Abstract

The localized surface-plasmon resonance absorption of metal nanoparticles is currently utilized in many fields such as near-infrared (NIR) curing and biomedical applications. In this paper, we study theoretically the influence of an oxide (SiO2, ZrO2, or TiO2) shell on a metal (Ag, Au, or Cu) nanoparticle from the point of view of shifting the resonance peak to a more desirable color or NIR wavelengths while conserving the intensity of the absorption or extinction peak. The computational models used in the studies include the Mie theory and the four-flux method. We find shifts of up to hundreds or even close to 1000 nm. Among the material combinations studied, the largest shifts are obtained with Ag-TiO2 core-shell nanoparticles when going from a few nanometers sized core without an oxide shell to a 100 nm size core with a 100 nm thick shell. However, the huge shifts happen together with severe intensity loss of the absorption peak, leading to a more conservative estimate of practically useful shifts of a few hundreds of nanometers.

© 2013 Optical Society of America

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    [CrossRef]
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    [CrossRef]
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  24. W. Vargas, P. Greenwood, J. Otterstedt, and G. Niklasson, “Light scattering in pigmented coatings: experiments and theory,” Sol. Energy 68, 553–561 (2000).
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  25. W. E. Vargas and G. A. Niklasson, “Pigment mass density and refractive index determination from optical measurements,” J. Phys. Condens. Matter 9, 1661–1669 (1997).
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  26. P. Johnson and R. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6, 4370–4379 (1972).
    [CrossRef]
  27. D.-Y. Liu, S.-Y. Ding, H.-X. Lin, B.-J. Liu, Z.-Z. Ye, F.-R. Fan, B. Ren, and Z.-Q. Tian, “Distinctive enhanced and tunable plasmon resonant absorption from controllable Au@Cu2O nanoparticles: experimental and theoretical modeling,” J. Phys. Chem. C 116, 4477–4483 (2012).
    [CrossRef]
  28. W. Vargas, “Light scattering and absorption in pigmented coatings: theory and experiments,” Ph.D. thesis (Uppsala University, 1997).
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    [CrossRef]
  31. M. Meier and A. Wokaun, “Enhanced fields on large metal particles: dynamic depolarization,” Opt. Lett. 8, 581–583 (1983).
    [CrossRef]

2012

R. Ghosh Chaudhuri and S. Paria, “Core/shell nanoparticles: classes, properties, synthesis mechanisms, characterization, and applications,” Chem. Rev. 112, 2373–2433 (2012).
[CrossRef]

D.-Y. Liu, S.-Y. Ding, H.-X. Lin, B.-J. Liu, Z.-Z. Ye, F.-R. Fan, B. Ren, and Z.-Q. Tian, “Distinctive enhanced and tunable plasmon resonant absorption from controllable Au@Cu2O nanoparticles: experimental and theoretical modeling,” J. Phys. Chem. C 116, 4477–4483 (2012).
[CrossRef]

2011

M. Garcia, “Surface plasmons in metallic nanoparticles: fundamentals and applications,” J. Phys. D 44, 283001 (2011).
[CrossRef]

2009

2008

2003

R. T. Tom, A. S. Nair, N. Singh, M. Aslam, C. L. Nagendra, R. Philip, K. Vijayamohanan, and T. Pradeep, “Freely dispersible Au@TiO2, Au@ZrO2, Ag@TiO2, and Ag@ZrO2 coreshell nanoparticles: one-step synthesis, characterization, spectroscopy, and optical limiting properties,” Langmuir 19, 3439–3445 (2003).
[CrossRef]

2002

Y. Lu, Y. Yin, Z. Li, and Y. Xia, “Synthesis and self-assembly of Au@SiO2 core-shell colloids,” Nano Lett. 2, 785–788 (2002).
[CrossRef]

2000

I. Pastoriza-Santos, D. Koktysh, A. Mamedov, M. Giersig, N. Kotov, and L. Liz-Marzán, “One-pot synthesis of Ag@TiO2 core-shell nanoparticles and their layer-by-layer assembly,” Langmuir 16, 2731–2735 (2000).
[CrossRef]

