Abstract

We present an effective medium theory for resonant plasmonic nanoparticle systems. By utilizing the notion of dressed polarizability to describe dipolar particle interactions, we show that even highly concentrated, resonant plasmonic particles can be correctly described by the effective medium theory. The effective permittivity tensor of a nanoparticle monolayer is found explicitly and the resulting absorbance spectrum is shown to agree with rigorous numerical results from the FDTD model. The effective theory based on dressed polarizability provides a powerful tool to tailor resonant optical behaviors and design diverse plasmonic devices.

© 2012 OSA

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  1. C. E. Talley, J. B. Jackson, C. Oubre, N. K. Grady, C. W. Hollars, S. M. Lane, T. R. Huser, P. Nordlander, and N. J. Halas, “Surface-enhanced Raman scattering from individual au nanoparticles and nanoparticle dimer substrates,” Nano Lett. 5(8), 1569–1574 (2005).
    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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2010 (1)

J. A. Fan, C. Wu, K. Bao, J. Bao, R. Bardhan, N. J. Halas, V. N. Manoharan, P. Nordlander, G. Shvets, and F. Capasso, “Self-assembled plasmonic nanoparticle clusters,” Science 328(5982), 1135–1138 (2010).
[CrossRef] [PubMed]

2009 (1)

2008 (2)

T. Ming, X. Kou, H. Chen, T. Wang, H.-L. Tam, K.-W. Cheah, J.-Y. Chen, and J. Wang, “Ordered gold nanostructure assemblies formed by droplet evaporation,” Angew. Chem. Int. Ed. Engl. 47(50), 9685–9690 (2008).
[CrossRef] [PubMed]

K. Nakayama, K. Tanabe, and H. A. Atwater, “Plasmonic nanoparticle enhanced light absorption in GaAs solar cells,” Appl. Phys. Lett. 93(12), 121904 (2008).
[CrossRef]

2007 (2)

W. Zhang, B. S. Yeo, T. Schmid, and R. Zenobi, “Single molecule tip-enhanced Raman spectroscopy with silver tips,” J. Phys. Chem. C 111(4), 1733–1738 (2007).
[CrossRef]

A. Vial, “Implementation of the critical points model in the recursive convolution method for modelling dispersive media with the finite-difference time domain method,” J. Opt. A, Pure Appl. Opt. 9(7), 745–748 (2007).
[CrossRef]

2006 (1)

P. G. Etchegoin, E. C. Le Ru, and M. Meyer, “An analytic model for the optical properties of gold,” J. Chem. Phys. 125(16), 164705 (2006).
[CrossRef] [PubMed]

2005 (2)

N. Engheta, A. Salandrino, and A. Alù, “Circuit elements at optical frequencies: Nanoinductors, nanocapacitors, and nanoresistors,” Phys. Rev. Lett. 95(9), 095504 (2005).
[CrossRef] [PubMed]

C. E. Talley, J. B. Jackson, C. Oubre, N. K. Grady, C. W. Hollars, S. M. Lane, T. R. Huser, P. Nordlander, and N. J. Halas, “Surface-enhanced Raman scattering from individual au nanoparticles and nanoparticle dimer substrates,” Nano Lett. 5(8), 1569–1574 (2005).
[CrossRef] [PubMed]

2004 (1)

P. Nordlander, C. Oubre, E. Prodan, K. Li, and M. I. Stockman, “Plasmon hybridization in nanoparticle dimers,” Nano Lett. 4(5), 899–903 (2004).
[CrossRef]

2003 (1)

E. Prodan, C. Radloff, N. J. Halas, and P. Nordlander, “A hybridization model for the plasmon response of complex nanostructures,” Science 302(5644), 419–422 (2003).
[CrossRef] [PubMed]

1998 (1)

1993 (1)

1991 (1)

R. Barrera, M. del Castillo-Mussot, G. Monsivais, P. Villaseor, and W. Mochán, “Optical properties of two-dimensional disordered systems on a substrate,” Phys. Rev. B Condens. Matter 43(17), 13819–13826 (1991).
[CrossRef] [PubMed]

1988 (1)

R. G. Barrera, G. Monsivais, and W. L. Mochán, “Renormalized polarizability in the Maxwell Garnett theory,” Phys. Rev. B Condens. Matter 38(8), 5371–5379 (1988).
[CrossRef] [PubMed]

