Abstract

The optical properties of metallic nanoparticles (NPs) can be described with analytical models based on fundamental quantum mechanical principles, of which the Drude model constitutes the classical limit. Here, we examine the plasmonic properties of silver and gold nanospheres and dimers, with radii ranging from 10 to 1 nm, extending from the classically described regime to the quantum size regime. We have studied the spectral extinction cross section by using the T-matrix method. The results indicate an increasingly substantial change in NP permittivity as the radius is reduced below 5 nm, showing a clear blueshift and weakening of the plasmon resonances for both silver and gold. As a consequence, we observe a dramatic change in the interaction of dimers, especially in the case of gold, where the introduction of quantum mechanically corrected optical properties quenches the plasmonic resonance and predicts an absence of the expected associated redshift.

© 2012 Optical Society of America

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  17. E. D. Palik, Handbook of Optical Constants of Solids(Academic, 1985).
  18. C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1983).
  19. M. I. Tribelsky, Europhys. Lett. 94, 14004 (2011).
    [CrossRef]

2012 (4)

J. A. Scholl, A. L. Koh, and J. A. Dionne, Nature 483, 421 (2012).
[CrossRef]

C. J. Cheng and W. M. Saltzman, Nat. Nanotechnol. 7, 346 (2012).
[CrossRef]

R. Esteban, A. G. Borisov, P. Nordlander, and J. Aizpurua, Nat. Commun. 3, 825 (2012).
[CrossRef]

K. J. Savage, M. M. Hawkeye, R. Esteban, A. G. Borisov, J. Aizpurua, and J. J. Baumberg, Nature 491, 574 (2012).
[CrossRef]

2011 (2)

A. Vial, T. Laroche, M. Dridi, and L. Le Cunff, Appl. Phys. A 103, 849 (2011).
[CrossRef]

M. I. Tribelsky, Europhys. Lett. 94, 14004 (2011).
[CrossRef]

2010 (1)

H. A. Atwater and A. Polman, Nat. Mater. 9, 205 (2010).
[CrossRef]

2008 (1)

S. Kim, J. Jin, Y.-J. Kim, I.-Y. Park, Y. Kim, and S.-W. Kim, Nature 453, 757 (2008).
[CrossRef]

2007 (1)

F. Hao and P. Nordlander, Chem. Phys. Lett. 446, 115 (2007).
[CrossRef]

2005 (1)

S. Berciaud, L. Cognet, P. Tamarat, and B. Lounis, Nano Lett. 5, 515 (2005).
[CrossRef]

2004 (1)

P. Nordlander, C. Oubre, E. Prodan, K. Li, and M. I. Stockman, Nano Lett. 4, 899 (2004).
[CrossRef]

1997 (2)

N. Shuming and S. R. Emory, Science 275, 5303 (1997).

K. Kneipp, Y. Wang, H. Kneipp, L. T. Perelman, I. Itzkan, R. R. Dasari, and M. S. Feld, Phys. Rev. Lett. 78, 1667 (1997).
[CrossRef]

1996 (1)

1983 (1)

W. A. Kraus and G. C. Schatz, J. Chem. Phys. 79, 6130 (1983).
[CrossRef]

1972 (1)

P. B. Johnson and R. W. Christy, Phys. Rev. B 6, 4370 (1972).
[CrossRef]

Aizpurua, J.

R. Esteban, A. G. Borisov, P. Nordlander, and J. Aizpurua, Nat. Commun. 3, 825 (2012).
[CrossRef]

K. J. Savage, M. M. Hawkeye, R. Esteban, A. G. Borisov, J. Aizpurua, and J. J. Baumberg, Nature 491, 574 (2012).
[CrossRef]

Atwater, H. A.

H. A. Atwater and A. Polman, Nat. Mater. 9, 205 (2010).
[CrossRef]

Baumberg, J. J.

K. J. Savage, M. M. Hawkeye, R. Esteban, A. G. Borisov, J. Aizpurua, and J. J. Baumberg, Nature 491, 574 (2012).
[CrossRef]

Berciaud, S.

S. Berciaud, L. Cognet, P. Tamarat, and B. Lounis, Nano Lett. 5, 515 (2005).
[CrossRef]

Bohren, C. F.

