What is it about matter that slows light?, The EM field effect

Hi Tor,

Much better! Thank you.

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Bit of a deviation but hopefully it helps..

Consider reflection from a mirror - optically flat but we know that in reality it is lumpy as hell. No single atom, electron, molecule, phonon or (probably) anything else you can suggest can 'know' the angle of the mirror without some form of communication with the rest of the surface (whistles? bells?.. well I hope you get the point). The inevitable (crazy) conclusion is that a single photon is reflected off a large area (in terms of atoms and molecules), possibly even the entire surface of the mirror. This gets worse, it is generally accepted that for both mirrors and lenses the maximum resolving power is determined by the diameter of the mirror or lens. When looking at distant stars we can easily get down to the level of counting photons - can single photons work out the diameter of a lens? :- apparently they can.
Lenses, as I'm sure we know, work by selectively slowing down light, exactly what we are looking at here, the point here being that it will not be possible to identify a 'single' interaction if there isn't one. It is possible that we may be looking at the right thing but possibly not in the right way.
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Please follow up my deviation - in the meantime I'll look at phonon/photon interaction. Would you mind emailing the picture to me? I'll email my email address to you until we work out how to get pictures onto the site.

-C2

C2,

I understand where you are coming from and it is always the immediate thought by anyone who start to think microscopic; the surface is never totally flat, and if you think, like most, the atoms is like a ball and likewise the photon, it will be similar to snooker, you have to hit the other ball correctly to make it bounce in the desired angle. Well, this is not the way it is or happens with light reflection. (I am opening a can of worms here)

Let’s take your mirror which I suppose is a metallic solid, grinded to a very smooth surface. What you have done is to expose as many atoms as you could at the surface-line, and the more exposed, the better reflection.

As I pointed out earlier, metals have conduction electrons and free valence energy bands. When photons (light) hits the metallic surface, conduction electron absorbs and gains energy from the photon’s E-field causing it to temporarily change valence band. However, the conduction electron will drop back to its original valence band and re-emit the photon, keeping the transverse momentum, but with a 180 degree phase shift due to the negative charged conduction electron. (So there is the light “bouncing” for you).

Now to you resolving power, but first; never think of light as one photon!!
What determines the resolving power is the intensity/density of light over hit lens surface area, then the optical performance of the glass (scattering, refraction of colours etc. etc.)

I am not quite sure what you mean by “we may be looking at the right thing but possibly not in the right way”??

Hi Tor,

No pictures! Makes things a lot more difficult (has my emailing failed?)

Main theme first.. phonons as the mechanism for delay of light travelling through a solid..

To establish the nature of my type of phonons I quote from Wikipedia (search "phonons wiki" and find thermodynamic properties)

A crystal lattice at zero temperature lies in its ground state, and contains no phonons...(Note: the random motion of the atoms in the lattice is what we usually think of as heat) Because these phonons are generated by the temperature of the lattice, they are sometimes referred to as thermal phonons.

The point I feel is important here is not that phonons are influenced by temperature as that the population density for any chosen energy is very much influenced by temperature. Without the pictures I can't be sure but my impression so far is that every 'encounter' should result in a delay - small population gives small delay and vice versa - hence the theory should lead to a temperature dependence which I don't think happens in reality.
The other alternative (pictures please!!!) is that you suggest the photons are generating their own phonons. Please clarify.
Deviations from main theme..
I am programmed to deal with single photons first - I am that way.

"maximum resolving power is determined by the diameter of the mirror or lens" - check, check, check. It's a theoretical limitation - argue with the theory and I'll try to follow but don't dismiss it as just dirty lenses - there is a lot more to it than that.


Later addition-
Re: possibly not looking at it in the right way - just for example - if phonons could be shown to represent the 'entire structure' then your suggestion would look very promising. Same thing, different angle.

-C2.

Hi C2,

Couple of things, it is very important to have some basic knowledge about physics before jumping to conclusions when reading about physical properties of phonons. Mind you, phonon is just another name for frequency due to its excitation. As you know we have frequencies from almost DC to cosmic rays and depending on the frequency interact different with solids, gases etc. What you are referring to are thermal phonons, which has nothing to do with our topic! Please do not confuse the issue.

