4584 JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 24, NO. 12, DECEMBER 2006 Polarization Mode Dispersion of Installed Fibers Misha Brodsky, Member, IEEE, Nicholas J. Frigo, Fellow, IEEE, Misha Boroditsky, Senior Member, IEEE, and Moshe Tur, Fellow, IEEE Invited Paper Abstract—Polarization mode dispersion (PMD), a potentially limiting impairment in high-speed long-distance fiber-optic com- munication systems, refers to the distortion of propagating optical pulses due to random birefringences in an optical system. Because these perturbations (which can be introduced through manufac- turing imperfections, cabling stresses, installation procedures, and environmental sensitivities of fiber and other in-line components) are unknowable and continually changing, PMD is unique among optical impairments. This makes PMD both a fascinating research subject and potentially one of the most challenging technical obstacles for future optoelectronic transmission. Mitigation and compensation techniques, proper emulation, and accurate predic- tion of PMD-induced outage probabilities critically depend on the understanding and modeling of the statistics of PMD in installed links. Using extensive data on buried fibers used in long-haul high- speed links, the authors discuss the proposition that most of the temporal PMD changes that are observed in installed routes arise primarily from a relatively small number of “hot spots” along the route that are exposed to the ambient environment, whereas the buried shielded sections remain largely stable for month-long time periods. It follows that the temporal variations of the differential group delay for any given channel constitute a distinct statistical distribution with its own channel-specific mean value. The impact of these observations on outage statistics is analyzed, and the implications for future optoelectronic fiber-based transmission are discussed. Index Terms—Communication systems, optical fiber communi- cation, optical fiber dispersion, optical fiber polarization. I. I NTRODUCTION F IBER optics revolutionized telecommunications over two decades ago, spurred by the promise of a low-loss trans- mission medium with seemingly infinite bandwidth. However, as the bandwidths of transported signals rapidly increased in the late 1980s, birefringence, which is a dependence of refractive index on the state of polarization (SOP), became recognized as a new impairment. Essentially, if the transit times for an optical fiber pulse were different for the x and y polarizations, for example, then an optical pulse launched in an arbitrary SOP Manuscript received September 18, 2006. M. Brodsky is with AT&T Labs Research, Middletown, NJ 07748 USA. N. J. Frigo is with the Physics Department, U.S. Naval Academy, Annapolis, MD 21402 USA. M. Boroditsky is with the Statistical Arbitrage Group, Knight Equity Markets, Jersey City, NJ 07310 USA. M. Tur is with the Faculty of Engineering, Tel Aviv University, Tel Aviv 69978, Israel. Color versions of Figs. 1–4 and 6–16 are available online at http:// ieeexplore.ieee.org. Digital Object Identifier 10.1109/JLT.2006.885781 would create two time-displaced replicas at the receiver, intro- ducing distortion errors. As pulse widths became shorter with higher bandwidths, this differential time displacement, called differential group delay (DGD, defined later), became more injurious. Even more troubling was the recognition that this im- pairment varied from fiber-to-fiber (even in the same lot), from wavelength to wavelength for a given fiber at any given time, and even at each wavelength over time. For carriers, this ran- domness begs the question of how to assess the likelihood that any given fiber will suffer an outage for a given system. Since billions of dollars of fiber were installed before these problems surfaced, and transmission rates are likely to increase, it is clear that this problem has enduring economic implications. Early views of these issues were fleshed out in the late 1980s and early 1990s, the impairment became known as “polariza- tion mode dispersion” (PMD), and research has continued to the present (the term PMD is also used to quantify the phenomenon by the introduction of a PMDvector, to be defined in Section II). As a measure of the maturity of the field, there have been several reviews [1], [2] (including one of over 130 pages [3]) since the earliest work of Poole and Wagner [4] as well as two recent books [5], [6] concerned with PMD: the theoretical foundations are well established. During the telecom bubble, the temporary overbuild of fiber routes with low-PMD fibers allowed the widespread deploy- ment of 10 Gb/s systems, mitigating the need for immediate PMD compensation. For a while, most carriers seemed to have enough recent vintage fiber to satisfy the increasing de- mand of their customers using multiple wavelength-division- multiplexed channels to form terabit per second links. However, as the telecommunications industry comes out from a long downturn, there is a renewed interest in PMD as “good” fibers have been cherry picked on existing routes and even better fiber is needed for the worldwide deployment of 40 Gb/s systems that has already begun. PMD-related research can be roughly divided in seven over- lapping subfields, each involving both theoretical and experi- mental work. 1) Development of low-PMD fiber. The PMD coefficient of the fiber, having units of picosecond per square root kilo- meter, is roughly proportional to the fiber birefringence and inversely proportional to the birefringence correlation length. The former parameter has been improved by better control over the drawing process, and the latter was shortened dramatically by the introduction of so-called 0733-8724/$20.00 © 2006 IEEE