IEEE PHOTONICS TECHNOLOGY LETTERS, VOL. 18, NO. 1, JANUARY 1, 2006 217 Autocorrelation Function of the Single PC Polarization-Mode Dispersion Emulator Yannick Keith Lize, Student Member, IEEE, Leigh Palmer, Student Member, IEEE, Maryse Aubé, Nicolas Godbout, Member, IEEE, Suzanne Lacroix, Member, IEEE, and Raman Kashyap, Member, IEEE Abstract—The discrete structure of multisection polariza- tion-mode dispersion (PMD) emulators is known to artificially correlate the PMD affecting different channels in a wavelength-di- vision multiplexing system, thus limiting their usefulness in accurately emulating broad-band PMD. We report on the correla- tion properties of a novel single polarization controller (PC) PMD emulator, which offers scalability with the number of emulator sections through component reuse. We report a background level of the PMD frequency autocorrelation function of 0.66%, for a 50-section emulator, the lowest experimentally demonstrated for a PMD emulator, which makes the single PC PMD emulator an instrument of choice for research and development of broad-band PMD mitigation strategies. Index Terms—Autocorrelation function, emulators, optical com- munication, polarization-mode dispersion (PMD). I. INTRODUCTION P OLARIZATION-MODE dispersion (PMD) emulators conveniently and efficiently replicate the effects of bire- fringence and polarization-mode coupling on long optical links. They are typically used to analyze system outages and test PMD mitigation strategies, which require rapid coverage of the PMD space. A number of emulator designs reported in the literature, or made commercially available, are based on cascading bire- fringent elements and controlling the mode coupling between them [2]–[4]. Although these designs can accurately model the first- and higher order PMD statistics expected for a long fiber link, if the emulators consist of relatively few elements they tend to introduce artificial PMD correlation between channels in wavelength-multiplexed systems. An alternative design, also commercially available, utilizes elements with variable differential group delay (DGD) to reproduce PMD [1], [5]–[7]. Again, although this design offers excellent accuracy for first- and second-order statistics, it provides no advantage with re- spect to achieving low channel correlation. Given the tight PMD tolerances for 40-Gb/s systems, accurate emulation of the PMD frequency response in optical fibers is essential for realistic wavelength-division multiplexing (WDM) system analysis. Manuscript received July 27, 2005; revised September 20, 2005. This work was supported in part by the Canadian Institute for Photonic Innovations (CIPI) and by the Natural Sciences and Engineering Research Council’s Canada Re- search Chairs Program. Y. K. Lize and R. Kashyap are with the Advanced Photonics Laboratory, Ecole Polytechnique de Montreal, University of Montreal, Montreal QC H3T 1J4, Canada (e-mail: yannick.lize@polymtl.ca). L. Palmer is with the Australian CRC, Photonics Research Laboratory, Uni- versity of Melbourne, Melbourne 3010, Australia. M. Aubé, N. Godbout, and S. Lacroix are with the Optical Fiber Laboratory, Ecole Polytechnique de Montreal, Montreal, University of Montreal, Montreal, QC H3T 1J4, Canada. Digital Object Identifier 10.1109/LPT.2001.861304 Fig. 1. Single polarization controller PMD emulator. SMF is spooled on each paddle for phase retardation. PMF induces fixed differential group delays. Random rotation between paddles induces random coupling in each length of PMF. A new class of multisection PMD emulator employing cor- related polarization scrambling has recently been reported [8], [9]. The reuse of a single modified Lefèvre polarization con- troller (PC) allows more sections to be included in an emulator and, if designed properly [9], provides accurate statistical repro- duction of all-order PMD with low insertion loss in a low-cost device. Fig. 1 illustrates how the polarization scrambling be- tween birefringent elements is implemented by winding a stan- dard single-mode fiber (SMF) onto the same set of three motor- ized paddles of an enlarged Lefèvre PC and splicing to sections of polarization-maintaining fiber (PMF). In this letter, we analyze the frequency autocorrelation func- tion (ACF) of single PC emulators, a figure of merit which gives a quantitative description of the frequency response of the PMD affecting a link [10]–[12]. We demonstrate through ex- perimental results and simulations that due to its scalability the single PC design can achieve very low background autocorrela- tion (BAC). Low BAC is of importance when emulating PMD since BAC is an artifact of PMD emulation which results in cor- related DGD between different WDM channels. We experimen- tally obtained a BAC of 0.66% for a 50-section emulator, which is 15 to 60 times lower than previously reported [11], [12]. This result is, to the best of our knowledge, the lowest experimentally demonstrated BAC for a PMD emulator. II. THEORY PMD can be described via a vector in the Stokes space, where is the angular optical frequency [13]. The PMD vector is derived from the frequency dependence of the Jones matrix [14] expressed as 1041-1135/$20.00 © 2005 IEEE