How Does Complex Epsilon Influence Wave Propagation and Attenuation?

[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.

---

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

 

[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

 

[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.

 

[ehild]

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

ehild

 

[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

 

[ehild]

Do you know the imaginary part of k?

ehild