Polarizaition and susceptibility

  1. 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. Andy Resnick

    Andy Resnick 6,143
    Science Advisor
    Education Advisor

    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. 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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