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# Four-wave mixing

Four-wave mixing is an intermodulation distortion in optical systems, similar to the third-order intercept point in electrical systems.

Four-wave mixing can be compared to the intermodulation distortion in standard electrical systems. When three wavelengths (λ_{1}, λ_{2}, and λ_{3}) interact in a nonlinear medium, they give rise to a fourth wavelength (λ^{4}) which is formed by the scattering of the incident photons, producing the fourth photon. It is easier to illustrate this if we use frequency instead of wavelength.

Given inputs f_{1}, f_{2}, and f_{3}, the nonlinear system will produce

with the most damaging signals to system performance calculated as

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

Doing the math with the three input signals, you will find that 12 interfering frequencies are produced, 3 of which lie on one of original incoming frequencies.

**Degenerate four-wave mixing
**

FWM is also present if only three components interact. In this case the term

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

couples three components, thus generating the so-called Degenerate Four-Wave Mixing, showing identical properties as in case of four interacting waves.

Four-Wave Mixing (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 causes in WDM systems is known as interchannel crosstalk. FWM can be mitigated by using uneven channel spacing or fiber that increases dispersion.

**Links**

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