slowing down light

[bwanaaa]

I always wondered about the ability of transparent objects to slow down light. Recent research has even managed to slow down light much further-to a velocity of mere centimeters per second. Are electric and magnetic fields also 'slowed' down the same way?

For example, Diamond which has a high index of refraction slows light down measurably. Would the path of an electron beam deflected by a magnet change with different kinetics as diamond is interposed around the beam?

 

[Denbo1991]

In the same way that visible light is slowed down by certain materials, propagating electromagnetic waves are slowed down in the same fashion. This is consistent, since visible light is just an electromagnetic wave within a certain wavelength.

Electron beams, on the other hand, are not quite the same as propagating electromagnetic waves, so they are not slowed by a material with a different index of refraction in the same fashion. Still, it would not be unreasonable to imagine a material that interacts with a beam of electrons that will slow down the beam. If you could work out some of the math and dimensional analysis, I'm sure you could also model a beam of particles in the same fashion for some cases.

 

[Born2bwire]

Light is electromagnetic waves. So the same things that are done to slow down light can be applied to electromagnetic waves of any frequency. Although there is a bit of handwaving when people talk of when they are discussing the speed of light. In our macroscopic view, there is the group velocity and phase velocity and on a more technical and pedantic level there is the velocity of the light itself (we can say in the form of photons). Group velocity is basically the speed and direction of the flow of power and information in light. It is the speed by which your encoded signal will travel in your fiber optic or whathaveyou. Phase velocity is the speed and direction of the phase of the wave which can be thought of as the speed by which the peaks and troughs of the wave travel. Phase velocity is not always the same as the group velocity.

Phase velocity is usually what is being discussed when you hear the more fantastic speed of light experiments. For example, there are some experiments which claim that they can get the speed of light to exceed the speed of light in vacuum, c. What they mean in this case is that the phase velocity is faster than c. But this is ok and still within the realm of special relativity because the information of the signal is still traveling at speeds equal or less than c.

The other thing to note is that the discussions of the speed of light is talking about the macroscopic group behavior for the most part. What happens in a bulk material is that the material is made up of a lattice of atoms where the atoms and their behavior are not interrelated and correlated across the bulk. So when a photon enters the bulk, it interacts with the bulk material as a whole. It does so by being absorbed into the bulk and exciting vibrational modes called phonons. These phonons are the heat that is produced by the absorption of light in a material. Ignoring the lossy nature though, the phonon absorbs the photon, and then after a short delay the phonon gives up its energy and emits a photon. The short delay is what causes the reduction in the group velocity of light. So the photons still "travel" at c, but their interactions with the bulk material cause the overall behavior of the transmission of the signal to slow down.

So this mechanism works for visible light and for light at all the other frequencies. But even more interesting is that we can make artificial subwavelength structures that when arranged in a bulk arrangement will cause similar effects. The design of metamaterials is one example. In a metamaterial, we design a unit cell that has specific behavior, usually a resonant behavior of capacitive and/or inductive properties, where the unit cell is much smaller than the wavelength of our signals. When we arrange a lattice of these unit cells then the bulk lattice now has very different properties and we can do things like making the effective permittivity and permeability of this bulk material to be both negative within a small bandwidth. Since these have to be subwavelength, most metamaterials are usually around the radio or microwave frequencies. We haven't really gotten up to the optical frequencies due to the required size scales involved. However, there is a lot of research in using nanoparticles and making use of plasmonic resonances in these nanoparticles to create these kind of behaviors in the terahertz, infrared and even visible light range.

 

[Farmer]

SNIP

Good post, but I think you have that flipped sir, group velocity can exceed c in materials, and in fact can be infinite or 0, depending on your definition. The phase velocity is always c.

Any introductory book on optics will explain the difference. In short, basic summary, the propagation of EM waves in materials is a series of "waves clashing" (or, more technically, photon scattering), and the resultant waves will interfere with eachother, the superposition of which may result in a larger or smaller resultant group velocity. This view focuses entirely on the absorption and emission of photons by individual atoms in the lattice, but is ignorant of photon-phonon coupling, like Born2bwire talked about. However you don't need phonon-photon coupling to explain the effect.

 

[bwanaaa]

I clearly did not explain myself. or maybe i did not explain myself clearly.

I am asking about the speed at which a magnetic FIELD propagates, not a wave. When you turn on a magnet, field lines grow in strength. Consider this arrangement: particle1 is x distance from the center of an electro-magnet and experiences force,F. particle2 happens to be 4 x as massive as particle1 and is located 2x distance away. Particle2 experiences force, 4F. You are looking at the magnet and the 2 particles from the side so you can see all 3. there is a light source equidistant from the 2 particles which is currently off. The electromagnet and the light are both switched on at the same time.

Will the particles demonstrate equal acceleration?

If the effect of magnetic fields traveled faster than light, would we see a doppler shift in the frequencies of light reflected from the particles? (even though the image of both particles would appear simultaneously because the speed of light is constant).

 

[Farmer]

A field can be a wave. Waves are fields. Propagating waves are solutions to Maxwell's equations, which are field equations, the distinction makes no difference. When you speak of "turning on" a magnetic field, you are speaking of a propagating wavefront. What has been said so far is pertinent to your original question.

