Chromatic Dispersion and Polarization Mode Dispersion (PMD)

Before reading this you may find the following tutorial useful:
Nonlinear Effects, Laser Basics, Distributed Feedback (DFB) Lasers, Optical Units Reference

Dispersion

Each wavelength in an optical network consists of on/off flashes of light representing data. A 10-Gbit/s wavelength corresponds to 10,000,000,000 bits being sent every second, meaning that each of these bits can last a maximum of 100 ps in time.

After traveling through many km of optical fiber, it is possible for pulses to spread out in time. Therefore, what were tightly defined 100 ps duration pulses at the beginning could possibly "smear" out into 120 ps, 150 ps, or even 200 ps pulses. It will then become increasingly difficult, if not impossible, to distinguish two adjacent bits, as they will have smeared into each other. The problem becomes worse at higher bit rates where the duration of the pulses (the "bit-period") becomes even smaller. This spreading of pulses in time is known as dispersion.

Chromatic Dispersion

The most well understood forms of dispersion occur because different wavelengths of light travel at slightly different speeds in optical fiber. Material dispersion causes different wavelengths to travel at different speeds due to the variation of refractive index of the fiber core with wavelength. However, a proportion of the light also travels in the cladding of the fiber, which has a different refractive index again and therefore propagates light through it at a different speed to the core – an effect known as waveguide dispersion. Material and waveguide dispersion are combined to give an overall effect called "chromatic dispersion."

In a Wavelength Division Multiplexing (WDM) system it is not necessarily a problem for each different signal wavelength to travel at a different speed, as they are demultiplexed at the end and detected separately anyway. Chromatic dispersion is still a problem, however, because each of these individual signal wavelengths contains a range of different wavelengths.

You may remember from the laser basics tutorial that standard Fabry-Perot lasers give out a broad range of wavelengths, actually spanning as much as 2 nm or so in total. Distributed Feedback (DFB) lasers have much purer emission, but nevertheless still contain maybe a 0.2 nm range of wavelengths.

A light pulse will typically have a curved shape when looking at its intensity with respect to time. At each of these points in time the pulse could contain the whole spread of wavelengths being emitted. With positive chromatic dispersion, the shorter wavelengths travel faster than the longer ones so that after a while, the shorter wavelengths have moved forward in time with respect to the longer wavelengths. Therefore the beginning of the pulse in time and the end of the pulse in time have spread further apart and the pulse has experienced chromatic dispersion.

Chromatic dispersion is measured in ps/nm/km, meaning that for every km of fiber traveled through, a pulse with a 1 nm spread of wavelengths will disperse by 1 ps for a dispersion of 1 ps/nm/km. Therefore you can see that with a 1 ps/nm/km chromatic dispersion, a 10-Gbit/s pulse with a 0.2nm spectral width will have spread by a whole bit period (100 ps) after 500 km of fiber and will then be completely indistinguishable.

The amount of chromatic dispersion experienced in optical fiber is dependent on the wavelength at which light is being transmitted, and a graph showing this for regular singlemode fibre is shown here. It is worth noting that there is a "slope" to the dispersion – meaning that each wavelength experiences a different amount of dispersion.

You will see that it is possible to have negative chromatic dispersion in which the longer wavelengths travel faster. This is the key to how clever people in white coats have been able to make sure that chromatic dispersion does not limit the distance of optical systems to a few hundred km. In the "Advanced Fiber Types" tutorial you will be able to see how chromatic dispersion can be corrected, or "compensated," through the use of such specially designed optical fibers. The "dispersion slope" previously mentioned, however, can make perfect compensation at all wavelengths quite tricky. It will also be shown how systems utilising the low loss 1550 nm region of optical fibre can pick a type of fiber that reduces the amount of chromatic dispersion experienced from the very large 15 or so ps/nm/km in the standard type.

Polarization Mode Dispersion (PMD)

The light used in optical networks is generally in the infrared region of the electromagnetic spectrum. These light waves, as part of the electromagnetic spectrum, have associated electric and magnetic fields. For a given light wave, there will be electric and magnetic fields that are perpendicular to each other, as well as being perpendicular to the direction of travel of the light.

Light emitted from a laser is made up of many individual waves that have their electric and magnetic fields in a range of random directions with respect to each other, although for each individual wave the electric and magnetic fields will always be perpendicular. Such light is said to be "unpolarized." If the electric fields could all be lined up with each other, then the same would be true for the magnetic fields and the light would be "linearly" polarized.

However, each wave’s random field orientation can be separated into a component that is vertical and one that is horizontal – in much the same way that vectors can be written as a horizontal and vertical component. In the language of physics, these different components of the field orientation are referred to as "polarization states" or "principal states."

When traveling through a perfectly straight length of perfectly cylindrical optical fiber, both of these polarization states will travel at exactly the same speed. However, real-world optical fiber is not so nice to us. There will be flaws in the fiber that cause it to be non-cylindrical, and there will also be points of stress on the fiber which are not spread in a symmetric manner. This spells trouble for the polarization states, and in fact causes them to travel at different speeds. At the end of the system these states will have separated slightly in time and therefore have caused the light pulses to spread out in time. The pulses will have experienced Polarization Mode Dispersion (PMD).

PMD is a random effect due to the imperfect symmetry and constantly fluctuating stresses that a fiber experiences, and so it is measured as an average value over time. This randomness makes it a lot more difficult to compensate for, and much research is still taking place in this area. PMD has not been a significant effect at the bit rates up to 10 Gbit/s deployed at the moment, but with the tight (25 ps) bit period of 40-Gbit/s systems it is expected to become an issue in the near future.

Key Points