Sum-frequency generation

Sum frequency generation (SFG) is an example of a second order non-linear optical process, in which two beams of light of different frequencies $\omega _{1}$ and $\omega _{2}$ interact, creating light with frequency $\omega _{3}=\omega _{1}+\omega _{2}$. It is a generalization of second harmonic generation. In the latter, $\omega _{1}=\omega _{2}$, both of which can be provided by a single light source. From a quantum mechanical perspective, SFG can be seen as result of combining two photons to produce a third. Since the energy of a photon is given by

$E_{\nu }=\hbar \omega ,$

the frequency summing $\omega _{3}=\omega _{1}+\omega _{2}$ is simply a statement that energy is conserved.

In a common SFG application, light from a tunable infrared laser is combined with light from a fixed frequency visible laser to produce an invisible sum frequency (SF) beam created by a wave mixing process.