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

Borisov, A. G.

K. J. Savage, M. M. Hawkeye, R. Esteban, A. G. Borisov, J. Aizpurua, and J. J. Baumberg, Nature 491, 574 (2012).
[CrossRef]

R. Esteban, A. G. Borisov, P. Nordlander, and J. Aizpurua, Nat. Commun. 3, 825 (2012).
[CrossRef]

Cheng, C. J.

C. J. Cheng and W. M. Saltzman, Nat. Nanotechnol. 7, 346 (2012).
[CrossRef]

Christy, R. W.

P. B. Johnson and R. W. Christy, Phys. Rev. B 6, 4370 (1972).
[CrossRef]

Cognet, L.

S. Berciaud, L. Cognet, P. Tamarat, and B. Lounis, Nano Lett. 5, 515 (2005).
[CrossRef]

Dasari, R. R.

K. Kneipp, Y. Wang, H. Kneipp, L. T. Perelman, I. Itzkan, R. R. Dasari, and M. S. Feld, Phys. Rev. Lett. 78, 1667 (1997).
[CrossRef]

Dionne, J. A.

J. A. Scholl, A. L. Koh, and J. A. Dionne, Nature 483, 421 (2012).
[CrossRef]

Dridi, M.

A. Vial, T. Laroche, M. Dridi, and L. Le Cunff, Appl. Phys. A 103, 849 (2011).
[CrossRef]

Emory, S. R.

N. Shuming and S. R. Emory, Science 275, 5303 (1997).

Esteban, R.

K. J. Savage, M. M. Hawkeye, R. Esteban, A. G. Borisov, J. Aizpurua, and J. J. Baumberg, Nature 491, 574 (2012).
[CrossRef]

R. Esteban, A. G. Borisov, P. Nordlander, and J. Aizpurua, Nat. Commun. 3, 825 (2012).
[CrossRef]

Feld, M. S.

K. Kneipp, Y. Wang, H. Kneipp, L. T. Perelman, I. Itzkan, R. R. Dasari, and M. S. Feld, Phys. Rev. Lett. 78, 1667 (1997).
[CrossRef]

Hao, F.

F. Hao and P. Nordlander, Chem. Phys. Lett. 446, 115 (2007).
[CrossRef]

Hawkeye, M. M.

K. J. Savage, M. M. Hawkeye, R. Esteban, A. G. Borisov, J. Aizpurua, and J. J. Baumberg, Nature 491, 574 (2012).
[CrossRef]

Huffman, D. R.

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

Itzkan, I.

K. Kneipp, Y. Wang, H. Kneipp, L. T. Perelman, I. Itzkan, R. R. Dasari, and M. S. Feld, Phys. Rev. Lett. 78, 1667 (1997).
[CrossRef]

Jin, J.

S. Kim, J. Jin, Y.-J. Kim, I.-Y. Park, Y. Kim, and S.-W. Kim, Nature 453, 757 (2008).
[CrossRef]

Johnson, P. B.

P. B. Johnson and R. W. Christy, Phys. Rev. B 6, 4370 (1972).
[CrossRef]

Kim, S.

S. Kim, J. Jin, Y.-J. Kim, I.-Y. Park, Y. Kim, and S.-W. Kim, Nature 453, 757 (2008).
[CrossRef]

Kim, S.-W.

S. Kim, J. Jin, Y.-J. Kim, I.-Y. Park, Y. Kim, and S.-W. Kim, Nature 453, 757 (2008).
[CrossRef]

Kim, Y.

S. Kim, J. Jin, Y.-J. Kim, I.-Y. Park, Y. Kim, and S.-W. Kim, Nature 453, 757 (2008).
[CrossRef]

Kim, Y.-J.

S. Kim, J. Jin, Y.-J. Kim, I.-Y. Park, Y. Kim, and S.-W. Kim, Nature 453, 757 (2008).
[CrossRef]

Kneipp, H.

K. Kneipp, Y. Wang, H. Kneipp, L. T. Perelman, I. Itzkan, R. R. Dasari, and M. S. Feld, Phys. Rev. Lett. 78, 1667 (1997).
[CrossRef]

Kneipp, K.

