# Polarizaition and susceptibility

by KFC
Tags: polarizaition, susceptibility
 P: 369 In some unit, the relation of (linear) polarization and susceptibility can be written of $$P(t) = \chi E(t)$$ but I also read some expression in other text reads $$P(\omega) = \chi(\omega) E(\omega)$$ why change the time to frequency? Why polarization depends on frequency?
 Sci Advisor P: 5,468 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)=$\int \chi(t-\tau)E(\tau)d\tau$ And taking the Fourier transform of this equation provides your second expression. If the material responds instantaneously and has no memory[$\chi(t-\tau) = \chi\delta(t-\tau)$], then the convolution integral reduces to your first expression. Having a frequency-dependent susceptibility is simply dispersion.
P: 369
 Quote by Andy Resnick 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)=$\int \chi(t-\tau)E(\tau)d\tau$ And taking the Fourier transform of this equation provides your second expression. If the material responds instantaneously and has no memory[$\chi(t-\tau) = \chi\delta(t-\tau)$], then the convolution integral reduces to your first expression. Having a frequency-dependent susceptibility is simply dispersion.
Oh ... I just wonder why in textbook they don't say it is a convolution! So you mean in frequency domain susceptibility is the repsonse function?

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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