1986 (1)

R. Rojas and F. Claro, “Electromagnetic response of an array of particles: normal-mode theory,” Phys. Rev. B Condens. Matter 34(6), 3730–3736 (1986).
[CrossRef] [PubMed]

1983 (1)

1978 (1)

R. Ruppin, “Validity range of the Maxwell-Garnett theory,” Phys. Status Solidi B 87(2), 619–624 (1978).
[CrossRef]

1972 (1)

P. B. Johnson and R. W. Christy, “Optical constants of the Noble Metals,” Phys. Rev. B 6(12), 4370–4379 (1972).
[CrossRef]

Alù, A.

N. Engheta, A. Salandrino, and A. Alù, “Circuit elements at optical frequencies: Nanoinductors, nanocapacitors, and nanoresistors,” Phys. Rev. Lett. 95(9), 095504 (2005).
[CrossRef] [PubMed]

Atwater, H. A.

K. Nakayama, K. Tanabe, and H. A. Atwater, “Plasmonic nanoparticle enhanced light absorption in GaAs solar cells,” Appl. Phys. Lett. 93(12), 121904 (2008).
[CrossRef]

Aussenegg, F. R.

Bao, J.

J. A. Fan, C. Wu, K. Bao, J. Bao, R. Bardhan, N. J. Halas, V. N. Manoharan, P. Nordlander, G. Shvets, and F. Capasso, “Self-assembled plasmonic nanoparticle clusters,” Science 328(5982), 1135–1138 (2010).
[CrossRef] [PubMed]

Bao, K.

J. A. Fan, C. Wu, K. Bao, J. Bao, R. Bardhan, N. J. Halas, V. N. Manoharan, P. Nordlander, G. Shvets, and F. Capasso, “Self-assembled plasmonic nanoparticle clusters,” Science 328(5982), 1135–1138 (2010).
[CrossRef] [PubMed]

Bardhan, R.

J. A. Fan, C. Wu, K. Bao, J. Bao, R. Bardhan, N. J. Halas, V. N. Manoharan, P. Nordlander, G. Shvets, and F. Capasso, “Self-assembled plasmonic nanoparticle clusters,” Science 328(5982), 1135–1138 (2010).
[CrossRef] [PubMed]

Barrera, R.

R. Barrera, M. del Castillo-Mussot, G. Monsivais, P. Villaseor, and W. Mochán, “Optical properties of two-dimensional disordered systems on a substrate,” Phys. Rev. B Condens. Matter 43(17), 13819–13826 (1991).
[CrossRef] [PubMed]

Barrera, R. G.

R. G. Barrera, G. Monsivais, and W. L. Mochán, “Renormalized polarizability in the Maxwell Garnett theory,” Phys. Rev. B Condens. Matter 38(8), 5371–5379 (1988).
[CrossRef] [PubMed]

Capasso, F.

J. A. Fan, C. Wu, K. Bao, J. Bao, R. Bardhan, N. J. Halas, V. N. Manoharan, P. Nordlander, G. Shvets, and F. Capasso, “Self-assembled plasmonic nanoparticle clusters,” Science 328(5982), 1135–1138 (2010).
[CrossRef] [PubMed]

Cheah, K.-W.

T. Ming, X. Kou, H. Chen, T. Wang, H.-L. Tam, K.-W. Cheah, J.-Y. Chen, and J. Wang, “Ordered gold nanostructure assemblies formed by droplet evaporation,” Angew. Chem. Int. Ed. Engl. 47(50), 9685–9690 (2008).
[CrossRef] [PubMed]

Chen, H.

T. Ming, X. Kou, H. Chen, T. Wang, H.-L. Tam, K.-W. Cheah, J.-Y. Chen, and J. Wang, “Ordered gold nanostructure assemblies formed by droplet evaporation,” Angew. Chem. Int. Ed. Engl. 47(50), 9685–9690 (2008).
[CrossRef] [PubMed]

Chen, J.-Y.

