# Homework Help: Wave attenuation, complex e

1. Nov 8, 2011

### mathman44

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?

2. Nov 8, 2011

### ehild

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. Nov 8, 2011

### mathman44

Well a plane wave for an em wave is

$$E=A\exp{(kr-wt)}$$

I'm just not seeing how to proceed from here.

4. Nov 9, 2011

### ehild

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
5. Nov 9, 2011

### mathman44

Hi. We have $$k=\frac{2pi}{\lambda} = \frac{2*pi*n}{\lambda_o} = \frac{2*pi*\sqrt{\epsilon}}{\lambda_o}$$

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. Nov 10, 2011

### ehild

Do you know the imaginary part of k?

ehild