How exactly does photon polarization work?

[Jake1]

Hi everyone, I'm working on a pretty relaxed end-of-the-year school project, the only objective of which is to explain a mathematical concept to the class. I've chosen quantum cryptography. By Monday, I would like to be able to:

1. Define quantum mechanics for the class.
2. Explain the math behind photon polarization.
3. Explain how the BB84 (sending photons with laser pulses) and Eckert (communicating with two entangled photons) quantum key distribution protocols work.
4. Explain the applications of quantum cryptography.

I can accomplish all but the second objective by myself. I understand Wikipedia's explanation of the BB84 protocol pretty well, but I do not understand the actual mathematics behind photon polarization. I don't know what "rectilinear" or "diagonal" base states are, I don't know how photons are actually polarized, and I don't understand why measuring a rectilinear photon as if it were diagonal forces it to assume a random diagonal state. I can't simply settle for a qualitative understanding of these concepts, either, as this project must have a firm basis in actual math.

 

So, as a student with a firm understanding of calculus and a very light understanding of physics, which online resources can I use to learn about the mathematics behind photon polarization? I need to be able to actually explain polarization in terms of the functions physicists use to describe quantum mechanics.

 

Thanks in advanced for your help.

[Sensei]

Photons emitted by your LCD/LED monitors are the most likely polarized. You just need polarization filter to see effects.

 

I have made photos and showed in this thread:

http://www.scienceforums.net/topic/80366-particle-location/page-3#entry783255

Have you read this?

http://en.wikipedia.org/wiki/Polarization_%28waves%29

Edited May 18, 2014 by Sensei