Abstract

The optical absorption in small cubic particles and thin films, composed of an ionic crystal or a free-electron metal, is calculated by using both a local dielectric constant and more-exact microscopic methods. It is found that a local theory gives a qualitatively correct description of the absorption in cubes but not in thin films. The electric field is calculated in thin metallic films, and the results are applied to the theory of surface-enhanced Raman scattering.

© 1981 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. The symbol ωp stands for two somewhat different quantities. If ωp is related to the total number of charges, as in Eqs. (2) and (4a), it has units cm3/2 sec−1. If it is related to the number of charges per unit volume, as in Eqs. (3) and (4b), it has units sec−1, and only in this case is it actually a frequency.
  2. R. Fuchs, “Theory of the optical properties of ionic crystal cubes,” Phys. Rev. B 11, 1732–1740 (1975); “Theory of the optical properties of small cubes,” Phys. Lett. 48A, 353–354 (1974).
    [Crossref]
  3. R. Fuchs and S. H. Liu, “Sum rule for the polarizability of small particles,” Phys. Rev. B 14, 5521–5522 (1976).
    [Crossref]
  4. T. S. Chen, F. S. de Wette, and L. Kleinman, “Infrared absorption in MgO microcrystals,” Phys. Rev. B 18, 958–962 (1978).
    [Crossref]
  5. R. Fuchs, “Infrared absorption in MgO microcrystals,” Phys. Rev. B 18, 7160–7162 (1978).
    [Crossref]
  6. W. E. Jones and R. Fuchs, “Surface modes of vibration and optical properties of an ionic crystal slab,” Phys. Rev. B 4, 3581–3603 (1971); R. Fuchs, “Nonlocal optical properties of an ionic crystal film,” Phys. Lett. 43A, 42–44 (1973).
    [Crossref]
  7. W. E. Jones, K. L. Kliewer, and R. Fuchs, “A nonlocal theory of the optical properties of thin metallic films,” Phys. Rev. 178, 1201–1203 (1969).
    [Crossref]
  8. G. Mukhopadhay and S. Lundqvist, “The electromagnetic field near a metal surface,” Phys. Scr. 17, 69–81 (1979).
    [Crossref]
  9. C. Y. Chen, E. Burstein, and S. Lundqvist, “Giant Raman scattering by pyridine and CN absorbed on silver,” Solid State Commun. 32, 63–66 (1979).
    [Crossref]
  10. R. London, “Theory of the first-order Raman effect in crystals,” Proc. R. Soc. (London) A 275, 218–232 (1963).
    [Crossref]
  11. Although the idea that electrons can leave the film is not consistent with the infinite potential barriers at the surfaces, we believe that our calculation of Eq. (7) is not greatly in error.

1979 (2)

G. Mukhopadhay and S. Lundqvist, “The electromagnetic field near a metal surface,” Phys. Scr. 17, 69–81 (1979).
[Crossref]

C. Y. Chen, E. Burstein, and S. Lundqvist, “Giant Raman scattering by pyridine and CN absorbed on silver,” Solid State Commun. 32, 63–66 (1979).
[Crossref]

1978 (2)

T. S. Chen, F. S. de Wette, and L. Kleinman, “Infrared absorption in MgO microcrystals,” Phys. Rev. B 18, 958–962 (1978).
[Crossref]

R. Fuchs, “Infrared absorption in MgO microcrystals,” Phys. Rev. B 18, 7160–7162 (1978).
[Crossref]

1976 (1)

R. Fuchs and S. H. Liu, “Sum rule for the polarizability of small particles,” Phys. Rev. B 14, 5521–5522 (1976).
[Crossref]

1975 (1)

R. Fuchs, “Theory of the optical properties of ionic crystal cubes,” Phys. Rev. B 11, 1732–1740 (1975); “Theory of the optical properties of small cubes,” Phys. Lett. 48A, 353–354 (1974).
[Crossref]

1971 (1)

W. E. Jones and R. Fuchs, “Surface modes of vibration and optical properties of an ionic crystal slab,” Phys. Rev. B 4, 3581–3603 (1971); R. Fuchs, “Nonlocal optical properties of an ionic crystal film,” Phys. Lett. 43A, 42–44 (1973).
[Crossref]

1969 (1)

W. E. Jones, K. L. Kliewer, and R. Fuchs, “A nonlocal theory of the optical properties of thin metallic films,” Phys. Rev. 178, 1201–1203 (1969).
[Crossref]

1963 (1)

R. London, “Theory of the first-order Raman effect in crystals,” Proc. R. Soc. (London) A 275, 218–232 (1963).
[Crossref]

Burstein, E.

