Sum-frequency generation
Sum-frequency generation is a second order nonlinear optical process based on the mixing of two input photons at frequencies and to generate a third photon at frequency. As with any optical phenomenon in nonlinear optics, this can only occur under conditions where:
the light is interacting with matter, that lacks centrosymmetry ;
the light has a very high intensity.
Sum-frequency generation is a "parametric process", meaning that the photons satisfy energy conservation, leaving the matter unchanged:
Second-harmonic generation
A special case of sum-frequency generation is second-harmonic generation, in which. In fact, in experimental physics, this is the most common type of sum-frequency generation. This is because in second-harmonic generation, only one input light beam is required, but if, two simultaneous beams are required, which can be more difficult to arrange. In practice, the term "sum-frequency generation" usually refers to the less common case in which.Phase-matching
For sum-frequency generation to occur efficiently, phase-matching conditions must be satisfied:where are the angular wavenumbers of the three waves as they travel through the medium. As this condition is satisfied more and more accurately, the sum-frequency generation becomes more and more efficient.