Retarded potentials in disspersive media

[hunt_mat]

Are there any equations for these? I have seen in books for the vacuum case but not for a dispersive media.

 

[vanhees71]

A very nice description of classical dispersion theory can be found in

A. Sommerfeld, Lectures on Theoretical Physics IV (Optics)

 

[hunt_mat]

Do they include the equations for a dispersive media though? I can get the basic theory from Griffiths (it's very well explained).

 

[vanhees71]

The classical dispersion theory gives you the (complex-valued) dielectric function $\epsilon(\omega)$ from a simple damped harmonic oscillator ansatz for the electrons in the medium interacting with the incoming em. wave.

Quantum-field theoretically you find very similar results as the retarded in-medium Green's function of the em. field. Quantum mechanical dispersion theory on this linear-response level is not so different from the classical theory.

 

[hunt_mat]

Interesting. I am not that interested in complex mediums, just a simple multiplicative description.

 

[Born2bwire]

Interesting. I am not that interested in complex mediums, just a simple multiplicative description.

You can't avoid it though. A dispersive media always implies a lossy media by virtue of the Kramers-Kronig relation. As vanhees states though, the simplest model for a dispersive media is a simple oscillator as modeled by the Debye relaxation (or its variants like the Cole-Cole, Cole-Davidson, etc.). I would use Debye relaxation as a basic start for modeling dielectric dispersion. As simple as it is, it's very useful in application as long as you realize that it is meant to be applied over a finite bandwidth.