Light propagation in dense media

[jeremyfiennes]

TL;DR

Web-available links

Do you have accessible web links discussing the pros and cons of the various theories of light propagation in dense media? I have done quire a bit of searching, but all seems rather superficial (Don Lincoln's video, f. ex.)
Thanks

 

[anorlunda]

You'll get better answers if your question is more specific.

What do you mean by pro/con? opaque/transparent? cheap/expensive? images/illumination?

What do you mean by dense media? I think glass is pretty dense.

Please elaborate your question.

 

[jeremyfiennes]

Looking through the replies to the questions on the topic, there seem to be two main theories: absorption-reemission and secondary wave. The latter is described in Feynman's 1963 lecture, but which I don't find very convincing. Are there links to in-depth discussions of the two. And how they explain the Fizeau effect, for instance. (Sorry, I thought I had posted this a few days ago. It doesn't seem to have got through.)

 

[hutchphd]

Feynman's 1963 lecture

Which lecture and what do you need convincing about? The fellow did know some physics after all.

 

[jeremyfiennes]

Exactly. That is what I had always thought. The ref is: <https://www.feynmanlectures.caltech.edu/I_31.html>.
He arrives at an equation (eq.31-19) that he says is "the 'explanation' of the index of refraction that we wished to obtain". But he doesn't give a numerical example to show that it in fact is. And he doesn't go into what a value for w₀ would be in a specific case, water for instance.
This is not however what I want to discuss. I'm after a link to a serious comparison between this and the rival absorption-reemission theory, as for instance described in <https://www.physlink.com/Education/AskExperts/ae509.cfm>:
"When light enters a material, photons are absorbed by the atoms in that material, increasing the energy of the atom. The atom will then lose energy after some tiny fraction of time, emitting a photon in the process. This photon, which is identical to the first, travels at the speed of light until it is absorbed by another atom and the process repeats. The delay between the time that the atom absorbs the photon and the excited atom releases as photon causes it to appear that light is slowing down"
But this is not a recognized source.

 

[tech99]

Exactly. That is what I had always thought. The ref is: <https://www.feynmanlectures.caltech.edu/I_31.html>.
He arrives at an equation (eq.31-19) that he says is "the 'explanation' of the index of refraction that we wished to obtain". But he doesn't give a numerical example to show that it in fact is. And he doesn't go into what a value for w₀ would be in a specific case, water for instance.
This is not however what I want to discuss. I'm after a link to a serious comparison between this and the rival absorption-reemission theory, as for instance described in <https://www.physlink.com/Education/AskExperts/ae509.cfm>:
"When light enters a material, photons are absorbed by the atoms in that material, increasing the energy of the atom. The atom will then lose energy after some tiny fraction of time, emitting a photon in the process. This photon, which is identical to the first, travels at the speed of light until it is absorbed by another atom and the process repeats. The delay between the time that the atom absorbs the photon and the excited atom releases as photon causes it to appear that light is slowing down"
But this is not a recognized source.

With the absorption-re-emission theory, it strikes me that the time delay would be somewhat random, and so light passing through the medium would acquire noise. But this is not the case, for instance, with optical fibres.

 

[hutchphd]

I don't understand your problem with Feynman's treatment. It is quite correct. He does not use the term "photon" at all, and other than saying the electron is like an oscillator it is entirely classical. He then extracts bunches of physics from this result. The concept of dispersion (and later phase and group velocity) is fundamental
Do not be listen to the guy in the back waving his hands about photons and time delays.
If you want a quantum description, you need to do quantum mechanics...

 

[vanhees71]

Well, Feynman is wise enough not to use the word photon where it isn't needed. This notion is so loaded with historical misconceptions, which are perpetuated forever since way too many introductory QM-textbook writers still copy the wrong handwaving statements from old quantum theory in their introductory chapter.

The classical linear-response theory, very clearly discussed in the Feynman Lectures vol. II is phenomenologically very succuessful, but of course it cannot predict the specifics of the in-medium Green's function (aka index of refraction) since for this you need indeed quantum theory. The semiclassical theory, where only the matter is quantized but the em. field is kept classical is sufficient, because the key issue is absorption and induced emission, both of which are well-described with the semiclassical model as far as you don't consider the interaction of single electrons but only classical em. waves).

