Abstract

We investigate plasmon resonances in gold nanoparticles to enhance the quantum yield of upconverting materials. For this purpose, we use a rate equation model that describes the upconversion of trivalent erbium based upconverters. Changes of the optical field acting on the upconverter and the changes to the transition probabilities of the upconverter in the proximity of a gold nanoparticle are calculated using Mie theory and exact electrodynamic theory respectively. With this data, the influence on the luminescence of the upconverter is determined using the rate equation model. The results show that upconversion luminescence can be increased in the proximity of a spherical gold nanoparticle due to the change in the optical field and the modification of the transition rates.

© 2011 OSA

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Errata

Stefan Fischer, Florian Hallermann, Toni Eichelkraut, Gero von Plessen, Karl W. Krämer, Daniel Biner, Heiko Steinkemper, Martin Hermle, and Jan Christoph Goldschmidt, "Plasmon enhanced upconversion luminescence near gold nanoparticles – simulation and analysis of the interactions: Errata," Opt. Express 21, 10606-10611 (2013)
https://www.osapublishing.org/oe/abstract.cfm?uri=oe-21-9-10606

References

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  28. B. R. Judd, “Optical absorption intensities of rare-earth ions,” Phys. Rev. 127(3), 750–761 (1962).
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    [CrossRef]
  32. H. Mertens, A. F. Koenderink, and A. Polman, “Plasmon-enhanced luminescence near noble-metal nanospheres: Comparison of exact theory and an improved Gersten and Nitzan model,” Phys. Rev. B 76(11), 115123 (2007).
    [CrossRef]
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    [CrossRef]

2011 (3)

J. C. Goldschmidt, S. Fischer, P. Löper, K. W. Krämer, D. Biner, M. Hermle, and S. W. Glunz, “Experimental analysis of upconversion with both coherent monochromatic irradiation and broad spectrum illumination,” Sol. Energy Mater. Sol. Cells 95(7), 1960–1963 (2011).
[CrossRef]

J. T. van Wijngaarden, M. M. van Schooneveld, C. de Mello Donegá, and A. Meijerink, “Enhancement of the decay rate by plasmon coupling for Eu 3+ in an Au nanoparticle model system,” Europhys. Lett. 93(5), 57005 (2011).
[CrossRef]

N. Liu, W. Qin, G. Qin, T. Jiang, and D. Zhao, “Highly plasmon-enhanced upconversion emissions from Au@β-NaYF4:Yb,Tm hybrid nanostructures,” Chem. Commun. (Camb.) 47(27), 7671–7673 (2011).
[CrossRef] [PubMed]

2010 (3)

S. Schietinger, T. Aichele, H.-Q. Wang, T. Nann, and O. Benson, “Plasmon-enhanced upconversion in single NaYF4:Yb3+/Er3+ codoped nanocrystals,” Nano Lett. 10(1), 134–138 (2010).
[CrossRef] [PubMed]

H. Zhang, Y. Li, I. A. Ivanov, Y. Qu, Y. Huang, and X. Duan, “Plasmonic Modulation of the Upconversion Fluorescence in NaYF4:Yb/Tm Hexaplate Nanocrystals Using Gold Nanoparticles or Nanoshells,” Angew. Chem. Int. Ed. 49, 2865–2868 (2010).

S. Fischer, J. C. Goldschmidt, P. Löper, G. H. Bauer, R. Brüggemann, K. Krämer, D. Biner, M. Hermle, and S. W. Glunz, “Enhancement of silicon solar cell efficiency by upconversion: Optical and electrical characterization,” J. Appl. Phys. 108(4), 044912 (2010).
[CrossRef]

2008 (1)

F. Hallermann, C. Rockstuhl, S. Fahr, G. Seifert, S. Wackerow, H. Graener, G. Plessen, and F. Lederer, “On the use of localized plasmon polaritons in solar cells,” Phys. Status Solidi A 205(12), 2844–2861 (2008).
[CrossRef]

2007 (6)

B. S. Richards and A. Shalav, “Enhancing the near-infrared spectral response of silicon optoelectronic devices via up-conversion,” IEEE Trans. Electron. Dev. 54(10), 2679–2684 (2007).
[CrossRef]

F. Kaminski, V. Sandoghdar, and M. Agio, “Finite-Difference Time-Domain Modeling of Decay Rates in the Near Field of Metal Nanostructures,” J. Comput. Theor. Nanosci. 4, 635–643 (2007).

G. Sun, J. B. Khurgin, and R. A. Soref, “Practicable enhancement of spontaneous emission using surface plasmons,” Appl. Phys. Lett. 90(11), 111107 (2007).
[CrossRef]

O. L. Muskens, V. Giannini, J. A. Sanchez-Gil, and J. Gómez Rivas, “Strong enhancement of the radiative decay rate of emitters by single plasmonic nanoantennas,” Nano Lett. 7(9), 2871–2875 (2007).
[CrossRef] [PubMed]

A. Shalav, B. S. Richards, and M. A. Green, “Luminescent layers for enhanced silicon solar cell performance: up-conversion,” Sol. Energy Mater. Sol. Cells 91(9), 829–842 (2007).
[CrossRef]

H. Mertens, A. F. Koenderink, and A. Polman, “Plasmon-enhanced luminescence near noble-metal nanospheres: Comparison of exact theory and an improved Gersten and Nitzan model,” Phys. Rev. B 76(11), 115123 (2007).
[CrossRef]

2006 (2)

H. Mertens and A. Polman, “Plasmon-enhanced erbium luminescence,” Appl. Phys. Lett. 89(21), 211107 (2006).
[CrossRef]

T. Trupke, A. Shalav, B. S. Richards, P. Würfel, and M. A. Green, “Efficiency enhancement of solar cells by luminescent up-conversion of sunlight,” Sol. Energy Mater. Sol. Cells 90(18-19), 3327–3338 (2006).
[CrossRef]

2005 (2)

P. Johansson, H. Xu, and M. Käll, “Surface-enhanced Raman scattering and fluorescence near metal nanoparticles,” Phys. Rev. B 72(3), 035427 (2005).
[CrossRef]

J. F. Suyver, A. Aebischer, S. Garcia-Revilla, P. Gerner, and H. U. Güdel, “Anomalous power dependence of sensitized upconversion luminescence,” Phys. Rev. B 71(12), 125123 (2005).
[CrossRef]

2004 (3)

L. Yang and B. Kruse, “Revised Kubelka-Munk theory. I. Theory and application,” J. Opt. Soc. Am. A 21(10), 1933–1941 (2004).
[CrossRef] [PubMed]

F. Auzel, “Upconversion and anti-Stokes processes with f and d ions in solids,” Chem. Rev. 104(1), 139–174 (2004).
[CrossRef] [PubMed]

