Dear AnObserver, you may surely refer to so-called non-linear optics. Indeed, as you mention it, the optical transfert functions of some material are not proportional to the incident light. You may know the green (wavelength = 0.532µm) and the red laser (wavelength = 1.016µm) pointers, the green is derived from the red from a non-linear material that double frequencies. Yes also, you need some basics of quantic mechanics to write the equations. The result is comparable to parametric amplification in electronics. While this is a second order effect, the refraction, as well as the birefringence, is explained in the first order, linear, of the response of the material that is the domain of geometrical optics.