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Nonlocal Optics

  • Ansgar Liebsch
Chapter
Part of the Physics of Solids and Liquids book series (PSLI)

Abstract

The microscopic electronic properties of metal surfaces can be probed with a variety of optical spectroscopies: ellipsometry, differential reflection spectroscopy, electroreflection, and attenuated total reflection. Surface photoemission and inverse photoemission are also intimately related to these microscopic properties since the amplitude and spatial variation of the local fields in the surface region determine the frequency dependence of the measured intensity. The proper treatment of the surface electronic structure and of its dynamical response characteristics require a generalization of classical Fresnel theory. In particular, the finite width of the surface density profile and the induced surface charge must be taken into account. Moreover, since these distributions vary rapidly on the scale of the wavelength, the nonlocal nature of the surface response cannot be omitted. Hence, near the surface the microscopic fields deviate appreciably from the standard Fresnel fields. At optical frequencies, the effect of these microscopic properties on observable quantities can be described in terms of two complex functions: d (w) and d (w). The real parts of these quantities specify the location of the normal and parallel induced surface currents; the imaginary parts represent the corresponding surface excitation spectra. The most prominent spectral feature in d (w) is the multipole surface plasmon, which has been identified on several simple metals. In the case of Ag, the surface excitations are strongly affected by d bands. The great sensitivity of surface optics with respect to the microscopic electronic structure is evident from the changes induced on surface charging. Optical spectroscopies are also well suited for investigating surface excitations localized in thin metallic overlayers.

