Considering a transmission speed of 10 Gb/s, the bit length (100 ps) can be determined and then used to

calculate the theoretical maximum PMD delay: Δτ = 0.1 * 100 ps = 10 ps

In practice, some systems can accept up to 13-14 ps, depending on the coding structure.

The result of this calculation according to different transmission speeds is summarized in the table below.

Bit rate per channel SDH SONET Equivalent timeslot PMD delay limit PMD coefficient with 400 km

55 Mb/s ––– OC-1 19.3 ns 2 ns <100 ps/√km

155 Mb/s STM-1 OC-3 6.43 ns 640 ps <32 ps/√km

622 Mb/s STM-4 OC-12 1.61 ns 160 ps <8 ps/√km

1.2 Gb/s ––– OC-24 803 ps 80 ps <4 ps/√km

2.5 Gb/s STM-16 OC-48 401 ps 40 ps <2 ps/√km

10 Gb/s STM-64 OC-192 100 ps 10 ps <0.5 ps/√km

40 Gb/s STM-256 OC-768 25.12 ps 2.5 ps <0.125 ps/√km

This PMD limits are used to determine the maximum admissible fiber length.

You will find below, for a typical transmission system, the maximum PMD coefficient as a function of length, at a

given transmission bit rate.

Introduction

Competitive market pressures demand that service providers continuously upgrade and maintain their networks to ensure they are able to deliver higher speed, higher quality applications and services to the customers. This requires verifying and ensuring that the network fiber infrastructure and equipment can meet exacting performance standards and operate reliably. Due to the increased transmission speed and implementation of DWDM systems, some important changes were made in the optical fiber characterization and system turn-up, requiring new test tools and procedures, described in different white papers. Polarization Mode Dispersion (PMD) testing is becoming essential in the fiber characterization process, but still one of the most difficult parameter to test, due to its sensitivity to a number of environmental constraints.

Polarization Mode Dispersion definition

PMD (Polarization Mode Dispersion) is caused by the differential arrival time of the different polarization components of the input light pulse, transmitted into an optical fiber. This light pulse can always be decomposed into pairs of orthogonal polarization modes. These polarization modes propagate at different speeds according to a slow and fast axis induced by the birefringence of the fiber.

Bi-refringence

Optical fibers are slightly bi-refringent. Bi-refringence is a property of material (e.g. optical fiber) where the effective index of refraction varies with the polarization state of the input light. The main causes of this bi-refringence are non-perfect concentricity and in homogeneity of the optical fiber in manufacturing design, as well as external stresses applied on the fiber cabling, such as bends, or twist.

Differential group delay

In a single mode fiber, light is guided through the whole core and in a part of the cladding (referring to Mode

field diameter), so that there is only a single propagation mode. However, as fibers are birefringent materials, this

propagation mode, is polarized in two different ways, following the polarization axis of the fiber (These axis are also

called Principal States of Polarization -PSP-). This leads to two polarization modes.

Figure 1: Electrical field vector decomposed into two polarization modes (fast and slow)

As any birefringent material, there is a difference of refractive index value between the two PSP, which means that

there is a fast PSP and slow PSP.

These slow and fast propagation axis, create a variation in the propagation speed of the orthogonal pair of

polarization modes of the light, presenting a different time arrival at the receiver side. This time difference is the

Differential Group Delay (DGD), so called PMD delay.

A light pulse transmitted through a “uniform”, Highly Birefringent (HiBi) or polarization maintaining, fiber could

be defined as the decomposition of the pulse into 2 orthogonal pulses (see figure 1) travelling at different, but

constant speed.

Figure 2: Differential group delay in HiBi fiber

However, in telecommunication optical fibers, birefringence levels and principal axis are not uniform over the total

link, and could be considered as the result of HiBi fibers randomly coupled together

As a consequence, there is a polarization mode coupling between fast and slow modes each time the principal

states of polarization orientation changes. This is called a strong mode coupling.

