Abstract

The Maxwell-Garnett’s and Toudert’s methods detailed in Appl. Opt. 48, 778 (2009), based on the Maxwell-Garnett and Yamaguchi effective medium models, respectively, have been used for calculating the absorbance α of a (BaF2/Ag)5/BaF2 nanocomposite thin film identical to the one presented in Fig. 1 of Appl. Opt. 48, 778 (2009)]. We propose that the discrepancies observed in this reference between the α spectra calculated by the two methods are due to a non rigorous use of both effective medium models by the author and show that adequate calculations lead to superposed spectra.

© 2010 Optical Society of America

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References

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  1. M. L. Protopapa, “Surface plasmon resonance of metal nanoparticles sandwiched between dielectric layers:theoretical modeling,” Appl. Opt. 48, 778–785 (2009).
    [Crossref] [PubMed]
  2. C. Jiang, S. Markutsya, and V. V. Tsukruk, “Collective and individual plasmon resonances in nanoparticle films obtained by spin-assisted layer-by-layer assembly,” Langmuir 20, 882–890 (2004).
    [Crossref]
  3. T. Girardeau, S. Camelio, D. Babonneau, J. Toudert, and A. Barranco, “Correlations between the microstructure of Ag-Si3N4 multilayers and their optical properties,” Thin Sol. Films 455, 313–317 (2004).
    [Crossref]
  4. T. Yamaguchi, S. Yoshida, and A. Kinbara, “Optical effect of the substrate on the anomalous absorption of aggregated silver films,” Thin Solid Films 21, 173–187(1974).
    [Crossref]
  5. V. A. Fedotov, V. I. Emel’yanov, K. F. McDonald, and N. I. Zheludev, “optical properties of closely packed nanoparticle films: spheroids and nanoshells,” J. Opt. A Pure Appl. Opt. 6, 155–160 (2004).
    [Crossref]
  6. J. Toudert, D. Babonneau, L. Simonot, S. Camelio, and T. Girardeau, “Quantitative modeling of the surface plasmon resonances of metal nanoclusters sandwiched between dielectric layers : influence of the nanocluster size, shape and organization,” Nanotechnology 19, 125709(2008).
    [Crossref] [PubMed]
  7. P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6, 4370–4379 (1972).
    [Crossref]

2009 (1)

2008 (1)

J. Toudert, D. Babonneau, L. Simonot, S. Camelio, and T. Girardeau, “Quantitative modeling of the surface plasmon resonances of metal nanoclusters sandwiched between dielectric layers : influence of the nanocluster size, shape and organization,” Nanotechnology 19, 125709(2008).
[Crossref] [PubMed]

2004 (3)

V. A. Fedotov, V. I. Emel’yanov, K. F. McDonald, and N. I. Zheludev, “optical properties of closely packed nanoparticle films: spheroids and nanoshells,” J. Opt. A Pure Appl. Opt. 6, 155–160 (2004).
[Crossref]

C. Jiang, S. Markutsya, and V. V. Tsukruk, “Collective and individual plasmon resonances in nanoparticle films obtained by spin-assisted layer-by-layer assembly,” Langmuir 20, 882–890 (2004).
[Crossref]

T. Girardeau, S. Camelio, D. Babonneau, J. Toudert, and A. Barranco, “Correlations between the microstructure of Ag-Si3N4 multilayers and their optical properties,” Thin Sol. Films 455, 313–317 (2004).
[Crossref]

1974 (1)

T. Yamaguchi, S. Yoshida, and A. Kinbara, “Optical effect of the substrate on the anomalous absorption of aggregated silver films,” Thin Solid Films 21, 173–187(1974).
[Crossref]

1972 (1)

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

Babonneau, D.

J. Toudert, D. Babonneau, L. Simonot, S. Camelio, and T. Girardeau, “Quantitative modeling of the surface plasmon resonances of metal nanoclusters sandwiched between dielectric layers : influence of the nanocluster size, shape and organization,” Nanotechnology 19, 125709(2008).
[Crossref] [PubMed]

T. Girardeau, S. Camelio, D. Babonneau, J. Toudert, and A. Barranco, “Correlations between the microstructure of Ag-Si3N4 multilayers and their optical properties,” Thin Sol. Films 455, 313–317 (2004).
[Crossref]

Barranco, A.

