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Metal optics near the plasma frequency

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Festkörperprobleme 22

Part of the book series: Advances in Solid State Physics ((ASSP,volume 22))

Abstract

Near the plasma frequency spatial dispersion is an important effect in metal optics, since it leads to optical excitation of plasma waves. We outline an extension of local metal optics, which takes this effect into account via the hydrodynamical approximation for the electron motion and appropriate additional boundary conditions. We discuss a number of successful applications including an analysis of the fields near the surface. Finally, we review other methods dealing with nonlocal optics near a metal surface and comment on the theoretical limitations and practical merits of the hydrodynamical approach.

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References

  1. M. Born, E. Wolf, Principles of Optics (Pergamon 1975).

    Google Scholar 

  2. D. Pines, Elementary Excitations in Solids, New York, Benjamin 1964.

    MATH  Google Scholar 

  3. H. Raether, Springer Tracts Mod. Phys. 38, 85 (1965).

    Google Scholar 

  4. F. Sauter, in Fachberichte der Physikertagung der DPG, Düsseldorf 1964.

    Google Scholar 

  5. F. Sauter, Z. Physik 203, 488 (1967).

    Article  ADS  Google Scholar 

  6. F. Forstmann, Z. Physik 203, 495 (1967).

    Article  ADS  Google Scholar 

  7. A. R. Melnyk, M. J. Harrison; Phys. Rev. Lett. 21, 85 (1970), Phys. Rev. B2, 835 (1970).

    Article  ADS  Google Scholar 

  8. I. Lindau, P. O. Nilsson, Phys. Lett A31, 352 (1970), Physica Scripta 3, 87 (1971).

    Article  ADS  Google Scholar 

  9. M. Anderegg, B. Feuerbacher, B. Fitton; Phys. Rev. Lett. 27, 1565 (1971).

    Article  ADS  Google Scholar 

  10. K. L. Kliewer, Surface Sci. 101, 57 (1980).

    Article  ADS  Google Scholar 

  11. P. J. Feibelman, Review: Surface Electromagnetic Fields, preprint.

    Google Scholar 

  12. F. Forstmann, H. Stenschke, Phys. Rev. Lett. 38, 1365 (1977).

    Article  ADS  Google Scholar 

  13. V. M. Agranovich, V. L. Ginzburg, Spatial Dispersion in Crystal Optics and the Theory of Excitons, (New York, Wiley 1966).

    Google Scholar 

  14. R. Becker, F. Sauter, Theorie der Elektrizität, Vol. III (Teubner, Stuttgart 1969) § 64.

    Google Scholar 

  15. The static pressure gradient of the electron gas is grad \(p = \frac{m}{3}v_F^2\) grad n. The factor 3/5 (instead of 1/3) for the dynamic pressure stems from the fact that the coherent high frequency density perturbations do not use the entire phase space and therefore lead to a stronger increase of the local Fermi energy than relaxation to local equilibrium would do. See Ref. 14 R. Becker, F. Sauter, Theorie der Elektrizität, Vol. III (Teubner, Stuttgart 1969) § 64 or J. D. Jackson, Classical Electrodynamics (Wiley 1962/1975).

    Google Scholar 

  16. L. D. Landau, E. M. Lifschitz, Lehrbuch der Theor. Physik Vol. VI.

    Google Scholar 

  17. F. Forstmann, H. Stenschke, Phys. Rev. B17, 1489 (1978).

    Article  ADS  Google Scholar 

  18. A. D. Boardman, R. Ruppin, Surface Sci. 112, 153 (1981).

    Article  ADS  Google Scholar 

  19. F. Abelès, Y. Borensztein, M. De Crescenzi, T. Lopez-Rios, Surf. Sci. 101, 123 (1980).

    Article  ADS  Google Scholar 

  20. R. Kötz, D. M. Kolb, F. Forstmann, Surface Sci. 91, 489 (1980).

    Article  Google Scholar 

  21. F. Sauter, F. Forstmann, K. Sturm, Helv. Phys. Acta 41, 1138 (1968).

    Google Scholar 

  22. P. J. Feibelman, Phys. Rev. Lett. 35, 617 (1975).

    Article  ADS  Google Scholar 

  23. T. Lopez-Rios, F. Abelès, G. Vuye, J. de Physique, 40, L343 (1979).

    Article  Google Scholar 

  24. T. Lopez-Rios, M. De Crescenzi, Y. Borensztein, Sol. State Commun. 30, 755 (1979).

    Article  ADS  Google Scholar 

  25. M. De Crescenzi, T. Lopez-Rios, G. Vuye, N. J. Mansor, Y. Borensztein, Thin Solid Films 57, 89 (1979).

    Article  Google Scholar 

  26. F. Abelès, in Advanced Optical Techniques, ed. A.C.S. van Heel (North Holland, Amsterdam) 1967.

    Google Scholar 

  27. A. Otto, in Optical Properties of Solids, New Developments. Ed. B. O. Seraphin (North Holland, Amsterdam) 1976, p. 678.