Keywords

Jellium Model Bulk Plasmon Surface Response Function Volume Plasmon Bulk Plasma Frequency 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. Abelés, F., and T. López—Ríos, Surf. Sci. 96, 32 (1980).Google Scholar
  2. Anderegg, M., B. Feuerbacher, and B. Fitton, Phys. Rev. Lett. 27, 1565 (1971).ADSCrossRefGoogle Scholar
  3. Apell, P., Phys. Scr. 24, 795 (1981).ADSCrossRefGoogle Scholar
  4. Apell, P., and C. Holmberg, Solid State Commun. 49, 693 (1984).ADSCrossRefGoogle Scholar
  5. Bachelet, G. B., D. R. Hamann, and M. Schlüter, Phys. Rev. B 26, 4199 (1982).Google Scholar
  6. Bagchi, A., Phys. Rev. B 15, 3060 (1977).Google Scholar
  7. Bagchi, A., R. G. Barrera, and A. K. Rajagopal, Phys. Rev. B 20, 4824 (1979).CrossRefGoogle Scholar
  8. Barman, S. R., K. Horn, P. Häberle, H. Ishida, and A. Liebsch, to be published (1997).Google Scholar
  9. Bartynski, R. A., E. Jensen, T. Gustafsson, and E. W. Plummer, Phys. Rev. B 32, 1921 (1985).Google Scholar
  10. Bennett, A. J., Phys. Rev. B 1, 203 (1970).ADSCrossRefGoogle Scholar
  11. Borensztein, Y., W. L. Mochân, J. Tarriba, R. G. Barrera, and A. Tadjeddine, Phys. Rev. Lett. 71, 2334 (1993).ADSCrossRefGoogle Scholar
  12. Borensztein, Y., M. Roy, and R. Alameh, Europhys. Lett. 31, 5 (1995).CrossRefGoogle Scholar
  13. Brodskii, A. M., and M. I. Urbakh, Surf. Sci. 94, 369 (1980).ADSCrossRefGoogle Scholar
  14. Burke, K., and W L Schaich, Phys. Rev. B 48, 14599 (1993).Google Scholar
  15. Burke, K., and W. L. Schaich, Phys. Rev. B 49, 11397 (1994).Google Scholar
  16. Del Sole, R., Solid State Commun. 37, 537 (1981).ADSCrossRefGoogle Scholar
  17. Del Sole, R., in Electromagnetic Waves: Recent Developments in Research; vol. 2: Photonic Probes of Surfaces, P. Halevi, ed. ( Elsevier, Amsterdam, 1995 ), p. 131.Google Scholar
  18. Del Sole, R., and E. Fiorino, Phys. R.v. B 29, 4631 (1984).Google Scholar
  19. Drube, W., F. J. Himpsel, and P. J. Feibelman, Phys. Rev. Lett. 60, 2070 (1988).ADSCrossRefGoogle Scholar
  20. Drude, P., Ann. Phys. 43, 126 (1891).CrossRefGoogle Scholar
  21. Drude, P., The Theory of Optics ( Dover, New York, 1959 ), p. 290.Google Scholar
  22. Dzhavakhidze, P. G., A. A. Kornyshev, A. Tadjeddine, and M. I. Urbakh, Phys. Rev. B 39, 13106 (1989).Google Scholar
  23. Epstein, S. T., and R. E. Johnson, J. Chem. Phys. 51, 188 (1969).ADSCrossRefGoogle Scholar
  24. Feibelman, P. J., Phys. Rev. B 12, 1319 (1975a).ADSCrossRefGoogle Scholar
  25. Feibelman, P. J., Phys. Rev. Lett. 35, 617 (1975b).ADSCrossRefGoogle Scholar
  26. Feibelman, P. J., Prog. Surf. Sci. 12, 287 (1982).ADSCrossRefGoogle Scholar
  27. Feibelman, P. J., Surf. Sci. 282, 129 (1993).ADSCrossRefGoogle Scholar
  28. Fernández, V., D. Pahlke, N. Esser, K. Stahrenberg, O. Hunderi, A. M. Bradshaw, and W. Richter, to be published (1997).Google Scholar
  29. Flätgen, G., K. Krischer, B. Pettinger, K. Doblhofer, H. Junkes, and G. Ertl, Science 269, 668 (1995).ADSCrossRefGoogle Scholar
  30. Flodstrom, S. A., and J. G. Endriz, Phys. Rev. Lett. 31, 893 (1973).ADSCrossRefGoogle Scholar
  31. Flodstrom, S. A., and J. G. Endriz, Phys. Rev. B 12, 1252 (1975).Google Scholar
  32. Forstmann, F., Z. Phys. 203, 495 (1967).ADSCrossRefGoogle Scholar
