Abstract

Differences between the point-dipole approximation and a more rigorous theory for studying the optical behavior of a granular metal film are discussed.

© 1988 Optical Society of America

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References

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  1. T. Yamaguchi, S. Yoshida, A. Kinbara, “Optical effect of the substrate on the anamolous absorption of aggregated silver films,” Thin Solid Films 21, 173–187 (1984).
    [CrossRef]
  2. R. Ruppin, “Infrared active modes of dielectric crystallites on a substrate,” Surf. Sci. 58, 550–556 (1976).
    [CrossRef]
  3. V. V. Truong, G. D. Scott, “Optical properties of aggregated noble metal films,”J. Opt. Soc. Am. 67, 502–510 (1977).
    [CrossRef]
  4. A. Wokaun, “Surface-enhanced electromagnetic processes,” in Solid State Physics, H. Ehrenreich, D. Turnbull, eds. (Academic, New York, 1984), Vol. 38.
    [CrossRef]
  5. G. Bosi, B. de Dormale, “Substrate related effects on the optical behavior of a granular surface: the Maxwell–Garnett theory revisited,” J. Appl. Phys. 58, 513–517 (1985).
    [CrossRef]
  6. See, for example, T. Yamaguchi, M. Sakai, N. Saito, “Optical properties of well-defined granular metal systems,” Phys. Rev. 32, 2126–2131 (1985).
    [CrossRef]
  7. P. B. Johnson, R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. 6, 4370–4379 (1972).
    [CrossRef]
  8. G. A. Niklasson, H. G. Craighead, “Optical response and fabrication of regular arrays of ultrasmall gold particles,” Thin Solid Films 125, 165–170 (1985).
    [CrossRef]

1985

G. Bosi, B. de Dormale, “Substrate related effects on the optical behavior of a granular surface: the Maxwell–Garnett theory revisited,” J. Appl. Phys. 58, 513–517 (1985).
[CrossRef]

See, for example, T. Yamaguchi, M. Sakai, N. Saito, “Optical properties of well-defined granular metal systems,” Phys. Rev. 32, 2126–2131 (1985).
[CrossRef]

G. A. Niklasson, H. G. Craighead, “Optical response and fabrication of regular arrays of ultrasmall gold particles,” Thin Solid Films 125, 165–170 (1985).
[CrossRef]

1984

T. Yamaguchi, S. Yoshida, A. Kinbara, “Optical effect of the substrate on the anamolous absorption of aggregated silver films,” Thin Solid Films 21, 173–187 (1984).
[CrossRef]

1977

1976

R. Ruppin, “Infrared active modes of dielectric crystallites on a substrate,” Surf. Sci. 58, 550–556 (1976).
[CrossRef]

1972

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

Bosi, G.

G. Bosi, B. de Dormale, “Substrate related effects on the optical behavior of a granular surface: the Maxwell–Garnett theory revisited,” J. Appl. Phys. 58, 513–517 (1985).
[CrossRef]

Christy, R. W.

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

Craighead, H. G.

G. A. Niklasson, H. G. Craighead, “Optical response and fabrication of regular arrays of ultrasmall gold particles,” Thin Solid Films 125, 165–170 (1985).
[CrossRef]

de Dormale, B.

G. Bosi, B. de Dormale, “Substrate related effects on the optical behavior of a granular surface: the Maxwell–Garnett theory revisited,” J. Appl. Phys. 58, 513–517 (1985).
[CrossRef]

Johnson, P. B.

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

Kinbara, A.

T. Yamaguchi, S. Yoshida, A. Kinbara, “Optical effect of the substrate on the anamolous absorption of aggregated silver films,” Thin Solid Films 21, 173–187 (1984).
[CrossRef]

Niklasson, G. A.

G. A. Niklasson, H. G. Craighead, “Optical response and fabrication of regular arrays of ultrasmall gold particles,” Thin Solid Films 125, 165–170 (1985).
[CrossRef]

Ruppin, R.

R. Ruppin, “Infrared active modes of dielectric crystallites on a substrate,” Surf. Sci. 58, 550–556 (1976).
[CrossRef]

Saito, N.

See, for example, T. Yamaguchi, M. Sakai, N. Saito, “Optical properties of well-defined granular metal systems,” Phys. Rev. 32, 2126–2131 (1985).
[CrossRef]

Sakai, M.

See, for example, T. Yamaguchi, M. Sakai, N. Saito, “Optical properties of well-defined granular metal systems,” Phys. Rev. 32, 2126–2131 (1985).
[CrossRef]

Scott, G. D.