K. W. Krämer, D. Biner, G. Frei, H. U. Güdel, M. P. Hehlen, and S. R. Lüthi, “Hexagonal sodium yttrium fluoride based green and blue emitting upconversion phosphors,” Chem. Mater. 16(7), 1244–1251 (2004).
[CrossRef]

2002 (1)

T. Trupke, M. A. Green, and P. Würfel, “Improving solar cell efficiencies by up-conversion of sub-band-gap light,” J. Appl. Phys. 92(7), 4117–4122 (2002).
[CrossRef]

2000 (1)

M. Pollnau, D. R. Gamelin, S. R. Lüthi, H. U. Güdel, and M. P. Hehlen, “Power dependence of upconversion luminescence in lanthanide and transition-metal-ion systems,” Phys. Rev. B 61(5), 3337–3346 (2000).
[CrossRef]

1996 (1)

P. Gibart, F. Auzel, J. C. Guillaume, and K. Zahraman, “Below band-gap IR response of substrate-free GaAs solar cells using two- photon up-conversion,” Jpn. J. Appl. Phys. 35, 4401–4402 (1996).
[CrossRef]

1988 (1)

Y. S. Kim, P. T. Leung, and T. F. George, “Classical decay rates for molecules in the presence of a spherical surface: A complete treatment,” Surf. Sci. 195(1-2), 1–14 (1988).
[CrossRef]

1987 (1)

O. L. Malta, P. A. Santa-Cruz, G. F. de Sa´, and F. Auzel, “Up-conversion yield in glass ceramics containing silver,” J. Solid State Chem. 68(2), 314–319 (1987).
[CrossRef]

1981 (1)

J. Gersten and A. Nitzan, “Spectroscopic properties of molecules interacting with small dielectric particles,” J. Chem. Phys. 75(3), 1139–1152 (1981).
[CrossRef]

1962 (2)

B. R. Judd, “Optical absorption intensities of rare-earth ions,” Phys. Rev. 127(3), 750–761 (1962).
[CrossRef]

G. S. Ofelt, “Intensities of crystal spectra of rare-earth ions,” J. Chem. Phys. 37(3), 511–520 (1962).
[CrossRef]

1961 (1)

W. Shockley and H. J. Queisser, “Detailed balance limit of efficiency of p-n junction solar cells,” J. Appl. Phys. 32(3), 510–519 (1961).
[CrossRef]

1931 (1)

P. Kubelka and F. Munk, “Ein Beitrag zur Optik der Farbanstriche,” Zeitschrift für technische Physik 11, 593–601 (1931).

1917 (1)

A. Einstein, “Zur Quantentheorie der Strahlung,” Phys. Z. 18, 121–128 (1917).

Aebischer, A.

J. F. Suyver, A. Aebischer, S. Garcia-Revilla, P. Gerner, and H. U. Güdel, “Anomalous power dependence of sensitized upconversion luminescence,” Phys. Rev. B 71(12), 125123 (2005).
[CrossRef]

Agio, M.

F. Kaminski, V. Sandoghdar, and M. Agio, “Finite-Difference Time-Domain Modeling of Decay Rates in the Near Field of Metal Nanostructures,” J. Comput. Theor. Nanosci. 4, 635–643 (2007).

Aichele, T.

S. Schietinger, T. Aichele, H.-Q. Wang, T. Nann, and O. Benson, “Plasmon-enhanced upconversion in single NaYF4:Yb3+/Er3+ codoped nanocrystals,” Nano Lett. 10(1), 134–138 (2010).
[CrossRef] [PubMed]

Auzel, F.

F. Auzel, “Upconversion and anti-Stokes processes with f and d ions in solids,” Chem. Rev. 104(1), 139–174 (2004).
[CrossRef] [PubMed]

P. Gibart, F. Auzel, J. C. Guillaume, and K. Zahraman, “Below band-gap IR response of substrate-free GaAs solar cells using two- photon up-conversion,” Jpn. J. Appl. Phys. 35, 4401–4402 (1996).
[CrossRef]

O. L. Malta, P. A. Santa-Cruz, G. F. de Sa´, and F. Auzel, “Up-conversion yield in glass ceramics containing silver,” J. Solid State Chem. 68(2), 314–319 (1987).
[CrossRef]

Bauer, G. H.

S. Fischer, J. C. Goldschmidt, P. Löper, G. H. Bauer, R. Brüggemann, K. Krämer, D. Biner, M. Hermle, and S. W. Glunz, “Enhancement of silicon solar cell efficiency by upconversion: Optical and electrical characterization,” J. Appl. Phys. 108(4), 044912 (2010).
[CrossRef]

Benson, O.

S. Schietinger, T. Aichele, H.-Q. Wang, T. Nann, and O. Benson, “Plasmon-enhanced upconversion in single NaYF4:Yb3+/Er3+ codoped nanocrystals,” Nano Lett. 10(1), 134–138 (2010).
[CrossRef] [PubMed]

Biner, D.

J. C. Goldschmidt, S. Fischer, P. Löper, K. W. Krämer, D. Biner, M. Hermle, and S. W. Glunz, “Experimental analysis of upconversion with both coherent monochromatic irradiation and broad spectrum illumination,” Sol. Energy Mater. Sol. Cells 95(7), 1960–1963 (2011).
[CrossRef]

S. Fischer, J. C. Goldschmidt, P. Löper, G. H. Bauer, R. Brüggemann, K. Krämer, D. Biner, M. Hermle, and S. W. Glunz, “Enhancement of silicon solar cell efficiency by upconversion: Optical and electrical characterization,” J. Appl. Phys. 108(4), 044912 (2010).
[CrossRef]

K. W. Krämer, D. Biner, G. Frei, H. U. Güdel, M. P. Hehlen, and S. R. Lüthi, “Hexagonal sodium yttrium fluoride based green and blue emitting upconversion phosphors,” Chem. Mater. 16(7), 1244–1251 (2004).
[CrossRef]

Brüggemann, R.

S. Fischer, J. C. Goldschmidt, P. Löper, G. H. Bauer, R. Brüggemann, K. Krämer, D. Biner, M. Hermle, and S. W. Glunz, “Enhancement of silicon solar cell efficiency by upconversion: Optical and electrical characterization,” J. Appl. Phys. 108(4), 044912 (2010).
[CrossRef]

de Mello Donegá, C.

J. T. van Wijngaarden, M. M. van Schooneveld, C. de Mello Donegá, and A. Meijerink, “Enhancement of the decay rate by plasmon coupling for Eu 3+ in an Au nanoparticle model system,” Europhys. Lett. 93(5), 57005 (2011).
[CrossRef]

de Sa´, G. F.

O. L. Malta, P. A. Santa-Cruz, G. F. de Sa´, and F. Auzel, “Up-conversion yield in glass ceramics containing silver,” J. Solid State Chem. 68(2), 314–319 (1987).
[CrossRef]

Duan, X.

