# Propagation of light in transparent media: absorption and reemission or scattering?

In the two Phys.SE questions What is the mechanism behind the slowdown of light/photons in a transparent medium? and Why glass is transparent? transparent media were discussed. But I'd like to clarify one detail: is a photon absorbed (and delayed) by the medium and then reemitted, or scattered instantly?

Is e.g. a laser beam still coherent after passing glass? As medium molecules are disordered, this should distort the phase of photons taking different paths.

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you might be interested in this trnmag.com/Stories/2002/010902/… –  anna v Aug 19 '11 at 5:07
There is always both some scattering and some additional phase factor due to interaction (this leads to lowered speed of propagation), altogether leading to a complex index of refraction (and attenuation of signal). But it depends on the medium how big or small that scattering is. You need to compute interaction cross-sections for photons vs. whatever constitutes the material, which might besides atoms and molecules be electronic liquid, phonons, impurities and much much more. –  Marek Aug 19 '11 at 7:09
@anna, the lede of that article is really misleading - as far as I can tell, the research is about counteracting dispersion of laser pulses in a medium, not counteracting scattering. It's simply not true that "the red dot will dissipate completely before it gets to the other side" of a pane of glass. If that were true, there would be no point to lenses in laser experiments! –  ptomato Aug 19 '11 at 16:06
@ptomato the picture has a 2cm thick glass. It shows where the dispersion would disperse too. I am sure that lenses used for laser work are much thinner. BTW I would call dispersion due to microscopic scattering. –  anna v Aug 19 '11 at 16:52
@Qmechanic there exists a pdf cpht.polytechnique.fr/cpth/couairon/advert/TRN010902.pdf . found this too physics.aps.org/articles/v5/104?referer=rss –  anna v Feb 14 at 5:43

There is no unambiguous correct answer to this question because it isn't well posed in terms of logical positivism: what is the difference between the two processes? There is no way to tell which happens if you don't muck up the intermediate state with a measurement.

If you mean this in terms of some quantum field theory with given fields and interactions and asymptotic states, then you can ask how the processes appear in a Feynman description. The scattering process in QED is always two-step, the absorption and emission are separate space-time points. But the emission can precede the absorption both in coordinate time and in proper time along the electron's world line, so you should include "emitted and then absorbed" to the list of possibilities.

Light does not have to be resonant in order to scatter off an atom. The amount of scattering/emission-reabsorption is smaller away from resonance. A light wave is also a long coherent field, and this field can acquire a phase push from the emission-reabsorption, leading the phase-velocity to be bigger than the speed of light.

The issue of "how come the phases add up coherently" is adressed by two things: there is a large scale difference between the atoms and the light wavelength. Each atom scatters the light independently and randomly into a spherical waves, which add up coherently in the original direction only to alter the phase velocity by a constant amount.

There is no scattering from the bulk of a perfect crystal, for long wavelengths, because there is still a discrete translation invariance which means momentum is conserved up to big jumps, and the big jumps give waves with the wrong frequency for long enough wavelengths. But there are discrete momentum additions which are allowed for a short wavelength x-ray in an atomic crystal, and if the photon momentum comes out different but at the same frequency due to the coherence in a different direction, that's called diffraction.

If you want scattering in a crystal, you need to scatter off defects which have a good amount of random variation in a box the size of one wavelength. Similarly, if you scatter of a fluid, you need fluctuations in density to be meaningful in one wavelength. This is easier for blue light than for red light, so transparent fluids scatter blue.

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I see a difference as, upon absorption the directional (also phase?) information is lost, and the propagation follows Huygens principle - whereas scattered photon (particle) still partially preserves its impulse. –  troyaner May 16 '12 at 22:38
@troyaner: no phase information is lost by absorption and reemission, if you multiply the incoming state by a phase, the outgoing state gives the same phase. –  Ron Maimon May 17 '12 at 0:13

A laser beam passing though transparent glass does not lose energy (or momentum) consequently there's no reason for it to become incoherent. But this is not directly related to the question of whether there is scattering or absorption and delayed emission.

There's a difficulty in relating what happens on a photon by photon basis with what happens in the classical limit. You know that light traveling through glass is slowed down, and it seems that this must be due to a delay between absorption and emission, and I suppose that this seems to imply that there must be a delay between absorption and emission in the quantum analysis of the situation.

"Quantum mechanics" is limited to situations where the particles are neither created nor destroyed; this can't include absorption and emission. And it's not terribly easy with large number of particles in the same state (as happens in a laser). The more general "Quantum Field Theory" allows creation and annihilation of particles (photons) so this is what's appropriate.

The quantum field theory that applies to photons interacting with electrons (atoms) is quantum electrodynamics (QED). In this theory, the speed of photons is random; they do not have to travel at speed c. So it's possible for a QED problem to have a delayed photon without a delay between absorption and emission (but the average speed will still be c, as far as I know).

A crystal (or other solid) lattice contains a large number of atoms. What determines whether or not a photon can be absorbed is whether the crystal lattice has an available vibration corresponding to the energy, momentum, and angular momentum of the incoming photon. If it does, then the solid will absorb that photon and it will not be transparent in that frequency.

If a photon has an energy that is not compatible with the crystal lattice then it must adjust its energy by borrowing energy. This can only happen for a time $\Delta E\;\Delta t \approx \hbar$. One supposes that energies where $\Delta E$ is small should have a slower speed of light (larger index of refraction).

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It really is a wonderful and very insightful answer, thank you. so the light is actually always absorbed (scattering being another form). one remark about coherence - my image was, that as photons start out at the same phase, but travel hand over hand along differently positioned atoms, their phases are distorted relatively to one another - is it correct? –  troyaner Aug 19 '11 at 22:15
You don't need to lose energy or momentum to become incoherent, you only need to get entangled with something. A photon which knocks a phonon into a different state will become incoherent with other photons (this process is suppressed if there are other photons around), because it is entangled with the phonon direction. The absorption/reemission off resonance is identical with scattering, since you can describe scattering as a sum over the intermediate available states of absorption followed by reemission, in an appropriate framework. –  Ron Maimon Aug 20 '11 at 4:41