in hollow gold nanospheres,” Opto-Electron. Rev. 22, 36–40 (2014).
    [Crossref]
  17. B. N. J. Persson, “Polarizability of small spherical metal particles: influence of the matix environment,” Surf. Sci. 281, 153–162 (1993).
    [Crossref]
  18. H. Baida, P. Billaud, S. Marhaba, D. Christofilos, E. Cottancin, A. Crut, J. Lermé, P. Maioli, M. Pellarin, N. Del Fatti, F. Vallée, A. Sánchez-Iglesias, I. Pastoriza-Santos, and L. M. Liz-Marzán, “Quantitative determination of the size dependence of surface plasmon resonance damping in single Ag@SiO2 nanoparticles,” Nano Lett. 9, 3463–3469 (2009).
    [Crossref] [PubMed]
  19. E. Cottancin, G. Celep, J. Lermé, M. Pellarin, J. Huntzinger, J. Vialle, and M. Broyer, “Optical properties of noble metal clusters as a function of the size: Comparison between experiments and a semi-quantal theory,” Theoretical Chemistry Accounts 116, 514–523 (2006).
    [Crossref]
  20. B. Palpant, B. Prével, J. Lermé, E. Cottancin, M. Pellarin, M. Treilleux, A. Perez, J. L. Vialle, and M. Broyer, “Optical properties of gold clusters in the size range 2–4 nm,” Phys. Rev. B 57, 1963–1970 (1998).
    [Crossref]
  21. G. Mie, “Beiträge zur Optik trüber Medien, speziell kolloidaler Metallösungen,” Ann. Phys. 25, 377–445 (1908).
    [Crossref]
  22. 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. B 48, 18178–18188 (1993).
    [Crossref]
  23. A. Kawabata and R. Kubo, “Electronic properties of fine metallic particles. ii. plasma resonance absorption,” Journal of the Physical Society of Japan 21, 1765–1772 (1966).
    [Crossref]
  24. P. Ascarelli and M. Cini, “Red shift of the surface plasmon resonance absorption by fine metal particles,” Solid State Commun. 18, 385–388 (1976).
    [Crossref]
  25. R. Ruppin, “Optical properties of small metal spheres,” Phys. Rev. B 11, 2871–2876 (1975).
    [Crossref]
  26. A. V. Uskov, I. E. Protsenko, N. A. Mortensen, and E. P. O’Reilly, “Broadening of plasmonic resonance due to electron collisions with nanoparticle boundary: a quantum mechanical consideration,” Plasmonics 9, 185–192 (2014).
    [Crossref]
  27. P. Apell and A. Ljungbert, “A general non-local theory for the electromagnetic response of a small metal particle,” Physica Scripta 26, 113–118 (1982).
    [Crossref]
  28. B. N. J. Persson and P. Apell, “Sum rules for surface response functions with application to the van der Waals interaction between an atom and a metal,” Phys. Rev. B. 27, 6058–6065 (1983).
    [Crossref]
  29. A. Liebsch, “Dynamical screening at simple-metal surfaces,” Phys. Rev. B 36, 7378–7388 (1987).
    [Crossref]
  30. P. J. Feibelman, “Surface electromagnetic fields,” Prog. Surf. Sci. 12, 287–407 (1982).
  31. A. Liebsch, “Surface-plasmon dispersion and size dependence of Mie resonance: Silver versus simple metals,” Phys. Rev. B 48, 11317–11328 (1993).
    [Crossref]
  32. K.-D. Tsuei, E. W. Plummer, A. Liebsch, E. Pehlke, K. Kempa, and P. Bakshi, “The normal modes at the surface of simple metals,” Surf. Sci. 247, 302–326 (1991).
    [Crossref]
  33. P. Johnson and R. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6, 4370–4379 (1972).
    [Crossref]
  34. K. Kolwas and A. Derkachova, “Damping rates of surface plasmons for particles of size from nano- to micrometers; reduction of the nonradiative decay,” J. Quant. Spectrocs. Radiat. Transfer 114, 45–55 (2013).
    [Crossref]
  35. J. Lermé, H. Baida, C. Bonnet, M. Broyer, E. Cottancin, A. Crut, P. Maioli, N. Del Fatti, F. Vallée, and M. Pellarin, “Size dependence of the surface plasmon resonance damping in metal nanospheres,” J. Phys. Chem. Lett. 1, 2922–2928 (2010).
  36. J. Lermé, “Size evolution of the surface plasmon resonance damping in silver nanoparticles: Confinement and dielectric effects,” J. Phys. Chem. C 115, 14098–14110 (2011).
    [Crossref]

2014 (2)

Y. Fan, J. Li, H. Chen, X. Lu, and X. Liu, “Size-dependence of the effective electron-phonon energy relaxation in hollow gold nanospheres,” Opto-Electron. Rev. 22, 36–40 (2014).
[Crossref]

A. V. Uskov, I. E. Protsenko, N. A. Mortensen, and E. P. O’Reilly, “Broadening of plasmonic resonance due to electron collisions with nanoparticle boundary: a quantum mechanical consideration,” Plasmonics 9, 185–192 (2014).
[Crossref]

2013 (3)

R. C. 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]

T. V. Teperik, P. Nordlander, J. Aizpurua, and A. G. Borisov, “Robust subnanometric plasmon ruler by rescaling of the nonlocal optical response,” Phys. Rev. Lett. 110, 263901 (2013).
[Crossref] [PubMed]

K. Kolwas and A. Derkachova, “Damping rates of surface plasmons for particles of size from nano- to micrometers; reduction of the nonradiative decay,” J. Quant. Spectrocs. Radiat. Transfer 114, 45–55 (2013).
[Crossref]

2012 (4)

A. Garcia-Etxarri, P. Apell, M. Käll, and J. Aizpurua, “A combination of concave/convex surfaces for field-enhancement optimization: the indented nanocone,” Opt. Express 20, 25201–25212 (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,” Science 337, 1072–1074 (2012).
[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]

E. Townsend and G. W. Bryant, “Plasmonic properties of metallic nanoparticles: The effects of size quantization,” Nano Letters 12, 429–434 (2012).
[Crossref]

2011 (1)

J. Lermé, “Size evolution of the surface plasmon resonance damping in silver nanoparticles: Confinement and dielectric effects,” J. Phys. Chem. C 115, 14098–14110 (2011).
[Crossref]

2010 (2)

J. Lermé, H. Baida, C. Bonnet, M. Broyer, E. Cottancin, A. Crut, P. Maioli, N. Del Fatti, F. Vallée, and M. Pellarin, “Size dependence of the surface plasmon resonance damping in metal nanospheres,” J. Phys. Chem. Lett. 1, 2922–2928 (2010).

