## 2 Dispersion-Managed Link and WDM System Modelling  
### Dispersion-Managed Link  
Figure 1 shows the WDM system and dispersion-managed optical transmission link to be analyzed through simulation in this paper. OPC is located in the middle of the entire transmission link in Figure 1. As will be mentioned later, the number of WDM channels transmitted over the link is 24, and the data rate of each channel is assumed to be 40 Gb/s. Though dispersion management is achieved by DCF added to all fiber spans of the first and second half-links with respect to midway-OPC, the dispersion maps are designed so that the cumulative dispersion becomes 0 ps/nm repeatedly at intervals of the fiber span group (FSG) as shown in Figure 2, rather than a structure in which the cumulative dispersion becomes 0 ps/nm for each fiber span. We divide these FSG spacings non-uniformly into 2, 4, 8, and 16 for each half-link. In other words, as shown in Figure 2, the zero-crossing place of cumulative dispersion in each half-link is not constant. Also, as can be seen in Figure 2, the dispersion maps are designed so that the zero-crossing places of cumulative dispersion in the first and the second half-link are symmetrical to each other with respect to midway-OPC. That is, if the zero-crossings of the cumulative dispersion occurs at the 2 nd, 4 th, 8 th, and 16 th fiber spans in the first half-link, then the zero-crossings in the second half-link must correspondingly occur in the order of 16 th, 8 th, 4 th, and 2 nd fiber spans. This dispersion map structure is hereafter referred to as the growth-decaying (GD) scheme, and in this paper, we simultaneously analyze the decaying-growth (DG) scheme, where the zero-crossing of the cumulative dispersion in each half-link is opposite to the GD scheme. The dispersion map proposed in this study has another symmetry. This symmetry is made by the cumulative dispersion distribution of successive FSGs. When the cumulative dispersion of the first FSG increases linearly to the middle point and then decreases, the cumulative dispersion of the next FSG decreases and then increases with the same slope. Also, the cumulative dispersion profile of consecutive FSGs configured in this way is symmetrical about the midway-OPC. In this paper, this symmetry has two forms for all proposed dispersion maps. In order to distinguish these two types, we denote AD (ascent-descent) and DA (descent-ascent) according to the distribution shape of the cumulative dispersion in the first FSG, as shown in Figure 2.  
Figure 1: The 40 Gb/s \(\times\) 24 channels WDM transmission system through the dispersion-managed link and the midway-OPC. The last factor considered to analyze the effect of the proposed dispersion maps on WDM channel distortion compensation is the increase/decrease rate of dispersion accumulated in the FSGs. The increase and decrease in the accumulated dispersion depends on the magnitude and sign of the residual dispersion of each fiber span. As shown in Figure 2, the cumulative dispersion reversal occurs at each intermediate position of all FSGs. And, as mentioned above, the number of fiber spans constituting the FSG in which zero-crossing of cumulative dispersion occurs is 2, 4, 8, and 16 in each half-link. Based on these features, the dispersion maps classified into the following four cases. The first case is that the residual dispersion assigned to all fiber spans is assumed to be same for all FSGs. The dispersion maps shown in Figure 1(a),b correspond to the first case. Analyzing the dispersion map of Figure 1(a), the rate of increase/decrease in the cumulative dispersion in all FSGs is the same regardless of the number of the fiber spans each FSG has. That is, if the rate of the cumulative dispersion in an FSG consisting of two fiber spans is \(\pm\)100 (ps/nm)/span, the increase/decrease rates of the cumulative dispersion in all other FSGs also have the same value. For this reason, we will call the dispersion map in Figure 1(a),b the 'fixed' scheme.