W. Vargas, P. Greenwood, J. Otterstedt, and G. Niklasson, “Light scattering in pigmented coatings: experiments and theory,” Sol. Energy 68, 553–561 (2000).
[CrossRef]

1999

S. J. Oldenburg, J. B. Jackson, S. L. Westcott, and N. J. Halas, “Infrared extinction properties of gold nanoshells,” Appl. Phys. Lett. 75, 2897–2899 (1999).
[CrossRef]

1998

S. Oldenburg, R. Averitt, S. Westcott, and N. Halas, “Nanoengineering of optical resonances,” Chem. Phys. Lett. 288, 243–247 (1998).
[CrossRef]

W. E. Vargas, “Generalized four-flux radiative transfer model,” Appl. Opt. 37, 2615–2623 (1998).
[CrossRef]

1997

W. E. Vargas and G. A. Niklasson, “Pigment mass density and refractive index determination from optical measurements,” J. Phys. Condens. Matter 9, 1661–1669 (1997).
[CrossRef]

1996

L. Liz-Marzán, M. Giersig, and P. Mulvaney, “Synthesis of nanosized gold-silica core-shell particles,” Langmuir 12, 4329–4335 (1996).
[CrossRef]

1986

1984

1983

1982

A. Wokaun, J. Gordon, and P. Liao, “Radiation damping in surface-enhanced Raman scattering,” Phys. Rev. Lett. 48, 957–960 (1982).
[CrossRef]

D. Wood and K. Nassau, “Refractive index of cubic zirconia stabilized with yttria,” Appl. Opt. 21, 2978–2981 (1982).
[CrossRef]

1972

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

1951

A. Aden and M. Kerker, “Scattering of electromagnetic waves from two concentric spheres,” J. Appl. Phys. 22, 1242–1246 (1951).
[CrossRef]

1908

G. Mie, “Beiträge zur optik trüber medien, speziell kolloidaler metallösungen,” Ann. Phys. 330, 377–445 (1908).
[CrossRef]

Aden, A.

A. Aden and M. Kerker, “Scattering of electromagnetic waves from two concentric spheres,” J. Appl. Phys. 22, 1242–1246 (1951).
[CrossRef]

Ala-Nissila, T.

K. Laaksonen, S. Suomela, T. Ala-Nissila, and R. M. Nieminen, are preparing a manuscript to be called “Influence of high-refractive-index oxide core on optical properties of metal nanoshells.”

Ashcroft, N.

N. Ashcroft and N. Mermin, Solid State Physics, Thomson Learning (Saunders College, 1976).

Aslam, M.

R. T. Tom, A. S. Nair, N. Singh, M. Aslam, C. L. Nagendra, R. Philip, K. Vijayamohanan, and T. Pradeep, “Freely dispersible Au@TiO2, Au@ZrO2, Ag@TiO2, and Ag@ZrO2 coreshell nanoparticles: one-step synthesis, characterization, spectroscopy, and optical limiting properties,” Langmuir 19, 3439–3445 (2003).
[CrossRef]

Averitt, R.

S. Oldenburg, R. Averitt, S. Westcott, and N. Halas, “Nanoengineering of optical resonances,” Chem. Phys. Lett. 288, 243–247 (1998).
[CrossRef]

Bohren, C. F.

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

Christy, R.

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

Crespo-Sosa, A.

Ding, S.-Y.

D.-Y. Liu, S.-Y. Ding, H.-X. Lin, B.-J. Liu, Z.-Z. Ye, F.-R. Fan, B. Ren, and Z.-Q. Tian, “Distinctive enhanced and tunable plasmon resonant absorption from controllable Au@Cu2O nanoparticles: experimental and theoretical modeling,” J. Phys. Chem. C 116, 4477–4483 (2012).
[CrossRef]

Fan, F.-R.

D.-Y. Liu, S.-Y. Ding, H.-X. Lin, B.-J. Liu, Z.-Z. Ye, F.-R. Fan, B. Ren, and Z.-Q. Tian, “Distinctive enhanced and tunable plasmon resonant absorption from controllable Au@Cu2O nanoparticles: experimental and theoretical modeling,” J. Phys. Chem. C 116, 4477–4483 (2012).
[CrossRef]

Garcia, M.

