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Everything about Sum Frequency Generation totally explained

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's necessary that the following two conditions happen:
1. Energy conservation: hbaromega_3 = hbaromega_1 + hbaromega_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 frequency visible laser to produce an invisible sum frequency (SF) beam created by a wave mixing process.

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