T. Ming, X. Kou, H. Chen, T. Wang, H.-L. Tam, K.-W. Cheah, J.-Y. Chen, and J. Wang, “Ordered gold nanostructure assemblies formed by droplet evaporation,” Angew. Chem. Int. Ed. Engl. 47(50), 9685–9690 (2008).
[CrossRef] [PubMed]

Christy, R. W.

P. B. Johnson and R. W. Christy, “Optical constants of the Noble Metals,” Phys. Rev. B 6(12), 4370–4379 (1972).
[CrossRef]

Claro, F.

R. Rojas and F. Claro, “Electromagnetic response of an array of particles: normal-mode theory,” Phys. Rev. B Condens. Matter 34(6), 3730–3736 (1986).
[CrossRef] [PubMed]

del Castillo-Mussot, M.

R. Barrera, M. del Castillo-Mussot, G. Monsivais, P. Villaseor, and W. Mochán, “Optical properties of two-dimensional disordered systems on a substrate,” Phys. Rev. B Condens. Matter 43(17), 13819–13826 (1991).
[CrossRef] [PubMed]

Engheta, N.

N. Engheta, A. Salandrino, and A. Alù, “Circuit elements at optical frequencies: Nanoinductors, nanocapacitors, and nanoresistors,” Phys. Rev. Lett. 95(9), 095504 (2005).
[CrossRef] [PubMed]

Etchegoin, P. G.

P. G. Etchegoin, E. C. Le Ru, and M. Meyer, “An analytic model for the optical properties of gold,” J. Chem. Phys. 125(16), 164705 (2006).
[CrossRef] [PubMed]

Fan, J. A.

J. A. Fan, C. Wu, K. Bao, J. Bao, R. Bardhan, N. J. Halas, V. N. Manoharan, P. Nordlander, G. Shvets, and F. Capasso, “Self-assembled plasmonic nanoparticle clusters,” Science 328(5982), 1135–1138 (2010).
[CrossRef] [PubMed]

Grady, N. K.

C. E. Talley, J. B. Jackson, C. Oubre, N. K. Grady, C. W. Hollars, S. M. Lane, T. R. Huser, P. Nordlander, and N. J. Halas, “Surface-enhanced Raman scattering from individual au nanoparticles and nanoparticle dimer substrates,” Nano Lett. 5(8), 1569–1574 (2005).
[CrossRef] [PubMed]

Halas, N. J.

J. A. Fan, C. Wu, K. Bao, J. Bao, R. Bardhan, N. J. Halas, V. N. Manoharan, P. Nordlander, G. Shvets, and F. Capasso, “Self-assembled plasmonic nanoparticle clusters,” Science 328(5982), 1135–1138 (2010).
[CrossRef] [PubMed]

C. E. Talley, J. B. Jackson, C. Oubre, N. K. Grady, C. W. Hollars, S. M. Lane, T. R. Huser, P. Nordlander, and N. J. Halas, “Surface-enhanced Raman scattering from individual au nanoparticles and nanoparticle dimer substrates,” Nano Lett. 5(8), 1569–1574 (2005).
[CrossRef] [PubMed]

E. Prodan, C. Radloff, N. J. Halas, and P. Nordlander, “A hybridization model for the plasmon response of complex nanostructures,” Science 302(5644), 419–422 (2003).
[CrossRef] [PubMed]

Hollars, C. W.

C. E. Talley, J. B. Jackson, C. Oubre, N. K. Grady, C. W. Hollars, S. M. Lane, T. R. Huser, P. Nordlander, and N. J. Halas, “Surface-enhanced Raman scattering from individual au nanoparticles and nanoparticle dimer substrates,” Nano Lett. 5(8), 1569–1574 (2005).
[CrossRef] [PubMed]

Huser, T. R.

C. E. Talley, J. B. Jackson, C. Oubre, N. K. Grady, C. W. Hollars, S. M. Lane, T. R. Huser, P. Nordlander, and N. J. Halas, “Surface-enhanced Raman scattering from individual au nanoparticles and nanoparticle dimer substrates,” Nano Lett. 5(8), 1569–1574 (2005).
[CrossRef] [PubMed]

Jackson, J. B.

C. E. Talley, J. B. Jackson, C. Oubre, N. K. Grady, C. W. Hollars, S. M. Lane, T. R. Huser, P. Nordlander, and N. J. Halas, “Surface-enhanced Raman scattering from individual au nanoparticles and nanoparticle dimer substrates,” Nano Lett. 5(8), 1569–1574 (2005).
[CrossRef] [PubMed]

Johnson, P. B.

