Four-wave mixing

# Four-wave mixing

Discussion

Encyclopedia
Four-wave mixing is an intermodulation
Intermodulation
Intermodulation or intermodulation distortion is the amplitude modulation of signals containing two or more different frequencies in a system with nonlinearities...

phenomenon in optical systems, whereby interactions between 3 wavelengths produce a 4th wavelength in the signal. It is similar to the third-order intercept point
Third-order intercept point
In telecommunications, a third-order intercept point is a measure for weakly nonlinear systems and devices, for example receivers, linear amplifiers and mixers. It is based on the idea that the device nonlinearity can be modeled using a low-order polynomial, derived by means of Taylor series...

in electrical systems. Four-wave mixing can be compared to the intermodulation distortion in standard electrical systems.

## Mechanism

When three wavelength
Wavelength
In physics, the wavelength of a sinusoidal wave is the spatial period of the waveâ€”the distance over which the wave's shape repeats.It is usually determined by considering the distance between consecutive corresponding points of the same phase, such as crests, troughs, or zero crossings, and is a...

s (λ1, λ2, and λ3) interact in a nonlinear medium, they give rise to a fourth wavelength (λ4) which is formed by the scattering of the incident photons, producing the fourth photon. It is easier to illustrate this if we use frequency
Frequency
Frequency is the number of occurrences of a repeating event per unit time. It is also referred to as temporal frequency.The period is the duration of one cycle in a repeating event, so the period is the reciprocal of the frequency...

Given inputs f1, f2, and f3, 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.

From calculation with the three input signals, it is found that 12 interfering frequencies are produced, 3 of which lie on one of original incoming frequencies.

## Degenerate four-wave mixing

Four-Wave Mixing (FWM) is also present if only three components interact. In this case the term

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

FWM is a fiber-optic characteristic that affects wavelength-division multiplexing
Wavelength-division multiplexing
In fiber-optic communications, wavelength-division multiplexing is a technology which multiplexes a number of optical carrier signals onto a single optical fiber by using different wavelengths of laser light...

(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
Coherence (physics)
In physics, coherence is a property of waves that enables stationary interference. More generally, coherence describes all properties of the correlation between physical quantities of a wave....

. 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.