S. Peng, J. M. McMahon, G. C. Schatz, S. K. Gray, and Y. Sun, “Reversing the size-dependence of surface plasmon resonances,” Proc. Natl. Acad. Sci. U.S.A. 107, 14530–14534 (2010).
[Crossref] [PubMed]

2009 (1)

H. Baida, P. Billaud, S. Marhaba, D. Christofilos, E. Cottancin, A. Crut, J. Lermé, P. Maioli, M. Pellarin, N. Del Fatti, F. Vallée, A. Sánchez-Iglesias, I. Pastoriza-Santos, and L. M. Liz-Marzán, “Quantitative determination of the size dependence of surface plasmon resonance damping in single Ag@SiO2 nanoparticles,” Nano Lett. 9, 3463–3469 (2009).
[Crossref] [PubMed]

2006 (1)

E. Cottancin, G. Celep, J. Lermé, M. Pellarin, J. Huntzinger, J. Vialle, and M. Broyer, “Optical properties of noble metal clusters as a function of the size: Comparison between experiments and a semi-quantal theory,” Theoretical Chemistry Accounts 116, 514–523 (2006).
[Crossref]

2002 (2)

C. Sönnichsen, T. Franzl, T. Wilk, G. von Plessen, J. Feldmann, O. Wilson, and P. Mulvaney, “Drastic reduction of plasmon damping in gold nanorods,” Phys. Rev. Lett. 88, 077402 (2002).
[Crossref] [PubMed]

C. Sönnichsen, T. Franzl, T. Wilk, G. von Plessen, and J. Feldmann, “Plasmon resonances in large noble-metal clusters,” New J. Phys. 4, 93 (2002).
[Crossref]

1998 (3)

T. Klar, M. Perner, S. Grosse, G. von Plessen, W. Spirkl, and J. Feldmann, “Surface-plasmon resonances in single metallic nanoparticles,” Phys. Rev. Lett. 80, 4249–4252 (1998).
[Crossref]

C. Yannouleas, “Microscopic description of the surface dipole plasmon in large NaN clusters (950 ≲ N ≲ 12050),” Phys. Rev. B 58, 6748–6751 (1998).
[Crossref]

B. Palpant, B. Prével, J. Lermé, E. Cottancin, M. Pellarin, M. Treilleux, A. Perez, J. L. Vialle, and M. Broyer, “Optical properties of gold clusters in the size range 2–4 nm,” Phys. Rev. B 57, 1963–1970 (1998).
[Crossref]

1993 (5)

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. B 48, 18178–18188 (1993).
[Crossref]

A. Liebsch, “Surface-plasmon dispersion and size dependence of Mie resonance: Silver versus simple metals,” Phys. Rev. B 48, 11317–11328 (1993).
[Crossref]

S. Fedrigo, W. Harbich, and J. Buttet, “Collective dipole oscillations in small silver clusters embedded in rare-gas matrices,” Phys. Rev. B 47, 10706–10715 (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. A 48, R1749–R1752 (1993).
[Crossref] [PubMed]

B. N. J. Persson, “Polarizability of small spherical metal particles: influence of the matix environment,” Surf. Sci. 281, 153–162 (1993).
[Crossref]

1991 (1)

K.-D. Tsuei, E. W. Plummer, A. Liebsch, E. Pehlke, K. Kempa, and P. Bakshi, “The normal modes at the surface of simple metals,” Surf. Sci. 247, 302–326 (1991).
[Crossref]

1987 (1)

A. Liebsch, “Dynamical screening at simple-metal surfaces,” Phys. Rev. B 36, 7378–7388 (1987).
[Crossref]

1986 (1)

Y. Borensztein, P. De Andrès, R. Monreal, T. Lopez-Rios, and F. Flores, “Blue shift of the dipolar plasma resonance in small silver particles on an alumina surface,” Phys. Rev. B 33, 2828–2830 (1986).
[Crossref]

1984 (1)

W. Ekardt, “Dynamical polarizability of small metal particles: Self-consistent spherical jellium background model,” Phys. Rev. Lett. 52, 1925–1928 (1984).
[Crossref]

1983 (1)

B. N. J. Persson and P. Apell, “Sum rules for surface response functions with application to the van der Waals interaction between an atom and a metal,” Phys. Rev. B. 27, 6058–6065 (1983).
[Crossref]

1982 (2)

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

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

1976 (1)

P. Ascarelli and M. Cini, “Red shift of the surface plasmon resonance absorption by fine metal particles,” Solid State Commun. 18, 385–388 (1976).
[Crossref]

1975 (1)

R. Ruppin, “Optical properties of small metal spheres,” Phys. Rev. B 11, 2871–2876 (1975).
[Crossref]

1972 (1)

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

1966 (1)

A. Kawabata and R. Kubo, “Electronic properties of fine metallic particles. ii. plasma resonance absorption,” Journal of the Physical Society of Japan 21, 1765–1772 (1966).
[Crossref]

1908 (1)

G. Mie, “Beiträge zur Optik trüber Medien, speziell kolloidaler Metallösungen,” Ann. Phys. 25, 377–445 (1908).
[Crossref]

Aizpurua, J.

T. V. Teperik, P. Nordlander, J. Aizpurua, and A. G. Borisov, “Robust subnanometric plasmon ruler by rescaling of the nonlocal optical response,” Phys. Rev. Lett. 110, 263901 (2013).
[Crossref] [PubMed]

A. Garcia-Etxarri, P. Apell, M. Käll, and J. Aizpurua, “A combination of concave/convex surfaces for field-enhancement optimization: the indented nanocone,” Opt. Express 20, 25201–25212 (2012).
[Crossref] [PubMed]

Antosiewicz, T. J.

R. C. 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.

A. Garcia-Etxarri, P. Apell, M. Käll, and J. Aizpurua, “A combination of concave/convex surfaces for field-enhancement optimization: the indented nanocone,” Opt. Express 20, 25201–25212 (2012).
[Crossref] [PubMed]

B. N. J. Persson and P. Apell, “Sum rules for surface response functions with application to the van der Waals interaction between an atom and a metal,” Phys. Rev. B. 27, 6058–6065 (1983).
[Crossref]

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

Apell, S. P.

