How does refraction work on the quantum level?

[Ai52487963]

A friend of mine and I were discussing particle states during exam revision and the refraction of light came up. His question was, 'how does light know to bend in a medium'?

My shot at the answer was that the individual photon that comes into the medium doesn't 'know' to change trajectory until it comes into contact with the medium. A ray of light will continue on straight for a long time until it hits a bit of space station glass and bends, for example. But since the spaces between atoms in a medium are so much larger than photons, a number will sail right through the medium without interacting with the glass and not refract. It's the collection of photons that bends, but not individual ones.

His retort was that even individual photons, sailing between the relatively monstrous distances between carbon atoms in the glass know the glass is there and bend their trajectory accordingly.

My question is: if the photons didn't interact with the carbon in the glass, how do they know the glass is there? Don't photons have to interact with things in order to change their trajectory or do the idividual photons themselves know to refract, even if they don't touch any of the atoms in the glass?

 

[zush]

Actually, the photons are affected by the the atoms, specifically, they are absorbed and re-emitted by the electrons in the atom.

 

[Rear Naked]

Actually, the photons are affected by the the atoms, specifically, they are absorbed and re-emitted by the electrons in the atom.

I believe this is a different process than light passing through a medium.


Very interesting question. I'm very interested in the answer.

 

[zush]

I believe this is a different process than light passing through a medium.

No, it's actually the same process. Whenever light interacts with a medium, (reflection or refraction) the interaction is an electron from the medium absorbing the photon and re-emitting it. There's a very good book on this by Richard Feynman called https://www.amazon.com/dp/0691024170/?tag=pfamazon01-20

 

[Drakkith]

I've seen several times in these forums where it has been said that the absorbtion and re-emission of photons in a material does NOT explain refraction, reflection, etc. I don't know for sure though.

 

[nhmllr]

You really should read QED by Richard Feynman, it explains this.

The quick answer is that the photon doesn't bend in the way we think about it. Because media like water "slow down" light, the bend actually let's it reach it's destination faster than if it didn't.

He gave the example of a life guard that wants to get to a drowning person as fast as possible. He can run faster on the sand than he can swim in the water. If he runs right to the swimmer, he will spend too much time in the water. If he runs to the edge of the beach then swims to the swimmer, he covers too much distance. He has to negotiate a path in the middle to get to the swimmer the easiest.

[PLAIN]http://esfscience.files.wordpress.com/2009/04/lifeg.jpg

What Feynman explains in his book is that the fastest path that light can travel contributes most to the probability of it getting to the destination, whereas the slower paths do not, thereby demonstrating that the light bent to get where it wanted as fast as possible.

This seems arbitrary in a forum post. You should read the book, it's very enjoyable and not too long.

 

[Drakkith]

I'll have to read it some day. Sounds like a good read.

 

[ProTerran]

Is it appropriate to explain the refraction and dispersion of light using optical phonons phenomena?

 

[Rear Naked]

Do Photons Move Slower in a Solid Medium?
Do Photons Move Slower in a Solid Medium?

Contributed by ZapperZ. Edited and corrected by Gokul43201 and inha

This question appears often because it has been shown that in a normal, dispersive solid such as glass, the speed of light is slower than it is in vacuum. This FAQ will strictly deal with that scenario only and will not address light transport in anomalous medium, atomic vapor, metals, etc., and will only consider light within the visible range.

The process of describing light transport via the quantum mechanical description isn't trivial. The use of photons to explain such process involves the understanding of not just the properties of photons, but also the quantum mechanical properties of the material itself (something one learns in Solid State Physics). So this explanation will attempt to only provide a very general and rough idea of the process.

A common explanation that has been provided is that a photon moving through the material still moves at the speed of c, but when it encounters the atom of the material, it is absorbed by the atom via an atomic transition. After a very slight delay, a photon is then re-emitted. This explanation is incorrect and inconsistent with empirical observations. If this is what actually occurs, then the absorption spectrum will be discrete because atoms have only discrete energy states. Yet, in glass for example, we see almost the whole visible spectrum being transmitted with no discrete disruption in the measured speed. In fact, the index of refraction (which reflects the speed of light through that medium) varies continuously, rather than abruptly, with the frequency of light.

