# Polarization-mode dispersion mandates computation and control

Polarization-mode dispersion mandates computation and control

andrÉ girard and jarod guertin

exfo electro-optical engineering

Dispersion, or the widening of optical light pulses as they travel along fiber, must be accurately measured to reduce the subsequent limitations on optical-signal transmission range and modulation frequency

Investigations of fiber performance demonstrate that polarization-mode dispersion (PMD) can degrade the performance of high-speed Synchronous Optical Network/Synchronous Digital Hierarchy (Sonet/SDH) communications networks. Indeed, PMD must be measured not only after manufacturing, but also after cabling and installation. Otherwise, mechanical bends and pressure points in fiber can introduce birefringence and, therefore, PMD degradation. With the use of erbium-doped fiber amplifiers (Edfas) to increase fiber spans, all sources of dispersion must be minimized and controlled, or else the transmission gain in range is undermined by the modulation frequency limitation.

The two main optical-link parameters that affect the performance of optical fiber and cable in high-speed networks are maximum transmission range and maximum modulation frequency. The transmission range is a function of emitter output power, receiver sensibility and losses in the fiber. The modulation frequency is also limited by emitter and receiver frequency responses as well as by dispersion in the fiber. The effects of dispersion and its improved correction have led to the study of PMD and its general measurement techniques.

Dispersion in this context is the temporal dispersion that adversely affects a pulsed or modulated signal. Although many sources of dispersion exist, the effect is the same, due to the longer rising and falling time of the power signal compared to that of the input signal. In other words, dispersion consists of some power signals arriving at the receiver sooner and some later than the mean power time of arrival. For a modulated signal, dispersion becomes large enough so that the receiver cannot properly distinguish the encoded information. Dispersion must, therefore, be minimized because temporal spreading limits the maximum modulation frequency and how closely the encoded bits can be spaced.

Dispersion has been markedly reduced over the years mainly through component optimization. Initially, multimode fibers had large cores (100, 62.5 or 50 microns), and applied optical wavelengths of 850 and 1300 nm guided many propagation modes. That is, each spatial mode traveled a different path length for the same speed, thus leading to modal dispersion due to different arrival times. For example, for a 850-nm wavelength that traveled 100 km, the maximum modulation frequency was approximately 2 MHz because the dispersion was approximately 1 nsec/km. To reduce this problem, multimode fiber with a graded index core/cladding geometry and singlemode fiber were developed. Today, multimode fibers are restricted to local area network (LAN) applications with short distances and low frequencies.

Singlemode fiber with only one spatial propagation mode still shows significant dispersion, but to a lesser degree. Wavelength dependence of the core material refractive index causes the problem. This dependence results in different propagation velocities for different wavelengths. This chromatic dispersion occurs because of the finite spectral width of the sources: Each wavelength component travels at a different speed and reaches the receiver at a different time. At 1550 nm, a typical dispersion of 15 psec/nmkm limits the maximum frequency to 44 MHz for a length of 100 km with a light source width of 3 nm (Fabry-Perot laser).

Common singlemode fiber has a natural dispersion-free point at 1312 nm, but dispersion gradually increases on either side of this wavelength. On the other hand, the dispersion-free point of dispersion-shifted fiber is translated from 1312 to 1550 nm, whereas dispersion-flattened fiber has two dispersion-free regions at 1312 and 1550 nm. The easiest way to reduce this effect is to use narrow distributed-feedback lasers with widths of less than 0.01 nm and a dispersion of less than 0.15 psec/km.

The core material refractive index also has a polarization dependence resulting in a difference in propagation velocity due to birefringence and mode coupling. To better understand this phenomenon, polarization, birefringence and mode coupling must be investigated.

Light propagation can always be decomposed along two polarizations, which are orthogonal to each other and to the propagation direction. In the case of birefringent materials, each polarization state or mode travels at a different speed, resulting in temporal spreading or dispersion (see Figs. 1, 2 and 3). Birefringence is the dependence of the refractive index as a function of the angle between light polarization and the fast or slow axis of material.

Birefringence is a symptom of aniso tropy or asymmetry in the propagation media. It can be found in crystals due to asymmetric chemical bonds and in isotropic materials, where a force (mechanical, magnetic or electrical) creates a local asymmetric atomic distribution. Fibers contain random birefringence sites, so that even with a polarized input, other polarization projections are relatively accelerated or slowed down, and a statistical distribution of delays, called PMD delays, is obtained.

The mean value of these delays--the mean PMD delay--is referred to as the PMD delay coefficient or PMD coefficient due to its dependence on fiber length. Depending on the intensity of the coupling (energy exchange) between the polarization states or modes (called mode coupling), the PMD coefficient is expressed in psec/km for weak mode coupling (or fixed small birefringence) or psec/(km for strong mode coupling, typically the case for fibers used in the field.

Measurements show that in currently installed fibers, the PMD is typically of the order of 0.5 psec/(km, which sets a limit of 40 GHz for a transmission distance of 100 km. However, in installed networks with fiber amplifiers, the total length without repeaters could be extended to the range of 400 km. Fibers installed several years ago, such as depressed cladding fiber, often exhibit a much higher PMD coefficient, thus making upgrades to higher bit rates problematic.

It is impractical to try to measure dispersion in real time due to the high frequencies involved. There are two domains, however, on which determination of the PMD parameter is based: the time domain and the spectral domain. The two standard PMD definitions are the mean square deviation of time of flight, derived from the time-domain principle, and the mean differential group delay (DGD), obtained from the spectral-domain principle. The first definition is used by the Fourier transform wavelength scanning method and by the interferometric method, whereas the second definition is used by the extrema counting wavelength scanning method (fixed analyzer) and the polarimetric method (Jones Matrix Eigenanalysis).