R. C. 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]

Ascarelli, P.

P. Ascarelli and M. Cini, “Red shift of the surface plasmon resonance absorption by fine metal particles,” Solid State Commun. 18, 385–388 (1976).
[Crossref]

Baida, H.

J. Lermé, H. Baida, C. Bonnet, M. Broyer, E. Cottancin, A. Crut, P. Maioli, N. Del Fatti, F. Vallée, and M. Pellarin, “Size dependence of the surface plasmon resonance damping in metal nanospheres,” J. Phys. Chem. Lett. 1, 2922–2928 (2010).

H. Baida, P. Billaud, S. Marhaba, D. Christofilos, E. Cottancin, A. Crut, J. Lermé, P. Maioli, M. Pellarin, N. Del Fatti, F. Vallée, A. Sánchez-Iglesias, I. Pastoriza-Santos, and L. M. Liz-Marzán, “Quantitative determination of the size dependence of surface plasmon resonance damping in single Ag@SiO2 nanoparticles,” Nano Lett. 9, 3463–3469 (2009).
[Crossref] [PubMed]

Bakshi, P.

K.-D. Tsuei, E. W. Plummer, A. Liebsch, E. Pehlke, K. Kempa, and P. Bakshi, “The normal modes at the surface of simple metals,” Surf. Sci. 247, 302–326 (1991).
[Crossref]

Billaud, P.

H. Baida, P. Billaud, S. Marhaba, D. Christofilos, E. Cottancin, A. Crut, J. Lermé, P. Maioli, M. Pellarin, N. Del Fatti, F. Vallée, A. Sánchez-Iglesias, I. Pastoriza-Santos, and L. M. Liz-Marzán, “Quantitative determination of the size dependence of surface plasmon resonance damping in single Ag@SiO2 nanoparticles,” Nano Lett. 9, 3463–3469 (2009).
[Crossref] [PubMed]

Bonnet, C.

J. Lermé, H. Baida, C. Bonnet, M. Broyer, E. Cottancin, A. Crut, P. Maioli, N. Del Fatti, F. Vallée, and M. Pellarin, “Size dependence of the surface plasmon resonance damping in metal nanospheres,” J. Phys. Chem. Lett. 1, 2922–2928 (2010).

Borensztein, Y.

Y. Borensztein, P. De Andrès, R. Monreal, T. Lopez-Rios, and F. Flores, “Blue shift of the dipolar plasma resonance in small silver particles on an alumina surface,” Phys. Rev. B 33, 2828–2830 (1986).
[Crossref]

Borisov, A. G.

T. V. Teperik, P. Nordlander, J. Aizpurua, and A. G. Borisov, “Robust subnanometric plasmon ruler by rescaling of the nonlocal optical response,” Phys. Rev. Lett. 110, 263901 (2013).
[Crossref] [PubMed]

Broyer, M.

J. Lermé, H. Baida, C. Bonnet, M. Broyer, E. Cottancin, A. Crut, P. Maioli, N. Del Fatti, F. Vallée, and M. Pellarin, “Size dependence of the surface plasmon resonance damping in metal nanospheres,” J. Phys. Chem. Lett. 1, 2922–2928 (2010).

E. Cottancin, G. Celep, J. Lermé, M. Pellarin, J. Huntzinger, J. Vialle, and M. Broyer, “Optical properties of noble metal clusters as a function of the size: Comparison between experiments and a semi-quantal theory,” Theoretical Chemistry Accounts 116, 514–523 (2006).
[Crossref]

B. Palpant, B. Prével, J. Lermé, E. Cottancin, M. Pellarin, M. Treilleux, A. Perez, J. L. Vialle, and M. Broyer, “Optical properties of gold clusters in the size range 2–4 nm,” Phys. Rev. B 57, 1963–1970 (1998).
[Crossref]

Bryant, G. W.

E. Townsend and G. W. Bryant, “Plasmonic properties of metallic nanoparticles: The effects of size quantization,” Nano Letters 12, 429–434 (2012).
[Crossref]

Buttet, J.

S. Fedrigo, W. Harbich, and J. Buttet, “Collective dipole oscillations in small silver clusters embedded in rare-gas matrices,” Phys. Rev. B 47, 10706–10715 (1993).
[Crossref]

Celep, G.

E. Cottancin, G. Celep, J. Lermé, M. Pellarin, J. Huntzinger, J. Vialle, and M. Broyer, “Optical properties of noble metal clusters as a function of the size: Comparison between experiments and a semi-quantal theory,” Theoretical Chemistry Accounts 116, 514–523 (2006).
[Crossref]

Chen, H.

Y. Fan, J. Li, H. Chen, X. Lu, and X. Liu, “Size-dependence of the effective electron-phonon energy relaxation in hollow gold nanospheres,” Opto-Electron. Rev. 22, 36–40 (2014).
[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,” Science 337, 1072–1074 (2012).
[Crossref] [PubMed]

Christofilos, D.

H. Baida, P. Billaud, S. Marhaba, D. Christofilos, E. Cottancin, A. Crut, J. Lermé, P. Maioli, M. Pellarin, N. Del Fatti, F. Vallée, A. Sánchez-Iglesias, I. Pastoriza-Santos, and L. M. Liz-Marzán, “Quantitative determination of the size dependence of surface plasmon resonance damping in single Ag@SiO2 nanoparticles,” Nano Lett. 9, 3463–3469 (2009).
[Crossref] [PubMed]

Christy, R.

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

Cini, M.

P. Ascarelli and M. Cini, “Red shift of the surface plasmon resonance absorption by fine metal particles,” Solid State Commun. 18, 385–388 (1976).
[Crossref]

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,” Science 337, 1072–1074 (2012).
[Crossref] [PubMed]

Cottancin, E.

J. Lermé, H. Baida, C. Bonnet, M. Broyer, E. Cottancin, A. Crut, P. Maioli, N. Del Fatti, F. Vallée, and M. Pellarin, “Size dependence of the surface plasmon resonance damping in metal nanospheres,” J. Phys. Chem. Lett. 1, 2922–2928 (2010).

