Four Wave Mixing (FWM) Basics in Optical Fiber

This page describes FWM basics. The term FWM refers to Four Wave Mixing. It also mentions the 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 circuits. 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; this can form a new signal of an undesired wavelength. The figure below depicts the FWM effect in a two-channel WDM system on low-dispersion fiber cable.

The FWM effect usually occurs in nonlinear optical materials, e.g., photonic switches, fiber cables, etc. This interaction between waves will lead to interaction between the channels.

As shown in the figure above, when two input signals located at W1 and W2 traverse a fiber of length (L), it will produce outputs at four frequencies located at W1, W2, 2W1-W2, and 2W2-W1.

FWM depends on the following parameters:

• Dispersion
• Effective Area
• Channel spacing

FWM can be expressed as follows:

$FWM \sim \frac{Power^4}{Dispersion^2 \cdot EffectiveArea^2 \cdot ChannelSpacing^4}$

The figure above depicts the generation of a fourth wave when three channels are provided as input to the nonlinear fiber device or component. As shown, it produces a fourth component equal to w1+w2-w3. In general, when three waves at frequencies of $f_i$, $f_j$, and $f_k$ traverse a fiber, they will generate another signal as defined by the following equation:

$f_{ijk} = f_i + f_j - f_k$, where i, j is not equal to k

If there are N channels, the newly generated signals are expressed as follows:

$M = (1/2) \cdot N^2 \cdot (N-1)$

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 issues in the optical domain. It produces unwanted spurious components which cause the 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 the above equation, if the number of channels increases then mixing products at the output increase rapidly.

Reducing FWM Effects

The following methods can be employed in an Optical System to reduce FWM and to improve performance:

• By using modulation techniques such as DPSK, QAM, QPSK, etc.
• By using a Duobinary modulation scheme.
• By using a hybrid modulation scheme.