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Fractals: optical susceptibility and giant raman scattering

  • V. M. Shalaev
  • M. I. Stockman
Article

Abstract

A theory is developed which describes the optical properties of fractal clusters (i.e. of aggregates of non-trivial Hausdorff dimension consisting of interacting monomer particles). It is shown that with respect to these properties fractal clusters differ significantly from both gases and condensed media. The interaction between the monomers is assumed to be dipole-dipole. The theory is based on the self-consistent field equations; it takes into account the fluctuation nature of the fractal cluster (considerable probability for approach of monomers to each other despite an asymptotically zero integral density). An expression is obtained for the linear susceptibility. Combination of the monomers with the formation of a cluster entails the splitting, shift and broadening of the monomer spectra. These changes depend strongly on the fractal (Hausdorff) dimension of the cluster but do not depend on the number of monomers in it (for a cluster of non-trivial dimension). On the other hand, the monomers partially retain their individuality and the susceptibility — its quasi-resonance nature. Broadening, like the imaginary part of the susceptibility, does not depend on dissipation in an individual monomer. It is predicted that giant Raman scattering may occur at an impurity particle fixed near one of the cluster monomers when excitation takes place in the absorption band of the cluster. The enhancement factor for the scattering is also determined by the fractal dimension.

PACS

64.60 

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References

  1. 1.
    Mandelbrot, B.M.: Fractals, form, chance, and dimension. San Francisco: Freeman 1977; The fractal geometry of Nature. San Francisco: Freeman 1982Google Scholar
  2. 2.
    Zeldovich, Ya.B., Sokolov, D.D., Uspekhi Fiz. Nauk146, 493 (1985)Google Scholar
  3. 3.
    Witten, T.A., Sander, L.M.: Phys. Rev. B27, 5686 (1983)Google Scholar
  4. 4.
    Meakin, P.: Phys. Rev. Lett.51, 1119 (1983); J. Chem. Phys.81, 4637 (1981)Google Scholar
  5. 5.
    Vicsek, T.: Phys. Rev. Lett.53, 2281 (1984)Google Scholar
  6. 6.
    Weitz, D.A., Oliveria, M.: Phys. Rev. Lett.52, 1433 (1984)Google Scholar
  7. 7.
    Feder, J., Joessang, T., Rosenquist, E.: Phys. Rev. Lett.53, 1403 (1984)Google Scholar
  8. 8.
    Schaefer, D.W., Martin, J.E., Wiltzius, P., Cannel, D.S.: Phys. Rev. Lett.52, 2371 (1984)Google Scholar
  9. 9.
    Ersh, I.G., Muratov, L.C., Novozhilov, S.Yu., Stockman, B.M., Stockman, M.I.: Doklady AN SSSR287, 1239 (1986); Preprint Inst. Autom. Electrometry N 292 (1985)Google Scholar
  10. 10.
    Elam, W.T., Wolf, S.A., Sprague, J. et al.: Phys. Rev. Lett.54, 701 (1985)Google Scholar
  11. 11.
    Isaacson, J., Lubensky, T.S.: J. Phys. Lett. (Paris)41, L469 (1981)Google Scholar
  12. 12.
    Kreibig, U.: Z. Phys. D — Atoms, Molecules and Clusters3, 239 (1986)Google Scholar
  13. 13.
    Berry, M.V., Percival, I.C.: Opt. Acta, 1986,33, 577Google Scholar
  14. 14.
    Hui, P.M., Strond, D.: Phys. Rev. B33, 2163 (1986)Google Scholar
  15. 15.
    Shalaev, V.M., Stockman, M.I.: Zh. Eksp. Teor. Fiz.92, 509 (1987); Preprint Inst. Phys. N 391 F, Krasnoyarsk 1986Google Scholar
  16. 16.
    Yemelyanov, V.I., Koroteev, N.I.: Uspekhi Fiz. Nauk135, 345 (1981)Google Scholar
  17. 17.
    Moskovits, M.: Rev. Mod. Phys.57, 785 (1985)Google Scholar
  18. 18.
    Kittel, Ch.: Introduction to solid state physics, 4th Edn., Chap. 13. New York: J. Wiley 1973Google Scholar
  19. 19.
    Klimontovich, Yu.L., Osipov, M.A., Egibyan, L.V.: Kristallografiya30, 445 (1985)Google Scholar
  20. 20.
    Burstein, A.I. Uspekhi Fiz. Nauk.143, 553 (1984); Avtometriya,5, 65;6, 72 (1978)Google Scholar
  21. 21.
    Beitmen, G., Erdei, A.: Tables of integral transformations, Vol. 1. Moscow: Nauka 1969Google Scholar

Copyright information

© Springer-Verlag 1988

Authors and Affiliations

  • V. M. Shalaev
    • 1
  • M. I. Stockman
    • 2
  1. 1.Institute of PhysicsUSSR Academy of Sciences, Siberian BranchKrasnoyarskUSSR
  2. 2.Institute of Automation and ElectrometryUSSR Academy of Sciences, Siberian BranchNovosibirskUSSR

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