H. Baida, P. Billaud, S. Marhaba, D. Christofilos, E. Cottancin, A. Crut, J. Lermé, P. Maioli, M. Pellarin, N. Del Fatti, F. Vallée, A. Sánchez-Iglesias, I. Pastoriza-Santos, and L. M. Liz-Marzán, “Quantitative determination of the size dependence of surface plasmon resonance damping in single Ag@SiO2 nanoparticles,” Nano Lett. 9, 3463–3469 (2009).
[Crossref] [PubMed]

E. Cottancin, G. Celep, J. Lermé, M. Pellarin, J. Huntzinger, J. Vialle, and M. Broyer, “Optical properties of noble metal clusters as a function of the size: Comparison between experiments and a semi-quantal theory,” Theoretical Chemistry Accounts 116, 514–523 (2006).
[Crossref]

B. Palpant, B. Prével, J. Lermé, E. Cottancin, M. Pellarin, M. Treilleux, A. Perez, J. L. Vialle, and M. Broyer, “Optical properties of gold clusters in the size range 2–4 nm,” Phys. Rev. B 57, 1963–1970 (1998).
[Crossref]

Crut, A.

J. Lermé, H. Baida, C. Bonnet, M. Broyer, E. Cottancin, A. Crut, P. Maioli, N. Del Fatti, F. Vallée, and M. Pellarin, “Size dependence of the surface plasmon resonance damping in metal nanospheres,” J. Phys. Chem. Lett. 1, 2922–2928 (2010).

H. Baida, P. Billaud, S. Marhaba, D. Christofilos, E. Cottancin, A. Crut, J. Lermé, P. Maioli, M. Pellarin, N. Del Fatti, F. Vallée, A. Sánchez-Iglesias, I. Pastoriza-Santos, and L. M. Liz-Marzán, “Quantitative determination of the size dependence of surface plasmon resonance damping in single Ag@SiO2 nanoparticles,” Nano Lett. 9, 3463–3469 (2009).
[Crossref] [PubMed]

De Andrès, P.

Y. Borensztein, P. De Andrès, R. Monreal, T. Lopez-Rios, and F. Flores, “Blue shift of the dipolar plasma resonance in small silver particles on an alumina surface,” Phys. Rev. B 33, 2828–2830 (1986).
[Crossref]

Del Fatti, N.

J. Lermé, H. Baida, C. Bonnet, M. Broyer, E. Cottancin, A. Crut, P. Maioli, N. Del Fatti, F. Vallée, and M. Pellarin, “Size dependence of the surface plasmon resonance damping in metal nanospheres,” J. Phys. Chem. Lett. 1, 2922–2928 (2010).

H. Baida, P. Billaud, S. Marhaba, D. Christofilos, E. Cottancin, A. Crut, J. Lermé, P. Maioli, M. Pellarin, N. Del Fatti, F. Vallée, A. Sánchez-Iglesias, I. Pastoriza-Santos, and L. M. Liz-Marzán, “Quantitative determination of the size dependence of surface plasmon resonance damping in single Ag@SiO2 nanoparticles,” Nano Lett. 9, 3463–3469 (2009).
[Crossref] [PubMed]

Derkachova, A.

K. Kolwas and A. Derkachova, “Damping rates of surface plasmons for particles of size from nano- to micrometers; reduction of the nonradiative decay,” J. Quant. Spectrocs. Radiat. Transfer 114, 45–55 (2013).
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Y. Fan, J. Li, H. Chen, X. Lu, and X. Liu, “Size-dependence of the effective electron-phonon energy relaxation in hollow gold nanospheres,” Opto-Electron. Rev. 22, 36–40 (2014).
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S. Fedrigo, W. Harbich, and J. Buttet, “Collective dipole oscillations in small silver clusters embedded in rare-gas matrices,” Phys. Rev. B 47, 10706–10715 (1993).
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Feldmann, J.

C. Sönnichsen, T. Franzl, T. Wilk, G. von Plessen, J. Feldmann, O. Wilson, and P. Mulvaney, “Drastic reduction of plasmon damping in gold nanorods,” Phys. Rev. Lett. 88, 077402 (2002).
[Crossref] [PubMed]

C. Sönnichsen, T. Franzl, T. Wilk, G. von Plessen, and J. Feldmann, “Plasmon resonances in large noble-metal clusters,” New J. Phys. 4, 93 (2002).
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T. Klar, M. Perner, S. Grosse, G. von Plessen, W. Spirkl, and J. Feldmann, “Surface-plasmon resonances in single metallic nanoparticles,” Phys. Rev. Lett. 80, 4249–4252 (1998).
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Fernández-Domínguez, A. I.

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,” Science 337, 1072–1074 (2012).
[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]

Flores, F.

Y. Borensztein, P. De Andrès, R. Monreal, T. Lopez-Rios, and F. Flores, “Blue shift of the dipolar plasma resonance in small silver particles on an alumina surface,” Phys. Rev. B 33, 2828–2830 (1986).
[Crossref]

Franzl, T.

C. Sönnichsen, T. Franzl, T. Wilk, G. von Plessen, J. Feldmann, O. Wilson, and P. Mulvaney, “Drastic reduction of plasmon damping in gold nanorods,” Phys. Rev. Lett. 88, 077402 (2002).
[Crossref] [PubMed]

C. Sönnichsen, T. Franzl, T. Wilk, G. von Plessen, and J. Feldmann, “Plasmon resonances in large noble-metal clusters,” New J. Phys. 4, 93 (2002).
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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. B 48, 18178–18188 (1993).
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Garcia-Etxarri, A.

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]

Gray, S. K.

S. Peng, J. M. McMahon, G. C. Schatz, S. K. Gray, and Y. Sun, “Reversing the size-dependence of surface plasmon resonances,” Proc. Natl. Acad. Sci. U.S.A. 107, 14530–14534 (2010).
[Crossref] [PubMed]

Grosse, S.

T. Klar, M. Perner, S. Grosse, G. von Plessen, W. Spirkl, and J. Feldmann, “Surface-plasmon resonances in single metallic nanoparticles,” Phys. Rev. Lett. 80, 4249–4252 (1998).
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Harbich, W.

S. Fedrigo, W. Harbich, and J. Buttet, “Collective dipole oscillations in small silver clusters embedded in rare-gas matrices,” Phys. Rev. B 47, 10706–10715 (1993).
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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. B 48, 18178–18188 (1993).
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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,” Science 337, 1072–1074 (2012).
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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. B 48, 18178–18188 (1993).
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Huntzinger, J.

E. Cottancin, G. Celep, J. Lermé, M. Pellarin, J. Huntzinger, J. Vialle, and M. Broyer, “Optical properties of noble metal clusters as a function of the size: Comparison between experiments and a semi-quantal theory,” Theoretical Chemistry Accounts 116, 514–523 (2006).
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Kawabata, A.

