Nonlinear processes generating beams with the sum or difference of the frequencies of the input beams.

Crystal materials lacking inversion symmetry can exhibit a so-called χ(2) nonlinearity. In such nonlinear crystal materials, sum Frequency generation or difference frequency generation can occur, where two pump beams generate another beam with the sum or difference of the optical frequencies of the pump beams. Such a process requires Phase Matching to be efficient, and usually there is no simultaneous phase matching for sum and difference frequency generation.