Four-wave mixing (FWM) is an intermodulation phenomenon in nonlinear optics, whereby interactions between two or three wavelengths produce two or one new wavelengths. It is similar to the third-order intercept point in electrical systems. Four-wave mixing can be compared to the intermodulation distortion in standard electrical systems. It is a parametric nonlinear process, in that the energy of the incoming photons is conserved. FWM is a phase-sensitive process, in that the efficiency of the process is strongly affected by phase matching conditions. Mechanism When three frequencies (f1, f2, and f3) interact in a nonlinear medium, they give rise to a fourth frequency (f4) which is formed by the scattering of the incident photons, producing the fourth photon. Given inputs f1, f2, and f3, the nonlinear system will produce From calculations with the three input signals, it is found that 12 interfering frequencies are produced, three of which lie on one of the original incoming frequencies. Note that these three frequencies which lie at the original incoming frequencies are typically attributed to self-phase modulation and cross-phase modulation, and are naturally phase-matched unlike FWM. Sum and Difference frequency generation Two common forms of four-wave mixing are dubbed sum frequency generation and difference frequency generation. In sum frequency generation three fields are input and the output is a new high frequency field at the sum of the three input frequencies. In difference frequency generation, the typical output is the sum of two minus the third. A condition for efficient generation of FWM is phase matching: the associated k-vectors of the four components must add to zero when they are plane waves. This becomes significant since sum and difference frequencies generation is often enhanced when resonance in the mixing media is exploited. In many configurations the sum of the first two photons will be tuned close to a resonant state. However, close to resonances the index of refraction changes rapidly and makes addition four co-linear k-vectors fail to add exactly to zero—thus long mixing path lengths are not always possible as the four component lose phase lock. Consequently, beams are often focused both for intensity but also to shorten the mixing zone. In gaseous media an often overlooked complication is that light beams are rarely plane waves but are often focused for extra intensity, this can add an addition pi-phase shift to each k-vector in the phase matching condition. It is often very hard