A. Kawabata and R. Kubo, “Electronic properties of fine metallic particles. ii. plasma resonance absorption,” Journal of the Physical Society of Japan 21, 1765–1772 (1966).
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Kempa, K.

K.-D. Tsuei, E. W. Plummer, A. Liebsch, E. Pehlke, K. Kempa, and P. Bakshi, “The normal modes at the surface of simple metals,” Surf. Sci. 247, 302–326 (1991).
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Klar, T.

T. Klar, M. Perner, S. Grosse, G. von Plessen, W. Spirkl, and J. Feldmann, “Surface-plasmon resonances in single metallic nanoparticles,” Phys. Rev. Lett. 80, 4249–4252 (1998).
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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. A 48, R1749–R1752 (1993).
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Kolwas, K.

K. Kolwas and A. Derkachova, “Damping rates of surface plasmons for particles of size from nano- to micrometers; reduction of the nonradiative decay,” J. Quant. Spectrocs. Radiat. Transfer 114, 45–55 (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. B 48, 18178–18188 (1993).
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Kubo, R.

A. Kawabata and R. Kubo, “Electronic properties of fine metallic particles. ii. plasma resonance absorption,” Journal of the Physical Society of Japan 21, 1765–1772 (1966).
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Lermé, J.

J. Lermé, “Size evolution of the surface plasmon resonance damping in silver nanoparticles: Confinement and dielectric effects,” J. Phys. Chem. C 115, 14098–14110 (2011).
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J. Lermé, H. Baida, C. Bonnet, M. Broyer, E. Cottancin, A. Crut, P. Maioli, N. Del Fatti, F. Vallée, and M. Pellarin, “Size dependence of the surface plasmon resonance damping in metal nanospheres,” J. Phys. Chem. Lett. 1, 2922–2928 (2010).

H. Baida, P. Billaud, S. Marhaba, D. Christofilos, E. Cottancin, A. Crut, J. Lermé, P. Maioli, M. Pellarin, N. Del Fatti, F. Vallée, A. Sánchez-Iglesias, I. Pastoriza-Santos, and L. M. Liz-Marzán, “Quantitative determination of the size dependence of surface plasmon resonance damping in single Ag@SiO2 nanoparticles,” Nano Lett. 9, 3463–3469 (2009).
[Crossref] [PubMed]

E. Cottancin, G. Celep, J. Lermé, M. Pellarin, J. Huntzinger, J. Vialle, and M. Broyer, “Optical properties of noble metal clusters as a function of the size: Comparison between experiments and a semi-quantal theory,” Theoretical Chemistry Accounts 116, 514–523 (2006).
[Crossref]

B. Palpant, B. Prével, J. Lermé, E. Cottancin, M. Pellarin, M. Treilleux, A. Perez, J. L. Vialle, and M. Broyer, “Optical properties of gold clusters in the size range 2–4 nm,” Phys. Rev. B 57, 1963–1970 (1998).
[Crossref]

Li, J.

Y. Fan, J. Li, H. Chen, X. Lu, and X. Liu, “Size-dependence of the effective electron-phonon energy relaxation in hollow gold nanospheres,” Opto-Electron. Rev. 22, 36–40 (2014).
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A. Liebsch, “Surface-plasmon dispersion and size dependence of Mie resonance: Silver versus simple metals,” Phys. Rev. B 48, 11317–11328 (1993).
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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. A 48, R1749–R1752 (1993).
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K.-D. Tsuei, E. W. Plummer, A. Liebsch, E. Pehlke, K. Kempa, and P. Bakshi, “The normal modes at the surface of simple metals,” Surf. Sci. 247, 302–326 (1991).
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A. Liebsch, “Dynamical screening at simple-metal surfaces,” Phys. Rev. B 36, 7378–7388 (1987).
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Liu, X.

Y. Fan, J. Li, H. Chen, X. Lu, and X. Liu, “Size-dependence of the effective electron-phonon energy relaxation in hollow gold nanospheres,” Opto-Electron. Rev. 22, 36–40 (2014).
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Liz-Marzán, L. M.

H. Baida, P. Billaud, S. Marhaba, D. Christofilos, E. Cottancin, A. Crut, J. Lermé, P. Maioli, M. Pellarin, N. Del Fatti, F. Vallée, A. Sánchez-Iglesias, I. Pastoriza-Santos, and L. M. Liz-Marzán, “Quantitative determination of the size dependence of surface plasmon resonance damping in single Ag@SiO2 nanoparticles,” Nano Lett. 9, 3463–3469 (2009).
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P. Apell and A. Ljungbert, “A general non-local theory for the electromagnetic response of a small metal particle,” Physica Scripta 26, 113–118 (1982).
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Y. Borensztein, P. De Andrès, R. Monreal, T. Lopez-Rios, and F. Flores, “Blue shift of the dipolar plasma resonance in small silver particles on an alumina surface,” Phys. Rev. B 33, 2828–2830 (1986).
[Crossref]

Lu, X.

Y. Fan, J. Li, H. Chen, X. Lu, and X. Liu, “Size-dependence of the effective electron-phonon energy relaxation in hollow gold nanospheres,” Opto-Electron. Rev. 22, 36–40 (2014).
[Crossref]

Maier, S. A.

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,” Science 337, 1072–1074 (2012).
[Crossref] [PubMed]

Maioli, P.

J. Lermé, H. Baida, C. Bonnet, M. Broyer, E. Cottancin, A. Crut, P. Maioli, N. Del Fatti, F. Vallée, and M. Pellarin, “Size dependence of the surface plasmon resonance damping in metal nanospheres,” J. Phys. Chem. Lett. 1, 2922–2928 (2010).

H. Baida, P. Billaud, S. Marhaba, D. Christofilos, E. Cottancin, A. Crut, J. Lermé, P. Maioli, M. Pellarin, N. Del Fatti, F. Vallée, A. Sánchez-Iglesias, I. Pastoriza-Santos, and L. M. Liz-Marzán, “Quantitative determination of the size dependence of surface plasmon resonance damping in single Ag@SiO2 nanoparticles,” Nano Lett. 9, 3463–3469 (2009).
[Crossref] [PubMed]

Marhaba, S.

