# The dielectric function of a metal using LD model.

1. ### sixers0130

6
I'm studying the dispersive properties of metals using Lorentz-Drude model, but I'm confused about the equation set-up.

What is LD model different from the classical dielectric function using for other dielectrics? Namely: ε(w) = ε’ + iε’' where the imaginary part is the attenuation.

In LD model, ε is composed of intraband (free-electron) effects and interband (bound-electron) effects. Physically what do they mean?

Thanks for the help!

6
3. ### DrDu

4,247
You could be a bit more specific. Do you mean the first formula ## \epsilon=(ck/\omega)^2##? That is just the relation between the dielectric constant and the index of refraction ##\epsilon=n^2##.

It would be useful if you could cite the form of the LD model you are referring too.
I think the Lorentz Drude model assumes absorption (or equivalently imaginary part of epsilon) to be described by a sum of Lorentzian lines. The real part can then be obtained using Kramers Kronig relations. The absorption lines are due to inter- or intraband transitions.

4. ### sixers0130

6
Dear DrDu,

Thanks for the reply and sorry about the confusing! I mean the second formula from the page where numbers are used to plug in. I try to compare this one with LD model from the paper "Optical Properties of Metallic Films for Vertical-Cavity Optoelectronic Devices" where equations are stated in the attachment.

They look very similar. I try to compare if there is just some variable exchange but couldn't find it. So I'm just wondering what would the symbolic form of the second equation from the site would be.

Thanks so much for the help again!
(btw can someone teach me how to type equations within text?!)

File size:
2.7 KB
Views:
17
File size:
3.1 KB
Views:
16
File size:
3.9 KB
Views:
16
5. ### DrDu

4,247
The terms with the "b" (supposedly for band or bound) describe the reaction of bound electrons in a harmonic oscillator with frequency ##\omega_j##. Correspondingly the f_jare called oscillator strengths.

Up to the 1, the term with "f" can be seen to be of a similar form with ##\omega_j## being equalt to 0. Hence these electrons are unbound or free.