P. B. Johnson and R. W. Christy, “Optical constants of the Noble Metals,” Phys. Rev. B 6(12), 4370–4379 (1972).
[CrossRef]

Kou, X.

T. Ming, X. Kou, H. Chen, T. Wang, H.-L. Tam, K.-W. Cheah, J.-Y. Chen, and J. Wang, “Ordered gold nanostructure assemblies formed by droplet evaporation,” Angew. Chem. Int. Ed. Engl. 47(50), 9685–9690 (2008).
[CrossRef] [PubMed]

Kreibig, U.

Krenn, J. R.

Lane, S. M.

C. E. Talley, J. B. Jackson, C. Oubre, N. K. Grady, C. W. Hollars, S. M. Lane, T. R. Huser, P. Nordlander, and N. J. Halas, “Surface-enhanced Raman scattering from individual au nanoparticles and nanoparticle dimer substrates,” Nano Lett. 5(8), 1569–1574 (2005).
[CrossRef] [PubMed]

Le Ru, E. C.

P. G. Etchegoin, E. C. Le Ru, and M. Meyer, “An analytic model for the optical properties of gold,” J. Chem. Phys. 125(16), 164705 (2006).
[CrossRef] [PubMed]

Leitner, A.

Li, K.

P. Nordlander, C. Oubre, E. Prodan, K. Li, and M. I. Stockman, “Plasmon hybridization in nanoparticle dimers,” Nano Lett. 4(5), 899–903 (2004).
[CrossRef]

Manoharan, V. N.

J. A. Fan, C. Wu, K. Bao, J. Bao, R. Bardhan, N. J. Halas, V. N. Manoharan, P. Nordlander, G. Shvets, and F. Capasso, “Self-assembled plasmonic nanoparticle clusters,” Science 328(5982), 1135–1138 (2010).
[CrossRef] [PubMed]

Meier, M.

Meyer, M.

P. G. Etchegoin, E. C. Le Ru, and M. Meyer, “An analytic model for the optical properties of gold,” J. Chem. Phys. 125(16), 164705 (2006).
[CrossRef] [PubMed]

Ming, T.

T. Ming, X. Kou, H. Chen, T. Wang, H.-L. Tam, K.-W. Cheah, J.-Y. Chen, and J. Wang, “Ordered gold nanostructure assemblies formed by droplet evaporation,” Angew. Chem. Int. Ed. Engl. 47(50), 9685–9690 (2008).
[CrossRef] [PubMed]

Mochán, W.

R. Barrera, M. del Castillo-Mussot, G. Monsivais, P. Villaseor, and W. Mochán, “Optical properties of two-dimensional disordered systems on a substrate,” Phys. Rev. B Condens. Matter 43(17), 13819–13826 (1991).
[CrossRef] [PubMed]

Mochán, W. L.

R. G. Barrera, G. Monsivais, and W. L. Mochán, “Renormalized polarizability in the Maxwell Garnett theory,” Phys. Rev. B Condens. Matter 38(8), 5371–5379 (1988).
[CrossRef] [PubMed]

Monsivais, G.

R. Barrera, M. del Castillo-Mussot, G. Monsivais, P. Villaseor, and W. Mochán, “Optical properties of two-dimensional disordered systems on a substrate,” Phys. Rev. B Condens. Matter 43(17), 13819–13826 (1991).
[CrossRef] [PubMed]

R. G. Barrera, G. Monsivais, and W. L. Mochán, “Renormalized polarizability in the Maxwell Garnett theory,” Phys. Rev. B Condens. Matter 38(8), 5371–5379 (1988).
[CrossRef] [PubMed]

Moroz, A.

Nakayama, K.

K. Nakayama, K. Tanabe, and H. A. Atwater, “Plasmonic nanoparticle enhanced light absorption in GaAs solar cells,” Appl. Phys. Lett. 93(12), 121904 (2008).
[CrossRef]

Nordlander, P.

