Understanding polarization-mode dispersion
Feenix Y. Pan
Polarization-mode dispersion (PMD) occurs when light pulses in the two orthogonal polarization modes in single-mode optical fibers or components propagate at slightly different velocities. Differential group delay (DGD) is the unit used to describe PMD, and it refers to the difference in arrival time of two light pulses launched into a fiber link along orthogonal polarization modes. Differential group delay is usually measured in picoseconds. The terms PMD and DGD are also sometimes used interchangeably.
In silica and erbium-doped fibers, PMD is caused by a statistical deviation from perfect circularity of the core. The deviation is an artifact of the manufacturing process. This induces birefringence in the fiber due to the ovality of the waveguide and the external mechanical stress fields. In fiberoptic components such as isolators and circulators, PMD is caused by the use of highly birefringent optical elements. In fiber Bragg gratings, PMD is caused by a differential coupling of the orthogonal modes to the grating.
The simplest type of PMD occurs in fiberoptic components such as isolators, circulators, and fiber Bragg gratings, as well as in polarization-maintaining fiber. This type of PMD can be modeled by a single element with a fixed amount of birefringence and is referred to as first-order or non-mode-coupled PMD. A second type of PMD that occurs in single-mode optical fibers is referred to as higher-order or mode-coupled PMD. This type of PMD can be modeled as a series of concatenated elements, each with a random birefringence and a random orientation of the fast and slow axes (see Fig. 1).1
Given this random nature, the exact DGD of a section of single-mode fiber cannot be calculated. Instead, a statistical method is used to calculate the mean DGD and the standard deviation. In addition, the DGD varies with wavelength and drifts over time in installed fiber; thus, the measured DGD of a spool of fiber can be different than the measured DGD of the same fiber when it is installed.
The most serious consequences of PMD in a digital fiberoptic telecommunications link are pulse broadening and intersymbol interference, which are due to the different propagation velocities of the optical pulses that are in the orthogonal polarization modes. These effects can be observed by the closure of the "eye" in oscilloscope measurements at the receiver. If the pulse broadening is severe enough, an increased bit-error rate can result. As a rule of thumb, the composite DGD should be kept below 10% of a bit period in an uncompensated fiber link. This translates to 10 ps for a 10-Gbit/s system. This performance penalty is a major limitation for systems operating at 10 Gbit/s and above.
The unpredictability of PMD in installed fiber is what makes it such a difficult problem to address. Although current state-of-the-art single-mode fiber exhibits PMD values of approximately 0.1 ps/km1/2, some spans of fiber installed prior to the mid 1990s have PMD values ranging from 1 to 10 ps/km1/2. In addition, at that time, PMD was not routinely measured when the fiber was installed, so it becomes very difficult to predict which spans of fiber have high PMD. The net result is that severe complications can result when the transmitted per-channel bit rates are increased to more than 10 Gbit/s in older fiber spans.
PMD can be emulated
To cope with the challenges presented by PMD it is necessary to be able to emulate the characteristics of a fiber span with PMD. To this end, much effort has been devoted to designing and constructing PMD emulators that can accurately replicate what occurs in installed fiber. A PMD emulator can be used to test the response of a fiberoptic telecommunication system to a fiber span with high PMD and also to test the effectiveness of PMD compensators. In these cases it is more advantageous to use a PMD emulator instead of an actual fiber span, because single-mode fiber with PMD values comparable to those of fibers produced ten years ago is no longer available. In addition, it is easier to reproducibly modify the PMD parameters of an emulator as compared to standard fiber.
Several guidelines are used when designing a PMD emulator.2 The emulator must be able to produce a sufficient amount of DGD over a specified wavelength range. Any output component in the specified wavelength range must be able to access all the possible polarization states. Higher-order PMD must be accurately replicated. If the PMD emulator is used to test a PMD compensator, the wavelength range of the emulator must exceed that of the compensator. Finally, the PMD characteristics of the emulator must remain stable over time unless intentionally changed.
