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.
Preview
Unable to display preview. Download preview PDF.
References
M. Born, E. Wolf, Principles of Optics (Pergamon 1975).
D. Pines, Elementary Excitations in Solids, New York, Benjamin 1964.
H. Raether, Springer Tracts Mod. Phys. 38, 85 (1965).
F. Sauter, in Fachberichte der Physikertagung der DPG, Düsseldorf 1964.
F. Sauter, Z. Physik 203, 488 (1967).
F. Forstmann, Z. Physik 203, 495 (1967).
A. R. Melnyk, M. J. Harrison; Phys. Rev. Lett. 21, 85 (1970), Phys. Rev. B2, 835 (1970).
I. Lindau, P. O. Nilsson, Phys. Lett A31, 352 (1970), Physica Scripta 3, 87 (1971).
M. Anderegg, B. Feuerbacher, B. Fitton; Phys. Rev. Lett. 27, 1565 (1971).
K. L. Kliewer, Surface Sci. 101, 57 (1980).
P. J. Feibelman, Review: Surface Electromagnetic Fields, preprint.
F. Forstmann, H. Stenschke, Phys. Rev. Lett. 38, 1365 (1977).
V. M. Agranovich, V. L. Ginzburg, Spatial Dispersion in Crystal Optics and the Theory of Excitons, (New York, Wiley 1966).
R. Becker, F. Sauter, Theorie der Elektrizität, Vol. III (Teubner, Stuttgart 1969) § 64.
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).
L. D. Landau, E. M. Lifschitz, Lehrbuch der Theor. Physik Vol. VI.
F. Forstmann, H. Stenschke, Phys. Rev. B17, 1489 (1978).
A. D. Boardman, R. Ruppin, Surface Sci. 112, 153 (1981).
F. Abelès, Y. Borensztein, M. De Crescenzi, T. Lopez-Rios, Surf. Sci. 101, 123 (1980).
R. Kötz, D. M. Kolb, F. Forstmann, Surface Sci. 91, 489 (1980).
F. Sauter, F. Forstmann, K. Sturm, Helv. Phys. Acta 41, 1138 (1968).
P. J. Feibelman, Phys. Rev. Lett. 35, 617 (1975).
T. Lopez-Rios, F. Abelès, G. Vuye, J. de Physique, 40, L343 (1979).
T. Lopez-Rios, M. De Crescenzi, Y. Borensztein, Sol. State Commun. 30, 755 (1979).
M. De Crescenzi, T. Lopez-Rios, G. Vuye, N. J. Mansor, Y. Borensztein, Thin Solid Films 57, 89 (1979).
F. Abelès, in Advanced Optical Techniques, ed. A.C.S. van Heel (North Holland, Amsterdam) 1967.
A. Otto, in Optical Properties of Solids, New Developments. Ed. B. O. Seraphin (North Holland, Amsterdam) 1976, p. 678.
D. M. Kolb, J. de Physique 38, C5–167 (1977).
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).
F. Forstmann, R. Kötz, D. M. Kolb, Proceedings of the Third European Conference on Surface Science (ECOSS-3), Cannes (France), September 1980.
F. Abelès, T. Lopez-Rios, Surface Sci. 96, 32 (1980).
K. Kempa, F. Forstmann, R. Kötz, B. E. Hayden, Surface Sci. 118 (1982).
J. Zenneck, Ann. Physik 23, 846 (1907).
A. Sommerfeld, Ann. Physik 28, 665 (1909). A. Sommerfeld, Vorlesungen der Theor. Physik Band VI, § 32, Leipzig 1966.
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.
R. H. Ritchie, Phys. Rev. 106, 874 (1957), Progr. Theor. Phys. 29, 607 (1963).
R. H. Ritchie, Surface Sci. 34, 1 (1973).
H. Raether, Physics of Thin Films 9, 147 (1977).
A. A. Maradudin, in Festkörperprobleme (Advances in Solid State Physics) Vol. XXI, 25, J. Treusch (ed.), Vieweg, Braunschweig (1981).
