How can light cause atoms to oscillate without being absorbed?

  • Thread starter johng23
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  • #1
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If light travels through a perfectly transparent material, it will not be absorbed, and other than the reflection loss at the two interfaces, the energy that comes out will be equal to that which went in. Yet we know that the light field is causing all the atoms in its path to oscillate, thus giving them kinetic energy. How can this happen without the light beam being absorbed, ie losing that energy?

This is fundamental issue of mine, and it relates to the second part of my question. I am trying to understand and reconcile two explanations for the optical properties of metals:

In the band-theory view, metals are opaque to visible light because there are empty states above the Fermi level, so all of these frequencies can be absorbed. They become transparent somewhere in the UV, because the photon energy becomes large enough that the electron would have to transfer to a state within the band gap.

In the free electron model, I can derive the dielectric function and I find that the metal is opaque up to the plasma frequency, and transparent above. Clearly this has to do with whether the atoms can oscillate exactly in phase with the electromagnetic wave, or whether they lag (as they do above the plasma frequency). However, I'm not 100% clear on the physical picture.

In the region where it is opaque, the atoms can polarize effectively instantly, so they move exactly out of phase with the light, and (as I am imagining it) this allows them to screen the field. In this picture, the fact that they can oscillate with the field is what is allowing them to absorb the energy. Then when the frequency increases to a certain point, the atom's response time becomes substantial, and they lag. I am imagining that this causes them to oscillate with a smaller amplitude (which eventually goes to zero), so that the amount of screening is getting less and less. But this must be wrong, because I know that absorption doesn't turn off gradually - it turns off abruptly, at the plasma frequency. And the amplitude argument can't be quite right, because at the plasma frequency that oscillations are resonant, so they should have large amplitudes.

(This is of course where the first part comes in - shouldn't all oscillations absorb energy?)

So, secondly, once I have the intuition for the free electron description, how do I relate this to the band-theory explanation? Is the availability of empty states above the Fermi level equivalent to the ability of the electrons to polarize in response to the applied field? More to the point, how do I visualize the available states for a metal? Do these higher energy states correspond to modes of oscillation of the free-electron sea?

Sorry for the long question!
 

Answers and Replies

  • #2
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the electrons are undamped and therefore emit as much as they absorb.
the only effect is to change the phase velocity of the light.
this clearly does depend on the amplitude of the oscillation.
In metals the electrons are free to move till the resulting field completely cancels the field due to the light.
In non-metals and in metals above the plasma freq the resulting field only partially cancels the field due to the light.

I wonder what a laser would do at the plasmon freq in a nonmetal
(looks like it would be totally reflected but then in a nonmetal the electrons may not be free to move sufficiently far for this to happen)

http://en.wikipedia.org/wiki/Free_electron_model#Dielectric_function_of_the_electron_gas

http://en.wikipedia.org/wiki/Plasmon_frequency
 
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  • #3
DaveC426913
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If light travels through a perfectly transparent material, it will not be absorbed, and other than the reflection loss at the two interfaces, the energy that comes out will be equal to that which went in. Yet we know that the light field is causing all the atoms in its path to oscillate, thus giving them kinetic energy. How can this happen without the light beam being absorbed, ie losing that energy?
Why do you insist that both these things are true?

You said perfectly transparent.

If this is an ideal material, then what makes you think light must imparting it with net energy? That would be so if it were a real material.
 
  • #4
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But even if it is an ideal material, and there is no damping, how can the light set the atoms moving with no energy loss? Haven't you just "gotten something for nothing"? Even for an idealized material, shouldn't that be impossible?
 
  • #5
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energy goes from the light into the electron causing it to move.
then the energy comes back out as light
energy in equals energy out.
 
  • #6
DaveC426913
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energy goes from the light into the electron causing it to move.
then the energy comes back out as light
energy in equals energy out.
OK but if so, the electron has not 'gained kinetic energy', as he claims:

...the light field is causing all the atoms in its path to oscillate, thus giving them kinetic energy...

john, if the material is perfectly transparent, it will transmit the energy without absorbing the energy, i.e. it will not heat up, i.e. will not retain any kinetic energy.
 
  • #7
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if the electron moves then it certainly 'gained kinetic energy'.
how could it emit light if it doesnt move?
 
  • #8
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Well here's part of my issue I think. Suppose I have a pulse of light that exists in the material for a short time, and sets an atom moving at some frequency. With no damping, the atom can continue oscillating indefinitely, and it emits light continuously at frequency w. A photon doesn't have any specified length in time, so I could consider it to emit a single photon even if it oscillates for an hour. Of course the real issue is that it absorbs a wavepacket so it has to emit something which is also localized in time...
 
  • #9
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How about the other parts of the question :biggrin:
 
  • #10
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what do you think?
 
  • #11
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What do you mean? Didn't I already write quite a bit about what I think?

Anyway, let's say I accept that atoms can absorb and emit the same amount of energy, so that no net energy transfer occurs. But then I still don't understand how this becomes impossible once the atoms begin to lag behind the driving field and go out of phase with it.
 
  • #12
Jano L.
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Try to calculate time average of the electric power P = qE(t)v(t) for the harmonically driven mechanical oscilator:

x'' + 2bx' + omega_0 x = a_0 sin(omega t)

It turns out that when the damping term (-2b v(t)) is zero, the force and the motion are in phase or antiphase and average power is zero. While with the nonzero damping, the oscillations get phase lag and energy gets absorbed (because of damping).
 

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