What is the meaning of the high-frequency dielectric permittivity limit for polaritons?

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Summary:

Questions about the high-frequency limit of the dielectric permittivity in metals, and especially why it appears in the polariton dielectric function.

Main Question or Discussion Point

During the derivation of the dielectric function of a plasma (Kittel 8. ed. chap. 14), this somewhat mysterious quantity ε(∞) is inserted to account for the high-frequency dielectric contribution of the ionic background. In some ways, I see how this is related to the "external" charge density in the general electronic ε, but I don't quite see exactly why it is multiplied in exactly like it is.. Or why it is sometimes referred to as an "optical constant". And I would be especially grateful for any insight in why it is also inserted in the polariton dispersion relation, as the ion background is not really "external" with respect to phonons.

So can anyone give me some insight? Thanks in advance!
 

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Lord Jestocost
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At the end, ##\epsilon_\infty## refers within the framework of a model to all contributions to the overall permittivity of the material which are considered to be about constant in the considered frequency range.
 
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