M. Garcia, “Surface plasmons in metallic nanoparticles: fundamentals and applications,” J. Phys. D 44, 283001 (2011).
[CrossRef]

Ghosh, G.

E. Palik and G. Ghosh, Handbook of Optical Constants of Solids (Academic, 1998).

Ghosh Chaudhuri, R.

R. Ghosh Chaudhuri and S. Paria, “Core/shell nanoparticles: classes, properties, synthesis mechanisms, characterization, and applications,” Chem. Rev. 112, 2373–2433 (2012).
[CrossRef]

Giersig, M.

I. Pastoriza-Santos, D. Koktysh, A. Mamedov, M. Giersig, N. Kotov, and L. Liz-Marzán, “One-pot synthesis of Ag@TiO2 core-shell nanoparticles and their layer-by-layer assembly,” Langmuir 16, 2731–2735 (2000).
[CrossRef]

L. Liz-Marzán, M. Giersig, and P. Mulvaney, “Synthesis of nanosized gold-silica core-shell particles,” Langmuir 12, 4329–4335 (1996).
[CrossRef]

Gordon, J.

A. Wokaun, J. Gordon, and P. Liao, “Radiation damping in surface-enhanced Raman scattering,” Phys. Rev. Lett. 48, 957–960 (1982).
[CrossRef]

Gouesbet, G.

Greenwood, P.

W. Vargas, P. Greenwood, J. Otterstedt, and G. Niklasson, “Light scattering in pigmented coatings: experiments and theory,” Sol. Energy 68, 553–561 (2000).
[CrossRef]

Halas, N.

S. Oldenburg, R. Averitt, S. Westcott, and N. Halas, “Nanoengineering of optical resonances,” Chem. Phys. Lett. 288, 243–247 (1998).
[CrossRef]

Halas, N. J.

S. J. Oldenburg, J. B. Jackson, S. L. Westcott, and N. J. Halas, “Infrared extinction properties of gold nanoshells,” Appl. Phys. Lett. 75, 2897–2899 (1999).
[CrossRef]

Huffman, D. R.

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

Jackson, J. B.

S. J. Oldenburg, J. B. Jackson, S. L. Westcott, and N. J. Halas, “Infrared extinction properties of gold nanoshells,” Appl. Phys. Lett. 75, 2897–2899 (1999).
[CrossRef]

Johnson, P.

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

Kerker, M.

A. Aden and M. Kerker, “Scattering of electromagnetic waves from two concentric spheres,” J. Appl. Phys. 22, 1242–1246 (1951).
[CrossRef]

Koktysh, D.

I. Pastoriza-Santos, D. Koktysh, A. Mamedov, M. Giersig, N. Kotov, and L. Liz-Marzán, “One-pot synthesis of Ag@TiO2 core-shell nanoparticles and their layer-by-layer assembly,” Langmuir 16, 2731–2735 (2000).
[CrossRef]

Kotov, N.

I. Pastoriza-Santos, D. Koktysh, A. Mamedov, M. Giersig, N. Kotov, and L. Liz-Marzán, “One-pot synthesis of Ag@TiO2 core-shell nanoparticles and their layer-by-layer assembly,” Langmuir 16, 2731–2735 (2000).
[CrossRef]

Kreibig, U.

U. Kreibig and M. Vollmer, Optical Properties of Metal Clusters (Springer, 1995).

Laaksonen, K.

K. Laaksonen, S. Suomela, T. Ala-Nissila, and R. M. Nieminen, are preparing a manuscript to be called “Influence of high-refractive-index oxide core on optical properties of metal nanoshells.”

Lakowicz, J.

J. Lakowicz, Principles of Fluorescence Spectroscopy (Springer, 2006).

Letoulouzan, J.

Li, Z.

Y. Lu, Y. Yin, Z. Li, and Y. Xia, “Synthesis and self-assembly of Au@SiO2 core-shell colloids,” Nano Lett. 2, 785–788 (2002).
[CrossRef]

Liao, P.