Photons do NOT generate phonons. Phonons is the designation for vibration generated by the lattice of atoms in a solid as thoroughly explained.

If you want to understand the topic of light, you can not deal with a single photon! If anything experience light, it experiences a stream of photons, and solids deals with streams of photons, that is the only way it can know it’s the frequency of light.

As I have said, resolving power of a lens system is dependent on many different parameters, but the governing parameter is the amount of light/size of lens.

PS: I have sent the picture again via email, but there seems to be a problem at your end.

Reminder: If anyone can give an explanation on how to insert a picture in the post, I would be grateful!

We have pictures..



I've asked Tor to post up some background on phonons so we can establish some common ground.

Hi Tor,

I think we've carried on long enough. My interest lies in the interaction of single photons with matter whereas yours lies in the interaction of many photons. The two approaches are divided by a common reality.

I withdraw any comment about the validity of your explanation because, as we have established, I don't understood it.

-C2

c2,

OK, I think we got off the topic anyway.

You will probably find it hard to explore the process of a single photon interacting with matter. Just be aware that a photon is still a hypotetic particle representing a quanta of an electromagnetic field.

Best of luck

Tor

Nick writes:

"There is only one way light can really slow down. And that is by interacting with the EM field of matter."

Correct.

"I have been told it is absorption and emission of light in a medium that slows it down. But this doesn't actually CHANGE the SPEED of light."

For the full treatment, you'll need any undergraduate E-M textbook, but here's the gist.

The light doesn't just interact with the EM field of matter as if the two were separate. Light IS the electromagnetic wave rippling through the matter -- there's not a separate 'wave-that-was-in-the-vacuum', with separate induced fields on top of it. There is a single traveling electromagnetic field, which has at every point ONE electric field vector and (at right angles) one magnetic field vector.

First of all, we can ignore quantum effects to answer your question, and we can treat light as a classical electromagnetic wave.

The slowing-down of light in matter can be very accurately modeled by treating the matter as a simple bulk material. Let's simplify further and let the material be glass or plastic.

In a vacuum, a traveling electromagnetic wave follows a simple law of induction: (1) a changing magnetic field generates an electric field at right angles to the change, and (2) the changing electric field generates a magnetic field at right angles to the change. The two fields generate each other as they travel along. These laws of induction are most compactly summarized by Maxwell's Equations, which are basically all you need.

Vacuum is said to have an electric permeability and a magnetic permeability. That just means that if you put a voltage across a vacuum, the vacuum acts like a capacitor and stores' a certain amount of energy in an electric field. This energy 'really is' in the electric field.

Vacuum is also said to have a magnetic permeability. That just means that when you create a magnetic potential difference across a vacuum, it acts like a magnetic material and stores a certain amount of energy in a magnetic field. The magnetic energy 'really is' in the magnetic field.

Now suppose you have a microwave waveguide, a metal horn with a square aperture, facing into vacuum. y rapidly reversing the fields, you can 'shake loose' an electromagnetic wave into the vacuum. The electromagnetic wave can carry as much power as you can generate. If you freeze-frame the traveling electromagnetic wave, the total energy in the wave is equal to the total energy stored in the electric and magnetic fields.

Now suppose we cover the mouth of the microwave horn with resistive cloth called space cloth. If the space cloth has the exact same electrical resistivity as vacuum ( 288 ohms per square ), the electromagnetic wave gets soaked up by the space cloth just as if the wave had gone off into space and disappeared. If the electrical resistivity of the space cloth is DIFFERENT from the electrical impedance of vacuum, part of the microwave beam bounces off of the spacecloth with either a positive or negative phase.

It might seem odd that vacuum has an electrical impedance measured in ohms, but it does. Since you can push power through a vacuum with a microwave generator, vacuum must have a measurable impedance, corresponding to how much power you can push into a vacuum with a given amount of voltage ( a.k.a. electromotive force ).

A microwave beam behaves exactly like light in a vacuum, and travels at exactly the same velocity as light -- because a microwave beam IS light with a longer wavelength -- just as ultraviolet light and gamma rays are light with a shorter wavelength.

OK, that's how "light" behaves in a vacuum. Light is a traveling electromagnetic wave -- they're one in the same thing.

