Wave attenuation, complex e

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  • #1
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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.

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I could attempt this if I knew where to start... not much help, but could anyone offer a hint?
 

Answers and Replies

  • #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
 
  • #3
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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.
 
  • #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:
  • #5
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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
 
  • #6
ehild
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Do you know the imaginary part of k?

ehild
 

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