ELECTRONICS LETTERS 28th May 1998 Vol. 34 No. 11 Impact of polarisation-mode dispersion in dispersion-managed soliton systems X. Zhang, M. Karlsson, P. Andrekson and K. Bertilsson Since enhanced power solitons are usually applied in dispersion- managed soliton systems, it might be expected that dispersion- managed solitons have a stronger resistance to polarisation-mode dispersion than conventional solitons. However, it is shown that dispersion-managed solitons behave similarly to conventional solitons in terms of resistance to polarisation-mode dispersion. Dispersion-managed systems incorporate two or more fibre seg- ments with different group-velocity dispersions (GVDs), simultane- ously allowing for both high local and small path-averaged dispersion. With respect to nonlinearities, such systems behave quite differently to those with uniform GVD, even if the path-averaged dispersions are identical to the uniform GVD. A high local disper- sion significantly reduces both modulation instability gain and bandwidth [1, 2], and low path-averaged dispersion gives very long dispersion length. For dispersion-managed solitons, enhanced power solitons can be applied. Such solitons would be expected to resist the impact of polarisation-mode dispersion (PMD) [3] since the local GVD is high, and power enhancement will increase the cross-phase modulation (XPM) between the two orthogonal polarisation com- ponents. In [4], we analysed the influence of PMD on solitons in a fibre with a uniform GVD, i.e. conventional solitons. It was found that the main broadening mechanism of PMD-perturbed solitons is the dispersive radiation [3, 4]. The GVD must not be too large in a dispersive radiation-limited system, but, conversely, it cannot be too weak since the beneficial effects from XPM then vanish. Conse- quently, we found that there is an optimum choice of GVD which minimises the broadening due to PMD. In dispersion-managed soliton systems, enhanced power solitons have higher energy and the path-averaged GVD is still kept low (this means that dispersion length is very long and the Manakov equation is less violated). Therefore, it may be expected that enhanced power solitons can bet- ter resist the influence of PMD as compared to conventional solitons. However, enhanced power solitons are not real solitons, so that dispersive radiation arises and may be very strong in some cases. Thus, there are a number of questions to be answered: are the disper- sion-managed solitons more resistant to PMD? Is the influence of PMD dependent on the local GVD? Are dispersion-managed solitons with a larger path-averaged GVD more resistant to PMD? In this Letter, we aim to answer these questions. The theoretical model is nearly identical to that in [4]. The corre- lation length, i.e the length over which one polarisation state is com- pletely coupled to another by randomly rotating the birefringence axes, is 0.5km, which is equal to the simulation step-size. In the sim- ulations, we use initial conditions: A (0,t ) = √(9/8·N 2 )sech(t /t 0 ) for conventional solitons, and A (0, t ) = √(9/8·N 2 )exp(–t 2 /2t 0 2 ) for disper- sion-managed solitons, t 0 being related to the full width at half maxi- mum (FWHM) of pulses (t 0 = FWHM/1.763 for secant pulses and t 0 = FWHM/1.665 for Gaussian pulses). N 2 is the so-called power enhancement factor. The power enhancement factor is expected to be related to the dispersion perturbation factor: Here, D P and D N are the positive and negative GVDs, respectively, with corresponding lengths, L P and L N , respectively; is the average GVD over the length of L P + L N ; t 0 is the soliton pulsewidth; λ is the signal operating wavelength (1.55 μm here); c is the velocity of light. It was found that a power enhancement factor N 2 of > 1.5 for disper- sion-managed solitons can be applied if initial pulses are Gaussian, even when the dispersion perturbation factor γ is very small [5]. This is not true for initial sech-shaped pulses. Therefore, initial Gaussian pulses are always used here irrespective of how large the dispersion perturbation factor is. Next, an 8bit sequence (11101000) of a 10Gbit/s signal consisting of 20ps wide (FWHM) pulses is considered. The fibre loss is 0.25dB/ km and a Kerr nonlinearity of 2.43W –1 km –1 are used for all consid- ered fibres. Since the dispersive radiation may become large, we will use eye closures to determine the broadening of pulses instead of the FWHM, so as to include the interaction of pulses induced by disper- sive radiation. In the receiver, an optical Fabry-Perot filter with a bandwidth of 40GHz and an electrical fourth-order Bessel filter with a bandwidth of 8GHz were used. The eye closure is defined as the ratio of eye opening for a back-to-back system to the eye opening for a system with transmission fibre. For all simulations considering PMD, the results are obtained based on an average over 400 trials, each having a different set of random birefringence axis rotations and phase variations. We have already found that a high power enhancement factor can be applied when the compensation period covers several amplifier spans [5]. First, we consider inserting a 2km dispersion-compensa- tion fibre (DCF) in the middle of three amplifier spans for an ampli- fier span of 40km (i.e. 40 + 38 + 2 + 40km). In the configuration, D P = 1ps/nm km and D N = –53ps/nm km are used; thus = 0.1ps/nm km. For such a dispersion-managed soliton system, almost no eye penalty for a distance of up to 2000km is obtained if PMD influence is not considered, which is shown in Fig. 1. In Fig. 1, power enhancement factors N 2 of 2, 2.5 and 3 are used. Correspondingly, the behaviour of dispersion-managed solitons with the influence of PMD is also shown in Fig. 1, in which PMD with an average differ- ential group delay (DGD) of 0.5ps/√km for all fibres is considered. D – Fig. 1 Eye closures against transmission distance for propagation of dis- persion-managed solitons in dispersion map with 2km DCF in every three spans ( 40 + 38 +2 + 40 k m) Two cases considered: without PMD and with PMD in simulations. Three power enhancement factors (N 2 ) are shown for comparison. Dis- persion perturbation factor for this map is γ = 2.11. ——— N 2 = 2 – – – – N 2 = 2.5 — ··· — N 2 = 3 ··········· conventional solitons with PMD and N 2 = 1.21 Average GVD = 0.1ps/nm km Fig. 2 N ormalised transmission distance with respect to conventional solitons against dispersion perturbation factor γ for same dispersion map as in Fig. 1 Average dispersion is maintained to = 0.1ps/nm km for all cases 2km DCF inserted in every three spans; average GVD = 0.1ps/nm km D – D –