I was reading about second-harmonic generation (SHG) crystals (or frequency-doubling crystals) used to produce green laser light from IR.
What low-level process in the crystal is actually driving the combination of two photons into one? I'm thinking of a process at the QED level (or at least motivating what happens at that level). The wikipedia entry on SHG doesn't really address this (it just mentions it's a non-linear phenomena..).
Or put another way - what's the simplest system possible (theoretically) that can show the phenomena even if at a very low efficiency?
Edit: A supplement to the question, is what entropy-related constraints are there on the incoming photons in these processes, in order to avoid for example turning heat into nicer higher-energy photons?