By Mark Albert
Mitigating chromatic dispersion and PMD requires reliable and accurate measurement methods and solutions. Measurement methods include phase-shift modulation, polarization-phase shift, fixed analyzer, and interferometric, along with the Jones matrix eigenanalysis.
Optical fiber and component manufacturers need reliable and accurate measurement equipment to successfully develop solutions to reduce and mitigate chromatic and polarization-mode dispersion (PMD) at data rates of 10 Gbit/s, 40 Gbit/s, and higher. A number of established methods are available for measuring chromatic dispersion and PMD, each suitable to varying degrees for design, manufacturing, and field-test applications.
Chromatic dispersion arises from the variation of a fiber's refractive index with wavelength. It causes different wavelength components of optical signals to arrive at different times at the fiber end. As a result, pulses spread out and adjacent bits eventually overlap, which leads to transmission errors (see Fig. 1). The difference in arrival time between different wavelengths is referred to as group delay and is measured in picoseconds. Chromatic dispersion is defined as the change of group delay over wavelength, and is expressed in (ps/nm), or (ps/nm·km) for fiber.
Chromatic dispersion in optical fiber is typically interpolated from group-delay data measured at coarse wavelength intervals. For standard single-mode fiber the three-term Sellmeier equation is the recommended interpolation function. Other functions are available for different applications. The dispersion characteristics of optical components are often less well defined and can require measurement with fine wavelength resolution.
Polarization-mode dispersion describes the phenomenon that different polarization states propagate at different speeds (see Fig. 2). It is caused by birefringence of the optical-transmission medium and leads to pulse broadening. The difference in arrival time between the principal polarization states is called differential group delay. Average differential group delay over wavelength and/or time is often referred to as PMD, just like the phenomenon itself. Polarization-mode dispersion is statistical in nature and varies with wavelength, time, temperature, and mechanical stress on the fiber.
In long fiber with random mode-coupling, differential group delay follows a Maxwell distribution, and is proportional to the square root of the fiber length. Accordingly, the parameter of interest is average differential group delay in (ps/√km), the so-called PMD coefficient. Narrowband devices with weak mode-coupling are often characterized for instantaneous differential group delay in picoseconds over wavelength.
To reduce loss and dispersion, optical fiber manufacturers have been introducing new fiber types with reduced PMD coefficient. These fiber types also feature lower chromatic dispersion, but have a higher dispersion slope, so their dispersion varies more with wavelength.
For combating chromatic dispersion the de facto accepted solution is dispersion-compensating modules. These contain specially doped dispersion-compensating fiber (DCF) that has almost constant negative dispersion across the C-band. This flat dispersion profile poses a problem. Because standard fiber has a sloped dispersion characteristic, dispersion-compensating fiber can only correct the dispersion at a specific wavelength. At other wavelengths, signals are compensated too little or too much.
To compensate the residual dispersion, chirped fiber Bragg gratings are installed for every wavelength after the DWDM demultiplexer. Their dispersion slope is the inverse of the slope of standard fiber. One concern in the design and manufacturing of these gratings is inherent group-delay ripple. If left unchecked it may cause portions of the pulse to shift in time, which may result in severe distortions.
Compensating for PMD remains a challenge. With modern optical fiber, PMD is not a limiting factor at 10 Gbit/s, but it becomes a severe issue at 40 Gbit/s and above. Because PMD changes with temperature and other environmental factors, any compensation must be adaptive. Experimental concepts link a feedback mechanism at the receiver end to a polarization controller along the fiber span, but implementation costs are still prohibitive. The prevalent method today is to alleviate PMD by deploying new fibers with lower PMD coefficient.
As optical-fiber, component, and system vendors develop devices to support higher data rates, they need appropriate tools for measuring chromatic dispersion and PMD with the needed resolution and accuracy. Commercially available test equipment relies on established methods:
Phase-shift modulation method. The phase-shift modulation method is the industry standard for measuring group delay, chromatic dispersion, and amplitude. The light from a tunable laser source is intensity modulated with a sinewave of a selectable frequency. The measurement light is launched into the device under test (DUT). Phase and amplitude of the output light are then compared with the input light at selectable wavelength intervals. The phase shift directly expresses the relative group delay of the DUT, and the amplitude comparison yields the insertion loss or gain of the device. For an accurate comparison of amplitudes and phases this method relies on close proximity of transmitter and receiver, which makes the method mostly suitable for laboratory or manufacturing test applications.
