|Jun3-09, 12:11 PM||#1|
Polarizaition and susceptibility
In some unit, the relation of (linear) polarization and susceptibility can be written of
[tex]P(t) = \chi E(t)[/tex]
but I also read some expression in other text reads
[tex]P(\omega) = \chi(\omega) E(\omega)[/tex]
why change the time to frequency? Why polarization depends on frequency?
|Jun3-09, 12:27 PM||#2|
Your equations are not really written correctly. The first one, the time dependent one, should really be written as a convolution: The polarization of a linear isotropic medium with a local but noninstantaneous response (but still independent of time) is:
And taking the Fourier transform of this equation provides your second expression.
If the material responds instantaneously and has no memory[[itex]\chi(t-\tau) = \chi\delta(t-\tau)[/itex]], then the convolution integral reduces to your first expression.
Having a frequency-dependent susceptibility is simply dispersion.
|Jun3-09, 12:54 PM||#3|
BTW, can you tell me one text in which the author show clearly the convolution relation b/w polarization, susceptibility and field? I am writing a short report and need a reference
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