A. Wokaun, J. Gordon, and P. Liao, “Radiation damping in surface-enhanced Raman scattering,” Phys. Rev. Lett. 48, 957–960 (1982).
[CrossRef]

Lin, H.-X.

D.-Y. Liu, S.-Y. Ding, H.-X. Lin, B.-J. Liu, Z.-Z. Ye, F.-R. Fan, B. Ren, and Z.-Q. Tian, “Distinctive enhanced and tunable plasmon resonant absorption from controllable Au@Cu2O nanoparticles: experimental and theoretical modeling,” J. Phys. Chem. C 116, 4477–4483 (2012).
[CrossRef]

Liu, B.-J.

D.-Y. Liu, S.-Y. Ding, H.-X. Lin, B.-J. Liu, Z.-Z. Ye, F.-R. Fan, B. Ren, and Z.-Q. Tian, “Distinctive enhanced and tunable plasmon resonant absorption from controllable Au@Cu2O nanoparticles: experimental and theoretical modeling,” J. Phys. Chem. C 116, 4477–4483 (2012).
[CrossRef]

Liu, D.-Y.

D.-Y. Liu, S.-Y. Ding, H.-X. Lin, B.-J. Liu, Z.-Z. Ye, F.-R. Fan, B. Ren, and Z.-Q. Tian, “Distinctive enhanced and tunable plasmon resonant absorption from controllable Au@Cu2O nanoparticles: experimental and theoretical modeling,” J. Phys. Chem. C 116, 4477–4483 (2012).
[CrossRef]

Liz-Marzán, L.

I. Pastoriza-Santos, D. Koktysh, A. Mamedov, M. Giersig, N. Kotov, and L. Liz-Marzán, “One-pot synthesis of Ag@TiO2 core-shell nanoparticles and their layer-by-layer assembly,” Langmuir 16, 2731–2735 (2000).
[CrossRef]

L. Liz-Marzán, M. Giersig, and P. Mulvaney, “Synthesis of nanosized gold-silica core-shell particles,” Langmuir 12, 4329–4335 (1996).
[CrossRef]

Lu, Y.

Y. Lu, Y. Yin, Z. Li, and Y. Xia, “Synthesis and self-assembly of Au@SiO2 core-shell colloids,” Nano Lett. 2, 785–788 (2002).
[CrossRef]

Maheu, B.

Mamedov, A.

I. Pastoriza-Santos, D. Koktysh, A. Mamedov, M. Giersig, N. Kotov, and L. Liz-Marzán, “One-pot synthesis of Ag@TiO2 core-shell nanoparticles and their layer-by-layer assembly,” Langmuir 16, 2731–2735 (2000).
[CrossRef]

Meier, M.

Mermin, N.

N. Ashcroft and N. Mermin, Solid State Physics, Thomson Learning (Saunders College, 1976).

Mie, G.

G. Mie, “Beiträge zur optik trüber medien, speziell kolloidaler metallösungen,” Ann. Phys. 330, 377–445 (1908).
[CrossRef]

Moroz, A.

Mulvaney, P.

L. Liz-Marzán, M. Giersig, and P. Mulvaney, “Synthesis of nanosized gold-silica core-shell particles,” Langmuir 12, 4329–4335 (1996).
[CrossRef]

Nagendra, C. L.

R. T. Tom, A. S. Nair, N. Singh, M. Aslam, C. L. Nagendra, R. Philip, K. Vijayamohanan, and T. Pradeep, “Freely dispersible Au@TiO2, Au@ZrO2, Ag@TiO2, and Ag@ZrO2 coreshell nanoparticles: one-step synthesis, characterization, spectroscopy, and optical limiting properties,” Langmuir 19, 3439–3445 (2003).
[CrossRef]

Nair, A. S.

R. T. Tom, A. S. Nair, N. Singh, M. Aslam, C. L. Nagendra, R. Philip, K. Vijayamohanan, and T. Pradeep, “Freely dispersible Au@TiO2, Au@ZrO2, Ag@TiO2, and Ag@ZrO2 coreshell nanoparticles: one-step synthesis, characterization, spectroscopy, and optical limiting properties,” Langmuir 19, 3439–3445 (2003).
[CrossRef]

Nassau, K.

Nieminen, R. M.