H. Zhang, Y. Li, I. A. Ivanov, Y. Qu, Y. Huang, and X. Duan, “Plasmonic Modulation of the Upconversion Fluorescence in NaYF4:Yb/Tm Hexaplate Nanocrystals Using Gold Nanoparticles or Nanoshells,” Angew. Chem. Int. Ed. 49, 2865–2868 (2010).

Einstein, A.

A. Einstein, “Zur Quantentheorie der Strahlung,” Phys. Z. 18, 121–128 (1917).

Fahr, S.

F. Hallermann, C. Rockstuhl, S. Fahr, G. Seifert, S. Wackerow, H. Graener, G. Plessen, and F. Lederer, “On the use of localized plasmon polaritons in solar cells,” Phys. Status Solidi A 205(12), 2844–2861 (2008).
[CrossRef]

Fischer, S.

J. C. Goldschmidt, S. Fischer, P. Löper, K. W. Krämer, D. Biner, M. Hermle, and S. W. Glunz, “Experimental analysis of upconversion with both coherent monochromatic irradiation and broad spectrum illumination,” Sol. Energy Mater. Sol. Cells 95(7), 1960–1963 (2011).
[CrossRef]

S. Fischer, J. C. Goldschmidt, P. Löper, G. H. Bauer, R. Brüggemann, K. Krämer, D. Biner, M. Hermle, and S. W. Glunz, “Enhancement of silicon solar cell efficiency by upconversion: Optical and electrical characterization,” J. Appl. Phys. 108(4), 044912 (2010).
[CrossRef]

Frei, G.

K. W. Krämer, D. Biner, G. Frei, H. U. Güdel, M. P. Hehlen, and S. R. Lüthi, “Hexagonal sodium yttrium fluoride based green and blue emitting upconversion phosphors,” Chem. Mater. 16(7), 1244–1251 (2004).
[CrossRef]

Gamelin, D. R.

M. Pollnau, D. R. Gamelin, S. R. Lüthi, H. U. Güdel, and M. P. Hehlen, “Power dependence of upconversion luminescence in lanthanide and transition-metal-ion systems,” Phys. Rev. B 61(5), 3337–3346 (2000).
[CrossRef]

Garcia-Revilla, S.

J. F. Suyver, A. Aebischer, S. Garcia-Revilla, P. Gerner, and H. U. Güdel, “Anomalous power dependence of sensitized upconversion luminescence,” Phys. Rev. B 71(12), 125123 (2005).
[CrossRef]

George, T. F.

Y. S. Kim, P. T. Leung, and T. F. George, “Classical decay rates for molecules in the presence of a spherical surface: A complete treatment,” Surf. Sci. 195(1-2), 1–14 (1988).
[CrossRef]

Gerner, P.

J. F. Suyver, A. Aebischer, S. Garcia-Revilla, P. Gerner, and H. U. Güdel, “Anomalous power dependence of sensitized upconversion luminescence,” Phys. Rev. B 71(12), 125123 (2005).
[CrossRef]

Gersten, J.

J. Gersten and A. Nitzan, “Spectroscopic properties of molecules interacting with small dielectric particles,” J. Chem. Phys. 75(3), 1139–1152 (1981).
[CrossRef]

Giannini, V.

O. L. Muskens, V. Giannini, J. A. Sanchez-Gil, and J. Gómez Rivas, “Strong enhancement of the radiative decay rate of emitters by single plasmonic nanoantennas,” Nano Lett. 7(9), 2871–2875 (2007).
[CrossRef] [PubMed]

Gibart, P.

P. Gibart, F. Auzel, J. C. Guillaume, and K. Zahraman, “Below band-gap IR response of substrate-free GaAs solar cells using two- photon up-conversion,” Jpn. J. Appl. Phys. 35, 4401–4402 (1996).
[CrossRef]

Glunz, S. W.

J. C. Goldschmidt, S. Fischer, P. Löper, K. W. Krämer, D. Biner, M. Hermle, and S. W. Glunz, “Experimental analysis of upconversion with both coherent monochromatic irradiation and broad spectrum illumination,” Sol. Energy Mater. Sol. Cells 95(7), 1960–1963 (2011).
[CrossRef]

S. Fischer, J. C. Goldschmidt, P. Löper, G. H. Bauer, R. Brüggemann, K. Krämer, D. Biner, M. Hermle, and S. W. Glunz, “Enhancement of silicon solar cell efficiency by upconversion: Optical and electrical characterization,” J. Appl. Phys. 108(4), 044912 (2010).
[CrossRef]

Goldschmidt, J. C.

J. C. Goldschmidt, S. Fischer, P. Löper, K. W. Krämer, D. Biner, M. Hermle, and S. W. Glunz, “Experimental analysis of upconversion with both coherent monochromatic irradiation and broad spectrum illumination,” Sol. Energy Mater. Sol. Cells 95(7), 1960–1963 (2011).
[CrossRef]

S. Fischer, J. C. Goldschmidt, P. Löper, G. H. Bauer, R. Brüggemann, K. Krämer, D. Biner, M. Hermle, and S. W. Glunz, “Enhancement of silicon solar cell efficiency by upconversion: Optical and electrical characterization,” J. Appl. Phys. 108(4), 044912 (2010).
[CrossRef]

Gómez Rivas, J.

O. L. Muskens, V. Giannini, J. A. Sanchez-Gil, and J. Gómez Rivas, “Strong enhancement of the radiative decay rate of emitters by single plasmonic nanoantennas,” Nano Lett. 7(9), 2871–2875 (2007).
[CrossRef] [PubMed]

Graener, H.

F. Hallermann, C. Rockstuhl, S. Fahr, G. Seifert, S. Wackerow, H. Graener, G. Plessen, and F. Lederer, “On the use of localized plasmon polaritons in solar cells,” Phys. Status Solidi A 205(12), 2844–2861 (2008).
[CrossRef]

Green, M. A.

A. Shalav, B. S. Richards, and M. A. Green, “Luminescent layers for enhanced silicon solar cell performance: up-conversion,” Sol. Energy Mater. Sol. Cells 91(9), 829–842 (2007).
[CrossRef]

T. Trupke, A. Shalav, B. S. Richards, P. Würfel, and M. A. Green, “Efficiency enhancement of solar cells by luminescent up-conversion of sunlight,” Sol. Energy Mater. Sol. Cells 90(18-19), 3327–3338 (2006).
[CrossRef]

T. Trupke, M. A. Green, and P. Würfel, “Improving solar cell efficiencies by up-conversion of sub-band-gap light,” J. Appl. Phys. 92(7), 4117–4122 (2002).
[CrossRef]

Güdel, H. U.

