# Imaginary part of dielectric constant.

1. Jun 16, 2010

### Ravian

in ac fields permittivity becomes complex quantity and has real and imaginary parts. in metals (may be few exceptions but i dont know) imaginary part is always positive and represents loss factor or energy absorbed. why the plot of imaginary part of dielectric constant as function of energy is exponentially decaying curve (it decreases with the increase in energy)?secondly img. part of dielectric constant is also related to conductivity so can we infer that energy lost to the metals appears as conductivity? but then it is directly proportional to conductivity but conductivity plots (as function of energy again) show structures. finally permittivity becomes complex because ac fields are complex or their is any other reason? i am studying electrodynamics of continuous media of landau and lifgarbagez.

2. Jun 17, 2010

### DrDu

I would not think of the complex part of permittivity in metals as energy absobed. The reason is that even an ideal electron gas, which is non-absorptive, has a high imaginary part. In fact, absorption only occurs is both the real part n and the complex part k are both non-zero as absorption is proportional to n*k. In an ideal metal, permittivity is purely imaginary so that there is no absorption.
Second, permittivity (or better polarizability) and conductivity are up to a factor i omega identical. Take in mind that conductivity also is a complex quantity in general.
I wouldn´t say that permittivity becomes complex because AC fields become complex but because the reaction to an oscillating field is exponentially decaying in the metal.

3. Jun 18, 2010

### Ravian

Landau (pg 276, 2nd Ed. eq: 80.6) does say that imaginary part of dielectric fun. (e2)represents loss and almost similar arguments are used by Jackson's book. Is not absorption proportional to k only by alpha=4pi*k/lambda. non-zero k means e2 is non zero (e2=2*n*k) whick means absorption. probably in metals both n & k decrease exponentially so is e2. metals are dispersive medium so absorption and reflection does take place that is why they appear to be shiny.e2=4pi*sigma/omega where sigma is real conductivity. [img. sigma is related to real part of epsilon] what i do not understand is the shape of e2 as function of energy which is decaying exponentially. can we identify metals, semiconductors insulators just by looking at the plot of e2 vs photon energy. one more thing i.e. what are units of e2 (F/m?).

4. Jun 18, 2010

### DrDu

Sorry, I confused permittivity and index of refraction. You are right, if the imaginary part of epsilon (is that the e2 you are talking about) is non-zero, the substance is absorbant. However, in an ideal metal without resistance, epsilon would be real and negative, at least up to a point called plasma frequency where it becomes zero.