K. Kneipp, Y. Wang, H. Kneipp, L. T. Perelman, I. Itzkan, R. R. Dasari, and M. S. Feld, Phys. Rev. Lett. 78, 1667 (1997).
[CrossRef]

Koh, A. L.

J. A. Scholl, A. L. Koh, and J. A. Dionne, Nature 483, 421 (2012).
[CrossRef]

Kraus, W. A.

W. A. Kraus and G. C. Schatz, J. Chem. Phys. 79, 6130 (1983).
[CrossRef]

Laroche, T.

A. Vial, T. Laroche, M. Dridi, and L. Le Cunff, Appl. Phys. A 103, 849 (2011).
[CrossRef]

Le Cunff, L.

A. Vial, T. Laroche, M. Dridi, and L. Le Cunff, Appl. Phys. A 103, 849 (2011).
[CrossRef]

Li, K.

P. Nordlander, C. Oubre, E. Prodan, K. Li, and M. I. Stockman, Nano Lett. 4, 899 (2004).
[CrossRef]

Lounis, B.

S. Berciaud, L. Cognet, P. Tamarat, and B. Lounis, Nano Lett. 5, 515 (2005).
[CrossRef]

Mackowski, D.

D. Mackowski, “SCSMFO. FOR: calculation of the scattering properties for a cluster of spheres,” User guide accompanying the SCSMFO. FOR code (1999).

Mackowski, D. W.

Mishchenko, M. I.

Nordlander, P.

R. Esteban, A. G. Borisov, P. Nordlander, and J. Aizpurua, Nat. Commun. 3, 825 (2012).
[CrossRef]

F. Hao and P. Nordlander, Chem. Phys. Lett. 446, 115 (2007).
[CrossRef]

P. Nordlander, C. Oubre, E. Prodan, K. Li, and M. I. Stockman, Nano Lett. 4, 899 (2004).
[CrossRef]

Oubre, C.

P. Nordlander, C. Oubre, E. Prodan, K. Li, and M. I. Stockman, Nano Lett. 4, 899 (2004).
[CrossRef]

Palik, E. D.

E. D. Palik, Handbook of Optical Constants of Solids(Academic, 1985).

Park, I.-Y.

S. Kim, J. Jin, Y.-J. Kim, I.-Y. Park, Y. Kim, and S.-W. Kim, Nature 453, 757 (2008).
[CrossRef]

Perelman, L. T.

K. Kneipp, Y. Wang, H. Kneipp, L. T. Perelman, I. Itzkan, R. R. Dasari, and M. S. Feld, Phys. Rev. Lett. 78, 1667 (1997).
[CrossRef]

Polman, A.

H. A. Atwater and A. Polman, Nat. Mater. 9, 205 (2010).
[CrossRef]

Prodan, E.

P. Nordlander, C. Oubre, E. Prodan, K. Li, and M. I. Stockman, Nano Lett. 4, 899 (2004).
[CrossRef]

Saltzman, W. M.

C. J. Cheng and W. M. Saltzman, Nat. Nanotechnol. 7, 346 (2012).
[CrossRef]

Savage, K. J.

K. J. Savage, M. M. Hawkeye, R. Esteban, A. G. Borisov, J. Aizpurua, and J. J. Baumberg, Nature 491, 574 (2012).
[CrossRef]

Schatz, G. C.

W. A. Kraus and G. C. Schatz, J. Chem. Phys. 79, 6130 (1983).
[CrossRef]

Scholl, J. A.

J. A. Scholl, A. L. Koh, and J. A. Dionne, Nature 483, 421 (2012).
[CrossRef]

Shuming, N.

N. Shuming and S. R. Emory, Science 275, 5303 (1997).

Stockman, M. I.

P. Nordlander, C. Oubre, E. Prodan, K. Li, and M. I. Stockman, Nano Lett. 4, 899 (2004).
[CrossRef]

Tamarat, P.

S. Berciaud, L. Cognet, P. Tamarat, and B. Lounis, Nano Lett. 5, 515 (2005).
[CrossRef]

Tribelsky, M. I.

M. I. Tribelsky, Europhys. Lett. 94, 14004 (2011).
[CrossRef]

Vial, A.

A. Vial, T. Laroche, M. Dridi, and L. Le Cunff, Appl. Phys. A 103, 849 (2011).
[CrossRef]

Wang, Y.