OK, let's step up the frequency to visible light and have it impact a sheet of plastic at a right angle. The light slows down. It's not a trick of path length -- the light actually slows down, in terms of the measured time to cross a unit distance. The plastic is said to have an index of refraction, measured by how much the light slows down. Refractive bending of light results from the light slowing down, because the wave fronts on either side of the boundary have to line up ).

Something else happens at the boundary -- a percentage of the wave bounces off the plastic, because there's an impedance mismatch -- the measured electrical impedance is different inside the plastic. The reflected wave tells you that the wave-in-vacuum doesn't just keep going 'as is' into the plastic. The plastic can not only change the velocity of the wave. but can cause part of the wave to rebound, which is why plastic looks shiny.

Inside the plastic, the movement of the electromagnetic wave is still governed by the laws of induction -- a changing electric field generates a magnetic field, and a changing magnetic field generates a magenetic field.

The difference is that each atom in the plastic has a positive nucleus and negative electrons. The electrons can move slightly in response to the electric field of the light. The slight movement of charge is caused a displacement current. The displacement of charge causes an induced electric field and an induced magnetic field.

Here's where it gets interesting. Maxwell's Equations don't just work in a vacuum -- they also work around electric currents. You can in principle solve Maxwell's equations for any arbitrarily complex configuration of moving charges and fields. Here we get lucky -- the solution is still a simple traveling ( plane ) wave.

So why is it slower?

The reason, in a nutshell, is that the electrons take time to respond to the electric field of the incoming light -- there's a phase delay. When the electrons do respond, they move so as to absorb energy from the incoming electric field ( like charging up a capacitor ). The induced electric field is roughly OPPOSITE to the incoming electric field. In other words, the original wave can be thought of as constantly being absorbed and re-emitted by the more sluggish charged matter.

Let's switch to an even simpler question, why does a TV wave slow down in plastic ribbon wire or coaxial cable? Suppose we start without the plastic, and just have two parallel conductors in a vacuum. If you hook the parallel wires up to a TV signal, the signal travels at the speed of light in vacuum -- because when you apply Maxwell's Equations to the electric and magnetic fields in the space around the wire, that space is vacuum, so you plug in the electric and magnetic permeability of vacuum.

Another way of solving the parallel-wire problem ( which comes out the same )
is to treat the wire as a series of small series inductors ( representing the inductance of wire in vacuum ) bridged by small capacitors between the wires, representing the distributed capacitance of two wires close together in vacuum. That's also a model for a delay line -- because the larger the capacitors are, the longer it takes them to charge up, causing a phase delay.
The end result is the same -- a TV wave travels along parallel wires at the speed of light if there's nothing between the wires.

If we add plastic insulation between the wires, the inductance is essentially unchanged, but the capacitance between the wires is markedly increased, and the signal slows down by 20 % to a third. This slowdown helps keep the signal from leaking out of the ribbon wire, because the speed and wavelength no longer match up with vacuum.

Again, to properly understand this you'll need to experiment with Maxwell's Equations, which are differential equations -- they express the electric field AT ANY POINT in terms of the change-of-magnetic field at that same point, and vice versa. You'll also need some calculus to see why the solutions are traveling plane waves of a particular velocity. That may seem like a lot of work, but it gives you a powerfully generalized understanding of how waves work, and why most faster-than-light schemes don't work.

Quantum mechanics wasn't needed in the above, because the quantum mechanics is folded into the index of refraction and dielectric constant, which for most transparent materials are fairly constant across the visible spectrum. ( Up in the ultraviolet range, glass and plastic have strong quantum mechanical resonances that can cause two slightly different frequencies of light to behave very differently ). However at ordinary visible-light wavelengths, the only quatum-nechanical effect is a slight variation of refractive index with frequency, which causes a prism to spread colors of light.

At the tail end of wiki entry about something else (sorry I can't find it again) came the comment..

The interaction of the photon with the (whatever) effectively gives it the property of 'mass' and for this reason it can no longer travel at the speed of light.

I think I am convinced by this explanation.. I'd give Nick 10/10.

-C2.

This post has been edited by Confused2 on Aug 4 2006, 04:06 PM