J. F. Suyver, A. Aebischer, S. Garcia-Revilla, P. Gerner, and H. U. Güdel, “Anomalous power dependence of sensitized upconversion luminescence,” Phys. Rev. B 71(12), 125123 (2005).
[CrossRef]

K. W. Krämer, D. Biner, G. Frei, H. U. Güdel, M. P. Hehlen, and S. R. Lüthi, “Hexagonal sodium yttrium fluoride based green and blue emitting upconversion phosphors,” Chem. Mater. 16(7), 1244–1251 (2004).
[CrossRef]

M. Pollnau, D. R. Gamelin, S. R. Lüthi, H. U. Güdel, and M. P. Hehlen, “Power dependence of upconversion luminescence in lanthanide and transition-metal-ion systems,” Phys. Rev. B 61(5), 3337–3346 (2000).
[CrossRef]

Guillaume, J. C.

P. Gibart, F. Auzel, J. C. Guillaume, and K. Zahraman, “Below band-gap IR response of substrate-free GaAs solar cells using two- photon up-conversion,” Jpn. J. Appl. Phys. 35, 4401–4402 (1996).
[CrossRef]

Hallermann, F.

F. Hallermann, C. Rockstuhl, S. Fahr, G. Seifert, S. Wackerow, H. Graener, G. Plessen, and F. Lederer, “On the use of localized plasmon polaritons in solar cells,” Phys. Status Solidi A 205(12), 2844–2861 (2008).
[CrossRef]

Hehlen, M. P.

K. W. Krämer, D. Biner, G. Frei, H. U. Güdel, M. P. Hehlen, and S. R. Lüthi, “Hexagonal sodium yttrium fluoride based green and blue emitting upconversion phosphors,” Chem. Mater. 16(7), 1244–1251 (2004).
[CrossRef]

M. Pollnau, D. R. Gamelin, S. R. Lüthi, H. U. Güdel, and M. P. Hehlen, “Power dependence of upconversion luminescence in lanthanide and transition-metal-ion systems,” Phys. Rev. B 61(5), 3337–3346 (2000).
[CrossRef]

Hermle, M.

J. C. Goldschmidt, S. Fischer, P. Löper, K. W. Krämer, D. Biner, M. Hermle, and S. W. Glunz, “Experimental analysis of upconversion with both coherent monochromatic irradiation and broad spectrum illumination,” Sol. Energy Mater. Sol. Cells 95(7), 1960–1963 (2011).
[CrossRef]

S. Fischer, J. C. Goldschmidt, P. Löper, G. H. Bauer, R. Brüggemann, K. Krämer, D. Biner, M. Hermle, and S. W. Glunz, “Enhancement of silicon solar cell efficiency by upconversion: Optical and electrical characterization,” J. Appl. Phys. 108(4), 044912 (2010).
[CrossRef]

Huang, Y.

H. Zhang, Y. Li, I. A. Ivanov, Y. Qu, Y. Huang, and X. Duan, “Plasmonic Modulation of the Upconversion Fluorescence in NaYF4:Yb/Tm Hexaplate Nanocrystals Using Gold Nanoparticles or Nanoshells,” Angew. Chem. Int. Ed. 49, 2865–2868 (2010).

Ivanov, I. A.

H. Zhang, Y. Li, I. A. Ivanov, Y. Qu, Y. Huang, and X. Duan, “Plasmonic Modulation of the Upconversion Fluorescence in NaYF4:Yb/Tm Hexaplate Nanocrystals Using Gold Nanoparticles or Nanoshells,” Angew. Chem. Int. Ed. 49, 2865–2868 (2010).

Jiang, T.

N. Liu, W. Qin, G. Qin, T. Jiang, and D. Zhao, “Highly plasmon-enhanced upconversion emissions from Au@β-NaYF4:Yb,Tm hybrid nanostructures,” Chem. Commun. (Camb.) 47(27), 7671–7673 (2011).
[CrossRef] [PubMed]

Johansson, P.

P. Johansson, H. Xu, and M. Käll, “Surface-enhanced Raman scattering and fluorescence near metal nanoparticles,” Phys. Rev. B 72(3), 035427 (2005).
[CrossRef]

Judd, B. R.

B. R. Judd, “Optical absorption intensities of rare-earth ions,” Phys. Rev. 127(3), 750–761 (1962).
[CrossRef]

Käll, M.

P. Johansson, H. Xu, and M. Käll, “Surface-enhanced Raman scattering and fluorescence near metal nanoparticles,” Phys. Rev. B 72(3), 035427 (2005).
[CrossRef]

Kaminski, F.

F. Kaminski, V. Sandoghdar, and M. Agio, “Finite-Difference Time-Domain Modeling of Decay Rates in the Near Field of Metal Nanostructures,” J. Comput. Theor. Nanosci. 4, 635–643 (2007).

Khurgin, J. B.

G. Sun, J. B. Khurgin, and R. A. Soref, “Practicable enhancement of spontaneous emission using surface plasmons,” Appl. Phys. Lett. 90(11), 111107 (2007).
[CrossRef]

Kim, Y. S.

Y. S. Kim, P. T. Leung, and T. F. George, “Classical decay rates for molecules in the presence of a spherical surface: A complete treatment,” Surf. Sci. 195(1-2), 1–14 (1988).
[CrossRef]

Koenderink, A. F.

H. Mertens, A. F. Koenderink, and A. Polman, “Plasmon-enhanced luminescence near noble-metal nanospheres: Comparison of exact theory and an improved Gersten and Nitzan model,” Phys. Rev. B 76(11), 115123 (2007).
[CrossRef]

Krämer, K.

S. Fischer, J. C. Goldschmidt, P. Löper, G. H. Bauer, R. Brüggemann, K. Krämer, D. Biner, M. Hermle, and S. W. Glunz, “Enhancement of silicon solar cell efficiency by upconversion: Optical and electrical characterization,” J. Appl. Phys. 108(4), 044912 (2010).
[CrossRef]

Krämer, K. W.

J. C. Goldschmidt, S. Fischer, P. Löper, K. W. Krämer, D. Biner, M. Hermle, and S. W. Glunz, “Experimental analysis of upconversion with both coherent monochromatic irradiation and broad spectrum illumination,” Sol. Energy Mater. Sol. Cells 95(7), 1960–1963 (2011).
[CrossRef]

K. W. Krämer, D. Biner, G. Frei, H. U. Güdel, M. P. Hehlen, and S. R. Lüthi, “Hexagonal sodium yttrium fluoride based green and blue emitting upconversion phosphors,” Chem. Mater. 16(7), 1244–1251 (2004).
[CrossRef]

Kruse, B.

Kubelka, P.

P. Kubelka and F. Munk, “Ein Beitrag zur Optik der Farbanstriche,” Zeitschrift für technische Physik 11, 593–601 (1931).

Lederer, F.

F. Hallermann, C. Rockstuhl, S. Fahr, G. Seifert, S. Wackerow, H. Graener, G. Plessen, and F. Lederer, “On the use of localized plasmon polaritons in solar cells,” Phys. Status Solidi A 205(12), 2844–2861 (2008).
[CrossRef]

Leung, P. T.