Figure 3: Strong mode coupling in telecommunication fibers

The speed of light in strong mode coupling fiber depends, obviously, on the input state of polarization (even such

a complex system has a slow and fast Principal State of Polarization), but also on the way of polarization light

rotates according to the wavelength: The State of Polarization, as well as the delay between the fast and slow axis,

is dependent from the wavelength.

The function of DGD vs. wavelength is constantly changing (figure 6). The biggest factor affecting this function

is temperature. Only a few degrees of variation is enough to completely skew the data. In addition, any human

intervention on the fiber link, changing the fiber layout, will have the same consequences.

Figure 4: DGD variation over a wavelength range

“From [the] data. DGD varies slowly over time but rapidly over wavelength…data showed good agreement with a

Maxwellian distribution. The frequency averaged mean DGD [emphasis added] varied about 10% or less during

periods that showed significant temperature swings”

Analysis and comparison of measured DGD data on buried single-mode fibers. Allen et. al2002

As PMD depends on random optical fiber’s birefringence, it cannot be characterized directly: The instantaneous

DGD cannot be used directly, because it does not have a reproducible value. DGD values fluctuate randomly around

an average (mean) value, describing a Maxwellian curve, as shown on the figure 3.

One commonly accepted parameter to be measured in order to characterize the PMD delay is the mean DGD

across a certain wavelength range. The mean DGD is the efficient value of the differential group delay density of

probability of the total fiber link, it is called the PMD delay, expressed in [ps].

Doubling the mean DGD, the fiber length had to be increased by a factor 4; and that to triple the DGD, it had to

be increased by a factor 9. So “the average DGD scales as the square root of the length of the fiber.”

The polarization mode dispersion is defined with up to four main parameters:

• PMD delay [ps] or mean DGD

• PMD coefficient

• Second order PMD delay or DGD2 [ps/nm]

• Second order PMD coefficient (PMD2, in ps/(nm.km)).

Second order PMD

The second order PMD gives the delay created by the PMD variation linked to the wavelength, and therefore is

interesting for DWDM and very high speed transmission systems. It provides the indication of the wavelength

dependency of the PMD delay.

• rate of change of DGD vs Wavelength

• It describes the change of direction of PSPs

Second order PMD has to be added to chromatic dispersion figures, and therefore is limiting the link distance.

Why does PMD appear?

Several factors are involved in the generation of PMD. Fiber optic cables which have been employed in the outside

plant are not perfect.

• Manufacturing defects.

– The fiber core is not perfectly circular along its overall length

– The fiber core is not perfectly concentric with the cladding

– The fiber can be twisted or bent at some points along the span.

• PMD constraints increase with:

– Channel bit rate

– Fiber length (number of sections)

– Number of channels (increase missing channel possibility)

?PMD decreases with:

?Better fiber manufacturing control (fiber geometry)

?PMD compensation modules

?PMD is more an issues for old G.652 fibers (<1996) than newer G.652, G.653, G.655 fibers

At any given signal wavelength the PMD is an unstable phenomenon, unpredictable. Instantaneous PMD varies

with ? time, T? movement. PMD is not intrinsic and requires statistical predictions as it fluctuates over the

network life cycle.

Limiting fiber parameter

The mean DGD causes the transmission pulse to broaden when traveling along the fiber, generating distortion

and increasing bit-error-rate (BER) of the optical system. The consequence is limitation of the transmission

distance for a given bit rate.

If the maximum PMD delay is known, the maximum admissible fiber length can be deduced.

L = 聂2/聂c max2

The statistical character of the PMD is taken into account where defining the maximum tolerable PMD delay as

10% of the bit length TB for a system, without disturbing the network performance by more than 1 dB loss, at

1550 nm, with NRZ coding

Considering a transmission speed of 10 Gb/s, the bit length (100 ps) can be determined and then used to

calculate the theoretical maximum PMD delay: Δτ = 0.1 * 100 ps = 10 ps

In practice, some systems can accept up to 13-14 ps, depending on the coding structure.