T. Girardeau, S. Camelio, D. Babonneau, J. Toudert, and A. Barranco, “Correlations between the microstructure of Ag-Si3N4 multilayers and their optical properties,” Thin Sol. Films 455, 313–317 (2004).
[Crossref]

Camelio, S.

J. Toudert, D. Babonneau, L. Simonot, S. Camelio, and T. Girardeau, “Quantitative modeling of the surface plasmon resonances of metal nanoclusters sandwiched between dielectric layers : influence of the nanocluster size, shape and organization,” Nanotechnology 19, 125709(2008).
[Crossref] [PubMed]

T. Girardeau, S. Camelio, D. Babonneau, J. Toudert, and A. Barranco, “Correlations between the microstructure of Ag-Si3N4 multilayers and their optical properties,” Thin Sol. Films 455, 313–317 (2004).
[Crossref]

Christy, R. W.

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

Emel’yanov, V. I.

V. A. Fedotov, V. I. Emel’yanov, K. F. McDonald, and N. I. Zheludev, “optical properties of closely packed nanoparticle films: spheroids and nanoshells,” J. Opt. A Pure Appl. Opt. 6, 155–160 (2004).
[Crossref]

Fedotov, V. A.

V. A. Fedotov, V. I. Emel’yanov, K. F. McDonald, and N. I. Zheludev, “optical properties of closely packed nanoparticle films: spheroids and nanoshells,” J. Opt. A Pure Appl. Opt. 6, 155–160 (2004).
[Crossref]

Girardeau, T.

J. Toudert, D. Babonneau, L. Simonot, S. Camelio, and T. Girardeau, “Quantitative modeling of the surface plasmon resonances of metal nanoclusters sandwiched between dielectric layers : influence of the nanocluster size, shape and organization,” Nanotechnology 19, 125709(2008).
[Crossref] [PubMed]

T. Girardeau, S. Camelio, D. Babonneau, J. Toudert, and A. Barranco, “Correlations between the microstructure of Ag-Si3N4 multilayers and their optical properties,” Thin Sol. Films 455, 313–317 (2004).
[Crossref]

Jiang, C.

C. Jiang, S. Markutsya, and V. V. Tsukruk, “Collective and individual plasmon resonances in nanoparticle films obtained by spin-assisted layer-by-layer assembly,” Langmuir 20, 882–890 (2004).
[Crossref]

Johnson, P. B.

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

Kinbara, A.

T. Yamaguchi, S. Yoshida, and A. Kinbara, “Optical effect of the substrate on the anomalous absorption of aggregated silver films,” Thin Solid Films 21, 173–187(1974).
[Crossref]

Markutsya, S.

C. Jiang, S. Markutsya, and V. V. Tsukruk, “Collective and individual plasmon resonances in nanoparticle films obtained by spin-assisted layer-by-layer assembly,” Langmuir 20, 882–890 (2004).
[Crossref]

McDonald, K. F.

V. A. Fedotov, V. I. Emel’yanov, K. F. McDonald, and N. I. Zheludev, “optical properties of closely packed nanoparticle films: spheroids and nanoshells,” J. Opt. A Pure Appl. Opt. 6, 155–160 (2004).
[Crossref]

Protopapa, M. L.

Simonot, L.

J. Toudert, D. Babonneau, L. Simonot, S. Camelio, and T. Girardeau, “Quantitative modeling of the surface plasmon resonances of metal nanoclusters sandwiched between dielectric layers : influence of the nanocluster size, shape and organization,” Nanotechnology 19, 125709(2008).
[Crossref] [PubMed]

Toudert, J.

J. Toudert, D. Babonneau, L. Simonot, S. Camelio, and T. Girardeau, “Quantitative modeling of the surface plasmon resonances of metal nanoclusters sandwiched between dielectric layers : influence of the nanocluster size, shape and organization,” Nanotechnology 19, 125709(2008).
[Crossref] [PubMed]

T. Girardeau, S. Camelio, D. Babonneau, J. Toudert, and A. Barranco, “Correlations between the microstructure of Ag-Si3N4 multilayers and their optical properties,” Thin Sol. Films 455, 313–317 (2004).
[Crossref]

Tsukruk, V. V.

C. Jiang, S. Markutsya, and V. V. Tsukruk, “Collective and individual plasmon resonances in nanoparticle films obtained by spin-assisted layer-by-layer assembly,” Langmuir 20, 882–890 (2004).
[Crossref]

Yamaguchi, T.