K. Sturm, Z. Physik 209, 329 (1968).
J. Bennett, Phys. Rev. B1, 203 (1970).
K. J. Krane, H. Raether, Phys. Rev. Lett. 37, 1355 (1976).
A. Tadjeddine, D. M. Kolb, R. Kötz, Surface Sci. 101, 277 (1980).
P. J. Feibelman, Phys. Rev. B12, 1319 (1975).
P. J. Feibelman, Phys. Rev. B23, 2629 (1981).
K. Kempa, F. Forstmann, to be published.
P. Apell, Physica Scripta (1982).
M. P. Seah, W. A. Dench, Surf. and Interf. Analysis 1, 1 (1979).
K. L. Kliewer, Phys. Rev. B14, 1412 (1976).
H. Petersen, S. B. M. Hagström, Phys. Rev. Lett. 41, 1314 (1978), H. Petersen, Z. Physik B31, 171 (1978).
H. J. Levinson, E. W. Plummer, P. J. Feibelman, Phys. Rev. Lett. 43, 952 (1979).
J. G. Endriz, Phys. Rev. B7, 3464 (1973).
N. Barberan, J. E. Inglesfield, J. Phys. C14, 3114 (1981).
S. I. Pekar, Zh. Eksp. Teor. Fiz. 33, 1022 (1957) [Sov. Phys.-JETP 6, 785 (1958)]; ibid. 34, 1176 (1958) [ibid. 7, 813 (1958)].
G. D. Mahan and J. J. Hopfield, Phys. Rev. A135, 428 (1964).
G. S. Agarwal, D. N. Pattanayak and E. Wolf, Phys. Rev. B10, 1447 (1974); Phys. Rev. B11, 1342 (1975) and references therein.
M. F. Bishop and A. A. Maradudin, Phys. Rev. B14, 3384 (1976).
A. K. Rajagopal and F. Forstmann, unpublished.
G. E. H. Reuter and E. H. Sondheimer, Proc. Roy. Soc. Lond. A195, 336 (1948).
K. L. Kliewer and R. Fuchs, Phys. Rev. 172, 607 (1968); R. Fuchs and K. L. Kliewer, Phys. Rev. 185, 905 (1969).
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.
D. L. Johnson and P. R. Rimbey, Phys. Rev. B14, 2398 (1976).
P. R. Rimbey and G. D. Mahan, Solid State Comm. 15, 35 (1974).
R. Zeyher, J. L. Birman and W. Brenig, Phys. Rev. B6, 4613 (1972).
P. R. Rimbey, Phys. Rev. B15, 1215 (1977).
F. Flores, F. García-Moliner and R. Monreal, Phys. Rev. B15, 5076 (1977).
F. García-Moliner and F. Flores, J. de Physique 38, 851 (1977).
P. Garik and N. W. Ashcroft, Solid State Commun. 39, 1183 (1981).
G. Mukhopadhyay and S. Lundqvist, Physica Scripta 17, 69 (1978); Solid State Commun. 21, 629 (1977).
R. G. Barrera and A. Bagchi, Phys. Rev. B20, 3186 (1979).
N. D. Lang and W. Kohn, Phys. Rev. B1, 4555 (1970).
see Ref. [11], P. J. Feibelman, Review: Surface Electromagnetic Fields, preprint, further references therein.
A. Bagchi, R. G. Barrera and A. K. Rajagopal, Phys. Rev. B20, 4827 (1979).
J. E. Sipe; Phys. Rev B22, 1589 (1980).
R. G. Barrera and A. Bagchi, Phys. Rev. B24, 1612 (1981).
It is usual and sufficient to replace ∈t by its k = 0 limit, so that the transverse fields can be calculated easily.
J. Lindhard, Kgl. Danske Videnskab. Selskab, Mat. Fys. Medd. 28, 8 (1954).
D. Pines and P. Nozieres, Theory of Quantum Liquids, (Benjamin, New York, 1966).
B. N. J. Persson, J. Phys. C13, 435 (1980).
P. Apell, Physica Scripta 23, 284 (1981).
G. Mukhopadhyay, Solid State Commun. 28, 277 (1978).
P. Apell, Physica Scripta 17, 535 (1978).
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
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1982 Friedr. Vieweg & Sohn Verlagsgesellschaft mbH
About this chapter
Cite this chapter
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
Download citation
DOI: https://doi.org/10.1007/BFb0107944
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-528-08028-0
Online ISBN: 978-3-540-75370-4
eBook Packages: Springer Book Archive