When selecting the modulation frequency one needs to consider the side bands inherent to amplitude modulation of the laser source. A relatively high modulation frequency yields best group-delay resolution, accuracy, and sensitivity, but also produces wide sidebands that broaden the laser linewidth and lead to an averaging of group delay over a small wavelength band. For measuring details such as group-delay ripple on gratings, a lower modulation frequency must be selected. However, it comes at the expense of reduced group-delay resolution and more noise in the measurement.
Polarization phase-shift method. Inserting a polarization controller and polarization beamsplitter into the optical path allows use of the polarization phase-shift method, which measures PMD simultaneously with chromatic dispersion and amplitude (see Fig. 3). When performing a measurement, the polarization controller first directs the modulated light input in one of the two principle axes of polarization. After passing through the DUT the light is separated into two linearly polarized orthogonal states, and amplitude and phase of each state compared with the input light. Then, a similar measurement is performed with the input light polarization rotated by 90$deg; to the second principle axis of polarization.
The results of these measurements define the so-called optical transfer function matrix, which allows the computation of amplitude, relative group delay, chromatic dispersion, and differential group delay, as well average differential group delay or PMD. A key advantage of this method is that all parameters are determined as a function of optical wavelength under identical measurement conditions.
Jones matrix eigenanalysis. The "gold standard" for measuring PMD is the Jones matrix eigenanalysis. It determines differential group delay from the change in the Jones matrix across wavelength intervals. The Jones matrix mathematically describes the transmission properties of an optical device. It relates magnitude, phase, and polarization state of the output light to magnitude, phase, and polarization state of the input light.
The measurement setup is relatively simple. Light from a tunable narrow-band optical source is directed through a polarization controller into the DUT at angles of 0°, 45°, and 90°. On the receiving end a polarimeter measures level and polarization of the output light for the different input states (see Fig. 4). From these data the Jones matrixes are calculated along a series of discrete wavelengths, and the differential group delay is then computed for the centers between adjacent wavelength pairs.
The wavelength step size must be chosen to match the differential group delay of the device. For unambiguous measurement results, the change in polarization state between two wavelength steps must not exceed 180°. Therefore, measuring high differential-group-delay values requires narrow and very accurate wavelength steps. Low differential-group-delay values require large steps to obtain a significant change of the Jones matrix. Measuring differential group delay on narrowband devices creates a challenge because sufficient detail requires narrow wavelength steps. In addition, to be able to measure low differential group delay with sufficient accuracy, a tunable laser with very good wavelength accuracy and very low source spontaneous emission must be used.
Fixed-analyzer method. Another method for measuring PMD is the fixed-analyzer method, also known as the wavelength-scanning method. It determines average differential group delay from the random evolution of the output state of polarization as wavelength is scanned. Polarized light from a broadband light source is launched into the DUT, and then measured by an optical spectrum analyzer (OSA) through a variable polarizer. The OSA records light intensity as it varies with wavelength due to changes in the output state of polarization. An alternative approach uses light from a tunable laser directed into the DUT through a polarizer and analyzed at the receiving end by a polarimeter.
The average differential group delay, or PMD, can then be calculated from the number of peaks and valleys (extrema) in the power-level curve and the wavelengths of the first and last extremum. To achieve good accuracy, the number of extrema must be statistically significant. Accordingly, a wide enough wavelength range must be selected. The method has limitations when measuring devices with low PMD because of the low number of resulting extrema. Since the measurement setup can be easily divided into transmitter and receiver, the method is suitable for measurements of installed fiber in the field. However, the measurement results are sensitive to fiber movements.
Interferometric method. The interferometric method is a reliable and versatile technique for measuring PMD in the field. Measurement setups vary, but generally the output light from a broadband light source is coupled through a polarizer into a DUT, and then into an interferometer with two orthogonally polarized arms. Changing the length of one of the paths introduces a delay between the two orthogonally polarized lightwaves. At the point at which this delay exactly compensates the differential group delay in the DUT, the photodetector detects an interference pattern.
For DUTs without mode coupling, average differential group delay can be determined directly from the position of the mirror. For devices with strong mode coupling, such as most fibers, PMD can be calculated from a Gaussian distribution fitted to the interference pattern. The method is fast and robust against fiber movements. It achieves the best accuracy when testing optical fiber with high PMD values. Technological enhancements exist that make the method more suitable for measuring small PMD values and narrowband devices such as DWDM filters (see table).
Mark Albert is a product marketing manager for optical test equipment at Tektronix, 14200 SW Karl Braun Dr., Beaverton, OR 97077. He can be reached at firstname.lastname@example.org.
1. Derickson, Dennis, ed., Fiber Optic Test and Measurement, Prentice Hall PTR, Upper Saddle River, NJ, 1998.
2. Sano, K., Kudou, T. and Ozeki, T., Proc. ECOC 1996, Oslo, TuP.09 (1996)