J. A. Fan, C. Wu, K. Bao, J. Bao, R. Bardhan, N. J. Halas, V. N. Manoharan, P. Nordlander, G. Shvets, and F. Capasso, “Self-assembled plasmonic nanoparticle clusters,” Science 328(5982), 1135–1138 (2010).
[CrossRef] [PubMed]

C. E. Talley, J. B. Jackson, C. Oubre, N. K. Grady, C. W. Hollars, S. M. Lane, T. R. Huser, P. Nordlander, and N. J. Halas, “Surface-enhanced Raman scattering from individual au nanoparticles and nanoparticle dimer substrates,” Nano Lett. 5(8), 1569–1574 (2005).
[CrossRef] [PubMed]

P. Nordlander, C. Oubre, E. Prodan, K. Li, and M. I. Stockman, “Plasmon hybridization in nanoparticle dimers,” Nano Lett. 4(5), 899–903 (2004).
[CrossRef]

E. Prodan, C. Radloff, N. J. Halas, and P. Nordlander, “A hybridization model for the plasmon response of complex nanostructures,” Science 302(5644), 419–422 (2003).
[CrossRef] [PubMed]

Oubre, C.

C. E. Talley, J. B. Jackson, C. Oubre, N. K. Grady, C. W. Hollars, S. M. Lane, T. R. Huser, P. Nordlander, and N. J. Halas, “Surface-enhanced Raman scattering from individual au nanoparticles and nanoparticle dimer substrates,” Nano Lett. 5(8), 1569–1574 (2005).
[CrossRef] [PubMed]

P. Nordlander, C. Oubre, E. Prodan, K. Li, and M. I. Stockman, “Plasmon hybridization in nanoparticle dimers,” Nano Lett. 4(5), 899–903 (2004).
[CrossRef]

Prodan, E.

P. Nordlander, C. Oubre, E. Prodan, K. Li, and M. I. Stockman, “Plasmon hybridization in nanoparticle dimers,” Nano Lett. 4(5), 899–903 (2004).
[CrossRef]

E. Prodan, C. Radloff, N. J. Halas, and P. Nordlander, “A hybridization model for the plasmon response of complex nanostructures,” Science 302(5644), 419–422 (2003).
[CrossRef] [PubMed]

Quinten, M.

Radloff, C.

E. Prodan, C. Radloff, N. J. Halas, and P. Nordlander, “A hybridization model for the plasmon response of complex nanostructures,” Science 302(5644), 419–422 (2003).
[CrossRef] [PubMed]

Rojas, R.

R. Rojas and F. Claro, “Electromagnetic response of an array of particles: normal-mode theory,” Phys. Rev. B Condens. Matter 34(6), 3730–3736 (1986).
[CrossRef] [PubMed]

Ruppin, R.

R. Ruppin, “Validity range of the Maxwell-Garnett theory,” Phys. Status Solidi B 87(2), 619–624 (1978).
[CrossRef]

Salandrino, A.

N. Engheta, A. Salandrino, and A. Alù, “Circuit elements at optical frequencies: Nanoinductors, nanocapacitors, and nanoresistors,” Phys. Rev. Lett. 95(9), 095504 (2005).
[CrossRef] [PubMed]

Schmid, T.

W. Zhang, B. S. Yeo, T. Schmid, and R. Zenobi, “Single molecule tip-enhanced Raman spectroscopy with silver tips,” J. Phys. Chem. C 111(4), 1733–1738 (2007).
[CrossRef]

Shvets, G.

J. A. Fan, C. Wu, K. Bao, J. Bao, R. Bardhan, N. J. Halas, V. N. Manoharan, P. Nordlander, G. Shvets, and F. Capasso, “Self-assembled plasmonic nanoparticle clusters,” Science 328(5982), 1135–1138 (2010).
[CrossRef] [PubMed]

Stockman, M. I.

P. Nordlander, C. Oubre, E. Prodan, K. Li, and M. I. Stockman, “Plasmon hybridization in nanoparticle dimers,” Nano Lett. 4(5), 899–903 (2004).
[CrossRef]

Talley, C. E.

C. E. Talley, J. B. Jackson, C. Oubre, N. K. Grady, C. W. Hollars, S. M. Lane, T. R. Huser, P. Nordlander, and N. J. Halas, “Surface-enhanced Raman scattering from individual au nanoparticles and nanoparticle dimer substrates,” Nano Lett. 5(8), 1569–1574 (2005).
[CrossRef] [PubMed]

Tam, H.-L.

