Polarization Mode Dispersion
In optical fibers, there is usually some slight difference in the propagation characteristics of light waves with different polarization states. A differential group delay can occur even for fibers which according to the design should have a rotational symmetry and thus exhibit no birefringence. This effect can result from random imperfections or bending of the fibers, or from other kinds of mechanical stress, and is also affected by temperature changes, mainly because those can cause mechanical stress. Mainly due to the influence of bending, the PMD of a fiber cable can be completely different from that of the contained fiber on a spool. By comparing PMD values of different fibers in the coiled state, one can hardly predict how those values were compared to the straight fiber; in particular, spun fibers exhibit much lower values in the straight state while not looking much better than unspun fibers on a spool.
Polarization mode dispersion is based on birefringence – more precisely, the differential group delay (as a measure for PMD) is the derivative of the difference of propagation constants (a measure for the birefringence) with respect to angular optical frequency.
Second-order PMD is the derivative of the differential group delay with respect to angular frequency  – effectively the second-order derivative of the difference of propagation constants.
The terms polarization mode dispersion (PMD) and differential group delay (DGD) are often used interchangeably, but sometimes with slightly different meanings. Some authors call the phenomenon PMD and consider DGD to be its magnitude. Others define PMD as the statistical standard deviation of DGD in some wavelength interval. Note that for optical fibers the DGD can have a substantial and complicated dependence on the optical wavelength and temperature.
Detrimental Effects of PMD
Polarization mode dispersion can have adverse effects on optical data transmission in fiber-optic links over long distances at very high data rates because portions of the transmitted signals in different polarization modes will arrive at slightly different times. Effectively, this can cause some level of pulse broadening or even pulse splitting. That leads to inter-symbol interference, and thus a degradation of the received signal, leading to an increased bit error rate. In order not to exceed the accepted level of bit error rate, one then has to limit the transmission rate.
Effects of polarization mode dispersion often need to be described statistically because they depend in a complicated way on a substantial number of factors, some of which are hard or impossible to predict. For example, temperature changes can lead to mechanical stress in the fibers, with a substantial dependence on additional factors like the type of buffer layer used in the cable, and those affect PMD. For short fiber sections, where the local birefringence stays approximately constant, the DGD is proportional to the fiber length. For longer sections, however, different portions of fiber contribute uncorrelated amounts to the DGD, and the total r.m.s. value of the differential group delay scales only with the square root of the fiber length. Therefore, PMD is often quantified with units of ps km−1/2.
There are certain polarimetric fiber-optic sensors where tiny polarization changes of light in fibers needs to be detected. For example, there are sensors for electric currents which are based on the Faraday effect, i.e., on the rotation of the polarization direction in proportion to a magnetic field which is generated by an electric current. Obviously, additional polarization changes due to random birefringence of the sensor fiber should be suppressed as much as possible.
Reducing the Effects of PMD
The first measure for reducing PMD is to choose an optical fiber with reduced PMD and ideally also a reduced sensitivity of PMD to external factors. Modern telecom fibers have fairly stringent PMD specifications, but fibers laid in the early 1990s often exhibit much stronger PMD, which is often not even specified. Note also that details of the deployment of such cables have some influence. Furthermore, aging effects can substantially deteriorate polarization properties of fiber cables, e.g. related to changed elasticity of aged polymer materials .
In principle, the problem could be solved by using well-defined polarization states in polarization-maintaining fibers, but this approach is usually not practical for various reasons: it would not only be necessary to use the more expensive and more lossy polarization-maintaining fibers for all components (including e.g. fiber amplifiers), but also the polarization directions would have to be aligned at many interfaces.
Another theoretical possibility would be to determine the so-called principal polarization states of a fiber span, and inject the optical signals only into one such state. For a sufficiently narrow optical bandwidth, there would then be no pulse broadening, although for larger bandwidths there is a polarization-related contribution to chromatic dispersion (with its sign being different for the two principle states). However, this method is usually not practical, partly because the c polarization states change with time.
A common ( because more practical) solution is to use spun fibers, where the fiber is twisted during the fiber drawing process. That way, telecom fibers with substantially improved PMD performance can be obtained. See the article on spun fibers for details.
For achieving the highest possible bit rates, particularly with older fibers and in long fiber-optic links, it can be necessary to compensate the polarization mode dispersion. There are devices for introducing an adjustable amount of PMD in order to compensate PMD of a fiber-optic link. Essentially, such a device may contain
- a fiber polarization controller, followed by
- a polarizer and a variable optical delay line which is applied only to light of one polarization direction, and
- another polarizer acting as a beam combiner.
By adjusting the delay line, one can minimize the overall PMD.
Note that temperature changes can make the PMD effect time-dependent; for highest data rates, it may therefore be necessary to apply an automatic feedback system. If the system has multiple wavelength channels (→ wavelength division multiplexing), the compensation may have to be done separately for each channel because the effect is wavelength dependent.
Minimizing the Sensitivity to PMD
Another strategy can be to limit the capacity of each transmission channel, but using many different channels in a single fiber, e.g. with the technique of wavelength division multiplexing.
There are also advanced modulation schemes with reduced symbol rate (for a given bit rate), which are less sensitive to PMD.
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|||D. A. Nolan et al., “Fibers with low polarization-mode dispersion”, J. Lightwave Technol. 22 (4), 1066 (2004), DOI:10.1109/JLT.2004.825240|
|||K. Borzycki, “Influence of temperature and aging on polarization mode dispersion of tight-buffered optical fibers and cables”, J. Telecommunications and Information Technology 3, 96 (2005)|
|||A. Mecozzi, “Theory of polarization mode dispersion with linear birefringence”, Opt. Lett. 33 (12), 1315 (2008), DOI:10.1364/OL.33.001315|
|||ITU standard G.666 (07/05), “Characteristics of PMD compensators and PMD compensating receivers”, International Telecommunication Union (2005)|
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