Y. S. Kim, P. T. Leung, and T. F. George, “Classical decay rates for molecules in the presence of a spherical surface: A complete treatment,” Surf. Sci. 195(1-2), 1–14 (1988).
[CrossRef]

Li, Y.

H. Zhang, Y. Li, I. A. Ivanov, Y. Qu, Y. Huang, and X. Duan, “Plasmonic Modulation of the Upconversion Fluorescence in NaYF4:Yb/Tm Hexaplate Nanocrystals Using Gold Nanoparticles or Nanoshells,” Angew. Chem. Int. Ed. 49, 2865–2868 (2010).

Liu, N.

N. Liu, W. Qin, G. Qin, T. Jiang, and D. Zhao, “Highly plasmon-enhanced upconversion emissions from Au@β-NaYF4:Yb,Tm hybrid nanostructures,” Chem. Commun. (Camb.) 47(27), 7671–7673 (2011).
[CrossRef] [PubMed]

Löper, P.

J. C. Goldschmidt, S. Fischer, P. Löper, K. W. Krämer, D. Biner, M. Hermle, and S. W. Glunz, “Experimental analysis of upconversion with both coherent monochromatic irradiation and broad spectrum illumination,” Sol. Energy Mater. Sol. Cells 95(7), 1960–1963 (2011).
[CrossRef]

S. Fischer, J. C. Goldschmidt, P. Löper, G. H. Bauer, R. Brüggemann, K. Krämer, D. Biner, M. Hermle, and S. W. Glunz, “Enhancement of silicon solar cell efficiency by upconversion: Optical and electrical characterization,” J. Appl. Phys. 108(4), 044912 (2010).
[CrossRef]

Lüthi, S. R.

K. W. Krämer, D. Biner, G. Frei, H. U. Güdel, M. P. Hehlen, and S. R. Lüthi, “Hexagonal sodium yttrium fluoride based green and blue emitting upconversion phosphors,” Chem. Mater. 16(7), 1244–1251 (2004).
[CrossRef]

M. Pollnau, D. R. Gamelin, S. R. Lüthi, H. U. Güdel, and M. P. Hehlen, “Power dependence of upconversion luminescence in lanthanide and transition-metal-ion systems,” Phys. Rev. B 61(5), 3337–3346 (2000).
[CrossRef]

Malta, O. L.

O. L. Malta, P. A. Santa-Cruz, G. F. de Sa´, and F. Auzel, “Up-conversion yield in glass ceramics containing silver,” J. Solid State Chem. 68(2), 314–319 (1987).
[CrossRef]

Meijerink, A.

J. T. van Wijngaarden, M. M. van Schooneveld, C. de Mello Donegá, and A. Meijerink, “Enhancement of the decay rate by plasmon coupling for Eu 3+ in an Au nanoparticle model system,” Europhys. Lett. 93(5), 57005 (2011).
[CrossRef]

Mertens, H.

H. Mertens, A. F. Koenderink, and A. Polman, “Plasmon-enhanced luminescence near noble-metal nanospheres: Comparison of exact theory and an improved Gersten and Nitzan model,” Phys. Rev. B 76(11), 115123 (2007).
[CrossRef]

H. Mertens and A. Polman, “Plasmon-enhanced erbium luminescence,” Appl. Phys. Lett. 89(21), 211107 (2006).
[CrossRef]

Munk, F.

P. Kubelka and F. Munk, “Ein Beitrag zur Optik der Farbanstriche,” Zeitschrift für technische Physik 11, 593–601 (1931).

Muskens, O. L.

O. L. Muskens, V. Giannini, J. A. Sanchez-Gil, and J. Gómez Rivas, “Strong enhancement of the radiative decay rate of emitters by single plasmonic nanoantennas,” Nano Lett. 7(9), 2871–2875 (2007).
[CrossRef] [PubMed]

Nann, T.

S. Schietinger, T. Aichele, H.-Q. Wang, T. Nann, and O. Benson, “Plasmon-enhanced upconversion in single NaYF4:Yb3+/Er3+ codoped nanocrystals,” Nano Lett. 10(1), 134–138 (2010).
[CrossRef] [PubMed]

Nitzan, A.

J. Gersten and A. Nitzan, “Spectroscopic properties of molecules interacting with small dielectric particles,” J. Chem. Phys. 75(3), 1139–1152 (1981).
[CrossRef]

Ofelt, G. S.

G. S. Ofelt, “Intensities of crystal spectra of rare-earth ions,” J. Chem. Phys. 37(3), 511–520 (1962).
[CrossRef]

Plessen, G.

F. Hallermann, C. Rockstuhl, S. Fahr, G. Seifert, S. Wackerow, H. Graener, G. Plessen, and F. Lederer, “On the use of localized plasmon polaritons in solar cells,” Phys. Status Solidi A 205(12), 2844–2861 (2008).
[CrossRef]

Pollnau, M.

M. Pollnau, D. R. Gamelin, S. R. Lüthi, H. U. Güdel, and M. P. Hehlen, “Power dependence of upconversion luminescence in lanthanide and transition-metal-ion systems,” Phys. Rev. B 61(5), 3337–3346 (2000).
[CrossRef]

Polman, A.

H. Mertens, A. F. Koenderink, and A. Polman, “Plasmon-enhanced luminescence near noble-metal nanospheres: Comparison of exact theory and an improved Gersten and Nitzan model,” Phys. Rev. B 76(11), 115123 (2007).
[CrossRef]

H. Mertens and A. Polman, “Plasmon-enhanced erbium luminescence,” Appl. Phys. Lett. 89(21), 211107 (2006).
[CrossRef]

Qin, G.

N. Liu, W. Qin, G. Qin, T. Jiang, and D. Zhao, “Highly plasmon-enhanced upconversion emissions from Au@β-NaYF4:Yb,Tm hybrid nanostructures,” Chem. Commun. (Camb.) 47(27), 7671–7673 (2011).
[CrossRef] [PubMed]

Qin, W.

N. Liu, W. Qin, G. Qin, T. Jiang, and D. Zhao, “Highly plasmon-enhanced upconversion emissions from Au@β-NaYF4:Yb,Tm hybrid nanostructures,” Chem. Commun. (Camb.) 47(27), 7671–7673 (2011).
[CrossRef] [PubMed]

Qu, Y.

H. Zhang, Y. Li, I. A. Ivanov, Y. Qu, Y. Huang, and X. Duan, “Plasmonic Modulation of the Upconversion Fluorescence in NaYF4:Yb/Tm Hexaplate Nanocrystals Using Gold Nanoparticles or Nanoshells,” Angew. Chem. Int. Ed. 49, 2865–2868 (2010).

Queisser, H. J.

W. Shockley and H. J. Queisser, “Detailed balance limit of efficiency of p-n junction solar cells,” J. Appl. Phys. 32(3), 510–519 (1961).
[CrossRef]

Richards, B. S.

