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Could someone kindly explain the relation between dielectric funciton (e) and frequency, wavevetor? What is the condition for wavevector e(k=0, w), e(k, w=0) and why?

Thanks a lot

- Thread starter sinayu71
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- #1

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Could someone kindly explain the relation between dielectric funciton (e) and frequency, wavevetor? What is the condition for wavevector e(k=0, w), e(k, w=0) and why?

Thanks a lot

- #2

olgranpappy

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olgranpappy

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not necessarily. the response of the system is a property *of the system* and is independent of the probe used be it light or electrons or neutrons or etc.Are we talking probing with light here?

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Claude Bile

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Only in a vacuum. Inside a medium, particularly media whose permittivity varies as a function of position (waveguides, photonic crystals for example), the dispersion relation can get quite complex.

Sinayu71 - There is no simple way to obtain how the permittivity changes with frequency, since this function ultimately depends on the band structure of the medium.

For a regular, isotropic medium however, the permittivity does have a characteristic shape (minus the kinks and other perturbations), approximated in the optical region of the spectrum by the Selmier (sp?) equations.

Claude.

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thank you :shy:

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olgranpappy

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In the first example you give (plasma oscillation) one thinks of all the electrons moving together in the whole macroscopic metal--this response is obviously of macroscopic wavelength ([tex]k \to 0[/tex]) but finite frequency. For finite wavelength the plasma frequency is not the same as the k=0 case discussed in textbooks and is much more difficult to determine.

In the second example, one considers the static ([tex]\omega = 0[/tex]) screening of a point charge. If the point charge were not at rest in the solid the problem would again be more difficult.

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