Nonlinear Fiber Optics - 4 ed. Agrawal

5.5. Higher-Order Effects 165
Figure 5.21: (a) Temporal and (b) spectral evolutions of a second-order (N = 2) soliton when τ R
= 0.01, depicting soliton’s fission induced by intrapulse Raman scattering.
In the case of higher-order solitons, one must solve the generalized NLS equation
(5.5.8) numerically. To focus on the effects of intrapulse Raman scattering, we set
δ 3 = 0 and s = 0 in this equation. Pulse evolution inside fibers is then governed by
i ∂u
∂ξ + 1 ∂ 2 u
2 ∂τ 2 + |u|2 u = τ R u ∂|u|2
∂τ . (5.5.20)
Figure 5.21 shows the spectral and temporal evolution of a second-order soliton (N =
2) by solving Eq. (5.5.20) numerically with τ R = 0.01. The effect of intrapulse Raman
scattering on higher-order solitons is similar to the case of self-steepening. In particular,
even relatively small values of τ R lead to the fission of higher-order solitons into its
constituents [197].
A comparison of Figures 5.19 and 5.21 shows the similarity and the differences
for two different higher-order nonlinear mechanisms. An important difference is that
relatively smaller values of τ R compared with s can induce soliton fission over a given
distance. For example, if s = 0.01 is chosen in Figure 5.19, the soliton does not split
over the distance z = 5L D . This feature indicates that the effects of τ R are likely to
dominate in practice over those of self-steepening. Another difference is that both
solitons are delayed in the case of self-steepening, while in the Raman case the lowintensity
soliton appears not to have shifted in both the spectral and temporal domains.
This feature is related to the T0 −4 dependence of the RIFS on the soliton width in Eq.
(5.5.19). The second soliton is much wider than the first one, and thus its spectrum