# Four-wave mixing

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Four-wave mixing (FWM) is an intermodulation phenomenon in non-linear optics, whereby interactions between two wavelengths produce two extra wavelengths in the signal. 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.

## Mechanism

When three frequencies (f1, f2, and f3) interact in a nonlinear medium, they give rise to a fourth wavelength (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

$\pm f_{1} \pm f_{2} \pm f_{3}$

with the most damaging signals to system performance calculated as

$f_{ijk} = f_{i} + f_{j} - f_{k}, \mathrm{where}\, i, j \neq k$

since these frequencies will lie close to one of the incoming frequencies.

From calculations with the three input signals, it is found that 12 interfering frequencies are produced, three of which lie on one of original incoming frequencies.

## Degenerate four-wave mixing

Four-wave mixing is also present if only two components interact. In this case the term

$f_{0} = f_{1} + f_{1} - f_{2}$

couples three components, thus generating so-called degenerate four-wave mixing, showing identical properties as in case of three interacting waves.

FWM is a fiber-optic characteristic that affects wavelength-division multiplexing (WDM) systems, where multiple optical wavelengths are spaced at equal intervals or channel spacing. The effects of FWM are pronounced with decreased channel spacing of wavelengths and at high signal power levels. High chromatic dispersion decreases FWM effects, as the signals lose coherence. The interference FWM caused in WDM systems is known as interchannel crosstalk. FWM can be mitigated by using uneven channel spacing or fiber that increases dispersion.