    Google Scholar 

  28. D. M. Kolb, J. de Physique 38, C5–167 (1977).

    Article  Google Scholar 

  29. J. D. E. McIntyre, in: Advances in Electrochemistry and Electrochemical Engineering, Vol. 9, Ed. R. H. Muller (Wiley-Interscience, New York, 1973), p. 61.; J. D. E. McIntyre, Surface Sci. 37, 658 (1973).

    Google Scholar 

  30. F. Forstmann, R. Kötz, D. M. Kolb, Proceedings of the Third European Conference on Surface Science (ECOSS-3), Cannes (France), September 1980.

    Google Scholar 

  31. F. Abelès, T. Lopez-Rios, Surface Sci. 96, 32 (1980).

    Article  ADS  Google Scholar 

  32. K. Kempa, F. Forstmann, R. Kötz, B. E. Hayden, Surface Sci. 118 (1982).

    Google Scholar 

  33. J. Zenneck, Ann. Physik 23, 846 (1907).

    Article  ADS  Google Scholar 

  34. A. Sommerfeld, Ann. Physik 28, 665 (1909). A. Sommerfeld, Vorlesungen der Theor. Physik Band VI, § 32, Leipzig 1966.

    Article  ADS  Google Scholar 

  35. Eq. (2.10) is often squared and solved for k 2x . Then a second solution for ω > ωp is found which does not solve (2.10). It is not an eigenmode but yields the condition for the Brewster angle.

    Google Scholar 

  36. R. H. Ritchie, Phys. Rev. 106, 874 (1957), Progr. Theor. Phys. 29, 607 (1963).

    Article  ADS  MathSciNet  Google Scholar 

  37. R. H. Ritchie, Surface Sci. 34, 1 (1973).

    Article  ADS  Google Scholar 

  38. H. Raether, Physics of Thin Films 9, 147 (1977).

    Google Scholar 

  39. A. A. Maradudin, in Festkörperprobleme (Advances in Solid State Physics) Vol. XXI, 25, J. Treusch (ed.), Vieweg, Braunschweig (1981).

    Google Scholar 

  40. K. Sturm, Z. Physik 209, 329 (1968).

    Article  ADS  Google Scholar 

  41. J. Bennett, Phys. Rev. B1, 203 (1970).

    Article  ADS  Google Scholar 

  42. K. J. Krane, H. Raether, Phys. Rev. Lett. 37, 1355 (1976).

    Article  ADS  Google Scholar 

  43. A. Tadjeddine, D. M. Kolb, R. Kötz, Surface Sci. 101, 277 (1980).

    Article  ADS  Google Scholar 

  44. P. J. Feibelman, Phys. Rev. B12, 1319 (1975).

    Article  ADS  Google Scholar 

  45. P. J. Feibelman, Phys. Rev. B23, 2629 (1981).

    Article  ADS  Google Scholar 

  46. K. Kempa, F. Forstmann, to be published.

    Google Scholar 

  47. P. Apell, Physica Scripta (1982).

    Google Scholar 

  48. M. P. Seah, W. A. Dench, Surf. and Interf. Analysis 1, 1 (1979).

    Article  Google Scholar 

  49. K. L. Kliewer, Phys. Rev. B14, 1412 (1976).

    Article  ADS  Google Scholar 

  50. H. Petersen, S. B. M. Hagström, Phys. Rev. Lett. 41, 1314 (1978), H. Petersen, Z. Physik B31, 171 (1978).

    Article  ADS  Google Scholar 

  51. H. J. Levinson, E. W. Plummer, P. J. Feibelman, Phys. Rev. Lett. 43, 952 (1979).

    Article  ADS  Google Scholar 

  52. J. G. Endriz, Phys. Rev. B7, 3464 (1973).

    Article  ADS  Google Scholar 

  53. N. Barberan, J. E. Inglesfield, J. Phys. C14, 3114 (1981).

    Article  ADS  Google Scholar 

  54. S. I. Pekar, Zh. Eksp. Teor. Fiz. 33, 1022 (1957) [Sov. Phys.-JETP 6, 785 (1958)]; ibid. 34, 1176 (1958) [ibid. 7, 813 (1958)].