C. Y. Chen, E. Burstein, and S. Lundqvist, “Giant Raman scattering by pyridine and CN absorbed on silver,” Solid State Commun. 32, 63–66 (1979).
[Crossref]

Chen, C. Y.

C. Y. Chen, E. Burstein, and S. Lundqvist, “Giant Raman scattering by pyridine and CN absorbed on silver,” Solid State Commun. 32, 63–66 (1979).
[Crossref]

Chen, T. S.

T. S. Chen, F. S. de Wette, and L. Kleinman, “Infrared absorption in MgO microcrystals,” Phys. Rev. B 18, 958–962 (1978).
[Crossref]

de Wette, F. S.

T. S. Chen, F. S. de Wette, and L. Kleinman, “Infrared absorption in MgO microcrystals,” Phys. Rev. B 18, 958–962 (1978).
[Crossref]

Fuchs, R.

R. Fuchs, “Infrared absorption in MgO microcrystals,” Phys. Rev. B 18, 7160–7162 (1978).
[Crossref]

R. Fuchs and S. H. Liu, “Sum rule for the polarizability of small particles,” Phys. Rev. B 14, 5521–5522 (1976).
[Crossref]

R. Fuchs, “Theory of the optical properties of ionic crystal cubes,” Phys. Rev. B 11, 1732–1740 (1975); “Theory of the optical properties of small cubes,” Phys. Lett. 48A, 353–354 (1974).
[Crossref]

W. E. Jones and R. Fuchs, “Surface modes of vibration and optical properties of an ionic crystal slab,” Phys. Rev. B 4, 3581–3603 (1971); R. Fuchs, “Nonlocal optical properties of an ionic crystal film,” Phys. Lett. 43A, 42–44 (1973).
[Crossref]

W. E. Jones, K. L. Kliewer, and R. Fuchs, “A nonlocal theory of the optical properties of thin metallic films,” Phys. Rev. 178, 1201–1203 (1969).
[Crossref]

Jones, W. E.

W. E. Jones and R. Fuchs, “Surface modes of vibration and optical properties of an ionic crystal slab,” Phys. Rev. B 4, 3581–3603 (1971); R. Fuchs, “Nonlocal optical properties of an ionic crystal film,” Phys. Lett. 43A, 42–44 (1973).
[Crossref]

W. E. Jones, K. L. Kliewer, and R. Fuchs, “A nonlocal theory of the optical properties of thin metallic films,” Phys. Rev. 178, 1201–1203 (1969).
[Crossref]

Kleinman, L.

T. S. Chen, F. S. de Wette, and L. Kleinman, “Infrared absorption in MgO microcrystals,” Phys. Rev. B 18, 958–962 (1978).
[Crossref]

Kliewer, K. L.

W. E. Jones, K. L. Kliewer, and R. Fuchs, “A nonlocal theory of the optical properties of thin metallic films,” Phys. Rev. 178, 1201–1203 (1969).
[Crossref]

Liu, S. H.

R. Fuchs and S. H. Liu, “Sum rule for the polarizability of small particles,” Phys. Rev. B 14, 5521–5522 (1976).
[Crossref]

London, R.

R. London, “Theory of the first-order Raman effect in crystals,” Proc. R. Soc. (London) A 275, 218–232 (1963).
[Crossref]

Lundqvist, S.

C. Y. Chen, E. Burstein, and S. Lundqvist, “Giant Raman scattering by pyridine and CN absorbed on silver,” Solid State Commun. 32, 63–66 (1979).
[Crossref]

G. Mukhopadhay and S. Lundqvist, “The electromagnetic field near a metal surface,” Phys. Scr. 17, 69–81 (1979).
[Crossref]

Mukhopadhay, G.

