Sum-frequency generation

Sum-frequency generation (SFG) is an example of a second order non-linear optical process. This phenomenon is based on the annihilation of two input photons at frequencies $\omega _{1}$ and $\omega _{2}$ while, simultaneously, one photon at frequency $\omega _{3}$ is generated. In order that the sum-frequency generation takes place it is necessary that the following two conditions happen:

1. Energy conservation: $\hbar \omega _{3}=\hbar \omega _{1}+\hbar \omega _{2}$

2. Momentum conservation: $\hbar k_{3}=\hbar k_{1}+\hbar k_{2}$

The first condition shows the relationship of the frequencies between the input and output photons. It is possible to notice that the sum-frequency generation 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. The second condition implicates the k-vector conservation, in fact $\Delta k=k_{3}-k_{2}-k_{1}=0$; this condition is called phase matching condition.

In a common SFG application, light from a tunable infrared laser is combined with light from a fixed infrared frequency in order to produce visible light through wave mixing process.