Sum frequency generation

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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 ω1 and ω2 while, simultaneously, one photon at frequency ω3 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, ω1 = ω2, both of which can be provided by a single light source. The second condition implicates the k-vector conservation, in fact Δk = k3 − k2 − k1 = 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.


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