定义：
光纤中传播的光波传输性质随偏振的变化

在光纤中，具有不同偏振态的光波之间的传输性质在某些方面不同。尽管光纤设计时应该具有旋转对称性，不应具有双折射，还是会存在差分群延时。这一效应来自于随机缺陷，光纤弯曲或者其它机械应力，还会受温度变化的影响。光缆光纤中与缠在圆筒上的相同的光纤的PMD完全不通，主要是因为弯曲的影响。通常用于光纤链路中的光纤光缆已经被优化，具有很低的PMD，但是安装这些光缆还是会受到影响。

 偏振模式色散（PMD）与差分群延时（DGD）可以互用，有时意义略有不同。一些作者称PMD为一种现象，而考虑DGD时主要考虑它的大小。也有定义PMD为波导间隙中的DGD的统计标准偏差。在光纤中，DGD对波长的依赖很复杂。 

一些作者采用二阶PMD代表差分群延时对角频率的导数，,尽管这里并没有涉及到二阶导数。 

对通信系统有害的效应 
偏振模式色散在长距离光纤链路中传输非常高的数据速率的光纤通信系统中会产生很不利的影响，因为具有不同偏振模式的传输信号会在略微不同的时间到达接收器。这相当于产生了一定程度的脉冲展宽，引起字节间干扰，于是接收信号失真，比特误码率提高。

 理论上来说，可以确定光纤的主偏振态，注入的光信号都是出于这一偏振态。光带宽足够窄的时候，就不会出现脉冲展宽，而对于稍大的带宽，就会存在偏振引起的色散（两个主偏振态的符号不同）。但是这一方法不实际，因为主偏振态是随时间变化的。 

需要统计描述偏振模式色散效应，不仅需要考虑随机的时间变化还需要考虑到对光纤长度的依赖性。光纤很短的区域，DGD正比于光纤长度。较长的光纤情况，不同部分的光纤对DGD的贡献是不相关的，因此DGD的总方均根仅仅与光纤长度的平方根成正比。 

减小PMD效应 
最直接的方法减小PMD是减小光纤中的PMD。现在的电信光纤PMD标准很高，而1990s早期的光纤则具有非常强的PMD。 

为了能实现很高的比特速率，需要在光纤链路中进行偏振模式色散补偿。而随着温度变化，PMD效应与时间有关，因此有必要采用自动反馈系统。如果系统具有多个波长信道（参阅波分复用），补偿需要对每个信道分别补偿，因为该效应是与波长有关的。 

理论上，可以采用保偏光纤来减小这一效应，但是这样也不实际，因为：保偏光纤更加昂贵并且损耗更大，不需要所有的器件（例如，光纤放大器）都采用保偏光纤；另外，需要在许多界面处调整偏振态的方向。 

另一个方案是限制每个传输信道的容量，在单根光纤中采用多个信道，例如，采用波分复用技术。 

最后，还可以采用高级调制方式来降低字节速率，对PMD不是很敏感。

Acronym: PMD

Definition: the polarization dependence of the propagation characteristics of light waves in optical fibers

More general term: 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 [6] – 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

Communication Systems

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.

The dependence of PMD on the fiber length is not necessarily linear!

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.

Fiber-optic Sensors

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

Optimized Fibers

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 [10].

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.

PMD Compensation

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.

Bibliography