H. Baida, P. Billaud, S. Marhaba, D. Christofilos, E. Cottancin, A. Crut, J. Lermé, P. Maioli, M. Pellarin, N. Del Fatti, F. Vallée, A. Sánchez-Iglesias, I. Pastoriza-Santos, and L. M. Liz-Marzán, “Quantitative determination of the size dependence of surface plasmon resonance damping in single Ag@SiO2 nanoparticles,” Nano Lett. 9, 3463–3469 (2009).
[Crossref] [PubMed]

McMahon, J. M.

S. Peng, J. M. McMahon, G. C. Schatz, S. K. Gray, and Y. Sun, “Reversing the size-dependence of surface plasmon resonances,” Proc. Natl. Acad. Sci. U.S.A. 107, 14530–14534 (2010).
[Crossref] [PubMed]

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. A 48, R1749–R1752 (1993).
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G. Mie, “Beiträge zur Optik trüber Medien, speziell kolloidaler Metallösungen,” Ann. Phys. 25, 377–445 (1908).
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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,” Science 337, 1072–1074 (2012).
[Crossref] [PubMed]

Monreal, R.

Y. Borensztein, P. De Andrès, R. Monreal, T. Lopez-Rios, and F. Flores, “Blue shift of the dipolar plasma resonance in small silver particles on an alumina surface,” Phys. Rev. B 33, 2828–2830 (1986).
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Monreal, R. C.

R. C. 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).
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Mortensen, N. A.

A. V. Uskov, I. E. Protsenko, N. A. Mortensen, and E. P. O’Reilly, “Broadening of plasmonic resonance due to electron collisions with nanoparticle boundary: a quantum mechanical consideration,” Plasmonics 9, 185–192 (2014).
[Crossref]

Mulvaney, P.

C. Sönnichsen, T. Franzl, T. Wilk, G. von Plessen, J. Feldmann, O. Wilson, and P. Mulvaney, “Drastic reduction of plasmon damping in gold nanorods,” Phys. Rev. Lett. 88, 077402 (2002).
[Crossref] [PubMed]

Nordlander, P.

T. V. Teperik, P. Nordlander, J. Aizpurua, and A. G. Borisov, “Robust subnanometric plasmon ruler by rescaling of the nonlocal optical response,” Phys. Rev. Lett. 110, 263901 (2013).
[Crossref] [PubMed]

O’Reilly, E. P.

A. V. Uskov, I. E. Protsenko, N. A. Mortensen, and E. P. O’Reilly, “Broadening of plasmonic resonance due to electron collisions with nanoparticle boundary: a quantum mechanical consideration,” Plasmonics 9, 185–192 (2014).
[Crossref]

Palpant, B.

B. Palpant, B. Prével, J. Lermé, E. Cottancin, M. Pellarin, M. Treilleux, A. Perez, J. L. Vialle, and M. Broyer, “Optical properties of gold clusters in the size range 2–4 nm,” Phys. Rev. B 57, 1963–1970 (1998).
[Crossref]

Pastoriza-Santos, I.

H. Baida, P. Billaud, S. Marhaba, D. Christofilos, E. Cottancin, A. Crut, J. Lermé, P. Maioli, M. Pellarin, N. Del Fatti, F. Vallée, A. Sánchez-Iglesias, I. Pastoriza-Santos, and L. M. Liz-Marzán, “Quantitative determination of the size dependence of surface plasmon resonance damping in single Ag@SiO2 nanoparticles,” Nano Lett. 9, 3463–3469 (2009).
[Crossref] [PubMed]

Pehlke, E.

K.-D. Tsuei, E. W. Plummer, A. Liebsch, E. Pehlke, K. Kempa, and P. Bakshi, “The normal modes at the surface of simple metals,” Surf. Sci. 247, 302–326 (1991).
[Crossref]

Pellarin, M.

J. Lermé, H. Baida, C. Bonnet, M. Broyer, E. Cottancin, A. Crut, P. Maioli, N. Del Fatti, F. Vallée, and M. Pellarin, “Size dependence of the surface plasmon resonance damping in metal nanospheres,” J. Phys. Chem. Lett. 1, 2922–2928 (2010).

H. Baida, P. Billaud, S. Marhaba, D. Christofilos, E. Cottancin, A. Crut, J. Lermé, P. Maioli, M. Pellarin, N. Del Fatti, F. Vallée, A. Sánchez-Iglesias, I. Pastoriza-Santos, and L. M. Liz-Marzán, “Quantitative determination of the size dependence of surface plasmon resonance damping in single Ag@SiO2 nanoparticles,” Nano Lett. 9, 3463–3469 (2009).
[Crossref] [PubMed]

E. Cottancin, G. Celep, J. Lermé, M. Pellarin, J. Huntzinger, J. Vialle, and M. Broyer, “Optical properties of noble metal clusters as a function of the size: Comparison between experiments and a semi-quantal theory,” Theoretical Chemistry Accounts 116, 514–523 (2006).
[Crossref]

B. Palpant, B. Prével, J. Lermé, E. Cottancin, M. Pellarin, M. Treilleux, A. Perez, J. L. Vialle, and M. Broyer, “Optical properties of gold clusters in the size range 2–4 nm,” Phys. Rev. B 57, 1963–1970 (1998).
[Crossref]

Pendry, J. B.

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,” Science 337, 1072–1074 (2012).
[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]

Peng, S.

S. Peng, J. M. McMahon, G. C. Schatz, S. K. Gray, and Y. Sun, “Reversing the size-dependence of surface plasmon resonances,” Proc. Natl. Acad. Sci. U.S.A. 107, 14530–14534 (2010).
[Crossref] [PubMed]

Perez, A.

B. Palpant, B. Prével, J. Lermé, E. Cottancin, M. Pellarin, M. Treilleux, A. Perez, J. L. Vialle, and M. Broyer, “Optical properties of gold clusters in the size range 2–4 nm,” Phys. Rev. B 57, 1963–1970 (1998).
[Crossref]

Perner, M.

T. Klar, M. Perner, S. Grosse, G. von Plessen, W. Spirkl, and J. Feldmann, “Surface-plasmon resonances in single metallic nanoparticles,” Phys. Rev. Lett. 80, 4249–4252 (1998).
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K.-D. Tsuei, E. W. Plummer, A. Liebsch, E. Pehlke, K. Kempa, and P. Bakshi, “The normal modes at the surface of simple metals,” Surf. Sci. 247, 302–326 (1991).
[Crossref]

Prével, B.

B. Palpant, B. Prével, J. Lermé, E. Cottancin, M. Pellarin, M. Treilleux, A. Perez, J. L. Vialle, and M. Broyer, “Optical properties of gold clusters in the size range 2–4 nm,” Phys. Rev. B 57, 1963–1970 (1998).
[Crossref]

Protsenko, I. E.