Since diamonds are considered "non-magnetic," or respond weakly to external magnetic fields in the bulk, I would expect that placing a diamond within a magnetic field will result in little or no deformation of that field. You also speak about some fixed magnetic field and some light source as if they would interact strongly (by doppler shift, maybe you mean some kind of phase shift from interference). They don't, incoherent light does not interfere.

 

[Born2bwire]

Good post, but I think you have that flipped sir, group velocity can exceed c in materials, and in fact can be infinite or 0, depending on your definition. The phase velocity is always c.

Any introductory book on optics will explain the difference. In short, basic summary, the propagation of EM waves in materials is a series of "waves clashing" (or, more technically, photon scattering), and the resultant waves will interfere with eachother, the superposition of which may result in a larger or smaller resultant group velocity. This view focuses entirely on the absorption and emission of photons by individual atoms in the lattice, but is ignorant of photon-phonon coupling, like Born2bwire talked about. However you don't need phonon-photon coupling to explain the effect.

The phase velocity is \omega / k where k is the wavenumber and the group velocity is \partial \omega / \partial k, that is the partial derivative of \omega with respect to k. The wavenumber is dependent upon the frequency, permittivity and permeability of the medium. Thus, it is simple to see that in a medium where the permittivity and/or permeability (like in a dielectric) are non-unity then the phase velocity drops below c. On the whole, the group velocity cannot be infinite. I have heard smatterings on Wikipedia about obtaining group velocities faster than c that carry all these caveats that keep it from breaking special relativity. However, on the whole I think those can be sidelined in such a discussion as one does not come across such circumstances very often. In fact, I do not know offhand what conditions would merit such phenomenon.

I clearly did not explain myself. or maybe i did not explain myself clearly.

I am asking about the speed at which a magnetic FIELD propagates, not a wave. When you turn on a magnet, field lines grow in strength. Consider this arrangement: particle1 is x distance from the center of an electro-magnet and experiences force,F. particle2 happens to be 4 x as massive as particle1 and is located 2x distance away. Particle2 experiences force, 4F. You are looking at the magnet and the 2 particles from the side so you can see all 3. there is a light source equidistant from the 2 particles which is currently off. The electromagnet and the light are both switched on at the same time.

Will the particles demonstrate equal acceleration?

If the effect of magnetic fields traveled faster than light, would we see a doppler shift in the frequencies of light reflected from the particles? (even though the image of both particles would appear simultaneously because the speed of light is constant).

Like Farmer stated, anytime you are talking about a time-varying situation you are talking about electromagnetic waves. The fields only truly decouple when we have a static case (Although you will here how the fields are effectively decoupled at very low frequencies in what we call the quasi-static regime. But in those cases the fields are still retarded by the relevant speed of light.). So yes, in essence any changes in the sources will be time delayed at the recievers as the changes propagate at the speed of light.

 

[Farmer]

The phase velocity is \omega / k where k is the wavenumber and the group velocity is \partial \omega / \partial k, that is the partial derivative of \omega with respect to k. The wavenumber is dependent upon the frequency, permittivity and permeability of the medium. Thus, it is simple to see that in a medium where the permittivity and/or permeability (like in a dielectric) are non-unity then the phase velocity drops below c. On the whole, the group velocity cannot be infinite. I have heard smatterings on Wikipedia about obtaining group velocities faster than c that carry all these caveats that keep it from breaking special relativity. However, on the whole I think those can be sidelined in such a discussion as one does not come across such circumstances very often. In fact, I do not know offhand what conditions would merit such phenomenon.

In the bulk, where quantities like permeability and permittivity take meaning, yes, I would agree that the apparent phase velocity certainly decreases when entering a material, hence to address the OP when he discusses photons traveling at speeds other than c. What I aim to say is that the incoming wave and the scattered waves, if considered by themselves, all have a phase velocity of c, as they are incident or scattered photons. When superposed to form the bulk effect, of course, the overall field will have a different dispersion relation from any single wave, as there is a phase difference dependent on the geometrical arrangement of the scatterers (i.e., the individual atoms of the dielectric and their spacing).

 

[C1]

Space-Time Cloak Possible, Could Make Events Disappear
http://news.nationalgeographic.com/...cloak-events-space-time-bank-robbery-science/

 

[sao123]

A field can be a wave. Waves are fields. Propagating waves are solutions to Maxwell's equations, which are field equations, the distinction makes no difference. When you speak of "turning on" a magnetic field, you are speaking of a propagating wavefront. What has been said so far is pertinent to your original question.

Since diamonds are considered "non-magnetic," or respond weakly to external magnetic fields in the bulk, I would expect that placing a diamond within a magnetic field will result in little or no deformation of that field. You also speak about some fixed magnetic field and some light source as if they would interact strongly (by doppler shift, maybe you mean some kind of phase shift from interference). They don't, incoherent light does not interfere.

Is not the strict interpretation of a field the following... any single point of a electromagnetic field, is equal to the sum of all the wave strengths also located at that point at that exact moment...
AKA fields are propogated only by continuous waves?