# What are Dispersion Compensating Fibers?

### >> The Background

In recent years there has been a lot of work on dispersion-compensating fibers (DCFs), which are being used extensively for upgrading the installed 1310nm optimized optical fiber links for operation at 1550nm. In the following two sections, we will discuss the basic principle behind dispersion compensation, and the characteristics of dispersion compensating fibers (DCFs).

### >> What is Dispersion Compensation

Let’s look at a pulse (with spectral width of Δλ_{0}) which is propagating through a fiber characterized by the propagation constant β. The spectral width Δλ_{0} could be due to either the finite spectral width of the laser source itself or the finite duration of a Fourier transform-limited pulse. We consider the propagation of such a pulse with the group velocity given by:

For a conventional single mode fiber with zero dispersion around 1300nm, a typical variation of ν_{g} with wavelength is shown by the solid curve in the following figure.

As we can see from the above figure, ν_{g }has a maximum value at the zero dispersion wavelength and on either side it monotonically decreases with wavelength. So, if the central wavelength of the pulse is around 1.55 μm, then the longer wavelengths will travel slower than the smaller wavelengths of the pulse. Because of this (chromatic dispersion) the pulse will get broadened. The leading edge of the output pulse is blue shifted and the trailing edge is red shifted.

Now, after propagating through such a fiber for a certain length L_{1}, we allow the pulse to propagate through another fiber where the group velocity varies, as shown by the dashed cure in the above figure. The longer wavelengths will now travel faster than the shorter wavelengths and the pulse will tend to reshape itself into its original form. This is the basic principle behind dispersion compensation.

Now the total dispersion of a single mode fiber is given by:

Thus, d^{2}β/dω^{2} < 0 implies operation at λ_{0} > λ_{z} (λ_{z} is the zero dispersion wavelength) and conversely.

Let (D_{t})_{1} and (D_{t})_{2} be the dispersion coefficient of the first and second fiber, respectively. Thus, if the lengths of the two fibers (L_{1} and L_{2}) are such that

then the pulse emanating from the second fiber will be identical to the pulse entering the first fiber.

In order to fully understand this, let’s look at the following figure.

In the above figure (a), we can see the broadening of an unchirped pulse as it propagates through a fiber characterized by (D_{t})_{1} > 0 (λ_{0} > λ_{z}). Thus, because of the physics discussed above, the pulse gets broadened and chirps, the front end of the pulse gets blue shifted, and the trailing edge of the pulse gets red shifted. The pulse is said to be negatively chirped. If such a negatively chirped pulse is now propagated through another fiber of length L_{2} characterized by (D_{t})_{2} < 0, then the chirped pulse will get compressed (see (b) of the above figure), and, if the length satisfies the previous equation, then the pulse dispersion will be exactly compensated.

### >> Dispersion Compensating Fiber

Conventional single mode fibers are characterized by large (~ 5-6 μm) core radii and zero dispersion occurs around 1300 nm. Operation around λ0 at 1300nm thus leads to very low pulse broadening, but the attenuation is higher than at 1550 nm. Thus, to exploit the low-loss window around 1550nm, new fiber designs were developed that had zero dispersion around 1550nm wavelength region. These fibers are called Dispersion Shifted Fibers (DSF) and have typically a triangular refractive index profiled core. using DSFs operating at 1550nm, one can achieve zero dispersion as well as minimum loss in silica-based fibers.

Now, in many countries, tens of millions of kilometers of conventional single mode fibers (CSFs) already exist n the underground ducts operating at 1300nm. One could increase the transmission capacity by operating these fibers at 1550nm and using WDM techniques and optical amplifiers. But, then there will be significant residual (positive) dispersion. On the other hand, replacing these fibers by DSFs would involve huge costs. As such, in recent years, there has been considerable work in upgrading the installed 1310nm optimized optical fiber links for operating at 1550nm. This is achieved by developing fibers with very large negative dispersion coefficients, a few hundred meters to a kilometer, which can be used to compensate for dispersion over tens of kilometers of the fiber in the link.

Compensation of dispersion at a wavelength around 1550nm in a 1310nm optimized single mode fiber can be achieved by specially designed fibers whose dispersion coefficient (D) is negative and large at 1550nm. These types of fibers are know as Dispersion Compensating Fibers (DCFs).

Since the DCF has to be added to an existing fiber optic limit, it would increase the total loss of the system and, hence, would pose problems in detection at the end. The length of the DCF required for compensation can be reduced by having fibers with very large negative dispersion coefficients. Thus, there has been considerable research effort to achieve DCFs with very large (negative) dispersion coefficients.

As an example, if we consider propagation in a 50 km length fiber (i.e., L = 50km) with D = + 16 ps/km*nm, then to compensate the dispersion by a 2 km long fiber we must have D’ = –400 ps/km*nm.

The higher the dispersion coefficient of the compensating fiber, the smaller will be required length of the compensating fiber. The next figure shows the waveforms at the input to a 50km conventional single mode fiber, the output without the dispersion compensator, and the output with a DCF with D = -548 ps/km*nm and of length 1.44 km. Note that without the compensating fiber, no information can be retrieved wile the DCF fully restores the pulses.

To achieve a very high negative value of D, the core of the compensating fiber has to be doped with relatively high GeO_{2} compared with the conventional fibers. Unfortunately, the total fiber loss (α) increases because of this doping. Hence, for DCFs a measure of the dispersion compensation efficiency is given by the figure of merit (FOM), which is defined as the ratio of the dispersion coefficient to the total loss and has a unit of ps/(dB-nm)

FOM(ps/(dB*nm)) = |D|/α

A typical refractive index profile of DCF is shown in the following figure which has D around – 300 ps/(km*nm) and FOM around – 400 ps/(dB*nm).