K. Kneipp, Y. Wang, H. Kneipp, L. T. Perelman, I. Itzkan, R. R. Dasari, and M. S. Feld, Phys. Rev. Lett. 78, 1667 (1997).
[CrossRef]

Appl. Phys. A (1)

A. Vial, T. Laroche, M. Dridi, and L. Le Cunff, Appl. Phys. A 103, 849 (2011).
[CrossRef]

Chem. Phys. Lett. (1)

F. Hao and P. Nordlander, Chem. Phys. Lett. 446, 115 (2007).
[CrossRef]

Europhys. Lett. (1)

M. I. Tribelsky, Europhys. Lett. 94, 14004 (2011).
[CrossRef]

J. Chem. Phys. (1)

W. A. Kraus and G. C. Schatz, J. Chem. Phys. 79, 6130 (1983).
[CrossRef]

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

Nano Lett. (2)

S. Berciaud, L. Cognet, P. Tamarat, and B. Lounis, Nano Lett. 5, 515 (2005).
[CrossRef]

P. Nordlander, C. Oubre, E. Prodan, K. Li, and M. I. Stockman, Nano Lett. 4, 899 (2004).
[CrossRef]

Nat. Commun. (1)

R. Esteban, A. G. Borisov, P. Nordlander, and J. Aizpurua, Nat. Commun. 3, 825 (2012).
[CrossRef]

Nat. Mater. (1)

H. A. Atwater and A. Polman, Nat. Mater. 9, 205 (2010).
[CrossRef]

Nat. Nanotechnol. (1)

C. J. Cheng and W. M. Saltzman, Nat. Nanotechnol. 7, 346 (2012).
[CrossRef]

Nature (3)

J. A. Scholl, A. L. Koh, and J. A. Dionne, Nature 483, 421 (2012).
[CrossRef]

K. J. Savage, M. M. Hawkeye, R. Esteban, A. G. Borisov, J. Aizpurua, and J. J. Baumberg, Nature 491, 574 (2012).
[CrossRef]

S. Kim, J. Jin, Y.-J. Kim, I.-Y. Park, Y. Kim, and S.-W. Kim, Nature 453, 757 (2008).
[CrossRef]

Phys. Rev. B (1)

P. B. Johnson and R. W. Christy, Phys. Rev. B 6, 4370 (1972).
[CrossRef]

Phys. Rev. Lett. (1)

K. Kneipp, Y. Wang, H. Kneipp, L. T. Perelman, I. Itzkan, R. R. Dasari, and M. S. Feld, Phys. Rev. Lett. 78, 1667 (1997).
[CrossRef]

Science (1)

N. Shuming and S. R. Emory, Science 275, 5303 (1997).

Other (3)

D. Mackowski, “SCSMFO. FOR: calculation of the scattering properties for a cluster of spheres,” User guide accompanying the SCSMFO. FOR code (1999).

E. D. Palik, Handbook of Optical Constants of Solids(Academic, 1985).

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

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Figures (4)

Fig. 1.
Fig. 1.

(a) Real and (b) imaginary parts of the relative electric permittivity of silver as a function of the particle radius for three different energies. Bulk values taken from Johnson and Christy [16] as well as Palik [17] are also shown. The insets show zoomed areas between R=8nm and R=10nm.

Fig. 2.
Fig. 2.

Spectral extinction efficiency for both single particles and dimers of radius R=4nm made of (a) silver and (b) gold, calculated with both bulk and QM-corrected optical properties.

Fig. 3.
Fig. 3.

Spectral real and imaginary parts of the relative electric permittivity for the case R=4nm. Both bulk and QM-corrected values are shown. (a) Silver and (b) gold.

Fig. 4.
Fig. 4.

Spectral shift (left axis, “*” symbol) and peak increment (right axis, “o” symbol) of the spectral extinction resonance shown in Fig. 2 as a function of the dimer gap lgap, Δλmax, and ΔQextmax represent the difference with respect to the isolated particle case. (a) Silver and (b) gold.

Equations (3)

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

ε(ω)=εIB+ωp2ifSifωif2ω2iγω,
QextQabs=4xI{ε1ε+2},
QextQabs=12xεi.

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