    Google Scholar 

  55. G. D. Mahan and J. J. Hopfield, Phys. Rev. A135, 428 (1964).

    Article  ADS  Google Scholar 

  56. G. S. Agarwal, D. N. Pattanayak and E. Wolf, Phys. Rev. B10, 1447 (1974); Phys. Rev. B11, 1342 (1975) and references therein.

    Article  ADS  MathSciNet  Google Scholar 

  57. M. F. Bishop and A. A. Maradudin, Phys. Rev. B14, 3384 (1976).

    Article  ADS  Google Scholar 

  58. A. K. Rajagopal and F. Forstmann, unpublished.

    Google Scholar 

  59. G. E. H. Reuter and E. H. Sondheimer, Proc. Roy. Soc. Lond. A195, 336 (1948).

    Article  MATH  ADS  Google Scholar 

  60. K. L. Kliewer and R. Fuchs, Phys. Rev. 172, 607 (1968); R. Fuchs and K. L. Kliewer, Phys. Rev. 185, 905 (1969).

    Article  ADS  Google Scholar 

  61. K. L. Kliewer, in Photoemission and the Electronic Properties of Surfaces, ed. B. Feuerbacher, B. Fitton, R. F. Willis (Wiley, New York, 1978), p. 45.

    Google Scholar 

  62. D. L. Johnson and P. R. Rimbey, Phys. Rev. B14, 2398 (1976).

    Article  ADS  Google Scholar 

  63. P. R. Rimbey and G. D. Mahan, Solid State Comm. 15, 35 (1974).

    Article  ADS  Google Scholar 

  64. R. Zeyher, J. L. Birman and W. Brenig, Phys. Rev. B6, 4613 (1972).

    Article  ADS  Google Scholar 

  65. P. R. Rimbey, Phys. Rev. B15, 1215 (1977).

    Article  ADS  Google Scholar 

  66. F. Flores, F. García-Moliner and R. Monreal, Phys. Rev. B15, 5076 (1977).

    Article  ADS  Google Scholar 

  67. F. García-Moliner and F. Flores, J. de Physique 38, 851 (1977).

    Article  Google Scholar 

  68. P. Garik and N. W. Ashcroft, Solid State Commun. 39, 1183 (1981).

    Article  ADS  Google Scholar 

  69. G. Mukhopadhyay and S. Lundqvist, Physica Scripta 17, 69 (1978); Solid State Commun. 21, 629 (1977).

    Article  ADS  Google Scholar 

  70. R. G. Barrera and A. Bagchi, Phys. Rev. B20, 3186 (1979).

    Article  ADS  Google Scholar 

  71. N. D. Lang and W. Kohn, Phys. Rev. B1, 4555 (1970).

    Article  ADS  Google Scholar 

  72. see Ref. [11], P. J. Feibelman, Review: Surface Electromagnetic Fields, preprint, further references therein.

    Google Scholar 

  73. A. Bagchi, R. G. Barrera and A. K. Rajagopal, Phys. Rev. B20, 4827 (1979).

    Article  ADS  Google Scholar 

  74. J. E. Sipe; Phys. Rev B22, 1589 (1980).

    Article  ADS  Google Scholar 

  75. R. G. Barrera and A. Bagchi, Phys. Rev. B24, 1612 (1981).

    Article  ADS  Google Scholar 

  76. It is usual and sufficient to replace ∈t by its k = 0 limit, so that the transverse fields can be calculated easily.

    Google Scholar 

  77. J. Lindhard, Kgl. Danske Videnskab. Selskab, Mat. Fys. Medd. 28, 8 (1954).

    MathSciNet  Google Scholar 

  78. D. Pines and P. Nozieres, Theory of Quantum Liquids, (Benjamin, New York, 1966).

    Google Scholar 

  79. B. N. J. Persson, J. Phys. C13, 435 (1980).

    Article  ADS  Google Scholar 

  80. P. Apell, Physica Scripta 23, 284 (1981).

    Article  ADS  Google Scholar 

  81. G. Mukhopadhyay, Solid State Commun. 28, 277 (1978).

    Article  ADS  Google Scholar 

  82. P. Apell, Physica Scripta 17, 535 (1978).

    Article  ADS  Google Scholar 

  83. Lately we got aware of the work of Maniv and Metiu, who published calculations similar to Feibelman's: T. Maniv and H. Metiu, J. Chem. Phys. 76, 696 (1982). 3

    Article  ADS  Google Scholar 

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© 1982 Friedr. Vieweg & Sohn Verlagsgesellschaft mbH

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Forstmann, F., Gerhardts, R.R. (1982). Metal optics near the plasma frequency. In: Grosse Aachen, P. (eds) Festkörperprobleme 22. Advances in Solid State Physics, vol 22. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0107944

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  • DOI: https://doi.org/10.1007/BFb0107944

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