Truong, V. V.

Wokaun, A.

A. Wokaun, “Surface-enhanced electromagnetic processes,” in Solid State Physics, H. Ehrenreich, D. Turnbull, eds. (Academic, New York, 1984), Vol. 38.
[CrossRef]

Yamaguchi, T.

See, for example, T. Yamaguchi, M. Sakai, N. Saito, “Optical properties of well-defined granular metal systems,” Phys. Rev. 32, 2126–2131 (1985).
[CrossRef]

T. Yamaguchi, S. Yoshida, A. Kinbara, “Optical effect of the substrate on the anamolous absorption of aggregated silver films,” Thin Solid Films 21, 173–187 (1984).
[CrossRef]

Yoshida, S.

T. Yamaguchi, S. Yoshida, A. Kinbara, “Optical effect of the substrate on the anamolous absorption of aggregated silver films,” Thin Solid Films 21, 173–187 (1984).
[CrossRef]

J. Appl. Phys.

G. Bosi, B. de Dormale, “Substrate related effects on the optical behavior of a granular surface: the Maxwell–Garnett theory revisited,” J. Appl. Phys. 58, 513–517 (1985).
[CrossRef]

J. Opt. Soc. Am.

Phys. Rev.

See, for example, T. Yamaguchi, M. Sakai, N. Saito, “Optical properties of well-defined granular metal systems,” Phys. Rev. 32, 2126–2131 (1985).
[CrossRef]

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

Surf. Sci.

R. Ruppin, “Infrared active modes of dielectric crystallites on a substrate,” Surf. Sci. 58, 550–556 (1976).
[CrossRef]

Thin Solid Films

G. A. Niklasson, H. G. Craighead, “Optical response and fabrication of regular arrays of ultrasmall gold particles,” Thin Solid Films 125, 165–170 (1985).
[CrossRef]

T. Yamaguchi, S. Yoshida, A. Kinbara, “Optical effect of the substrate on the anamolous absorption of aggregated silver films,” Thin Solid Films 21, 173–187 (1984).
[CrossRef]

Other

A. Wokaun, “Surface-enhanced electromagnetic processes,” in Solid State Physics, H. Ehrenreich, D. Turnbull, eds. (Academic, New York, 1984), Vol. 38.
[CrossRef]

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Figures (4)

Fig. 1
Fig. 1

Real and imaginary parts of the effective dielectric constant as a function of the filling factor Q, assuming bulk optical properties for the Ag particles. Symbols: ——, BD theory; - - - -, PDA.

Fig. 2
Fig. 2

Real and imaginary parts of the effective dielectric constant = (1∥i2∥) as a function of the photon energy E. The parameters characterizing the Ag granular film are Q = 0.45, a particle diameter of 3.7 nm, and a substrate refractive index of 1.46. Symbols: ——, BD theory; - - - -, PDA.

Fig. 3
Fig. 3

Real and imaginary parts of the effective dielectric constant = (1⊥i2⊥) as a function of the photon energy E. The parameters are as described for Fig. 2. Symbols: ——, BD theory; - - - -, PDA.

Fig. 4
Fig. 4

Transmittance for a square lattice of Au particles deposited upon sapphire with a refractive index of 1.76. Curves c and d are calculated by the PDA, assuming, respectively, spheroidal particles of axial ratio 1.5 and spherical particles. Curve a gives experimental measurements as given in Ref. 8, and curve b gives the calculated transmittance obtained by using the multiple-image approach.

Equations (8)

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= 1 + Q ( 1 ) / [ F ( 1 ) + 1 ] ,
= { 1 Q ( 1 ) / [ F ( 1 ) + 1 ] } 1 .
F = 1 / 3 [ ( s 1 ) / 24 ( s + 1 ) ] 0.989 Q 3 / 2 / ( s + 1 ) ,
F = 1 / 3 [ ( s 1 ) / 12 ( s + 1 ) ] + 1.979 s Q 3 / 2 / ( s + 1 ) ,
= 1 + 3 Q D / ( 1 1.079 Q D ) ,
= [ 1 3 Q D / ( 1 + 2.158 Q D ) ] 1 ,
D = 2 ( 1 ) ( s + 1 ) ( + 2 ) n = 0 x n / ( n + 1 ) 3 ,
D = 2 s ( s + 1 ) ( 1 ) ( + 2 ) n = 0 x n { 2 ( n + 1 ) 3 [ m = 0 x m ( m + 1 ) 2 ] [ ( n + 1 ) 2 m = 0 x m ( m + 1 ) ] 1 } ,

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