B. S. Richards and A. Shalav, “Enhancing the near-infrared spectral response of silicon optoelectronic devices via up-conversion,” IEEE Trans. Electron. Dev. 54(10), 2679–2684 (2007).
[CrossRef]

A. Shalav, B. S. Richards, and M. A. Green, “Luminescent layers for enhanced silicon solar cell performance: up-conversion,” Sol. Energy Mater. Sol. Cells 91(9), 829–842 (2007).
[CrossRef]

T. Trupke, A. Shalav, B. S. Richards, P. Würfel, and M. A. Green, “Efficiency enhancement of solar cells by luminescent up-conversion of sunlight,” Sol. Energy Mater. Sol. Cells 90(18-19), 3327–3338 (2006).
[CrossRef]

Rockstuhl, C.

F. Hallermann, C. Rockstuhl, S. Fahr, G. Seifert, S. Wackerow, H. Graener, G. Plessen, and F. Lederer, “On the use of localized plasmon polaritons in solar cells,” Phys. Status Solidi A 205(12), 2844–2861 (2008).
[CrossRef]

Sanchez-Gil, J. A.

O. L. Muskens, V. Giannini, J. A. Sanchez-Gil, and J. Gómez Rivas, “Strong enhancement of the radiative decay rate of emitters by single plasmonic nanoantennas,” Nano Lett. 7(9), 2871–2875 (2007).
[CrossRef] [PubMed]

Sandoghdar, V.

F. Kaminski, V. Sandoghdar, and M. Agio, “Finite-Difference Time-Domain Modeling of Decay Rates in the Near Field of Metal Nanostructures,” J. Comput. Theor. Nanosci. 4, 635–643 (2007).

Santa-Cruz, P. A.

O. L. Malta, P. A. Santa-Cruz, G. F. de Sa´, and F. Auzel, “Up-conversion yield in glass ceramics containing silver,” J. Solid State Chem. 68(2), 314–319 (1987).
[CrossRef]

Schietinger, S.

S. Schietinger, T. Aichele, H.-Q. Wang, T. Nann, and O. Benson, “Plasmon-enhanced upconversion in single NaYF4:Yb3+/Er3+ codoped nanocrystals,” Nano Lett. 10(1), 134–138 (2010).
[CrossRef] [PubMed]

Seifert, G.

F. Hallermann, C. Rockstuhl, S. Fahr, G. Seifert, S. Wackerow, H. Graener, G. Plessen, and F. Lederer, “On the use of localized plasmon polaritons in solar cells,” Phys. Status Solidi A 205(12), 2844–2861 (2008).
[CrossRef]

Shalav, A.

B. S. Richards and A. Shalav, “Enhancing the near-infrared spectral response of silicon optoelectronic devices via up-conversion,” IEEE Trans. Electron. Dev. 54(10), 2679–2684 (2007).
[CrossRef]

A. Shalav, B. S. Richards, and M. A. Green, “Luminescent layers for enhanced silicon solar cell performance: up-conversion,” Sol. Energy Mater. Sol. Cells 91(9), 829–842 (2007).
[CrossRef]

T. Trupke, A. Shalav, B. S. Richards, P. Würfel, and M. A. Green, “Efficiency enhancement of solar cells by luminescent up-conversion of sunlight,” Sol. Energy Mater. Sol. Cells 90(18-19), 3327–3338 (2006).
[CrossRef]

Shockley, W.

W. Shockley and H. J. Queisser, “Detailed balance limit of efficiency of p-n junction solar cells,” J. Appl. Phys. 32(3), 510–519 (1961).
[CrossRef]

Soref, R. A.

G. Sun, J. B. Khurgin, and R. A. Soref, “Practicable enhancement of spontaneous emission using surface plasmons,” Appl. Phys. Lett. 90(11), 111107 (2007).
[CrossRef]

Sun, G.

G. Sun, J. B. Khurgin, and R. A. Soref, “Practicable enhancement of spontaneous emission using surface plasmons,” Appl. Phys. Lett. 90(11), 111107 (2007).
[CrossRef]

Suyver, J. F.

J. F. Suyver, A. Aebischer, S. Garcia-Revilla, P. Gerner, and H. U. Güdel, “Anomalous power dependence of sensitized upconversion luminescence,” Phys. Rev. B 71(12), 125123 (2005).
[CrossRef]

Trupke, T.

T. Trupke, A. Shalav, B. S. Richards, P. Würfel, and M. A. Green, “Efficiency enhancement of solar cells by luminescent up-conversion of sunlight,” Sol. Energy Mater. Sol. Cells 90(18-19), 3327–3338 (2006).
[CrossRef]

T. Trupke, M. A. Green, and P. Würfel, “Improving solar cell efficiencies by up-conversion of sub-band-gap light,” J. Appl. Phys. 92(7), 4117–4122 (2002).
[CrossRef]

van Schooneveld, M. M.

J. T. van Wijngaarden, M. M. van Schooneveld, C. de Mello Donegá, and A. Meijerink, “Enhancement of the decay rate by plasmon coupling for Eu 3+ in an Au nanoparticle model system,” Europhys. Lett. 93(5), 57005 (2011).
[CrossRef]

van Wijngaarden, J. T.

J. T. van Wijngaarden, M. M. van Schooneveld, C. de Mello Donegá, and A. Meijerink, “Enhancement of the decay rate by plasmon coupling for Eu 3+ in an Au nanoparticle model system,” Europhys. Lett. 93(5), 57005 (2011).
[CrossRef]

Wackerow, S.

F. Hallermann, C. Rockstuhl, S. Fahr, G. Seifert, S. Wackerow, H. Graener, G. Plessen, and F. Lederer, “On the use of localized plasmon polaritons in solar cells,” Phys. Status Solidi A 205(12), 2844–2861 (2008).
[CrossRef]

Wang, H.-Q.

S. Schietinger, T. Aichele, H.-Q. Wang, T. Nann, and O. Benson, “Plasmon-enhanced upconversion in single NaYF4:Yb3+/Er3+ codoped nanocrystals,” Nano Lett. 10(1), 134–138 (2010).
[CrossRef] [PubMed]

Würfel, P.

T. Trupke, A. Shalav, B. S. Richards, P. Würfel, and M. A. Green, “Efficiency enhancement of solar cells by luminescent up-conversion of sunlight,” Sol. Energy Mater. Sol. Cells 90(18-19), 3327–3338 (2006).
[CrossRef]

T. Trupke, M. A. Green, and P. Würfel, “Improving solar cell efficiencies by up-conversion of sub-band-gap light,” J. Appl. Phys. 92(7), 4117–4122 (2002).
[CrossRef]

Xu, H.

P. Johansson, H. Xu, and M. Käll, “Surface-enhanced Raman scattering and fluorescence near metal nanoparticles,” Phys. Rev. B 72(3), 035427 (2005).
[CrossRef]

Yang, L.

