IEEE PHOTONICS TECHNOLOGY LETTERS, VOL. 13, NO. 10, OCTOBER 2001 1079 Polarization-Mode Dispersion-Induced Outages in Soliton Transmission Systems Chongjin Xie, Henrik Sunnerud, Magnus Karlsson, and Peter A. Andrekson, Member, IEEE Abstract—The bit-error-rate (BER) degradation of conven- tional soliton systems due to polarization-mode dispersion (PMD) is investigated. It is found that the interplay between the dispersive waves generated by PMD and adjacent soliton pulses will seriously degrade the BER of soliton systems, and make them even worse than linear systems if all other transmission impairments are neglected. In order to achieve soliton robustness to PMD, some techniques to eliminate or reduce the dispersive waves must be employed, such as soliton control methods or dispersion-managed solitons. Different systems are estimated and compared in terms of PMD-induced outage probability. Index Terms—Optical fiber communications, polarization, po- larization-mode dispersion, solitons. I. INTRODUCTION P OLARIZATION-MODE dispersion (PMD) is one of the limiting factors for high-speed optical transmission sys- tems, especially when the system bit rate increases to 40 Gb/s and beyond. It is well known that, thanks to fiber nonlinearity, solitons can resist the random pulse broadening caused by PMD. The self-trapping effects between the two polarization compo- nents of the soliton pulses can maintain the pulse shape, and keep the soliton pulses from splitting during propagation. The effects of PMD on the soliton systems have been studied both theoretically and experimentally, and it has been shown that soli- tons are robust to PMD [1]–[7]. However, all these previous works only took single pulse behavior into consideration, i.e., the pulsewidth broadening, which is obviously not sufficient to understand the influences of PMD on the whole soliton system performance. In this letter, the bit-error-rate (BER) degradation of the con- ventional soliton systems [i.e., soliton systems with constant group velocity dispersion (GVD)] due to PMD is investigated, and the influences of PMD on the soliton systems are quantified in terms of outage probability [8]. We find that, although the soliton pulses do not split due to PMD during propagation, dis- persive waves are generated and will interact with other soliton pulses, as well as cause a slight soliton pulse broadening. The in- Manuscript received March 9, 2001. C. Xie was with the Department of Microelectronics, Photonics Laboratory, Chalmers University of Technology, SE-412 96 Göteborg, Sweden. He is now with Bell Laboratories, Lucent Technologies, Holmdel, NJ 07733 USA (e-mail: chongjin@lucent.com). H. Sunnerud and M. Karlsson are with the Department of Microelectronics, Photonics Laboratory, Chalmers University of Technology, SE-412 96 Göte- borg, Sweden. P. A. Andrekson is with the Department of Microelectronics, Photonics Lab- oratory, Chalmers University of Technology, SE-412 96 Göteborg, Sweden and also with CENiX Inc., Allentown, PA 18106 USA. Publisher Item Identifier S 1041-1135(01)08077-6. teraction between the dispersive waves and the solitons will se- riously degrade the system performance, and can make soliton systems even worse than linear systems if all other degrading mechanisms are neglected. We will also show that soliton con- trol methods and dispersion-managed (DM) solitons, which can reduce the dispersive waves, will recover the soliton robustness to PMD. II. NUMERICAL SIMULATION AND DISCUSSION In order to isolate the influences of PMD, a simple system model is used, which is similar to that used in the analytical theory in [8]. In this model, the system consists of a lossless fiber and an erbium-doped fiber amplifier (EDFA) preamplified re- ceiver. The receiver is composed by an EDFA with a noise figure 3 dB, followed by an optical Fabry–Pérot filter with a bandwidth of , a square law detector, and an electrical second-order But- terworth filter with a bandwidth equal to 0.6 , where is the bit rate. Only the amplified spontaneous emission (ASE) noise is considered in the calculation of BER, and the BER is opti- mized with respect to the decision level and sampling time. In the simulations, we launch 40-Gb/s pseudorandom binary sequence (PRBS) sequences of solitons with pulsewidth equal to 5 ps. The coupling length of fiber is 500 m, and the total differential group delay (DGD) of the link is changed by changing the PMD coefficient of the fiber. In order to estimate the BER degradation due to PMD, we set the input power at the receiver 1 dB higher than the power that provides BER of when the system has no PMD (i.e., the power margin is 1 dB), and then calculate the BER property. In this case, all the BER degradation is caused by PMD. To get the statistical character- istics of BER, 10 000 independent fiber realizations are tested using Monte Carlo simulations. For each fiber realization, the BER is calculated based on ten runs of detection with different preamplifier ASE noise. Fig. 1 shows histograms of the pulse broadening for both the linear and soliton systems, when only a single pulse prop- agates along the fibers with PMD. For the linear system, a hy- perbolic secant pulse is used and both the GVD and the non- linearity of the fibers are neglected. It is clear that the soliton pulse broadening is smaller than that of the linear pulse, and the soliton can resist pulse broadening due to PMD, which is known as the soliton robustness to PMD [1]–[7]. However, if we look at the BER property of the same systems, the results are completely different. The BER degradation of the soliton system under these conditions is even more serious than that of the linear system, which is clearly shown in the BER histograms in Fig. 2 for the linear and soliton systems, where the same pa- rameters as in Fig. 1 are used. 1041–1135/01$10.00 © 2001 IEEE