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Homework Help: Wave attenuation, complex e

  1. Nov 8, 2011 #1
    Consider a wave propagating in a medium with complex epsilon (e).

    Show that the ratio of decay length to wavelength is roughly Re(e)/Im(e)
    when the decay length is long compared to the wavelength.

    ---

    I could attempt this if I knew where to start... not much help, but could anyone offer a hint?
     
  2. jcsd
  3. Nov 8, 2011 #2

    ehild

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    A plane electromagnetic wave of angular frequency ω propagates along the x axis in a medium of refractive index N. Write out the wave in the exponential form.

    The refractive index is N=√(ε/ε0). If ε is complex, so is N.

    ehild
     
  4. Nov 8, 2011 #3
    Well a plane wave for an em wave is

    [tex]E=A\exp{(kr-wt)}[/tex]

    I'm just not seeing how to proceed from here.
     
  5. Nov 9, 2011 #4

    ehild

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    How is related k to the wavelength? The wavelength in the medium to the refractive index? The refractive index to epsilon?

    ehild
     
    Last edited: Nov 9, 2011
  6. Nov 9, 2011 #5
    Hi. We have [tex]k=\frac{2pi}{\lambda} = \frac{2*pi*n}{\lambda_o} = \frac{2*pi*\sqrt{\epsilon}}{\lambda_o}[/tex]

    But of course epsilon has real and complex parts...

    The ratio of the wavelength to the decay length is lambda / (1/imaginary part of k) :S
     
  7. Nov 10, 2011 #6

    ehild

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    Do you know the imaginary part of k?

    ehild
     
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