Sum-frequency generation

Sum-frequency generation (SFG) is a second order nonlinear optical process based on the mixing of two input photons at frequencies ${\displaystyle \omega _{1}}$ and ${\displaystyle \omega _{2}}$ to generate a third photon at frequency ${\displaystyle \omega _{3}}$. As with any ${\displaystyle \chi ^{(2)}}$ optical phenomenon in nonlinear optics, this can only occur under conditions where: the light is interacting with matter, that lacks centrosymmetry (for example, surfaces and interfaces); the light has a very high intensity (typically from a pulsed laser). Sum-frequency generation is a "parametric process", meaning that the photons satisfy energy conservation, leaving the matter unchanged:

${\displaystyle \hbar \omega _{3}=\hbar \omega _{1}+\hbar \omega _{2}}$