Abstract

Some thin metallic films show anomalous optical properties, namely, that both energetic position and magnitude of the absorption bands depend on the film thickness. An interpretation, usually accepted, is based on a direct excitation of surface plasmons by means of the granular structure or the roughnesses of the films. The existence of these anomalous bands are explained, independently of the surface irregularities, if we assume a localized absorption.

© 1980 Optical Society of America

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References

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  1. P. Rouard, A. Meessen, Prog. Opt. 15, 77 (1977).
    [CrossRef]
  2. L. D. Landau, E. M. Lifshitz, Quantum Mechanics (Pergamon, London, 1959).
  3. F. Bassani, in Rendiconti della Scuola Internazionale E. Fermi, Course 34 (Academic, New York, 1966).
  4. See F. Abeles, Ed., Optical Properties of Solids (North-Holland, Amsterdam, 1972).
  5. R. Garron, Surf. Sci. à paraître.
  6. H. Mayey, M. H. El Naby, Z. Phys. 174, 280 (1963); H. Mayer, B. Hietel, in Proceedings, International Colloquium on Optical Properties and Electronic Structure of Metals and Alloys, Paris, F. Abeles, Ed. (North-Holland, Amsterdam, 1966).
    [CrossRef]
  7. R. Payan, D. Roux, C. R. Acad. Sci. 264, 285 (1967); R. Payan, D. Roux, C. R. Acad. Sci. 267, 1105 (1968); R. Payan, D. Roux, Opt Commun. 1, 37 (1969); R. Payan, Thèse, Université D’Aix-Marseille, C.N.R.S. A.O. 3406 et Ann Phys.4, 543 (1969).

1977 (1)

P. Rouard, A. Meessen, Prog. Opt. 15, 77 (1977).
[CrossRef]

1967 (1)

R. Payan, D. Roux, C. R. Acad. Sci. 264, 285 (1967); R. Payan, D. Roux, C. R. Acad. Sci. 267, 1105 (1968); R. Payan, D. Roux, Opt Commun. 1, 37 (1969); R. Payan, Thèse, Université D’Aix-Marseille, C.N.R.S. A.O. 3406 et Ann Phys.4, 543 (1969).

1963 (1)

H. Mayey, M. H. El Naby, Z. Phys. 174, 280 (1963); H. Mayer, B. Hietel, in Proceedings, International Colloquium on Optical Properties and Electronic Structure of Metals and Alloys, Paris, F. Abeles, Ed. (North-Holland, Amsterdam, 1966).
[CrossRef]

Bassani, F.

F. Bassani, in Rendiconti della Scuola Internazionale E. Fermi, Course 34 (Academic, New York, 1966).

El Naby, M. H.

H. Mayey, M. H. El Naby, Z. Phys. 174, 280 (1963); H. Mayer, B. Hietel, in Proceedings, International Colloquium on Optical Properties and Electronic Structure of Metals and Alloys, Paris, F. Abeles, Ed. (North-Holland, Amsterdam, 1966).
[CrossRef]

Garron, R.

R. Garron, Surf. Sci. à paraître.

Landau, L. D.

L. D. Landau, E. M. Lifshitz, Quantum Mechanics (Pergamon, London, 1959).

Lifshitz, E. M.

L. D. Landau, E. M. Lifshitz, Quantum Mechanics (Pergamon, London, 1959).

Mayey, H.

H. Mayey, M. H. El Naby, Z. Phys. 174, 280 (1963); H. Mayer, B. Hietel, in Proceedings, International Colloquium on Optical Properties and Electronic Structure of Metals and Alloys, Paris, F. Abeles, Ed. (North-Holland, Amsterdam, 1966).
[CrossRef]

Meessen, A.

P. Rouard, A. Meessen, Prog. Opt. 15, 77 (1977).
[CrossRef]

Payan, R.

R. Payan, D. Roux, C. R. Acad. Sci. 264, 285 (1967); R. Payan, D. Roux, C. R. Acad. Sci. 267, 1105 (1968); R. Payan, D. Roux, Opt Commun. 1, 37 (1969); R. Payan, Thèse, Université D’Aix-Marseille, C.N.R.S. A.O. 3406 et Ann Phys.4, 543 (1969).

Rouard, P.

P. Rouard, A. Meessen, Prog. Opt. 15, 77 (1977).
[CrossRef]

Roux, D.

R. Payan, D. Roux, C. R. Acad. Sci. 264, 285 (1967); R. Payan, D. Roux, C. R. Acad. Sci. 267, 1105 (1968); R. Payan, D. Roux, Opt Commun. 1, 37 (1969); R. Payan, Thèse, Université D’Aix-Marseille, C.N.R.S. A.O. 3406 et Ann Phys.4, 543 (1969).

C. R. Acad. Sci. (1)

R. Payan, D. Roux, C. R. Acad. Sci. 264, 285 (1967); R. Payan, D. Roux, C. R. Acad. Sci. 267, 1105 (1968); R. Payan, D. Roux, Opt Commun. 1, 37 (1969); R. Payan, Thèse, Université D’Aix-Marseille, C.N.R.S. A.O. 3406 et Ann Phys.4, 543 (1969).

