w₁ + w₂ = w₃ (or 1/l₁ + 1/l₂ = 1/l₃ in wavelength) It combines two low-energy (or low- frequency) photons into a high-energy photon. For example:

　1064nm + 532nm -----> 355nm

Frequency Doubling or Second Harmonic Generation (SHG) is a special case of sum frequency generation if the two input wavelengths are the same: 2w₁ = w₂ (or l₁ = 2l₂ in wavelength). The simplest scheme for frequency doubling is extracavity doubling. The laser passes through the nonlinear crystal only once as shown. However, if the power density of laser is low, focused beam, intracavity doubling and external resonant cavity are normally used to increase the power density on the crystals, for example, for doubling of cw Nd:YAG laser and Argon Ion lasers.

Frequency Tripling or Third Harmonic Generation (THG) is an other example of Sum Frequency Generation where, for THG of Nd:YAG laser, l₁ = 1064nm, l₂ = 532nm and generated wavelength l₃ = 355nm. By sum frequency of fundamental wavelength and THG of a Ti:Sapphire laser in BBO crystal, it can generate wavelength as short as 193nm.