9.4. DISPERSION-MANAGED SOLITONS 431
Input energy (pJ)0.001 0.010 0.100 1.000Pulse width (ps)05101520Input energy (pJ)0.0 0.5 1.0Input chirp 01234TmT 0(a) (b)Figure 9.15: (a) Changes inT 0 (upper curve) andTm(lower curve) with input pulse energyE 0
forα=0 (solid lines) and 0.25 dB/km (dashed lines). The inset shows the input chirpC 0 in the
two cases. (b) Evolution of the DM soliton over one map period forE 0 = 0 .1 pJ andLA=80 km.
Several conclusions can be drawn from Fig. 9.15. First, bothT 0 andTmdecrease
rapidly as pulse energy is increased. Second,T 0 attains its minimum value at a certain
pulse energyEcwhileTmkeeps decreasing slowly. Third,T 0 andTmdiffer from each
other considerably forE 0 >Ec. This behavior indicates that the pulse width changes
considerably in each fiber section when this regime is approached. An example of pulse
breathing is shown in Fig. 9.15(b) forE 0 = 0 .1 pJ in the case of lumped amplification.
The input chirpC 0 is relatively large (C 0 ≈ 1 .8) in this case. The most important feature
of Fig. 9.15 is the existence of a minimum value ofT 0 for a specific value of the pulse
energy. The input chirpC 0 =1 at that point. It is interesting to note that the minimum
value ofT 0 does not depend much on fiber losses and is about the same for the solid
and dashed curves although the value ofEcis much larger in the lumped amplification
case because of fiber losses.
As seen from Fig. 9.15, both the pulse width and the peak power of DM solitons
vary considerably within each map period. Figure 9.16(a) shows the width and chirp
variations over one map period for the DM soliton of Fig. 9.15(b). The pulse width
varies by more than a factor of 2 and becomes minimum nearly in the middle of each
fiber section where frequency chirp vanishes. The shortest pulse occurs in the middle
of the anomalous-GVD section in the case of ideal distributed amplification in which
fiber losses are compensated fully at every point along the fiber link. For comparison,
Fig. 9.16(b) shows the width and chirp variations for a DM soliton whose input energy
is close toEcwhere the input pulse is shortest. Breathing of the pulse is reduced
considerably together with the range of chirp variations. In both cases, the DM soliton
is quite different from a standard fundamental soliton as it does not maintain its shape,
width, or peak power. Nevertheless, its parameters repeat from period to period at
any location within the map. For this reason, DM solitons can be used for optical
communications in spite of oscillations in the pulse width. Moreover, such solitons
perform better from a system standpoint.