A. V. Uskov, I. E. Protsenko, N. A. Mortensen, and E. P. O’Reilly, “Broadening of plasmonic resonance due to electron collisions with nanoparticle boundary: a quantum mechanical consideration,” Plasmonics 9, 185–192 (2014).
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R. Ruppin, “Optical properties of small metal spheres,” Phys. Rev. B 11, 2871–2876 (1975).
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Sánchez-Iglesias, A.

H. Baida, P. Billaud, S. Marhaba, D. Christofilos, E. Cottancin, A. Crut, J. Lermé, P. Maioli, M. Pellarin, N. Del Fatti, F. Vallée, A. Sánchez-Iglesias, I. Pastoriza-Santos, and L. M. Liz-Marzán, “Quantitative determination of the size dependence of surface plasmon resonance damping in single Ag@SiO2 nanoparticles,” Nano Lett. 9, 3463–3469 (2009).
[Crossref] [PubMed]

Schatz, G. C.

S. Peng, J. M. McMahon, G. C. Schatz, S. K. Gray, and Y. Sun, “Reversing the size-dependence of surface plasmon resonances,” Proc. Natl. Acad. Sci. U.S.A. 107, 14530–14534 (2010).
[Crossref] [PubMed]

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,” Science 337, 1072–1074 (2012).
[Crossref] [PubMed]

Sönnichsen, C.

C. Sönnichsen, T. Franzl, T. Wilk, G. von Plessen, and J. Feldmann, “Plasmon resonances in large noble-metal clusters,” New J. Phys. 4, 93 (2002).
[Crossref]

C. Sönnichsen, T. Franzl, T. Wilk, G. von Plessen, J. Feldmann, O. Wilson, and P. Mulvaney, “Drastic reduction of plasmon damping in gold nanorods,” Phys. Rev. Lett. 88, 077402 (2002).
[Crossref] [PubMed]

Spirkl, W.

T. Klar, M. Perner, S. Grosse, G. von Plessen, W. Spirkl, and J. Feldmann, “Surface-plasmon resonances in single metallic nanoparticles,” Phys. Rev. Lett. 80, 4249–4252 (1998).
[Crossref]

Sun, Y.

S. Peng, J. M. McMahon, G. C. Schatz, S. K. Gray, and Y. Sun, “Reversing the size-dependence of surface plasmon resonances,” Proc. Natl. Acad. Sci. U.S.A. 107, 14530–14534 (2010).
[Crossref] [PubMed]

Teperik, T. V.

T. V. Teperik, P. Nordlander, J. Aizpurua, and A. G. Borisov, “Robust subnanometric plasmon ruler by rescaling of the nonlocal optical response,” Phys. Rev. Lett. 110, 263901 (2013).
[Crossref] [PubMed]

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. A 48, R1749–R1752 (1993).
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E. Townsend and G. W. Bryant, “Plasmonic properties of metallic nanoparticles: The effects of size quantization,” Nano Letters 12, 429–434 (2012).
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B. Palpant, B. Prével, J. Lermé, E. Cottancin, M. Pellarin, M. Treilleux, A. Perez, J. L. Vialle, and M. Broyer, “Optical properties of gold clusters in the size range 2–4 nm,” Phys. Rev. B 57, 1963–1970 (1998).
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[Crossref] [PubMed]

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A. V. Uskov, I. E. Protsenko, N. A. Mortensen, and E. P. O’Reilly, “Broadening of plasmonic resonance due to electron collisions with nanoparticle boundary: a quantum mechanical consideration,” Plasmonics 9, 185–192 (2014).
[Crossref]

Vallée, F.

J. Lermé, H. Baida, C. Bonnet, M. Broyer, E. Cottancin, A. Crut, P. Maioli, N. Del Fatti, F. Vallée, and M. Pellarin, “Size dependence of the surface plasmon resonance damping in metal nanospheres,” J. Phys. Chem. Lett. 1, 2922–2928 (2010).

H. Baida, P. Billaud, S. Marhaba, D. Christofilos, E. Cottancin, A. Crut, J. Lermé, P. Maioli, M. Pellarin, N. Del Fatti, F. Vallée, A. Sánchez-Iglesias, I. Pastoriza-Santos, and L. M. Liz-Marzán, “Quantitative determination of the size dependence of surface plasmon resonance damping in single Ag@SiO2 nanoparticles,” Nano Lett. 9, 3463–3469 (2009).
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[Crossref]

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B. Palpant, B. Prével, J. Lermé, E. Cottancin, M. Pellarin, M. Treilleux, A. Perez, J. L. Vialle, and M. Broyer, “Optical properties of gold clusters in the size range 2–4 nm,” Phys. Rev. B 57, 1963–1970 (1998).
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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).
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C. Sönnichsen, T. Franzl, T. Wilk, G. von Plessen, and J. Feldmann, “Plasmon resonances in large noble-metal clusters,” New J. Phys. 4, 93 (2002).
[Crossref]

C. Sönnichsen, T. Franzl, T. Wilk, G. von Plessen, J. Feldmann, O. Wilson, and P. Mulvaney, “Drastic reduction of plasmon damping in gold nanorods,” Phys. Rev. Lett. 88, 077402 (2002).
[Crossref] [PubMed]

Wilson, O.

C. Sönnichsen, T. Franzl, T. Wilk, G. von Plessen, J. Feldmann, O. Wilson, and P. Mulvaney, “Drastic reduction of plasmon damping in gold nanorods,” Phys. Rev. Lett. 88, 077402 (2002).
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J. Quant. Spectrocs. Radiat. Transfer (1)

K. Kolwas and A. Derkachova, “Damping rates of surface plasmons for particles of size from nano- to micrometers; reduction of the nonradiative decay,” J. Quant. Spectrocs. Radiat. Transfer 114, 45–55 (2013).
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H. Baida, P. Billaud, S. Marhaba, D. Christofilos, E. Cottancin, A. Crut, J. Lermé, P. Maioli, M. Pellarin, N. Del Fatti, F. Vallée, A. Sánchez-Iglesias, I. Pastoriza-Santos, and L. M. Liz-Marzán, “Quantitative determination of the size dependence of surface plasmon resonance damping in single Ag@SiO2 nanoparticles,” Nano Lett. 9, 3463–3469 (2009).
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E. Townsend and G. W. Bryant, “Plasmonic properties of metallic nanoparticles: The effects of size quantization,” Nano Letters 12, 429–434 (2012).
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R. C. 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).
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C. Sönnichsen, T. Franzl, T. Wilk, G. von Plessen, and J. Feldmann, “Plasmon resonances in large noble-metal clusters,” New J. Phys. 4, 93 (2002).
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[Crossref]