Secondly, if that assertion is true, then the index of refraction would ONLY depend on the type of atom in the material, and nothing else, since the atom is responsible for the absorption of the photon. Again, if this is true, then we see a problem when we apply this to carbon, let's say. The index of refraction of graphite and diamond are different from each other. Yet, both are made up of carbon atoms. In fact, if we look at graphite alone, the index of refraction is different along different crystal directions. Obviously, materials with identical atoms can have different index of refraction. So it points to the evidence that it may have nothing to do with an "atomic transition".

When atoms and molecules form a solid, they start to lose most of their individual identity and form a "collective behavior" with other atoms. It is as the result of this collective behavior that one obtains a metal, insulator, semiconductor, etc. Almost all of the properties of solids that we are familiar with are the results of the collective properties of the solid as a whole, not the properties of the individual atoms. The same applies to how a photon moves through a solid.

A solid has a network of ions and electrons fixed in a "lattice". Think of this as a network of balls connected to each other by springs. Because of this, they have what is known as "collective vibrational modes", often called phonons. These are quanta of lattice vibrations, similar to photons being the quanta of EM radiation. It is these vibrational modes that can absorb a photon. So when a photon encounters a solid, and it can interact with an available phonon mode (i.e. something similar to a resonance condition), this photon can be absorbed by the solid and then converted to heat (it is the energy of these vibrations or phonons that we commonly refer to as heat). The solid is then opaque to this particular photon (i.e. at that frequency). Now, unlike the atomic orbitals, the phonon spectrum can be broad and continuous over a large frequency range. That is why all materials have a "bandwidth" of transmission or absorption. The width here depends on how wide the phonon spectrum is.

On the other hand, if a photon has an energy beyond the phonon spectrum, then while it can still cause a disturbance of the lattice ions, the solid cannot sustain this vibration, because the phonon mode isn't available. This is similar to trying to oscillate something at a different frequency than the resonance frequency. So the lattice does not absorb this photon and it is re-emitted but with a very slight delay. This, naively, is the origin of the apparent slowdown of the light speed in the material. The emitted photon may encounter other lattice ions as it makes its way through the material and this accumulate the delay.

Moral of the story: the properties of a solid that we are familiar with have more to do with the "collective" behavior of a large number of atoms interacting with each other. In most cases, these do not reflect the properties of the individual, isolated atoms.

I happened to ask my physics prof. 2 weeks ago if the slowed speed of light was related to the lifetime of excited electrons and essentially he told me No, and used the example of light through glass.

Not sure how the explanation differs for a medium such as water.

 

[Born2bwire]

I've seen several times in these forums where it has been said that the absorbtion and re-emission of photons in a material does NOT explain refraction, reflection, etc. I don't know for sure though.

It doesn't, at least generally not in the way that most people use it to explain the phenomenon. As stated in the above quote from the FAQ, the photons are not absorbed and emitted by simple atomic transitions. Instead, the atoms of the material are now correlated with each other and exhibit a collective behavior. The absorption of a photon by an atom results in an excited electron state. The absorption of a photon by a bulk material results in a phonon, an excited vibrational state.

This can be taken as a rough explanation as to why the speed of light changes in a medium but it does not explain why refraction occurs though. In terms of photons, by accepting that the speed of propagation changes between mediums, then you can work out that the refraction of light is required for the conservation of the photon's momentum. This is what the swimming analogy in QED is explaining. When the photon is absorbed and then emitted, assuming a simple linear process here, the emitted photon must conserve the energy and momentum of the state prior to absorption. Conservation of energy is achieved by having the same frequency prior to absorption. Conservation of momentum is achieved by having a change in the direction of the photon's path (if we may take such deterministic liberties with a quantum picture).

As for QED, it is a bit of a frustrating book. It is too simple by far for most of us that already have an idea of quantum physics. He wrote the book to explain to laymen and so he drastically distills down the ideas. The result is that he talks about the conservation of momentum in light in terms of a swimmer but he doesn't mention things like momentum and so forth. In fact, the swimming analogy in regards to his book has nothing to do with momentum conservation. He uses it to state (I won't go as far as to call it explain) Fermat's principle which can be shown to be the classical limit of his path integrals.