Thus, an ideal PMD emulator would consist of a large number of concatenated sections of a birefringent material (with a Gaussian distribution of birefringence values) having automatic polarization controllers inserted between the sections. The polarization controllers would perform the task of inducing a variable phase shift and rotation between the optical signals propagating along the fast and slow axes of the sections of birefringent material. This ideal emulator would produce a Maxwellian distribution of PMD values over time and wavelength as the settings on the polarization controllers are randomly changed.
One practical implementation of an ideal PMD emulator uses a series of birefringent crystals that are individually mounted on motorized rotation stages. By separately rotating each of the stages, variable values of first-order and higher-order PMD can be produced. This approach has the advantages of compactness and ease of automation.
A second implementation uses a series of polarization-maintaining fibers connected by rotatable-key FC connectors (see Fig. 2). In this case, the various values of PMD are produced by rotating the key of the connector for each section. Using 15 sections of concatenated polarization-maintaining fiber, it has been shown that a nearly Maxwellian distribution of PMD values can be produced at a specific wavelength by randomly rotating the connector keys.3 This approach has the advantages of simple implementation and straightforward integration into a fiber-system testbed.
Compensating for PMD
As 10-Gbit/s and higher per-channel bit rates become more prevalent over the existing fiber plant, PMD compensators will oftentimes become a necessity in order to maintain the integrity of the optical signal. Recently, the first commercial PMD compensators have been introduced. Up until now, most of the research has been focused on developing compensators for first-order PMD. However, in light of evidence that higher-order PMD can also have a significant effect on signal integrity, higher-order PMD compensators have also been demonstrated.4, 5
The operation of a first-order PMD compensator is relatively straightforward. Using the analogy of two waveplates of equivalent retardance arranged in series, the composite retardance of the two waveplates can be adjusted from twice the retardance of each waveplate to zero by rotating the second waveplate with respect to the first. Similarly, if a device with a variable birefringence is inserted in line with a fiber component with PMD, the overall DGD can be reduced to zero by adjusting the birefringence of the compensating device to match the first fiber component, then rotating the fast axis of the compensating device so that it is perpendicular to the fast axis of the fiber component. In this case, the "rotation" is typically performed by one or more polarization controllers.
In a simple dynamic first-order PMD compensator, three elements are required: an automatic polarization controller, a tunable or static source of first-order PMD, and a feedback mechanism that monitors a specific figure of merit at the output and adjusts the polarization controller to maximize the figure of merit. When a first-order PMD compensator is used in a fiber span with a non-return-to-zero transmission format, the PMD tolerance of the span is increased from approximately 10% of the bit period to approximately 40%. However, chromatic-dispersion-enhanced second-order PMD distortion can reduce PMD tolerance to approximately 30% of the bit period.6 To address second-order PMD, experimental versions of higher-order PMD compensators have recently been demonstrated, and initial theoretical simulations have shown that a higher-order PMD compensator can produce a "cleaner" eye than a first-order PMD compensator.
1. D. Derickson, ed., Fiber Optic Test and Measurement, Prentice Hall (1997), p. 493.
2. J. N. Damask, OFC 2000, paper ThB3 (Baltimore, MD, Mar. 2000).
3. I. T. Lima et al., OFC 2000, paper ThB4 (Baltimore, MD, Mar. 2000).
4. L. E. Nelson et al., OFC 2000, paper ThB2 (Baltimore, MD, Mar. 2000).
5. A. Mecozzi et al., OFC 2000, paper WL2 (Baltimore, MD, Mar. 2000).
6. H. Bülow, "Limitation of Optical First-Order PMD Compensation," OFC `99, paper WE1 (San Diego, CA, Feb. 1999).
Eugene Rudkevich is president of Taliescent, 10088 E. Paseo San Rosendo, Tucson, AZ 85747; contact him at 520-574-7163 or email@example.com. Feenix Y. Pan is a Ph.D student at the Optical Sciences Center, University of Arizona.
FIGURE 1. Fiber span exhibiting higher-order PMD can be put in the form of a model containing a series of elements having random birefringence and orientation.
FIGURE 2. Higher-order PMD emulator is based on polarization-maintaining fiber and rotatable FC connectors.