Nonlinear Fiber Optics - 4 ed. Agrawal

8.4. Soliton Effects 307
Figure 8.19: Evolution of (a) pump and (b) Raman pulses over three walk-off lengths when both
pulses propagate in the anomalous-GVD regime of the fiber.
undistorted as a fundamental soliton. Numerical results show that this is possible if the
Raman pulse is formed at a distance at which the pump pulse, propagating as a higherorder
soliton, achieves its minimum width [150]. By contrast, if energy transfer to the
Raman pulse is delayed and occurs at a distance where the pump pulse has split into its
components (see Figure 5.6 for N = 3), the Raman pulse does not form a fundamental
soliton, and its energy rapidly disperses.
Equations (8.3.16) and (8.3.17) can be used to study ultrafast SRS in the anomalous-
GVD regime by simply changing the sign of the second-derivative terms. Figure 8.19
shows evolution of the pump and Raman pulses under conditions identical to those
used for Figure 8.11 except that L W /L D = 2. The pump pulse travels as a higher-order
soliton and is compressed as it propagates down the fiber, while also amplifying the
Raman seed. As in the case of normal GVD, energy transfer to the Raman pulse occurs
near z ≈ L W . If the pump pulse is shortest close to this distance, most of its energy is
transferred to the Raman pulse, which forms a soliton whose width is only a fraction
of the input pump pulse.
For the Raman soliton to form, L W should be comparable to the dispersion length
L D . In silica fibers L W and L D become comparable only for femtosecond pulses of
width ∼100 fs. For such ultrashort pump pulses, the distinction between pump and
Raman pulses gets blurred, as their spectra begin to overlap considerably. This can
be seen by noting that the Raman-gain peak in Figure 8.2 corresponds to a spectral
separation of about 13 THz, while the spectral width of a 100-fs pulse is ∼10 THz.