Zahraman, K.

P. Gibart, F. Auzel, J. C. Guillaume, and K. Zahraman, “Below band-gap IR response of substrate-free GaAs solar cells using two- photon up-conversion,” Jpn. J. Appl. Phys. 35, 4401–4402 (1996).
[CrossRef]

Zhang, H.

H. Zhang, Y. Li, I. A. Ivanov, Y. Qu, Y. Huang, and X. Duan, “Plasmonic Modulation of the Upconversion Fluorescence in NaYF4:Yb/Tm Hexaplate Nanocrystals Using Gold Nanoparticles or Nanoshells,” Angew. Chem. Int. Ed. 49, 2865–2868 (2010).

Zhao, D.

N. Liu, W. Qin, G. Qin, T. Jiang, and D. Zhao, “Highly plasmon-enhanced upconversion emissions from Au@β-NaYF4:Yb,Tm hybrid nanostructures,” Chem. Commun. (Camb.) 47(27), 7671–7673 (2011).
[CrossRef] [PubMed]

Angew. Chem. Int. Ed. (1)

H. Zhang, Y. Li, I. A. Ivanov, Y. Qu, Y. Huang, and X. Duan, “Plasmonic Modulation of the Upconversion Fluorescence in NaYF4:Yb/Tm Hexaplate Nanocrystals Using Gold Nanoparticles or Nanoshells,” Angew. Chem. Int. Ed. 49, 2865–2868 (2010).

Appl. Phys. Lett. (2)

H. Mertens and A. Polman, “Plasmon-enhanced erbium luminescence,” Appl. Phys. Lett. 89(21), 211107 (2006).
[CrossRef]

G. Sun, J. B. Khurgin, and R. A. Soref, “Practicable enhancement of spontaneous emission using surface plasmons,” Appl. Phys. Lett. 90(11), 111107 (2007).
[CrossRef]

Chem. Commun. (Camb.) (1)

N. Liu, W. Qin, G. Qin, T. Jiang, and D. Zhao, “Highly plasmon-enhanced upconversion emissions from Au@β-NaYF4:Yb,Tm hybrid nanostructures,” Chem. Commun. (Camb.) 47(27), 7671–7673 (2011).
[CrossRef] [PubMed]

Chem. Mater. (1)

K. W. Krämer, D. Biner, G. Frei, H. U. Güdel, M. P. Hehlen, and S. R. Lüthi, “Hexagonal sodium yttrium fluoride based green and blue emitting upconversion phosphors,” Chem. Mater. 16(7), 1244–1251 (2004).
[CrossRef]

Chem. Rev. (1)

F. Auzel, “Upconversion and anti-Stokes processes with f and d ions in solids,” Chem. Rev. 104(1), 139–174 (2004).
[CrossRef] [PubMed]

Europhys. Lett. (1)

J. T. van Wijngaarden, M. M. van Schooneveld, C. de Mello Donegá, and A. Meijerink, “Enhancement of the decay rate by plasmon coupling for Eu 3+ in an Au nanoparticle model system,” Europhys. Lett. 93(5), 57005 (2011).
[CrossRef]

IEEE Trans. Electron. Dev. (1)

B. S. Richards and A. Shalav, “Enhancing the near-infrared spectral response of silicon optoelectronic devices via up-conversion,” IEEE Trans. Electron. Dev. 54(10), 2679–2684 (2007).
[CrossRef]

J. Appl. Phys. (3)

S. Fischer, J. C. Goldschmidt, P. Löper, G. H. Bauer, R. Brüggemann, K. Krämer, D. Biner, M. Hermle, and S. W. Glunz, “Enhancement of silicon solar cell efficiency by upconversion: Optical and electrical characterization,” J. Appl. Phys. 108(4), 044912 (2010).
[CrossRef]

T. Trupke, M. A. Green, and P. Würfel, “Improving solar cell efficiencies by up-conversion of sub-band-gap light,” J. Appl. Phys. 92(7), 4117–4122 (2002).
[CrossRef]

W. Shockley and H. J. Queisser, “Detailed balance limit of efficiency of p-n junction solar cells,” J. Appl. Phys. 32(3), 510–519 (1961).
[CrossRef]

J. Chem. Phys. (2)

J. Gersten and A. Nitzan, “Spectroscopic properties of molecules interacting with small dielectric particles,” J. Chem. Phys. 75(3), 1139–1152 (1981).
[CrossRef]

G. S. Ofelt, “Intensities of crystal spectra of rare-earth ions,” J. Chem. Phys. 37(3), 511–520 (1962).
[CrossRef]

J. Comput. Theor. Nanosci. (1)

F. Kaminski, V. Sandoghdar, and M. Agio, “Finite-Difference Time-Domain Modeling of Decay Rates in the Near Field of Metal Nanostructures,” J. Comput. Theor. Nanosci. 4, 635–643 (2007).

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

J. Solid State Chem. (1)

O. L. Malta, P. A. Santa-Cruz, G. F. de Sa´, and F. Auzel, “Up-conversion yield in glass ceramics containing silver,” J. Solid State Chem. 68(2), 314–319 (1987).
[CrossRef]

Jpn. J. Appl. Phys. (1)

P. Gibart, F. Auzel, J. C. Guillaume, and K. Zahraman, “Below band-gap IR response of substrate-free GaAs solar cells using two- photon up-conversion,” Jpn. J. Appl. Phys. 35, 4401–4402 (1996).
[CrossRef]

Nano Lett. (2)

O. L. Muskens, V. Giannini, J. A. Sanchez-Gil, and J. Gómez Rivas, “Strong enhancement of the radiative decay rate of emitters by single plasmonic nanoantennas,” Nano Lett. 7(9), 2871–2875 (2007).
[CrossRef] [PubMed]

S. Schietinger, T. Aichele, H.-Q. Wang, T. Nann, and O. Benson, “Plasmon-enhanced upconversion in single NaYF4:Yb3+/Er3+ codoped nanocrystals,” Nano Lett. 10(1), 134–138 (2010).
[CrossRef] [PubMed]

Phys. Rev. (1)

B. R. Judd, “Optical absorption intensities of rare-earth ions,” Phys. Rev. 127(3), 750–761 (1962).
[CrossRef]

Phys. Rev. B (4)

H. Mertens, A. F. Koenderink, and A. Polman, “Plasmon-enhanced luminescence near noble-metal nanospheres: Comparison of exact theory and an improved Gersten and Nitzan model,” Phys. Rev. B 76(11), 115123 (2007).
[CrossRef]

M. Pollnau, D. R. Gamelin, S. R. Lüthi, H. U. Güdel, and M. P. Hehlen, “Power dependence of upconversion luminescence in lanthanide and transition-metal-ion systems,” Phys. Rev. B 61(5), 3337–3346 (2000).
[CrossRef]

