Speed of Light in Gas: FAQs & Explanations

[jostpuur]

The FAQ already contains some kind of answer to the question that why does light propagate slower in solids, but it's not fully clear to me why the speed is altered also for example in the atmosphere. There's no phonons in gas. A similar hand waving explanation would be nice for this matter also.

 

[smallphi]

The EM field of the light wave, Eincoming, makes the charged particles of the media (like electrons) oscillate. The oscillating charges create EM field themselves. The composite field Etotal = Eincoming+ Echarges has different phase velocity and amplitude.

The point is Eincoming doesn't 'slow down' in media but the field of the oscillating charges, Echarges, makes the total field propagate slower.

 

[CraigD]

Jostpuur,

The speed of light is constant, remember that most matter is 99% vaccum. What causes light to move "slower" in a solid is that the photons are absormed and re-emitted by the atoms that make up the matter.

Another way to think of it is this, if you drive straight from New York to LA it will take you x number of hours. If you drive from New York to LA but stop in Clevland, Chicago, Kansas City, Denver, and Las Vegas, it will take you even longer than driving without stoping.

CraigD, AMInstP
www.cymek.com

 

[ZapperZ]

Jostpuur,

The speed of light is constant, remember that most matter is 99% vaccum. What causes light to move "slower" in a solid is that the photons are absormed and re-emitted by the atoms that make up the matter.

Another way to think of it is this, if you drive straight from New York to LA it will take you x number of hours. If you drive from New York to LA but stop in Clevland, Chicago, Kansas City, Denver, and Las Vegas, it will take you even longer than driving without stoping.

CraigD, AMInstP
www.cymek.com

I think you are missing his question. He's asking for the effect in a GAS, not solid, which has been explained in our FAQ.

Zz.

 

[CraigD]

I think you are missing his question. He's asking for the effect in a GAS, not solid, which has been explained in our FAQ.

Zz.

It works the same, in a gas and a solid. Other effects can be added in solids that usually can't be seen in gases.

CraigD, AMInstP
www.cymek.com

 

[ZapperZ]

It works the same, in a gas and a solid. Other effects can be added in solids that usually can't be seen in gases.

CraigD, AMInstP
www.cymek.com

No it doesn't. The mechanism is different since there are no ordinary phonon modes in gasses. Lene Hau certainly didn't slow down light that way.

Zz.

 

[smallphi]

"Why the speed of light is reduced in a transparent medium"
Mary James and David Griffiths
American Journal of Physics -- April 1992 -- Volume 60, Issue 4, pp. 309-313
====================================================================

They constructed the wave inside the media perturbatively. In zero approximation, the incoming field E0 continues in the media at the usual speed of light in vacuum. That field creates polarization current J1 which creates extra field E1. The field E1 creates polarization current J2 which creates extra field E2 ...

The total field in the media is the sum E0 + E1 + E2 + ...
All those fields propagate at the speed of light in vacuum but their complex amplitudes sum up in a way that modifies exp(ikx) of the sum leading to speed smaller than in vacuum (see eq. 18 in article). Only complex amplitudes can modify exp(ikx) which means that phase delays between the waves are into play. The perturbative waves reflected from the media have all real amplitudes and therefore do not modify the phase speed of the total reflected wave.

Read the article for explicit details.

 

[cesiumfrog]

The speed of light is constant, remember that most matter is 99% vaccum. What causes light to move "slower" in a solid is that the photons are absormed and re-emitted by the atoms that make up the matter.

The obvious problem on the face of such explanations is that (gas) atoms are supposed to absorb only a few highly specific frequencies of light (whereas a continuous range of specific frequencies are individually slowed).

Is it even possible to express every sinusoid in terms of the given infinite discreet sequence of (higher frequency?) sinusoids (ie. those that the atom *can* absorb)?

"Why the speed of light is reduced in a transparent medium" Mary James and David Griffiths [..] 1992

Griffiths has certainly published some interesting electrodynamics!

 

[smallphi]

Classically if you put an atom in oscillating EM field, it will get polarized in synch with the field. That atomic polarization corresponds to shifting the effective positions of the positive and negative charges in the atom and correspondingly the oscillating charge emmits another EM wave.

I wonder what is the QM analogue of that description. As cesiumfrog pointed out, atoms interact only with certain frequencies of the EM field so I wonder how it is possible to have effect for all frequencies. Here I considered an individual atom so any possible collective effects are excluded from the question.

Is the classical picture above for one atom not true or what? How is it possible then for atoms to scatter light of any frequency? Would that be a collective effect?

 

[cesiumfrog]

So (having read the paper) classical EM tells us that if we can polarise (that is, induce electric dipole moments in the atoms or molecules comprising) a media (possibly gaseous), this alone is sufficient to explain both reflection from the media and also the slower speed of propagation within the media.

Very basic QM tells us that basic atoms will only absorb (and emit) discrete frequencies, but apparently this is irrelevant to the speed of light propagation. The remaining question seems to be: What, according to QM, happens to the charge distribution of a simple atom in an external (varying) electric field?

(It seems like a situation where the Hamiltonian would be fairly simple to write, surely someone has published a result showing recovery of linear dielectric behaviour in the limit of weak applied field?)

 

[CraigD]

Okay, I have to ask the question then, what is an oscillating EM field if it is not light?

CraigD, AMInstP
www.cymek.com

 

[ZapperZ]

Okay, I have to ask the question then, what is an oscillating EM field if it is not light?

And oscillating chain of charges! Look up "phonons"!

Zz.

 

[CraigD]

And oscillating chain of charges! Look up "phonons"!

Zz.

Okay, so we are talking about solids again. I thought we decided we were talking about a gas?