T. Ming, X. Kou, H. Chen, T. Wang, H.-L. Tam, K.-W. Cheah, J.-Y. Chen, and J. Wang, “Ordered gold nanostructure assemblies formed by droplet evaporation,” Angew. Chem. Int. Ed. Engl. 47(50), 9685–9690 (2008).
[CrossRef] [PubMed]

Tanabe, K.

K. Nakayama, K. Tanabe, and H. A. Atwater, “Plasmonic nanoparticle enhanced light absorption in GaAs solar cells,” Appl. Phys. Lett. 93(12), 121904 (2008).
[CrossRef]

Vial, A.

A. Vial, “Implementation of the critical points model in the recursive convolution method for modelling dispersive media with the finite-difference time domain method,” J. Opt. A, Pure Appl. Opt. 9(7), 745–748 (2007).
[CrossRef]

Villaseor, P.

R. Barrera, M. del Castillo-Mussot, G. Monsivais, P. Villaseor, and W. Mochán, “Optical properties of two-dimensional disordered systems on a substrate,” Phys. Rev. B Condens. Matter 43(17), 13819–13826 (1991).
[CrossRef] [PubMed]

Wang, J.

T. Ming, X. Kou, H. Chen, T. Wang, H.-L. Tam, K.-W. Cheah, J.-Y. Chen, and J. Wang, “Ordered gold nanostructure assemblies formed by droplet evaporation,” Angew. Chem. Int. Ed. Engl. 47(50), 9685–9690 (2008).
[CrossRef] [PubMed]

Wang, T.

T. Ming, X. Kou, H. Chen, T. Wang, H.-L. Tam, K.-W. Cheah, J.-Y. Chen, and J. Wang, “Ordered gold nanostructure assemblies formed by droplet evaporation,” Angew. Chem. Int. Ed. Engl. 47(50), 9685–9690 (2008).
[CrossRef] [PubMed]

Wokaun, A.

Wu, C.

J. A. Fan, C. Wu, K. Bao, J. Bao, R. Bardhan, N. J. Halas, V. N. Manoharan, P. Nordlander, G. Shvets, and F. Capasso, “Self-assembled plasmonic nanoparticle clusters,” Science 328(5982), 1135–1138 (2010).
[CrossRef] [PubMed]

Yeo, B. S.

W. Zhang, B. S. Yeo, T. Schmid, and R. Zenobi, “Single molecule tip-enhanced Raman spectroscopy with silver tips,” J. Phys. Chem. C 111(4), 1733–1738 (2007).
[CrossRef]

Zenobi, R.

W. Zhang, B. S. Yeo, T. Schmid, and R. Zenobi, “Single molecule tip-enhanced Raman spectroscopy with silver tips,” J. Phys. Chem. C 111(4), 1733–1738 (2007).
[CrossRef]

Zhang, W.

W. Zhang, B. S. Yeo, T. Schmid, and R. Zenobi, “Single molecule tip-enhanced Raman spectroscopy with silver tips,” J. Phys. Chem. C 111(4), 1733–1738 (2007).
[CrossRef]

Angew. Chem. Int. Ed. Engl. (1)

T. Ming, X. Kou, H. Chen, T. Wang, H.-L. Tam, K.-W. Cheah, J.-Y. Chen, and J. Wang, “Ordered gold nanostructure assemblies formed by droplet evaporation,” Angew. Chem. Int. Ed. Engl. 47(50), 9685–9690 (2008).
[CrossRef] [PubMed]

Appl. Opt. (1)

Appl. Phys. Lett. (1)

K. Nakayama, K. Tanabe, and H. A. Atwater, “Plasmonic nanoparticle enhanced light absorption in GaAs solar cells,” Appl. Phys. Lett. 93(12), 121904 (2008).
[CrossRef]

J. Chem. Phys. (1)

P. G. Etchegoin, E. C. Le Ru, and M. Meyer, “An analytic model for the optical properties of gold,” J. Chem. Phys. 125(16), 164705 (2006).
[CrossRef] [PubMed]