J. F. Suyver, A. Aebischer, S. Garcia-Revilla, P. Gerner, and H. U. Güdel, “Anomalous power dependence of sensitized upconversion luminescence,” Phys. Rev. B 71(12), 125123 (2005).
[CrossRef]

P. Johansson, H. Xu, and M. Käll, “Surface-enhanced Raman scattering and fluorescence near metal nanoparticles,” Phys. Rev. B 72(3), 035427 (2005).
[CrossRef]

Phys. Status Solidi A (1)

F. Hallermann, C. Rockstuhl, S. Fahr, G. Seifert, S. Wackerow, H. Graener, G. Plessen, and F. Lederer, “On the use of localized plasmon polaritons in solar cells,” Phys. Status Solidi A 205(12), 2844–2861 (2008).
[CrossRef]

Phys. Z. (1)

A. Einstein, “Zur Quantentheorie der Strahlung,” Phys. Z. 18, 121–128 (1917).

Sol. Energy Mater. Sol. Cells (3)

J. C. Goldschmidt, S. Fischer, P. Löper, K. W. Krämer, D. Biner, M. Hermle, and S. W. Glunz, “Experimental analysis of upconversion with both coherent monochromatic irradiation and broad spectrum illumination,” Sol. Energy Mater. Sol. Cells 95(7), 1960–1963 (2011).
[CrossRef]

T. Trupke, A. Shalav, B. S. Richards, P. Würfel, and M. A. Green, “Efficiency enhancement of solar cells by luminescent up-conversion of sunlight,” Sol. Energy Mater. Sol. Cells 90(18-19), 3327–3338 (2006).
[CrossRef]

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[CrossRef]

Surf. Sci. (1)

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[CrossRef]

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Other (3)

S. Fischer, H. Steinkemper, P. Löper, M. Hermle, and J. C. Goldschmidt, “Modeling upconversion of erbium doped microcrystals based on experimentally determined Einstein coefficienct,” arXiv:1110.2309v2 [physics.optics].

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Figures (6)

Fig. 1
Fig. 1

(a) Energy levels of the trivalent erbium in the host crystal NaYF4 with corresponding luminescence wavelengths of transitions from the excited states to the ground state (colored solid arrows). In the rate equation model, we assume an excitation with a wavelength of 1523 nm (red waved arrow). Higher energy levels can be populated by GSA followed by ESA (black dashed arrows). Another possibility to populate higher energy levels is ETU (dashed colored arrows), where energy is transferred from one ion, the donor (D), to a neighboring second ion, the acceptor (A). Cross-relaxation (CR) is the inverse process and included in the model as well. Additionally, we consider MPR to next lower energy levels (waved arrows). (b) Comparison of the simulated UC quantum yield ηSim,UC (red solid line) with the UC quantum yield, which was determined from calibrated photoluminescence measurements (black squares) [7]. Due to the non-linearity of UC, the UC quantum yield increases with increasing irradiance. Details on the UC model can be found in [23].

Fig. 2
Fig. 2

(a) The simulation was performed in a cubic volume with an edge length of 6 times the diameter of the gold nanoparticle, which is located in the center of the cube. The relative luminescence intensities of the various transitions of the upconverter were calculated for every position in the simulation volume. The values in the x-z-plane were calculated for every value of the y-axis. For a clear presentation, the graphs in this work show the x-z-plane at y = 0 nm, the center of the cube. (b) Enhancement of the quadratic optical field γE due to a spherical gold nanoparticle with a diameter of 200 nm (white circle in the center). The color scale was clipped at 5 for a clearer presentation and the white dashed line represents γE = 1. The strongest field enhancement with a value of 16 is reached close to the surface of the metal nanoparticle. The plot shows a cut in the x-z-plane of the cubic simulation volume in the center at y = 0 nm.

Fig. 3
Fig. 3

Schematic of the two polarizations considered for the simulations. For PPOL the Er3+ dipole oscillates parallel to the surface of the gold nanoparticle, while for SPOL the Er3+ dipole oscillates perpendicularly to the surface of the gold nanoparticle.

Fig. 4
Fig. 4

Impact of a spherical gold nanoparticle with a diameter of 200 nm on the relative luminescence of certain transitions. The rate equations of the UC model were solved for every spatial point, taking into account the relative change in the quadratic optical field and the relative changes of the transition probabilities due to the coupling of metal nanoparticle and the Er3+ dipole. The color scale shows the relative luminescence, which was calculated by dividing the luminescence with metal nanoparticle by that without the metal nanoparticle. The dashed white lines represent enhancement factors of 1. Two polarizations, PPOL and SPOL, were considered (see Fig. 3). The transitions from the energy levels 4I11/2, 4I9/2 and 4F9/2 to the ground state 4I15/2 in the x-z-plane at y = 0 nm are shown. The white circle in the middle of the graphs represents the spherical gold nanoparticle. For a clearer presentation, the color scale was clipped below 0.5 and above 2.

Fig. 5
Fig. 5

(a) Relative luminescence of various transitions of the UC for PPOL in dependence of the distance to the surface of the gold nanoparticle. While the luminescence of the two lowest transitions from 4I13/2 and 4I11/2 decrease slightly, the higher transitions with lower wavelength benefit from the nanoparticle. (b) Relative luminescence of various transitions of the UC for SPOL in dependence of the distance to the surface of the gold nanoparticle. For all distances and all transitions, the GNP increase the luminescence. For the transition from 4I11/2, the best suited distance is between 10 nm to 50 nm, where the luminescence is enhanced by a factor of 50. The strongest enhancement is reached for the transition from 4F9/2 with a value of 2270 for a distance of 10 nm to the surface of the gold nanoparticle. However, this transition contributes only marginally to the overall UC luminescence.

Fig. 6
Fig. 6

Relative luminescence averaged over spherical shells around the metal nanoparticle at a defined distance and for the weighted average of SPOL and PPOL. The black solid line shows the case without metal nanoparticle.

Tables (1)

Tables Icon

Table 1 Average relative luminescence for a homogenously dispersed upconverter. The average was calculated over all simulation points for SPOL, PPOL and weighted for SPOL and PPOL.

Equations (9)

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n ˙ =( M GSA + M ESA + M STE + M SPE + M MPR ) n + v ET ( n ,d)
W if SPE = A if
W if GSA/ESA =u( ω if ) B if =u( ω if ) π 2 c 3 ω if 3 g f g i A fi
W if STE = π 2 c 3 ω if 3 u( ω if ) A if =u( ω if ) B if .
I ν (ω)dω= c n u(ω)dω
L i = n i A if
η Sim,UC = i=3 6 n i A i1 + n 6 A 62 if n i M GSA + n i M ESA n f M STE η UC
A if,plasmon =( γ rad + γ nonrad ) A if
L i,plasmon = γ rad n i A if

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