- #1
johng23
- 294
- 1
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!
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!