Prog. Opt. (1)

P. Rouard, A. Meessen, Prog. Opt. 15, 77 (1977).
[CrossRef]

Z. Phys. (1)

H. Mayey, M. H. El Naby, Z. Phys. 174, 280 (1963); H. Mayer, B. Hietel, in Proceedings, International Colloquium on Optical Properties and Electronic Structure of Metals and Alloys, Paris, F. Abeles, Ed. (North-Holland, Amsterdam, 1966).
[CrossRef]

Other (4)

L. D. Landau, E. M. Lifshitz, Quantum Mechanics (Pergamon, London, 1959).

F. Bassani, in Rendiconti della Scuola Internazionale E. Fermi, Course 34 (Academic, New York, 1966).

See F. Abeles, Ed., Optical Properties of Solids (North-Holland, Amsterdam, 1972).

R. Garron, Surf. Sci. à paraître.

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Figures (3)

Fig. 3
Fig. 3

Courbes théoriques de la conductivité en fonction de l’énergie de la radiation incidente, pour équelques épaisseurs des couches. En pointillés, l’absorption de Drude calculée suivant les résultats de Mayer.6 Les épaisseurs décroissent depuis les courbes les plus basses vers les plus hautes.

Equations (24)

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A = A 0 exp [ i ( k · r - ω t ) ] ,
K = K 1 + i K 2
w ( ω , t , k v , k c ) = e 2 m 2 2 | 0 t d t V d r ψ c * ( k c , r , t ) Ap ψ v ( k v , r , t ) | 2 ,
d w d t = 2 π e 2 m 2 | V d r ψ c * ( k c , r ) A ( r ) p ψ v ( k v , r ) | 2 δ ( E c - E v - ω ) ,
d w d t = 2 π e 2 m 2 ω 2 2 e · M 2 δ ( E c - E v - ω )
e · M = δ V d r ψ c * ( k c , r ) e · ψ v ( k v , r )
d N = δ N d 3 k 4 π 3 / a 3 = δ N · a 3 d 3 k 4 π 3 ,
δ N = N ( ψ * ψ ) · δ V ,
d N = V 4 π 3 ( ψ * ψ ) d 3 k δ V .
d W = d N · ω d w d t = 2 e 2 2 π 2 m 2 ω V 2 e · M 2 ( ψ * ψ ) δ ( E c - E v - ω ) d 3 k δ V .
δ W = 2 e 2 2 π 2 m 2 ω V δ V Σ d Σ 2 ( ψ * ψ ) e · M 2 k ( E c - E v ) E c - E v = ω ,
δ W = 1 2 σ 2 δ V .
σ = 2 e 2 π 2 m 2 ω V Σ d Σ ( ψ * ψ ) e · M 2 k ( E c - E v ) E c - E v = h ω .
σ ( x ) = 2 e 2 π 2 m 2 ω Σ d Σ e · M 2 k ( E c - E v ) E c - E v = ω = constante = σ v 0 ,
W = 1 2 V σ ( x ) 2 δ V .
W = 1 2 σ V 2 δ V .
σ = V 2 σ ( x ) δ V / V 2 δ V .
σ ( x ) = 2 e 2 π 2 m 2 ω exp ( - 2 μ x ) Σ d Σ e · M 2 k ( E c - E v ) E c - E v = ω = exp ( - 2 μ x ) σ S 0 ,
2 = 0 2 exp [ - 2 K 2 ( x ) · x ] = 0 2 exp [ - ( 4 π / n c ) σ ( x ) · x ] ,
σ = 0 d [ σ v 0 + σ S 0 exp ( - 2 μ x ) ] exp { - ( 4 π / n c ) [ σ v 0 + σ S 0 · exp ( - 2 μ x ) ] x } 0 d exp { - ( 4 π / n c ) ] σ v 0 + σ S 0 exp ( - 2 μ x ) ] x } d x , d x .
( 4 π , n c ) σ S 0 x exp ( - 2 μ x ) 1.
σ = σ v 0 + σ S 0 1 2 μ + ( 4 π / n c ) σ v 0 - ( 4 π / n c ) σ S 0 [ 4 μ + ( 4 π / n c ) σ v 0 ] 2 1 ( 4 π / n c ) σ v 0 - ( 4 π / n c ) σ v 0 [ 2 μ + ( 4 π / n c ) σ v 0 ] 2 - 1 ( 4 π / n c ) σ v 0 exp [ - ( 4 π / n c ) σ v 0 d ] .
[ 2 K 2 = ( 4 π / n c ) σ v 0 2 μ ] σ = σ v 0 + σ S 0 K 2 μ 1 1 - exp ( - 2 K 2 d ) = σ v 0 + σ S 0 δ L 1 1 - exp ( - 2 K 2 d ) .
d σ S 0 d ω = - L δ [ 1 - exp ( - 2 K 2 d ) ] d σ v 0 d ω ,

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