How a mirror works: condensed matter explanation

[haushofer]

TL;DR Summary

fed up with phenomenological explanation of mirrors, need fundamental explanations

Dear all,

in the context of my teaching I was wondering what exactly the explanation is of how a mirror works at the atomic level. Apparently, the fact that reflecting materials are often also good conductors and hence big energy bands helps reflecting the photons. Does someone know a nice set of lecture notes where this is explained? So, questions like:

* how does the elecotromagnetic field / photons interact with the reflecting material as a solid state as a whole
* how exactly does the ability to reflect depend on the atomic structure of the material
* how can the law of reflection be explained within the "atomic paradigm" (instead of the maxwell- field approach)
* how does solid state physics explain the difference between reflecting materials and non-reflecting materials?
* do the photons interact with the free electrons of the material, or also with the bound ones from the atoms?

Well, hopefully you get the idea of my question. Of course, answers will also be appreciated :) Greetings!

sidenote: I'm a theoretical physicist who has forgotten most of his solid state physics...

 

[Vanadium 50]

Light wavelengths are around 5000 angstroms, and atoms are about an angstrom, so there are tens of millions of atoms responding at any instant to the EM fields of the wave. An atomic explanation is the wrong picture, as the light interacts collectively.

Some discussion in another context here.

 

[Lord Jestocost]

"Optical Properties of Solids" by M. S. Dresselhaus
[PDF]SOLID STATE PHYSICS PART II Optical Properties of Solids - MIT

 

[haushofer]

Light wavelengths are around 5000 angstroms, and atoms are about an angstrom, so there are tens of millions of atoms responding at any instant to the EM fields of the wave. An atomic explanation is the wrong picture, as the light interacts collectively.

Some discussion in another context here.

Thanks. I also had the idea that the picture of one single photon being absorbed and re-emitted (reflected) by a single electron is troublesome. Do you know of any references which cover this stuff in a pedagogical way?

 

[BvU]

Feynman !

 

[Dr_Nate]

Light wavelengths are around 5000 angstroms, and atoms are about an angstrom, so there are tens of millions of atoms responding at any instant to the EM fields of the wave. An atomic explanation is the wrong picture, as the light interacts collectively.

I disagree with the second sentence. The Lorentz model of the dielectric function is often explained in the context of the polarization of an atom. In fact, it is possible to perfectly fit the optical phonons of insulators (provided the phonons aren't anharmonic) with the Lorentz model. These oscillations are usually <200 meV and the IR wavelengths needed approach 1 millimeter.

 

[Dr_Nate]

Summary:: fed up with phenomenological explanation of mirrors, need fundamental explanations

You have so many questions, but I don't want to answer them all at once. I don't know if you've gone through them yet, but Milli Dresselhaus's notes are very detailed so you may get lost in it all.

The short answer to why mirrors work is that, in metals, the free electron density is high enough and the scattering is low enough that the free electrons form a plasma with a high reflectivity up to the plasma frequency.

Regarding what you said about bands: everything with charge in a material effects the reflectivity, but broad bands are not the reason why metals have high reflectivity.