Nonlinear optics is classified by the effect of an electric field applied to a medium. In nonlinear crystals, when a field is applied the dielectric polarization does not respond proportionally to it.
Nonlinear mediums are employed to change the wavelength of light. When two rays of the same frequency are phase matched incident to such a medium, they are absorbed and remitted from the surface as a single ray with double the frequency.
On an individual photon basis, two photons enter the material and are destroyed, while another is created with twice the frequency due to energy and momentum conservation. (Two are absorbed then a single re-emitted.)
My source of confusion:
Frequency mixing seems to occur if and only if photon absorption takes place. However, non-linear crystals are transparent, so most photons are not absorbed, and are instead scattered by the electric fields of surrounding atoms.
If very little absorption takes place, by what mechanism does frequency mixing take place?
Bonus question: If frequency mixing does take place, are all photons mixed? Or does unmixed light leave the crystal as well?