T. Yamaguchi, S. Yoshida, and A. Kinbara, “Optical effect of the substrate on the anomalous absorption of aggregated silver films,” Thin Solid Films 21, 173–187(1974).
[Crossref]

Yoshida, S.

T. Yamaguchi, S. Yoshida, and A. Kinbara, “Optical effect of the substrate on the anomalous absorption of aggregated silver films,” Thin Solid Films 21, 173–187(1974).
[Crossref]

Zheludev, N. I.

V. A. Fedotov, V. I. Emel’yanov, K. F. McDonald, and N. I. Zheludev, “optical properties of closely packed nanoparticle films: spheroids and nanoshells,” J. Opt. A Pure Appl. Opt. 6, 155–160 (2004).
[Crossref]

Appl. Opt. (1)

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

V. A. Fedotov, V. I. Emel’yanov, K. F. McDonald, and N. I. Zheludev, “optical properties of closely packed nanoparticle films: spheroids and nanoshells,” J. Opt. A Pure Appl. Opt. 6, 155–160 (2004).
[Crossref]

Langmuir (1)

C. Jiang, S. Markutsya, and V. V. Tsukruk, “Collective and individual plasmon resonances in nanoparticle films obtained by spin-assisted layer-by-layer assembly,” Langmuir 20, 882–890 (2004).
[Crossref]

Nanotechnology (1)

J. Toudert, D. Babonneau, L. Simonot, S. Camelio, and T. Girardeau, “Quantitative modeling of the surface plasmon resonances of metal nanoclusters sandwiched between dielectric layers : influence of the nanocluster size, shape and organization,” Nanotechnology 19, 125709(2008).
[Crossref] [PubMed]

Phys. Rev. B (1)

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

Thin Sol. Films (1)

T. Girardeau, S. Camelio, D. Babonneau, J. Toudert, and A. Barranco, “Correlations between the microstructure of Ag-Si3N4 multilayers and their optical properties,” Thin Sol. Films 455, 313–317 (2004).
[Crossref]

Thin Solid Films (1)

T. Yamaguchi, S. Yoshida, and A. Kinbara, “Optical effect of the substrate on the anomalous absorption of aggregated silver films,” Thin Solid Films 21, 173–187(1974).
[Crossref]

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Figures (3)

Fig. 1
Fig. 1

(a) Schematic representation of the Ba F 2 / ( Ag / Ba F 2 ) 5 multilayer, (b) Ba F 2 / ( effective medium/ Ba F 2 ) 5 stack used for calculating the absorbance of the multilayer by the Toudert method. The effective dielectric function ε eff , Yam of these layers is given by the Yamaguchi formula.

Fig. 2
Fig. 2

Calculated spectra of the extinction coefficient k eff , Yam ( d ) of the effective medium layers in the Ba F 2 / ( effective medium/ Ba F 2 ) 5 stack for various d values. (b) Absorbance spectra of the multilayer calculated by the “Toudert’s method” for several values of d (superposed full lines), which has been adjusted simultaneously in the Yamaguchi formula and in the multilayer model. Absorbance spectra calculated with d = 10 nm in the Yamaguchi formula and d = 12 nm in the multilayer model (Protopapa’s curve, red dotted line) and using the Maxwell-Garnett method with f = π D 3 / 6 a 3 = 0.00818 (blue dotted line) are also presented.

Fig. 3
Fig. 3

Absorbance spectra of the multilayer calculated using Toudert’s method (black line), the Maxwell-Garnett method with f = π D 3 / 6 a 3 = 0.00818 (blue dotted line), with f = 5 π D 3 / 6 a 2 L = 0.00711 (red dotted line), and considering the material as a Ba F 2 / effective medium / Ba F 2 trilayer with the central layer being described by the Maxwell-Garnett dielectric function with f = π D 3 / 6 a 3 = 0.00818 (green dotted line).

Equations (4)

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f = π D 3 / 6 a 3 .
α = 4 π k eff , MG / λ ,
α = ( ln ( 1 R ) ln ( T ) / L ) ,
ε eff , Yam = ε Ba F 2 [ 1 + π D 3 6 a 2 d ξ 1 0.188 D 3 a 3 ξ ] ,

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