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What is four wave mixing (FWM) in Optical Fiber Communication?

What is four wave mixing (FWM)?: FWM is the interaction of two or more wavelengths (channels) which results in sidebands (or ghost channels) and is caused by non-linear effects. Four-wave mixing (FWM) is an intermodulation phenomenon in non-linear 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.

The sidebands can coincide with other channels resulting in distortion. The effect on DWDM channels can be similar to noise if a number of channels are used. Nonlinear effects is important even at moderate powers and bit rates, at higher bit rates such as 10 Gb/s and above and/or at higher transmitted powers, it is important to consider the effect of nonlinearities. In case of WDM systems nonlinear effects happens. Nonlinear effect happen because of interaction of light waves with phonons (molecular vibrations) in the silica medium of optical fiber, other nonlinear effects are caused by the dependence of refractive index on the intensity of the optical power (applied electric field).
The four-wave-mixing process involves the conversion of two pump photons to a signal photon and an idler photon
The four-wave-mixing process involves the conversion of two pump photons to a signal photon and an idler photon

What is four wave mixing (FWM) in Optical Fiber Communication?
The practical issues

FWM is dependent on signal power, the effective fiber area, channel count, channel spacing and fiber type. FWM is therefore an issue of system design and type of fiber used. In systems using dispersion shifted fiber (DS) becomes a critical problem. Different wavelengths with the same propagation speed – or group velocity – traveling at a constant phase over a long period of time, increase the effect of FWM. The effects of FWM are greatest near the zero dispersion point of the fiber. A certain amount of chromatic dispersion (CD) leads to different group velocities resulting in a reduction of FWM. The influence of FWM can be reduced by irregular channel spacing.

Solution for Four Wave Mixing
Four-wave mixing is a severe problem in WDM systems using dispersion-shifted fiber but does not usually pose major problem in systems using standard fiber.

➥Unequal channel spacing. The positions of the channels can be chosen carefully so that the beat terms do not overlap with the data channels inside the receiver bandwidth.

Using higher wavelengths beyond 1560nm with DSF. Even with DSF, a significant amount of chromatic dispersion is present in this range, which reduces the effect of four-wave mixing.

Reducing transmitter power and the amplifier spacing.

 If the wavelengths can be demultiplexed and multiplexed in the middle of the transmission path,

How to Measure Four Wave Mixing FWM
The effects of FWM are only present with systems in service and are different for each particular system. The sum of all linear and non-linear distortions – including in-band crosstalk and noise from FWM – are covered by Q-factor measurements as the Q-factor provides a measure of the signal quality for a specific DWDM channel.

The appearance of mixture products in a particular channel can be addressed by a multi-tone power ratio (MTPR) measurement. The signal to noise-plus-distortion ratio of the transmitted signal in a DWDM channel is given as the ratio of the power level of that particular channel to the sum of all unwanted signals centered on the DWDM channel wavelength.

This ratio can be measured with an optical spectrum analyzer (OSA) for each channel used for transmission. The channel under investigation must be turned off during the measurement of the noise plus distortion.
Sidebands of three channels. Example for the fijk = fi + fj - fk scheme.
measurement of the noise plus distortion.
How the four wave is generated
In a WDM system using the angular frequencies ω1, … ωn, the intensity dependence of the refractive index not only induces phase shifts within a channel but also gives rise to signals at new frequencies such as 2ωij and ωi + ωj – ωk. This phenomenon is called four-wave mixing.

The four-wave mixing effect is independent of the bit rate but is critically dependent on the channel spacing and fiber chromatic dispersion.Decreasing the channel spacing increases the four-wave mixing effect. The effects of Four-Wave Mixing must be considered even for moderate-bit-rate systems when the channels are closely spaced and/or dispersion-shifted fibers are used.

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