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This Fourier Transfer Function properties?.

  1. Aug 1, 2015 #1
    Hi Everyone. I want to know what do you think about this Transfer function:

    [itex] T(\omega) = \frac{e^{i\omega\tau}}{1-\rho e^{i2\omega\tau}} [/itex]

    If[itex]\tau[/itex] is Real, this function is "good and pretty"(?), because it has a "nice" representation in time with its inverse transform: a delay plus a series of deltas displaced in time in [itex]n\tau[/itex] times [itex]\rho^n[/itex].
    But the question is: What about if [itex]\tau[/itex] is Complex?? Is there a magical property that i'm missing to deal with this?

    Sorry if i was mistaken on the election of the Forum. I don't know if this question may be in "Physics" because [itex] T(\omega) [/itex] is the Fabry-Perot Transfer Function, or in Engineering. And sorry for my English.

    Thanks!
     
  2. jcsd
  3. Aug 1, 2015 #2

    blue_leaf77

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    The simplest case of a FP resonator is that when the medium in between the mirrors is just vacuum, in that case ##\tau## is a constant with respect to frequency. By invoking that ##\tau## be complex (which physically means the intermediate medium is absorbing), this implies that this quantity must also be a function of frequency - there is no occurrence in reality where the index of refraction contained in ##\tau## is a constant complex number as this would violate Kramers-Kronig relation. Furthermore, there is no closed form of the dependence of refractive index on frequency as this is medium specific, so if ##\tau## is complex which also means ##\tau## is frequency dependent, the inverse FT of ##T(\omega)## won't be as nice as it is for free space case and I believe its analytical expression does not exist.
     
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