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

A. Vial, “Implementation of the critical points model in the recursive convolution method for modelling dispersive media with the finite-difference time domain method,” J. Opt. A, Pure Appl. Opt. 9(7), 745–748 (2007).
[CrossRef]

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

J. Phys. Chem. C (1)

W. Zhang, B. S. Yeo, T. Schmid, and R. Zenobi, “Single molecule tip-enhanced Raman spectroscopy with silver tips,” J. Phys. Chem. C 111(4), 1733–1738 (2007).
[CrossRef]

Nano Lett. (2)

P. Nordlander, C. Oubre, E. Prodan, K. Li, and M. I. Stockman, “Plasmon hybridization in nanoparticle dimers,” Nano Lett. 4(5), 899–903 (2004).
[CrossRef]

C. E. Talley, J. B. Jackson, C. Oubre, N. K. Grady, C. W. Hollars, S. M. Lane, T. R. Huser, P. Nordlander, and N. J. Halas, “Surface-enhanced Raman scattering from individual au nanoparticles and nanoparticle dimer substrates,” Nano Lett. 5(8), 1569–1574 (2005).
[CrossRef] [PubMed]

Opt. Lett. (2)

Phys. Rev. B (1)

P. B. Johnson and R. W. Christy, “Optical constants of the Noble Metals,” Phys. Rev. B 6(12), 4370–4379 (1972).
[CrossRef]

Phys. Rev. B Condens. Matter (3)

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Phys. Rev. Lett. (1)

N. Engheta, A. Salandrino, and A. Alù, “Circuit elements at optical frequencies: Nanoinductors, nanocapacitors, and nanoresistors,” Phys. Rev. Lett. 95(9), 095504 (2005).
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Science (2)

J. A. Fan, C. Wu, K. Bao, J. Bao, R. Bardhan, N. J. Halas, V. N. Manoharan, P. Nordlander, G. Shvets, and F. Capasso, “Self-assembled plasmonic nanoparticle clusters,” Science 328(5982), 1135–1138 (2010).
[CrossRef] [PubMed]

E. Prodan, C. Radloff, N. J. Halas, and P. Nordlander, “A hybridization model for the plasmon response of complex nanostructures,” Science 302(5644), 419–422 (2003).
[CrossRef] [PubMed]

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T. C. Choy, Effective Medium Theory: Principles and Applications (Oxford University Press, 1999).

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Figures (5)

Fig. 1
Fig. 1

(a) the field intensity profile (left) and the vector field plot (right) of a monolayer with a lattice constant of 23 nm at 537 nm resonant wavelength, and (b) the field intensity profile (left) and the vector field plot (right) of a single non-interacting particle at the same wavelength (c) Schematic of plasmonic interaction between metallic nanoparticles which enhance or quench polarization of each particle, and (d) the bare polarizability (blue line) and the dressed polarizability (red) normalized by the cubic of the particle radius, a 3 .

Fig. 2
Fig. 2

Original spherical coordinate system (r,θ,ϕ) centered at O and the spherical coordinate system (r',θ',ϕ') centered at O shifted from O by r 0 =( r 0 , θ 0 , ϕ 0 ) .

Fig. 3
Fig. 3

(a) Contour map of absorbance spectrum of gold nanoparticle monolayers, and the corresponding absorbance spectrum at a lattice constant of (b) 26 nm, (c) 23 nm and (d) 22 nm corresponding to the filling factor of f = 0.24, 0.34, 0.39 respectively. The absorbance spectra show increased absorbance and a red shift of the resonance for monolayers with shorter lattice constants.

Fig. 4
Fig. 4

Effective indices: (a) real part of effective refractive index n eff , (b) imaginary part of effective refractive index k eff and (c) figure of merit (FOM) which is defined by FOM= n eff k eff .

Fig. 5
Fig. 5

Absorbance spectrum for (a) the enhanced monolayer with dx = 23.6 nm dy = 28.6 nm (red line), (b) the isotropic monolayer dx = dy = 26 nm (black), and (c) the quenched monolayer dx = 28.6 nm, dy = 23.6 nm (blue). The enhanced and quenched monolayers have an anisotropic arrangement of gold nanoparticles of radius 10 nm along the x, y direction, but they have an identical filling factor f=0.24 because the geometric mean of their interparticle distances d ¯ is constant for each monolayer at 26 nm. These anisotropic absorbance characteristics cannot be obtained via the Maxwell-Garnett effective medium theory.

