# RF Wireless World

## What is FWM | Four Wave Mixing | FWM basics in Optical fiber

This page describes FWM basics. The term FWM refers to Four Wave Mixing. It also mentions effects of FWM and how to reduce it in optical fiber. Optical Four wave mixing is similar to third order intermodulation distortion seen in electronic or RF circuit.

FWM is the short form of Four Wave Mixing. This term is given to the most common interference found in DWDM optical fiber systems. In DWDM, multiple optical signals of various different wavelengths are combined; it will form a new signal of undesired wavelength.

The figure-1 depicts FWM effect in two channel WDM system on low dispersion fiber cable. The FWM effect usually occurs in nonlinear optical meterials e.g. photonic switch, fiber cable etc. This interaction between waves will lead to interaction between the channels. As shown in fig-1, when two input signals located at W1 and W2 traverse fiber of length (L), it will produce outputs at four frequencies located at W1, W2, 2W1-W2 and 2W2-W1. FWM depends on following parameters:
• Dispersion
• Effective Area
• Channel spacing

FWM can be expressed as follows:
FWM ~ { Power4 / (Dispersion2 x Effective Area2 x Channel Spacing4) } The figure-2 depicts generation of fourth wave when three channels are provided as input to the nonlinear fiber device or component. As shown it produces fourth component equal to w1+w2-w3.

In general, when three waves at frequencies of fi, fj and fk traverse a fiber, they will generate another signal as defined by following equation.
fijk = fi + fj - fk ,
Where i, j is not equal to k

If there are N channels, the newly generated signals are expressed as follows.
M = (1/2)*N2 * (N-1)
Where N = Number of input frequencies.
M = Mixing products generated at the output.
If there are 3 channels, this will create 9 additional signals.
From this it can be observed that if N increases, M increases rapidly.

### Effects of FWM-Four Wave Mixing

Four Wave Mixing is one of the most troublesome issue in optical domain. It produces unwanted spurious components which cause following problems.
• Produces interference between wanted optical signals.
• Produces additional noise which degrades the performance of the optical system.
• Some power will be lost from wanted wavelengths to the unwanted ones.
• As mentioned in above equation, if number of channel increases then mixing products at the output increases rapidly.

### Reducing FWM Effects

Following methods can be employed in Optical System to reduce FWM and to improve the performance.
• By using modulation technique such as DPSK, QAM, QPSK etc.
• By using Duobinary modulation scheme.
• By using hybrid modulation scheme.