CraigD, AMInstP
www.cymek.com

 

[ZapperZ]

Okay, so we are talking about solids again. I thought we decided we were talking about a gas?

But you also have the same polarization in gasses. I only gave ONE example to counter what you just said.

Zz.

 

[cesiumfrog]

I think that in this context (everything above suggests optical frequencies), an oscillating EM field *is* indeed light. ("Phonons" would normally describe oscillating mass-density, not specifically charge-density, and certainly never in the EM field itself)

Contrary to what seems to have been suggested, I so far see no evidence that phonons are related to the speed of light in even solid media (maybe ZapperZ can point us to reference otherwise), and close reading of the FAQ indicates phonons are only involved in *opacity* (ie. phonons may be produced from a wide range of photon frequencies but, if this occurs, the energy will be dissipated as heat rather than further contributing in any way to the slower but continuing propagation of incident light).

When light is incident on a material (solid or gaseous), the photons usually do not have the specific quantity of energy necessary to excite the electrons of ground state atoms into any higher orbital. Instead (thinking of light as a slowly oscillating variation in the EM field) the electric field will slightly perturb the ground state orbital (favouring the electron being on one side rather than the other), and this asymmetry leaves the atom with an electric dipole moment (the ground-state electron cloud is no longer perfectly aligned with the positive nucleus). Since the atoms have acquired oscillating electric dipole moment, they are producing EM waves of the exact same frequency as they are being driven at (the incident frequency), though out of phase (perhaps classically attributable to inertia). This new light wave interferes with the incident light wave, which just happens (as each layer of atoms contributes an equal phase delay) to result exactly in the total light wave propagating at a slower speed through the medium (in addition to an extra light wave propagating back outside of the medium, the "reflection"). This is the picture I think we will get from quantum mechanics (applying a classical field), based on the results from classical electrodynamics. What is interesting (imagining quantum field theory applied to this problem) is that it seems equivalent to saying that atoms can absorb any frequency of photon (but only for a much briefer time than those corresponding to atomic excitations), and hence that the explanation of slower light propagation truly is that alleged "myth" (which the FAQ purports to dispel).

 

[CraigD]

Thank you cesiumfrog.

CraigD, AMInstP
www.cymek.com

 

[smallphi]

Most QM textbooks have chapters on scattering of particles from a potential (of other particles). What I've never seen is QM treatment of scattering of photons from atoms which probably requires quantization of the EM field hence QED instead of QM. Probably that scattering is occurring for all frequences not only the ones that would correspond to atomic transitions.

 

[jostpuur]

The EM field of the light wave, Eincoming, makes the charged particles of the media (like electrons) oscillate. The oscillating charges create EM field themselves. The composite field Etotal = Eincoming+ Echarges has different phase velocity and amplitude.

The point is Eincoming doesn't 'slow down' in media but the field of the oscillating charges, Echarges, makes the total field propagate slower.

I sense difficulties with these thoughts. Why does refraction occur? It can be justified with path integrals, and the fact that photons move slower in some medium. (Or is it like this? I didn't check details, but this sounds reasonable, if I remember Feynman's popular QED explanations correctly.) Now if the photon actually doesn't slow down, and only more photons are emitted from the medium in the same direction, having some kind of macroscopic effect that the total EM-wave is slowing down, doesn't this mean that refraction should not occur at all?

 

[smallphi]

Refraction formulas are derived applying boundary conditions for the total EM field (see Griffifths or Jackson). It the total waves have different speeds at the boundary, refraction occurs.

If photos 'slowed down' in media, they would have to slow down also in strong electric field mimicking the interatomic electric field. Maxwell equations (from which refraction is derived) do not predict such thing.

 

[jostpuur]

But the paths of the original photons that came from vacuum to some media do not get altered at all? That is paradoxical.

It would of course help, if I (or we) knew something about photons. To my understanding they cannot be modeled with classical EM-packets and Maxwell's equations, because that is classical, and photons are not.

 

[Claude Bile]

Contrary to what seems to have been suggested, I so far see no evidence that phonons are related to the speed of light in even solid media (maybe ZapperZ can point us to reference otherwise), and close reading of the FAQ indicates phonons are only involved in *opacity* (ie. phonons may be produced from a wide range of photon frequencies but, if this occurs, the energy will be dissipated as heat rather than further contributing in any way to the slower but continuing propagation of incident light).

Refractive index is related to the band structure in a solid, the same band structure that determines phonon modes, so they are definitely linked. The Kramers-Kronig relations show how absorption and refractive index are intertwined.

This is the picture I think we will get from quantum mechanics (applying a classical field), based on the results from classical electrodynamics. What is interesting (imagining quantum field theory applied to this problem) is that it seems equivalent to saying that atoms can absorb any frequency of photon (but only for a much briefer time than those corresponding to atomic excitations), and hence that the explanation of slower light propagation truly is that alleged "myth" (which the FAQ purports to dispel).

There is no doubt that an incoming EM field perturbs the atom, however there are a few reasons why this is not equivalent to a true absorption event. Firstly, at no point is the energy of the wave being dissipated in any way. Secondly the electron does not jump into another eigenmode, which would normally happen in a true absorption event. Finally a true absorption/re-emission event is isotropic, whereas a "transmission" event is not. In fact, in a transmission event, I'm not sure if it even makes sense to regard it as a photon/atom interaction since there is no apparent collapse of the photonic wave-function.

@smallphi - In order for light to slow down, there must be some phase delay between the generated wave and incident (drive) field. This only happens if the oscillator possesses mass. The presence of atoms is therefore required for refraction to occur, light does not slow down on a whim.

Claude.