[function_seven]

If the material is being excited into oscillations that then re-emit "new" light, how is the color and direction preserved? Polarization filters tend to pass the full spectrum (or nearly so) of visible light, but my understanding of photon absorption and emittance is that the wavelengths are dependent on the electron energy levels. (I'm thinking of the same mechanism that produces lines on a spectrometer, indicating which elements are present in a sample.)

I guarantee I've misused a term or two above. Hopefully you get what I'm asking.

Taking a stab at my own question, the "rails" are field lines within the material, and not electrons themselves that interact. Is that close?

[amluto]

It’s because the “re-emission” is coherent in the sense that it’s in the same phase as the incoming light. As a decent analogy: when you sing a pure note, it “excites” (vibrates) air molecules as it travels, and those air molecules in turn bump into other molecules, all at random, but still all in phase so that whoever is listening hears the original note. Similarly, when light goes through ordinary glass, it wiggles the electrons in the glass, which in turn change the way the light propagates, refracting it while still preserving an image.

Any textbook on electricity and magnetism will cover this in a section called something like “Maxwell’s equations in materials”.

[roesel]

I have used the word "re-emit" in the sense of the Maxwell equations description of electromagnetic fields. You are right that the light definitely does not get absorbed and then re-emitted in the sense you mean. In such a case, everything you wrote would be correct. (I probably should have used a term like "radiate" and perhaps dipoles instead of electrons to be more clear.)

I was trying to describe the propagation of light in a material, where the optical field induces oscillations in the dipoles of the material, and these dipoles in turn excite the optical field. This happens constantly in every nanometer of the material, and it is difficult to experimentally separate the field into the "material" portion and the "vacuum" portion, because it exists as an everchanging mixture as long as there are dipoles around.

As for the "rails", the way I've had it explained to me is that in one direction of a polarizer, electrons are free to move, so they fully absorb the light polarized in that direction. In the perpendicular direction, they are bound, and the best they can do in reaction to a field is oscillate back and forth a tiny bit. These oscillations excite an optical field again and it propagates further until it finds another dipole to excite. I like to crudely imagine a polarizer as the grid of a nanoscopic egg slicer :D. Field oscillations will get absorbed along the metal wires, but in the perpendicular direction, it will just excite vibrations in the wires, which will radiate them out again, sort of like a guitar string.

Let me know if this was helpful, or if I've made a mistake somewhere :).

[Rayhem]

It's very likely an off-resonant, non-quantum excitation. If the incident light is at the resonance frequency of the atom, it will excite electrons which will spontaneously decay and throw off the energy. Far from resonance, though, the atoms will wiggle (classically) like a harmonic oscillator from forces due to the fields (similar to the answer here: https://physics.stackexchange.com/a/474/23322).