K. Laaksonen, S. Suomela, T. Ala-Nissila, and R. M. Nieminen, are preparing a manuscript to be called “Influence of high-refractive-index oxide core on optical properties of metal nanoshells.”

Niklasson, G.

W. Vargas, P. Greenwood, J. Otterstedt, and G. Niklasson, “Light scattering in pigmented coatings: experiments and theory,” Sol. Energy 68, 553–561 (2000).
[CrossRef]

G. Niklasson, “Modeling the optical properties of nanoparticles,” SPIE Newsroom, doi: 10.1117/2.1200603.0182 (2006).
[CrossRef]

Niklasson, G. A.

W. E. Vargas and G. A. Niklasson, “Pigment mass density and refractive index determination from optical measurements,” J. Phys. Condens. Matter 9, 1661–1669 (1997).
[CrossRef]

Oldenburg, S.

S. Oldenburg, R. Averitt, S. Westcott, and N. Halas, “Nanoengineering of optical resonances,” Chem. Phys. Lett. 288, 243–247 (1998).
[CrossRef]

Oldenburg, S. J.

S. J. Oldenburg, J. B. Jackson, S. L. Westcott, and N. J. Halas, “Infrared extinction properties of gold nanoshells,” Appl. Phys. Lett. 75, 2897–2899 (1999).
[CrossRef]

Otterstedt, J.

W. Vargas, P. Greenwood, J. Otterstedt, and G. Niklasson, “Light scattering in pigmented coatings: experiments and theory,” Sol. Energy 68, 553–561 (2000).
[CrossRef]

Pal, U.

Palik, E.

E. Palik and G. Ghosh, Handbook of Optical Constants of Solids (Academic, 1998).

Paria, S.

R. Ghosh Chaudhuri and S. Paria, “Core/shell nanoparticles: classes, properties, synthesis mechanisms, characterization, and applications,” Chem. Rev. 112, 2373–2433 (2012).
[CrossRef]

Pastoriza-Santos, I.

I. Pastoriza-Santos, D. Koktysh, A. Mamedov, M. Giersig, N. Kotov, and L. Liz-Marzán, “One-pot synthesis of Ag@TiO2 core-shell nanoparticles and their layer-by-layer assembly,” Langmuir 16, 2731–2735 (2000).
[CrossRef]

Peña, O.

Philip, R.

R. T. Tom, A. S. Nair, N. Singh, M. Aslam, C. L. Nagendra, R. Philip, K. Vijayamohanan, and T. Pradeep, “Freely dispersible Au@TiO2, Au@ZrO2, Ag@TiO2, and Ag@ZrO2 coreshell nanoparticles: one-step synthesis, characterization, spectroscopy, and optical limiting properties,” Langmuir 19, 3439–3445 (2003).
[CrossRef]

Pradeep, T.

R. T. Tom, A. S. Nair, N. Singh, M. Aslam, C. L. Nagendra, R. Philip, K. Vijayamohanan, and T. Pradeep, “Freely dispersible Au@TiO2, Au@ZrO2, Ag@TiO2, and Ag@ZrO2 coreshell nanoparticles: one-step synthesis, characterization, spectroscopy, and optical limiting properties,” Langmuir 19, 3439–3445 (2003).
[CrossRef]

Ren, B.

D.-Y. Liu, S.-Y. Ding, H.-X. Lin, B.-J. Liu, Z.-Z. Ye, F.-R. Fan, B. Ren, and Z.-Q. Tian, “Distinctive enhanced and tunable plasmon resonant absorption from controllable Au@Cu2O nanoparticles: experimental and theoretical modeling,” J. Phys. Chem. C 116, 4477–4483 (2012).
[CrossRef]

Rodríguez-Fernández, L.

Singh, N.

R. T. Tom, A. S. Nair, N. Singh, M. Aslam, C. L. Nagendra, R. Philip, K. Vijayamohanan, and T. Pradeep, “Freely dispersible Au@TiO2, Au@ZrO2, Ag@TiO2, and Ag@ZrO2 coreshell nanoparticles: one-step synthesis, characterization, spectroscopy, and optical limiting properties,” Langmuir 19, 3439–3445 (2003).
[CrossRef]

Suomela, S.