I guess what I am trying to say is that he presents these simplified analogies but because it is for laymen he does not connect it to the higher physics that you would recognize. So you may not come out any wiser since you can miss the physics that he is explaining in his descriptions. Another case in point is his talk that discusses why the stationary phase paths of the path integral lay out the classical paths. He does this by talking of the progression of the phase of the integrand of the path integral in terms of a stopwatch and how it cancels things out.

 

[lauratyso11n]

You really should read QED by Richard Feynman, it explains this.

The quick answer is that the photon doesn't bend in the way we think about it. Because media like water "slow down" light, the bend actually let's it reach it's destination faster than if it didn't.

He gave the example of a life guard that wants to get to a drowning person as fast as possible. He can run faster on the sand than he can swim in the water. If he runs right to the swimmer, he will spend too much time in the water. If he runs to the edge of the beach then swims to the swimmer, he covers too much distance. He has to negotiate a path in the middle to get to the swimmer the easiest.

http://esfscience.files.wordpress.com/2009/04/lifeg.jpg

What Feynman explains in his book is that the fastest path that light can travel contributes most to the probability of it getting to the destination, whereas the slower paths do not, thereby demonstrating that the light bent to get where it wanted as fast as possible.

This seems arbitrary in a forum post. You should read the book, it's very enjoyable and not too long.

And THIS is your explanation to the question: "How does light know which path to take to travel across non-homogenous media in the shortest possible time ?"

 

[DrDu]

I don't think the explanation in the FAQ, which stresses the role of phonons, is relevant in the optical region of the spectrum (as contrasted to infrared light). There are several sum rules which show that vibrations only contribute little to the refractive index in the visible part of the spectrum.
As far as the interaction of photons with matter is concerned, this is a form of scattering. Scattering can be thought of as a rapid succession of absorption and re-emission. If it occurs far away from a true absorption line, this is a virtual process whose duration is limited by time-energy uncertainty.
Nevertheless it is not so that this short time would create a delay which is then responsible for the changed speed of light. Rather the phase of the re-emitted photon does not coincide with the phase of the photon upon incidence. As this is basically a quantum mechanical phenomenon, scattering will occur only with a certain probability and in fact, after passing by an atom, we have a superposition of scattered and unscattered wave. It can be seen that this superposition of two waves with different phase, if happening repeatedly at successive atoms, will lead to a change in the wavelength of the light wave.

 

[Drakkith]

How does the change in wavelength affect the speed that light moves through a material?

 

[Antiphon]

First consider the classical case, then to over to the quantum.

In the classical case, suppose a plane wave impinges on a piece of glass. 96% of the incident field enters the glass, 4% is reflected. For the wave that enters, it slows down in the glass because the wave speed in the glass is v=1/sqrt(mu*epsilon) and epsilon in the glass is 2.3 times larger than in air. This slowing happens because in the glass the electric field is smaller than in air (by 2.3) but the magnetic field is the same magnitude. In Maxwell's equations, the time derivative of B is the same as curl(E) and will not have changed. This can happen when the magnitude of the electric field is smaller but has a shorter wavelength. When the wavelength gets shorter but the frequency stays the same, you have a reduced velocity.

In the quantum case, a photon enters the glass with 96% probability. That photon has a spatial wavelength and a frequency of oscillation. The photon energy doesn't change in the material so the frequency doesn't change. But the wavelength shortens because the effective momentum of the photon has increased. It becomes a modified particle through the interaction with the matter matrix called a polariton. These have an effective mass and travel slower than c.

An alternative quantum picture is that you have photons in a continual state of absorption and re-emission by the material matrix inducing a time delay.

 

[Drakkith]

Is a polariton similar to an electron "hole" in that it has certain properties but isn't exactly a "real" object? (If that makes sense)

 

[DrDu]

Is a polariton similar to an electron "hole" in that it has certain properties but isn't exactly a "real" object? (If that makes sense)

Yes, it is also a quasi-particle. It can be seen as a superposition of a photon and an electron-hole pair. I.e. the photon gets absorbed every now and then exciting an electron to a higher orbital and leaving a hole in an orbital which was occupied before. The electron and hole recombine and regenerate the photon and so on. The electron hole pair is sometimes called the polarization bubble (due to the form of its graphical representation in Feynman diagrams).