G. Mukhopadhay and S. Lundqvist, “The electromagnetic field near a metal surface,” Phys. Scr. 17, 69–81 (1979).
[Crossref]

Phys. Rev. (1)

W. E. Jones, K. L. Kliewer, and R. Fuchs, “A nonlocal theory of the optical properties of thin metallic films,” Phys. Rev. 178, 1201–1203 (1969).
[Crossref]

Phys. Rev. B (5)

R. Fuchs, “Theory of the optical properties of ionic crystal cubes,” Phys. Rev. B 11, 1732–1740 (1975); “Theory of the optical properties of small cubes,” Phys. Lett. 48A, 353–354 (1974).
[Crossref]

R. Fuchs and S. H. Liu, “Sum rule for the polarizability of small particles,” Phys. Rev. B 14, 5521–5522 (1976).
[Crossref]

T. S. Chen, F. S. de Wette, and L. Kleinman, “Infrared absorption in MgO microcrystals,” Phys. Rev. B 18, 958–962 (1978).
[Crossref]

R. Fuchs, “Infrared absorption in MgO microcrystals,” Phys. Rev. B 18, 7160–7162 (1978).
[Crossref]

W. E. Jones and R. Fuchs, “Surface modes of vibration and optical properties of an ionic crystal slab,” Phys. Rev. B 4, 3581–3603 (1971); R. Fuchs, “Nonlocal optical properties of an ionic crystal film,” Phys. Lett. 43A, 42–44 (1973).
[Crossref]

Phys. Scr. (1)

G. Mukhopadhay and S. Lundqvist, “The electromagnetic field near a metal surface,” Phys. Scr. 17, 69–81 (1979).
[Crossref]

Proc. R. Soc. (London) A (1)

R. London, “Theory of the first-order Raman effect in crystals,” Proc. R. Soc. (London) A 275, 218–232 (1963).
[Crossref]

Solid State Commun. (1)

C. Y. Chen, E. Burstein, and S. Lundqvist, “Giant Raman scattering by pyridine and CN absorbed on silver,” Solid State Commun. 32, 63–66 (1979).
[Crossref]

Other (2)

Although the idea that electrons can leave the film is not consistent with the infinite potential barriers at the surfaces, we believe that our calculation of Eq. (7) is not greatly in error.

The symbol ωp stands for two somewhat different quantities. If ωp is related to the total number of charges, as in Eqs. (2) and (4a), it has units cm3/2 sec−1. If it is related to the number of charges per unit volume, as in Eqs. (3) and (4b), it has units sec−1, and only in this case is it actually a frequency.

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (8)

Fig. 1
Fig. 1

Dipole strengths Cj as a function of depolarization factors nj for the six most prominent excitations of a cube.

Fig. 2
Fig. 2

Dipole strengths Cjxx, Cjyy, Cjzz as functions of the normal-mode frequencies ωj for a MgO cube containing 900 atoms calculated using lattice dynamics.

Fig. 3
Fig. 3

Dipole strengths Cj as a function of normal-mode frequencies ωj for MgO calculated using a local dielectric constant.

Fig. 4
Fig. 4

Lattice-dynamical (solid curve) and local (dashed curve) optical absorption of a MgO cube as functions of frequency.

Fig. 5
Fig. 5

Lattice-dynamical (points) and nonlocal (solid curve) optical absorption of a NaCl film, as functions of frequency Ω = ω/ωT.

Fig. 6
Fig. 6

Nonlocal (solid curve) and local (dashed curve) optical absorptance of a free-electron film as functions of frequency for p-polarized light incident at 75°. The electron density is that of potassium, and the film thickness is 46 Å.

Fig. 7
Fig. 7

Microscopic (solid curve) and local (dashed curve) optical absorptance of a free-electron film, as functions of frequency, using the same parameters as in Fig. 6.

Fig. 8
Fig. 8

Normal component of the electric field in a free-electron film as a function of position. The solid curve and the dot–dashed curve show the microscopic and nonlocal results, respectively. The frequency is 1/2 ωp.

Equations (8)

Equations on this page are rendered with MathJax. Learn more.

D ( r , ω ) = ( r - r , ω ) E ( r , ω ) d 3 r .
M μ = ν α μ ν E ν = 1 4 π ω p 2 j , ν C j μ ν ω j 2 - ω ( ω + i γ ) E ν .
¯ = 1 + 4 π M / E = 1 + ω p 2 j C j ω j 2 - ω ( ω + i γ ) .
0 ω α 2 μ ν ( ω ) d ω = 1 8 ω p 2 δ μ ν ,
0 ω ¯ 2 ( ω ) d ω = π 2 ω p 2 .
M μ = ν α μ ν E ν = v 4 π j , ν C j μ ν ( - 1 ) - 1 + n j E ν ,
C j μ ν = 4 π ω p 2 s s q s q s ( M s M s ) - 1 / 2 ξ j ( s , μ ) ξ j ( s , ν ) .
M = i j F H ep i i h vib j j H ep I ( E I - E j ) ( E I - E i ) .