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

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  1. The symboul 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 cm3/2sec-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).
  3. R. Fuchs and S. H. Liu, "Sum rule for the polarizability of small particles," Phys. Rev. B 14, 5521-5522 (1976).
  4. T. S. Chen, F. S. de Wette, and L. Kleinman, "Infrared absorption in MgO microcrystals," Phys. Rev. B 18, 958-962 (1978).
  5. R. Fuchs, "Infrared absorption in MgO microcrystals," Phys. Rev. B 18, 7160-7162 (1978).
  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).
  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).
  8. G. Mukhopadhay and S. Lundqvist, "The electromagnetic field near a metal surface," Phys. Scr. 17, 69-81 (1979).
  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).
  10. R. London, "Theory of the first-order Raman effect in crystals," Proc. R. Soc. (London) A 275, 218-232 (1963).
  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

G. Mukhopadhay and S. Lundqvist, "The electromagnetic field near a metal surface," Phys. Scr. 17, 69-81 (1979).

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).

1978

T. S. Chen, F. S. de Wette, and L. Kleinman, "Infrared absorption in MgO microcrystals," Phys. Rev. B 18, 958-962 (1978).

R. Fuchs, "Infrared absorption in MgO microcrystals," Phys. Rev. B 18, 7160-7162 (1978).

1976

R. Fuchs and S. H. Liu, "Sum rule for the polarizability of small particles," Phys. Rev. B 14, 5521-5522 (1976).

1975

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).

1971

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).

1969

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).

1963

R. London, "Theory of the first-order Raman effect in crystals," Proc. R. Soc. (London) A 275, 218-232 (1963).

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).

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).

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).

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).

Fuchs, R.

R. Fuchs, "Infrared absorption in MgO microcrystals," Phys. Rev. B 18, 7160-7162 (1978).

R. Fuchs and S. H. Liu, "Sum rule for the polarizability of small particles," Phys. Rev. B 14, 5521-5522 (1976).

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).

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).

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).

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).

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).

Kleinman, L.

T. S. Chen, F. S. de Wette, and L. Kleinman, "Infrared absorption in MgO microcrystals," Phys. Rev. B 18, 958-962 (1978).

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).

Liu, S. H.

R. Fuchs and S. H. Liu, "Sum rule for the polarizability of small particles," Phys. Rev. B 14, 5521-5522 (1976).

London, R.

R. London, "Theory of the first-order Raman effect in crystals," Proc. R. Soc. (London) A 275, 218-232 (1963).

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).

G. Mukhopadhay and S. Lundqvist, "The electromagnetic field near a metal surface," Phys. Scr. 17, 69-81 (1979).

Mukhopadhay, G.

G. Mukhopadhay and S. Lundqvist, "The electromagnetic field near a metal surface," Phys. Scr. 17, 69-81 (1979).

Phys. Rev.

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).

Phys. Rev. B

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).

R. Fuchs and S. H. Liu, "Sum rule for the polarizability of small particles," Phys. Rev. B 14, 5521-5522 (1976).

T. S. Chen, F. S. de Wette, and L. Kleinman, "Infrared absorption in MgO microcrystals," Phys. Rev. B 18, 958-962 (1978).

R. Fuchs, "Infrared absorption in MgO microcrystals," Phys. Rev. B 18, 7160-7162 (1978).

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).

Phys. Scr.

G. Mukhopadhay and S. Lundqvist, "The electromagnetic field near a metal surface," Phys. Scr. 17, 69-81 (1979).

Proc. R. Soc. London A

R. London, "Theory of the first-order Raman effect in crystals," Proc. R. Soc. (London) A 275, 218-232 (1963).

Solid State Commun.

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).

Other

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 symboul 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 cm3/2sec-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.

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