  33. Forstmann, F., and R. R. Gerhardts, Metal Optics Near the Plasma Frequency, Springer Tracts in Modern Physics 109 ( Springer, Berlin, 1986 ).Google Scholar
  34. Forstmann, F., and H. Stenschke, Phys. Rev. B 17, 1489 (1978).Google Scholar
  35. Gerhardts, R. R., and K. Kempa, Phys. Rev. B 30, 5704 (1984).Google Scholar
  36. Gesell, T. F., E. T. Arakawa, M. W. Williams, and R. N. Hamm, Phys. Rev. B 7, 5141 (1973).Google Scholar
  37. Gies, P., and R. R. Gerhardts, Europhys. Lett. 1, 513 (1986).ADSCrossRefGoogle Scholar
  38. Gies, P., and R. R. Gerhardts, Phys. Rev. B 36, 4422 (1987).Google Scholar
  39. Gies, P., R. R. Gerhardts, and T. Maniv, Phys. Rev. B 35, 458 (1987).Google Scholar
  40. Gross, E. K. U., and W. Kohn, Phys. Rev. Lett. 55, 2850 (1985); Erratum: ibid. 57, 923 (1986).CrossRefGoogle Scholar
  41. Hagemann, H. J., W. Gudat, and C. Kunz, J. Opt. Soc. Am. 65, 742 (1975).ADSCrossRefGoogle Scholar
  42. Hanke, W., and L. J. Sham, Phys. Rev. B 21 4656 (1980).Google Scholar
  43. Ishida, H., and A. Liebsch, Phys. Rev. B 42, 5505 (1990).Google Scholar
  44. Ishida, H., and A. Liebsch, Phys. Rev. B 45, 6171 (1992).Google Scholar
  45. Ishida, H., and A. Liebsch, to be published (1997).Google Scholar
  46. Jackson, J. D., Classical Electrodynamics ( Wiley, New York, 1962 ).Google Scholar
  47. Jezequel, G., Phys. Rev. Lett. 45, 1963 (1980).ADSCrossRefGoogle Scholar
  48. Johnson, P. B., and R. W. Christy, Phys. Rev. B 6, 4370 (1972).Google Scholar
  49. Kempa, K., A. Liebsch, and W. L. Schaich, Phys. Rev. B 38, 12645 (1988).Google Scholar
  50. Kempa, K., and W. L. Schaich, Phys. Rev. B 37, 6711 (1988).Google Scholar
  51. Kempa, K., and W. L. Schaich, Phys. Rev. B 39, 13139 (1989).Google Scholar
  52. Kim, B. O., E. W. Plummer, and A. Liebsch, to be published (1997).Google Scholar
  53. Kolb, D. M., in Surface Polaritons, V. M. Agranovich and D. L. Mills, eds. ( North Holland, Amsterdam, 1982 ), p. 299.CrossRefGoogle Scholar
  54. Kötz, R., and D. M. Kolb, Surf. Sci. 97, 575 (1980).ADSCrossRefGoogle Scholar
  55. Lang, N. D., and W. Kohn, Phys. Rev. B 1, 4555 (1970).Google Scholar
  56. Lang, N. D., and W. Kohn, Phys. Rev. B 7, 3541 (1973).Google Scholar
  57. Langreth, D. C., Phys. Rev. B 39, 10020 (1989).Google Scholar
  58. Lee, J. T., and W. L. Schaich, Phys. Rev. B 43, 4629 (1991a).Google Scholar
  59. Lee, J. T., and W. L. Schaich, Phys. Rev. B 44, 13010 (1991b).Google Scholar
  60. Levinson, H. J., E. W. Plummer, and P. J. Feibelman, Phys. Rev. Lett. 43, 952 (1979).ADSCrossRefGoogle Scholar
  61. Levinson, H. J., and E. W. Plummer, Phys. Rev. B 24, 628 (1981).Google Scholar
  62. Liebsch, A., Phys. Rev. B 36, 7378 (1987).Google Scholar
  63. Liebsch, A., G. Benemanskaya, and M. Lapushkin, Surf. Sci. 302, 303 (1994).ADSCrossRefGoogle Scholar
  64. Liebsch, A., G. Hincelin, and T. López—Ríos, Phys. Rev. B 41, 10463 (1990).Google Scholar
  65. Liebsch, A., and W. L. Schaich, Phys. Rev. B 52, 14219 (1995).Google Scholar
  66. Lindau, I., and P. O. Nilsson, Phys. Scr. 3, 87 (1971).ADSCrossRefGoogle Scholar
  67. López—Ríos, T., M. De Crescenzi, and Y. Borensztein, Solid State Commun. 30, 755 (1979).Google Scholar