Wavelength scanning method

In both wavelength scanning methods--Fourier transform and extrema counting--data acquisition is performed using either one of two available wavelength scanning setups (see Fig. 4).

In the test setup, the source output polarizer and the analyzer input polarizer are fixed at the same value for a constant launch polarization state. Then, the transmission power measurement versus wavelength is made. In the absence of device-under-test birefringence, the polarized light from the source always reaches the analyzer`s polarization at the same angle, and constant power is measured. However, where birefringence is involved, polarization turns in a cyclic fashion proportional to the birefringence. The polarizer output power also reflects these cycles. Therefore, the number of extrema can be counted and linked to PMD by a mathematical relation (the second PMD definition--the mean DGD from the spectral domain).

A variation of this method uses the Fourier transform of the wavelength scan to extract the PMD parameter. When the Fourier transform is performed, the square of the second moment of the Gaussian fit is used (first PMD definition--mean squared deviation of time of flight in the time domain). If the PMD definition used is not taken into account, the physical link between the two methods can be observed (see Fig. 5).

Some measurement limitations of these two techniques include:

PMD values are directly proportional to the spectral resolution (high PMD delays require high resolution).

Mathematical error (PMD delay uncertainty) is directly proportional to spectral range (a wider spectral range requires higher accuracy and resolution).

Determination of extrema is susceptible to noise and interpretation.

Source coherence must be greater than the PMD delay to be measured, to avoid source depolarization.

Measurement time is moderately long and, consequently, sensitive to changes in fiber status during measurement (such as vibration).

Communication is required between fiber input and fiber output, which is not applicable for field measurement.

The techniques are sensitive to launch polarization condition.

Interferometry method

The interferometric setup can also be used to measure PMD (see Fig. 6). Common measurement variations use a Michelson or Mach-Zender interferometer type with an open-air beam splitter, a cube beam splitter or a fiber-optic coupler.

In the Michelson interferometer setup, the moving mirror introduces a variable delay between the two interferometer arms, and each polarization state is recombined according to this delay. Scanning the delay makes source autocorrelation possible. Autocorrelation is a mathematical operation in which a function is relatively delayed and multiplied by its undelayed form. The delay is swept over a given integration range. The integration is performed by the detector, and the delay is swept by the movable mirror.

The concept of coherence is necessary to understand how an autocorrelation can be obtained with a continuous- wave signal. The concept of coherence is illustrated by comparing two signals with different frequencies.

The closer the frequencies (the more in phase), the longer they can be sufficiently synchronized to be combined through constructive interferences. In the absence of PMD, the autocorrelation measurement yields the coherence time autocorrelation of the source. The PMD parameter can be obtained because it increases both the effective coherence time of the source and its autocorrelation width.

The interferometer results can take either of the following two forms:

Weak mode coupling--This type of coupling occurs with single birefringent crystals and polarization-maintaining fibers where the fast and slow axes are unique and constant. In this case, the PMD delay is taken as the extrema spacing or as the centroid of the interferogram. The PMD coefficient is then given in units of psec/km, where km represents the unit length of the fiber cable under test.

Strong mode coupling--This type of coupling takes place with normal fiber used in the field or with a succession of randomly oriented birefringent crystals. In this case, the mean PMD delay is the second moment of the Gaussian fit of the interferogram. The units for the PMD coefficient are then given as psec/÷km.

Some important characteristics of the interferometry technique are:

A large PMD measurement requires a proportional movable mirror displacement.

Source coherence time has to be less than the PMD delay to be measured and, consequently, source spectral width must be large.

Measurement is fast and insensitive to fiber vibration.

It has a wide dynamic range.

It is sensitive to launch polarization condition.

With some PMD measurement test sets, the PMD measurement range runs to 30 psec with an optional extended range to 100 psec. A dynamic range of 40 dB is positioned well above most interferometric technique ranges, which usually limit the length of fiber to be tested. Some advanced PMD test sets provide an average measurement time of fewer than 15 seconds and perform automatic PMD computation.

Polarimetric method

The polarimeter, or Jones Matrix Eigenanalysis (JME or Stokes) parameter analyzer uses a complex method (amplitude and phase) that combines 2 ¥ 2 matrices and relates input to output polarization through a linear system (see Fig. 7). The test system measures the four Jones Matrix factors of the device under test for two close wavelengths. Three equations per wavelength are required because the fourth one is not independent.

To obtain these equations, the polarization transfer matrix is measured with a polarimeter for three different polarization launch conditions. The eigenvalues of the resulting matrices are then used to calculate the DGD between the two wavelengths. The results are then averaged over a wavelength range, and the mean value of the distribution is taken as the PMD parameter.

The limitations of this technique are:

Large PMD measurement requires finer wavelength steps and higher source resolution.

Dynamic range reduction is associated with an increase in wavelength resolution.

Wavelength range has to be wide enough for good statistics.

Source coherence has to be larger than the PMD delay to be measured to avoid depolarization

Measurement takes a long time and is sensitive to fiber vibration and thermal drift.

Because communication between fiber input and output is required, it is not applicable to field measurement. u

André Girard is director and Jarod Guertin is product manager of the Scientific Division, Laboratory and Marketing Group at Exfo Electro-Optical Engineering, Vanier, QC, Canada.