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Polarizaition and susceptibility

  1. Jun 3, 2009 #1

    KFC

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    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. jcsd
  3. Jun 3, 2009 #2

    Andy Resnick

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    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 frequency-dependent susceptibility is simply dispersion.
     
  4. Jun 3, 2009 #3

    KFC

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    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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