  68. López—Ríos, T., in Electromagnetic Waves: Recent Developments in Research; vol. 1: Spatial Dispersion in Solids and Plasmas, P. Halevi, ed. ( Elsevier, Amsterdam, 1992 ), p. 215.Google Scholar
  69. Mackinson, R. E. B., Proc. Roy. Soc. A 162, 367 (1937). Manie, T., and H. Metiu, Phys. Rev. B 22, 4731 (1980).Google Scholar
  70. Manninen, M., R. Nieminen, P. Hautojärvi, and J. Arponen, Phys. Rev. B 12, 4012 (1975).Google Scholar
  71. McIntyre, J. D. E., and D. E. Aspnes, Surf. Sci. 24, 417 (1971). Melnyk, A. R., and M. J. Harrison, Phys. Rev. Lett. 21, 85 (1968).Google Scholar
  72. Mochân, W. L., E. Fuchs, and R. G. Barrera, Phys. Rev. B 27, 771 (1983).Google Scholar
  73. Mochân, W. L., and R. G. Barrera, Phys. Rev. Lett. 55, 1192 (1985); Phys. Rev. B 32, 4984 (1985).Google Scholar
  74. Monin, J., Acta Electron. 16, 139 (1973).Google Scholar
  75. Monin, J., and S. G. A. Boutry, Phys. Rev. B 9, 1309 (1974).Google Scholar
  76. Mukhopadhyay, G., and S. Lundqvist, Phys. Scr. 17, 69 (1977).ADSCrossRefGoogle Scholar
  77. Pehlke, E., and A. Liebsch, unpublished (1991).Google Scholar
  78. Persson, B. N. J., and A. Apell, Phys. Rev. B 27, 6058 (1983).Google Scholar
  79. Persson, B. N. J., and E. Zaremba, Phys. Rev. B 30, 5669 (1984).Google Scholar
  80. Petersen, H., and S. B. M. Hagstrom, Phys. Rev. B 41, 1314 (1978).Google Scholar
  81. Plieth, W. J., and K. Naegele, Surf. Sci. 64, 484 (1977).ADSCrossRefGoogle Scholar
  82. Samuelsen, D., A. Yang, and W. Schattke, Surf. Sci. 287/288, 676 (1993).Google Scholar
  83. Sass, J. K., S. Stucki, and H. J. Lewerenz, Surf. Sci. 68, 429 (1977).ADSCrossRefGoogle Scholar
  84. Sauter, F., Z. Phys. 203, 488 (1967).ADSCrossRefGoogle Scholar
  85. Schaich, W. L., Phys. Rev. B 50, 17587 (1994a).Google Scholar
  86. Schaich, W. L., Surf. Sci. 318, L1157 (1994b).ADSCrossRefGoogle Scholar
  87. Schaich, W. L., and W. Chen, Phys. Rev. B 39, 10714 (1989).Google Scholar
  88. Schaich, W. L., and J. T. Lee, Phys. Rev. B 44, 5973 (1991).Google Scholar
  89. Schaich, W. L., and C. M. J. Wijers, Phys. Rev. B 51, 10189 (1995).Google Scholar
  90. Sipe, J. E., Phys. Rev. B 22, 1589 (1980).ADSCrossRefGoogle Scholar
  91. Sorbello, R. S., Solid State Commun. 56, 821 (1985).ADSCrossRefGoogle Scholar
  92. Sprunger, P. T., G. M. Watson, and E. W. Plummer, Surf. Sci. 269/270, 551 (1992).Google Scholar
  93. Sturm, K., Advances in Physics 31, 1 (1982).ADSCrossRefGoogle Scholar
  94. Sturm, K., and L. E. Oliveira, Phys. Rev. B 40, 3672 (1989).Google Scholar
  95. Tadjeddine, A., D. M. Kolb, and R. Kötz, Surf. Sci. 101, 277 (1980).ADSCrossRefGoogle Scholar
  96. Tarriba, J., and W. L. Mochân, Phys. Rev. B 46, RC 12902 (1992).Google Scholar
  97. Walldén, L., Phys. Rev. Lett. 54, 943 (1985).ADSCrossRefGoogle Scholar
  98. Wijers, C. M. J., and G. P. M. Poppe, Phys. Rev. B 46, 7605 (1992).Google Scholar
  99. Zaremba, E., and W. Kohn, Phys. Rev. B 13, 2270 (1976).Google Scholar

Copyright information

© Springer Science+Business Media New York 1997

Authors and Affiliations

  • Ansgar Liebsch
    • 1
  1. 1.Forschungszentrum JülichJülichGermany

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