K. Laaksonen, S. Suomela, T. Ala-Nissila, and R. M. Nieminen, are preparing a manuscript to be called “Influence of high-refractive-index oxide core on optical properties of metal nanoshells.”

Tian, Z.-Q.

D.-Y. Liu, S.-Y. Ding, H.-X. Lin, B.-J. Liu, Z.-Z. Ye, F.-R. Fan, B. Ren, and Z.-Q. Tian, “Distinctive enhanced and tunable plasmon resonant absorption from controllable Au@Cu2O nanoparticles: experimental and theoretical modeling,” J. Phys. Chem. C 116, 4477–4483 (2012).
[CrossRef]

Tom, R. T.

R. T. Tom, A. S. Nair, N. Singh, M. Aslam, C. L. Nagendra, R. Philip, K. Vijayamohanan, and T. Pradeep, “Freely dispersible Au@TiO2, Au@ZrO2, Ag@TiO2, and Ag@ZrO2 coreshell nanoparticles: one-step synthesis, characterization, spectroscopy, and optical limiting properties,” Langmuir 19, 3439–3445 (2003).
[CrossRef]

Vargas, W.

W. Vargas, P. Greenwood, J. Otterstedt, and G. Niklasson, “Light scattering in pigmented coatings: experiments and theory,” Sol. Energy 68, 553–561 (2000).
[CrossRef]

W. Vargas, “Light scattering and absorption in pigmented coatings: theory and experiments,” Ph.D. thesis (Uppsala University, 1997).

Vargas, W. E.

W. E. Vargas, “Generalized four-flux radiative transfer model,” Appl. Opt. 37, 2615–2623 (1998).
[CrossRef]

W. E. Vargas and G. A. Niklasson, “Pigment mass density and refractive index determination from optical measurements,” J. Phys. Condens. Matter 9, 1661–1669 (1997).
[CrossRef]

Vijayamohanan, K.

R. T. Tom, A. S. Nair, N. Singh, M. Aslam, C. L. Nagendra, R. Philip, K. Vijayamohanan, and T. Pradeep, “Freely dispersible Au@TiO2, Au@ZrO2, Ag@TiO2, and Ag@ZrO2 coreshell nanoparticles: one-step synthesis, characterization, spectroscopy, and optical limiting properties,” Langmuir 19, 3439–3445 (2003).
[CrossRef]

Vollmer, M.

U. Kreibig and M. Vollmer, Optical Properties of Metal Clusters (Springer, 1995).

Westcott, S.

S. Oldenburg, R. Averitt, S. Westcott, and N. Halas, “Nanoengineering of optical resonances,” Chem. Phys. Lett. 288, 243–247 (1998).
[CrossRef]

Westcott, S. L.

S. J. Oldenburg, J. B. Jackson, S. L. Westcott, and N. J. Halas, “Infrared extinction properties of gold nanoshells,” Appl. Phys. Lett. 75, 2897–2899 (1999).
[CrossRef]

Wokaun, A.

M. Meier and A. Wokaun, “Enhanced fields on large metal particles: dynamic depolarization,” Opt. Lett. 8, 581–583 (1983).
[CrossRef]

A. Wokaun, J. Gordon, and P. Liao, “Radiation damping in surface-enhanced Raman scattering,” Phys. Rev. Lett. 48, 957–960 (1982).
[CrossRef]

Wood, D.

Xia, Y.

Y. Lu, Y. Yin, Z. Li, and Y. Xia, “Synthesis and self-assembly of Au@SiO2 core-shell colloids,” Nano Lett. 2, 785–788 (2002).
[CrossRef]

Ye, Z.-Z.

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Figures (7)

Fig. 1.
Fig. 1.

Selected examples of the Mie results for the absorption (Qabs) and extinction (Qext) efficiencies of core-shell particles with different shell and core materials. R denotes the core radius and t the shell thickness.

Fig. 2.
Fig. 2.

Positions and intensities (QExtMax) of the dipole SPR peaks as a function of shell thickness for the core-shell particles with an Au and Ag core of radius R. The superscript Max in the extinction efficiency QExtMax denotes the maximum intensity value of the peak.