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[Crossref] [PubMed]

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C. Yannouleas, “Microscopic description of the surface dipole plasmon in large NaN clusters (950 ≲ N ≲ 12050),” Phys. Rev. B 58, 6748–6751 (1998).
[Crossref]

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[Crossref]

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[Crossref]

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[Crossref]

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. B 48, 18178–18188 (1993).
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[Crossref]

C. Sönnichsen, T. Franzl, T. Wilk, G. von Plessen, J. Feldmann, O. Wilson, and P. Mulvaney, “Drastic reduction of plasmon damping in gold nanorods,” Phys. Rev. Lett. 88, 077402 (2002).
[Crossref] [PubMed]

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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,” Science 337, 1072–1074 (2012).
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[Crossref]

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E. Cottancin, G. Celep, J. Lermé, M. Pellarin, J. Huntzinger, J. Vialle, and M. Broyer, “Optical properties of noble metal clusters as a function of the size: Comparison between experiments and a semi-quantal theory,” Theoretical Chemistry Accounts 116, 514–523 (2006).
[Crossref]

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Figures (4)

Fig. 1
Fig. 1

Absorption cross-sections (continuous blue lines) of silver spheres embedded in: (a) a host medium of dielectric function 1.5 (average value for spheres on a carbon substrate) and (b) a host medium of dielectric function 2.16 (SiO2). Calculations have been performed using the Time-Dependent Local Density Approximation for the dielectric response of the electronic density of Ag in the surface region. The cross-sections are normalized to the surface area of the sphere, the radius being 10 nm, 7.5 nm, 5 nm and 4 nm from top to bottom in each subfigure. Both show a blue-shift of the plasmon for decreasing size and a broadening of the peak. Dashed red lines are Lorentzians constructed from the width and peak position of the full calculation. They are a very good match to the spectra in (a) and not so good in (b). This reflects the detailed structure of the surface response function which is the major contribution to the absorption cross-section for these small spheres.

Fig. 2
Fig. 2

Color plot of the surface plasmon width as a function of inverse size and host permittivity for (a) the Random Phase Approximation and (b) the Time-dependent Local Density Approximation. The contours and the scale on top are in eV. Results are dominated by the surface effect we calculate. In both cases the width scales directly with the inverse size. Notice that the width is maximum for a host dielectric medium with permittivity 2.4–2.6.

Fig. 3
Fig. 3

(a) The linear coefficient of the plasmon width in vF/R, parameter A, as a function of the host permittivity for the Random Phase Approximation (dashed red line) and the Time-Dependent Local Density Approximation (solid blue line). The maximum of A leads to the maximum in the surface plasmon damping mechanism present in both approximations. (b) Quality factor of the surface plasmon in silver spheres for the TDLDA. Radius being 10 nm, 7.5 nm, 5 nm and 4 nm from top to bottom. We take the quality factor as resonance energy divided by width. To obtain the resonance energies, we changed the host dielectric permittivity in the range 1 – 6. Again we see how the maximum plasmon width comes in around 3 eV giving a minimum in the quality factor.

Fig. 4
Fig. 4

The surface plasmon width as a function of inverse size for (a) the Random Phase approximation and (b) the Time-dependent Local Density Approximation. Results are given for four different permittivities of the host medium differing from the value for SiO2 by less than 10%, and compared to the experimental results for Ag spheres coated with that material reported in [18] (circles). Notice the radiative damping taking over the physics as we approach particles larger than 25 nm. Then, the smallest damping is obtained for sizes of ca. 20 nm.

Equations (16)

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σ ( ω ) = 4 π ω c ε m Im [ α ( ω ) ] ,
α M ( ω ) = R 3 ε ( ω ) ε m ε ( ω ) + 2 ε m .
Im [ α M ( ω ) ] = 3 R 3 ε m ε 2 ( ω ) ( ε 1 ( ω ) + 2 ε m ) 2 + ( ε 2 ( ω ) ) 2 ,
ε 1 ( ω M ) + 2 ε m = 0 and Γ M = 2 ε 2 ( ω M ) [ ε 1 ( ω ) ω ] ω M ,
ε ( ω ) = ε d ( ω ) ω p 2 ω 2 + i ω / τ b ,
ω M = ω p Re [ ε d ( ω M ) ] + 2 ε m and Γ M = 1 τ b + Im [ ε d ( ω M ) ] ω M 3 ω p 2 1 + 1 2 ω M 3 ω p 2 [ Re [ ε d ( ω ) ] ω ] ω M ,
d r ( ω ) R = d r r ( R r ) δ ρ ( r , ω ) d r r 2 δ ρ ( r , ω ) ,
α ( ω ) = R 3 ( ε ( ω ) ε m ) ( 1 d r ( ω ) R ) ε ( ω ) + 2 ε m + 2 ( ε ( ω ) ε m ) d r ( ω ) R .
ε ( ω ) = ε d ( ω ) ω p 2 ω 2 Δ 2 + i ω / τ b ,
Im [ α ( ω ) ] = 3 R 3 ε ( ω ) ( ε ( ω ) ε m ) Im [ d r ( ω ) ] R [ ε ( ω ) + 2 ε m + 2 ( ε ( ω ) ε m ) Re [ d r ( ω ) ] R ] 2 + [ 2 ( ε ( ω ) ε m ) Im [ d r ( ω ) ] R ] 2 .
ε ( ω s ) + 2 ε m + 2 ( ε ( ω s ) ε m ) Re [ d r ( ω s ) ] R = 0 ,
Γ s 4 ( ε ( ω s ) ε m ) [ ε 1 ( ω ) ω ] ω s Im [ d r ( ω s ) ] R 12 ε m [ ε 1 ( ω ) ω ] ω s Im [ d r ( ω s ) ] R ,
[ ε 1 ( ω ) ω ] ω s 2 ω p 2 ω s 3 2 ( 2 ε m ) 3 2 ω p ,
lim ε m Γ s = 3 ω p 2 ε m Im [ d r ( ω s ) ] R .
lim ω 0 Im [ d r ( ω ) ] 0 .
Γ R = Γ 0 + A v F R ,

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