The result of this calculation according to different transmission speeds is summarized in the table below.

This graph is provided with the following assumptions: The PMD is considered to be Maxwellian, NRZ coding is

used, 1550 nm lasers are used, a maximum power penalty of 1 dB is acceptable, a BER is typically between 10-9

and 10-12. With this in mind, the following formula could be applied (L is the distance in km, B the bit rate in

Gb/s, PMD the PMD value in ps/√km:

Figure 6: Maximum distance vs. PMD coefficient and data bit rate

When testing PMD?

PMD testing is becoming a requirement when the transmission bit rate per channel rises or with the increase of

the corresponding distance. It appears that the measurement shall be at least performed when the bit rate is equal

or higher than 10 Gb/s. However, for fibers older than 1996 or for some applications, such as analog cable TV

applications, lower transmission bit rates will be affected by PMD.

As a summary, the main circumstances in which PMD measurement will be required are:

• Qualification during fiber manufacturing

• Qualification during cable manufacturing

• Installation of new fiber networks, for 10 Gb/s bit rate or higher.

• Installation of ultra long haul networks at 2.4 Gb/s or higher

• Upgrade of current networks for 10 Gb/s bit rate or higher

Fiber and cable manufacturers are specifying their fibers with 0.5 ps/√km maximum, according to the ITU-T

recommendations. However, current manufactured fibers are easily better than 0.2 .ps/√km

As PMD is a statistical measurement and, because it is sensitive to external environment, it is recommended to

perform different measurements at different time intervals so that long term fluctuation of DGD can be monitored,

providing better records of the fiber cable.

Figure 7: Drift representation of a long-term PMD delay measurement

High PMD Values

If the PMD measurement is higher than the tolerable limit for a given bit rate, the fiber is classified as ensitive?to

PMD for that particular transmission speed. For a passing PMD result (within the tolerable limit) at a given bit rate,

the fiber cannot be classified as on-PMD sensitive? Instead, it should be classified as 搒uitable for the particular

transmission rate?at the given time.

Currently, there is no simple and low-cost component that allows for the correction of a link with a high PMD value.

Although there are a number of components under qualification and development, at this time, very few PMD

compensators have been deployed in the field.

PMD is clearly important in limiting the distance (or the transmission bit rate) for a given network application.

Therefore, several solutions have been developed that allow for the compensation of the effect of PMD on the

transmission link, including transmitting over shorter distances, transmitting at lower bit rates per wavelength,

using low chirp lasers, using dispersion-managed RZ optical soliton transmission, or using forward error correction

(FEC) transmission.

PMD compensation techniques

It is particularly difficult to counteract PMD because of its statistical nature and its variation over the time and

wavelength. The stochastic nature of PMD is such that, reducing the impact of PMD does not necessarily imply the

complete cancellation of the effect, but the reduction of the outage probability due to PMD: This process is called

PMD mitigation.

Several PMD compensation techniques have been proposed in the past few years. They can be classified into two

main categories:

?Electrical PMD compensation

?Optical PMD compensation

Electrical compensation of PMD involves equalizing the electrical signal after the photodiode. This equalization can

be implemented in many ways: transversal filter (TF), non-linear decision feedback equalizer (DFE), phase diversity

detection. Electrical compensation schemes, in general, are robust and will improve the signal against all kinds of

transmission impairments. On the other hand, they do not perform as good as optical PMD compensators

and also they require high-speed electronics for better performance.

Optical PMD compensation is aimed to reduce the total PMD impairment caused by the transmission fiber and the

compensator. The block diagram of a general optical PMD compensation scheme is shown in Figure 8. It has an

adaptive counter element, a feedback signal and a control algorithm.

The adaptive counter element is the core of any PMD compensator. It must be able to counteract PMD

impairments and be tunable. The feedback signal is required to provide the PMD information to the controlling

algorithm of the compensator.