 

[DrDu]

I don't think there is really a discrepancy between the description in terms of absorption-reemission and secondary wave when done on a quantum mechanical level.

 

[jeremyfiennes]

Ok.

 

[vanhees71]

There is, of course, no discrepancy between the two treatments of the index of refraction of a homogeneous medium discussed above. The macroscopic approach as discussed by Feynman using the idea of polarization is a bit simpler, while the more microscopic (classical) approach is more intuitive. The latter is very nicely discussed in the (anyway very nice book)

M. Schwartz, Principles of Electrodynamics, Dover (1987)

 

[hutchphd]

"When light enters a material, photons are absorbed by the atoms in that material, increasing the energy of the atom. The atom will then lose energy after some tiny fraction of time, emitting a photon in the process. This photon, which is identical to the first, travels at the speed of light until it is absorbed by another atom and the process repeats. The delay between the time that the atom absorbs the photon and the excited atom releases as photon causes it to appear that light is slowing down"

But surely you do not think this is a good description of the process?

 

[jeremyfiennes]

There are these two options. I continue seeing problems with both. What I am after is a serious discussion of their merits and demerits, not just on a youtube video.

 

[vanhees71]

Which problems are you thinking about? Of course, a fully correct theory should use quantum many-body physics. Nevertheless the classical model is not that bad phenomenologically. The reason is that in this linear-response approximation you deal with a model using harmonic oscillators for small deviations of the charged particles from their mechanical equilibrium positions due to the incoming electromagnetic wave, and since the corresponding equations of motion are linear, the quantum theory is not too far from the classical approximation.

 

[hutchphd]

Which problems are you thinking about?

For me the Feynman treatment is far less bad than the pseudo-Drude model with time delays and photons bouncing. Feynman was always careful not to say things that were wrong because they were easier.

 

[Baluncore]

There are these two options. I continue seeing problems with both.

The "bouncing of photons" seems to go against Occam's razor and the Principle of Least Action.

 

[vanhees71]

For me the Feynman treatment is far less bad than the pseudo-Drude model with time delays and photons bouncing. Feynman was always careful not to say things that were wrong because they were easier.

I don't understand what you are talking about. There are no time delays nor photons bouncing in the approach via the superposition of the in-field and induced fields. The Drude model, modified for taking into account Fermi-Dirac statistics a la Sommerfeld, is better than you seem to think.

 

[hutchphd]

I don't understand what you are talking about.

I was referring to this (sorry I was not more clear)

<https://www.physlink.com/Education/AskExperts/ae509.cfm>:
"When light enters a material, photons are absorbed by the atoms in that material, increasing the energy of the atom. The atom will then lose energy after some tiny fraction of time, emitting a photon in the process. This photon, which is identical to the first, travels at the speed of light until it is absorbed by another atom and the process repeats. The delay between the time that the atom absorbs the photon and the excited atom releases as photon causes it to appear that light is slowing down"

Seems not so good to me.

 

[vanhees71]

No, doesn't seem to be good to me too.

 

[sophiecentaur]

No, doesn't seem to be good to me too.

Sounds bordering on the ridiculous to me. It makes the assumption that 'a material' consists of isolated atoms - i.e a gas.

Density of a gas - very low.

Title of the thread specifies Dense materials. That Hydrogen Atom model has a lot to answer for.

 

[tech99]

I had always assumed that the wave slowed down because it is electrically coupled to something having mass, which adds inductance to the medium.

 

[DrDu]

The propagation of light in dense media basically boils down to the calculation of the transverse dielectric function of the medium. This is possible with ab initio packages today. For the free electron gas, the theory has been developped by Lindhard and is part of the standard curriculum in solid state physics:
http://gymarkiv.sdu.dk/MFM/kdvs/mfm 20-29/mfm-28-8.pdf
Ab initio calculations can be performed e.g. with density functional packages like VASP or Quantum Expresso, see e.g.
https://ieeexplore.ieee.org/document/6602988