The dielectric function of a metal using LD model.

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Discussion Overview

The discussion focuses on the dielectric function of metals as described by the Lorentz-Drude (LD) model, comparing it to classical dielectric functions used for other materials. Participants explore the physical meanings of intraband and interband effects, seek symbolic forms of the dielectric function, and clarify aspects of the LD model.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant expresses confusion about how the LD model differs from the classical dielectric function, specifically regarding the roles of intraband and interband effects.
  • Another participant asks for the symbolic form of the dielectric function used in the LD model, referencing a specific tutorial page.
  • A reply suggests that the LD model describes absorption through a sum of Lorentzian lines and mentions the use of Kramers-Kronig relations to derive the real part of the dielectric function.
  • A participant clarifies their interest in a specific equation from the tutorial and compares it to the LD model, noting similarities and seeking further clarification on variable exchanges.
  • Discussion includes details about the terms in the LD model, where "b" represents bound electrons and "f" represents free electrons, with oscillator strengths associated with harmonic oscillators.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the specific symbolic form of the dielectric function or the exact relationship between the LD model and classical models, indicating ongoing uncertainty and exploration of the topic.

Contextual Notes

Some participants reference specific equations and models without fully resolving the differences or dependencies on definitions, leaving certain assumptions and mathematical steps unclear.

sixers0130
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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!
 
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btw, does anyone know what is the dielectric function (in symbolic form) they are using?

http://ab-initio.mit.edu/wiki/index.php/Meep_Tutorial/Material_dispersion
 
sixers0130 said:
btw, does anyone know what is the dielectric function (in symbolic form) they are using?

http://ab-initio.mit.edu/wiki/index.php/Meep_Tutorial/Material_dispersion
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.
 
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?!)
 

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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.
 

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