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The dispersion relations for surface plasma oscillations in normal metals are investigated for single- and multiple-film systems taking retardation effects into account. The simple dielectric function ε(ω)=1-ωp2/ω2 is found to be adequate for the high-frequency region in which oscillations remain undamped. Two types of possible modes of oscillation are found. One type corresponds to dispersion relations which behave linearly for not-so-high frequency, with a phase velocity always smaller than the velocity of light in the dielectric, but at least ten times larger than the Fermi velocity, while the other type consists of high-frequency modes (ω∼ωp). The role of these oscillations in the problem of transition radiation is reexamined. In the case of a thin metal film, a new interpretation is proposed for the peak observed in the transition radiation spectrum. Finally, the work is extended to superconducting metals where, in the frequency range ℏω\textless2Δ (2Δ is the superconducting energy gap), we have justified the use of a dielectric function of the same functional form as given above but with ωp2 replaced by an almost frequency-independent quantity ωps2, where ωps=c/λps and λps is the actual penetration depth. In this frequency range, the oscillations are essentially undamped and play an important role in the electromagnetic properties of the multiple-film systems, and particularly when the systems exhibit the ac Josephson effect.

@article{economou_surface_1969, title = {Surface {Plasmons} in {Thin} {Films}}, volume = {182}, url = {http://link.aps.org/doi/10.1103/PhysRev.182.539}, doi = {10.1103/PhysRev.182.539}, abstract = {The dispersion relations for surface plasma oscillations in normal metals are investigated for single- and multiple-film systems taking retardation effects into account. The simple dielectric function ε(ω)=1-ωp2/ω2 is found to be adequate for the high-frequency region in which oscillations remain undamped. Two types of possible modes of oscillation are found. One type corresponds to dispersion relations which behave linearly for not-so-high frequency, with a phase velocity always smaller than the velocity of light in the dielectric, but at least ten times larger than the Fermi velocity, while the other type consists of high-frequency modes (ω∼ωp). The role of these oscillations in the problem of transition radiation is reexamined. In the case of a thin metal film, a new interpretation is proposed for the peak observed in the transition radiation spectrum. Finally, the work is extended to superconducting metals where, in the frequency range ℏω{\textless}2Δ (2Δ is the superconducting energy gap), we have justified the use of a dielectric function of the same functional form as given above but with ωp2 replaced by an almost frequency-independent quantity ωps2, where ωps=c/λps and λps is the actual penetration depth. In this frequency range, the oscillations are essentially undamped and play an important role in the electromagnetic properties of the multiple-film systems, and particularly when the systems exhibit the ac Josephson effect.}, number = {2}, urldate = {2012-11-24TZ}, journal = {Physical Review}, author = {Economou, E. N.}, month = jun, year = {1969}, pages = {539--554} }

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