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Polarizaition and susceptibility 
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#1
Jun309, 12:11 PM

P: 369

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? 


#2
Jun309, 12:27 PM

Sci Advisor
P: 5,517

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:
P(t)=[itex]\int \chi(t\tau)E(\tau)d\tau[/itex] 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 frequencydependent susceptibility is simply dispersion. 


#3
Jun309, 12:54 PM

P: 369

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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