Equations (23)

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p= ε1 ε+2 a 3 E 0 α 0 E 0 ,
E loc = E 0 +Gp,
p= α 0 E loc = α 0 ( E 0 +Gp )= ( 1 α 0 G ) 1 α 0 E 0 .
α d = ( 1 α 0 G ) 1 α 0 γ α 0 ,
E int,d =( 1 α 0 a 3 )γ E 0 ,
d E d, =[ 1 r 3 ( 3 cos 2 θ1 )+ k 2 2r ( cos 2 θ+1 ) ]PdV,
r( r , θ , ϕ )= x 2 + y 2 + z 2 = r 2 + r 0 2 2 r r 0 cosγ ,
θ( r , θ , ϕ )= cos 1 ( z r )= cos 1 ( r cos θ + r 0 cos θ 0 r ),
ϕ( r , θ , ϕ )= tan 1 ( y x )= tan 1 ( r sin θ sin ϕ + r 0 sin θ 0 sin ϕ 0 r sin θ cos ϕ + r 0 sin θ 0 cos ϕ 0 ),
cosγ=cos( ϕ ϕ 0 )sin θ sin θ 0 +cosθcos θ 0 .
r( r , θ )= r 2 + d z 2 +2 r r 0 cos θ ,
θ( r , θ )= cos 1 ( r cos θ + d z r ),
P 0 a 0 π 0 2π 1 r ( r , θ ) 3 [ 3 cos 2 θ( r , θ )1 ] r 2 sin θ d r d θ d ϕ = 8π 3 ( a d z ) 3 P ,
P 0 a 0 π 0 2π k 2 2r( r , θ ) [ cos 2 θ( r , θ )+1 ] r 2 sin θ d r d θ d ϕ = 4π 15 ( a d z ) 3 ( 5 d z 2 a 2 ) k 2 P .
E d enhanced =2 ( a d z ) 3 8π 3 [ 1+ 1 10 ( 5 d z 2 a 2 ) k 2 ]P.
1 r( r , θ , ϕ ) = l=0 m=l +l 4π 2l+1 r l d l+1 Y lm * ( θ 0 , ϕ 0 ) Y lm ( θ , ϕ ) .
P 0 a 0 π 0 2π 1 r ( r , θ ) 3 [ 3 cos 2 θ( r , θ )1 ] r 2 sin θ d r d θ d ϕ 4π 3 ( a d y ) 3 P + 4π 5 ( a d y ) 5 +O( ( a d y ) 9 ),
P 0 a 0 π 0 2π k 2 2r( r , θ ) [ cos 2 θ( r , θ )+1 ] r 2 sin θ d r d θ d ϕ 2π 15 ( a d y ) 3 ( 5 d y 2 + a 2 ) k 2 P +O( ( a d y ) 9 k 2 a 2 ).
E d quenched =2 ( a d y ) 3 4π 3 [ ( 1+ 3 5 ( a d y ) 2 )+ 1 10 ( 5 d y 2 + a 2 ) k 2 ]P.
E d self = 4π 3 ( 1 k 2 a 2 )P.
E d layer = E d enhanced + E d quenched + E d self = 4π 3 [ k 2 a 2 +2{ ( a d z ) 3 ( 2+ k 2 5 ( 5 d z 2 a 2 ) ) ( a d y ) 3 ( 1 k 2 10 ( 5 d y 2 + a 2 ) )+ 3 5 ( a d y ) 5 } ]P.
a 3 G z = k 2 a 2 +2( a 3 d z 3 [ 2+ k 2 5 ( 5 d z 2 a 2 ) ] a 3 d y 3 [ 1 k 2 10 ( 5 d y 2 + a 2 ) ]+ 3 5 a 5 d y 5 ),
ε x eff = D E = fε E int,d ( λ,a,d )+( 1f ) E 0 f E int,d ( λ,a,d )+( 1f ) E 0 = [1+2f+(f1) a 3 G x ]ε+22f+(1f) a 3 G x [1f+(f1) a 3 G x ]ε+2+f+(1f) a 3 G x ,

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