Fig. 3.
Fig. 3.

Positions and intensities (QExtMax, i.e., the maximum intensity value of the peak) of the dipole SPR peaks as a function of shell thickness for the core-shell particles with a Cu core of radius R.

Fig. 4.
Fig. 4.

Extinctance (E) and absorptance (A) calculated by using the four-flux model for Ag-TiO2 [(a) and (c)] and Au-ZrO2 [(b) and (d)] nanoparticle dispersions with a core radius of 30 nm [(a) and (b)] and 50 nm [(c) and (d)] and a shell thickness of 0, 10, and 40 nm. The extinctance (E) is given by E=1T, where T is the transmittance. The four-flux calculations were carried out assuming a coating thickness of 10 μm and a constant particle volume fraction of 0.002.

Fig. 5.
Fig. 5.

Results of an effective refractive index of the medium model Eq. (24), lines compared to the Mie results (points) of Ag-TiO2 (a) and Au-ZrO2 (b) for core radii of 5, 10, 20, 30, and 40 nm as the shell thicknesses vary between 0 and 100 nm.

Fig. 6.
Fig. 6.

Positions and intensities (QExtMax) of the dipole SPR peaks as a function of shell thickness for the core-shell particles with an Au and Ag core of radius R. The superscript Max in the extinction efficiency QExtMax denotes the maximum intensity value of the peak. The refractive index of the surrounding medium is set to 1.5.

Fig. 7.
Fig. 7.

Positions and intensities (QExtMax, i.e., the maximum intensity value of the peak) of the dipole SPR peaks as a function of shell thickness for the core-shell particles with a Cu core of radius R. The refractive index of the surrounding medium is set to 1.5.

Tables (1)

Tables Icon

Table 1. Values Used for the Parameters of the Core Materials Needed in the Mie Calculations

Equations (25)

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εbulk(ω)=εfree(ω)+χIB(ω),
εfree(ω)=1ωp2ω2+iΓω,
Γ=vF,ωp=Nce2ε0meff,
Γ(R)=Γ+A0vFR,
ε(ω)=εbulk(ω)+ωp2ω2+iΓωωp2ω2+iΓ(R)ω,
x=|k|R=2πnmλR,m=nnm,
σext=2π|k|2L=1(2L+1)Re{aL+bL},
σsca=2π|k|2L=1(2L+1)(|aL|2+|bL|2),
σabs=σextσsca,
aL=mψL(mx)ψL(x)ψL(mx)ψL(x)mψL(mx)ξL(x)ψL(mx)ξL(x),
bL=ψL(mx)ψL(x)mψL(mx)ψL(x)ψL(mx)ξL(x)mψL(mx)ξL(x).
aL=ψLf(AL)m2ψL(y)g(AL)ξL(y)f(AL)m2ξLg(AL),
bL=m2ψnf(BL)ψL(y)g(BL)m2ξL(y)f(BL)ξLg(BL),
AL=m2ψL(m2x)ψL(m1x)m1ψL(m2x)ψL(m1x)m2χL(m2x)ψL(m1x)m1χL(m2x)ψL(m1x),
BL=m2ψL(m1x)ψL(m2x)m1ψL(m1x)ψL(m2x)m2χL(m2x)ψL(m1x)m1ψL(m1x)χL(m2x),
f(XL)=ψL(m2y)XLχL(m2y),
g(XL)=ψL(m2y)XLχL(m2y),
dIcdz=(α+β)Ic,
dJcdz=(α+β)Jc,
dIddz=ξβIdξ(1σd)αId+ξ(1σd)αJd+σcαIc+(1σc)αJc,
dJddz=ξβId+ξ(1σd)αJdξ(1σd)αIdσcαJc(1σc)αIc,
a1=i2x33(εεm)(1(εεm+1)x210)ε+2εm(εεm)(εεm+10)x210i2x33(εεm).
ε1[224+ε2210x223ε2x3],
ε1cs[224+(ε2cs)210x223ε2csx3],
εeff=ε2[εshell(1f)+εm(2+f)εshell(2f+1)+2εm(1f)],

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