Nonlinear Fiber Optics - 4 ed. Agrawal

6.6. Random Birefringence 219
Figure 6.15: PMD-induced pulse broadening as a function of fiber length for three values of
dispersion parameter. The analytical prediction is shown with a line containing solid dots. The
top trace shows the linear case for comparison. (After Ref. [162]; c○2002 IEEE.)
where σ T is defined as in Eq. (6.6.4). A comparison with the linear case (γ = 0) shows
that pulse broadening is reduced considerably in the case of solitons.
Numerical simulations based on Eq. (6.6.17) confirm this prediction. Figure 6.15
shows PMD-induced pulse broadening as a function of fiber length for fibers with
the PMD parameter D p = 0.2 ps/ √ km, average DGD of 4.5 ps, correlation length
l c = 0.5 km, and dispersion parameter D = 0.1 to 1 ps/(km-nm). Input pulses of 5-
ps FWHM are launched with enough peak power to form a fundamental soliton. The
traces in Figure 6.15 represent an average over 1000 runs [162]. The top trace shows
the linear for comparison. Clearly, pulse broadening is reduced for solitons but its magnitude
depends on D. ForD > 0.5 ps/(km-nm) numerical results agree well with the
analytical prediction given in Eq. (6.6.18). For small values of D, GVD is so small that
birefringence effects begin to dominate even for solitons. Similar results are found for
dispersion-managed solitons [159]. In this case, PMD-induced broadening depends
on the strength of dispersion map and can be less that predicted by Eq. (6.6.18) for
stronger maps [162].
The effects of PMD on solitons has been observed in several experiments for both
the conventional and dispersion-managed solitons [161]. The results show that the
pulse width at the output end of fiber fluctuates with time in both the linear and nonlinear
propagation regimes but the range over which pulse width fluctuates is reduced
considerably for solitons. As shown in Figure 6.16, this range depends on the instantaneous
value of DGD. Whereas the range of width fluctuations increases with DGD for
linear pulses, it remains relatively constant for solitons. It is this feature that indicates
the robustness of solitons to birefringence fluctuations. It should be stressed that the
average and RMS values of pulse-width fluctuations are not sufficient to quantify the
data in Figure 6.16 because their statistical distribution is far from being Gaussian. A