Nonlinear Fiber Optics - 4 ed. Agrawal

308 Chapter 8. Stimulated Raman Scattering
Figure 8.20: Pulse spectra of 30-ps input pulses at the output of a 250-m-long fiber for peak
powers in the range of 50 to 900 W. The autocorrelation trace on the right side corresponds to
the Stokes tail in the topmost spectrum. (After Ref. [151]; c○1985 Nauka.)
Equations (8.3.16) and (8.3.17) do not provide a realistic description of ultrafast SRS
with femtosecond pump pulses, particularly in the case of anomalous GVD where the
input pulse may shorten considerably during early stages of propagation.
An alternative approach is provided by the generalized propagation equation of
Section 2.3. Equation (2.3.43) includes the effect of Raman gain through the last term
proportional to the parameter T R . As discussed there, T R is related to the slope of the
Raman gain near origin in Figure 8.2. Effects of this Raman-gain term on the evolution
of femtosecond pulses have been discussed in Section 5.5.4. Figure 5.21 shows the
pulse shapes and spectra for a pump pulse whose peak power corresponds to a secondorder
soliton (N = 2). As seen there, the input pulse splits into two pulses within one
soliton period.
The same behavior can also be interpreted in terms of intrapulse Raman scattering
[151], a phenomenon that can occur even before the threshold of noise-induced
SRS is reached. The basic idea is the following. The input pulse, propagating as a
higher-order soliton, narrows its width and broadens its spectrum during the initial
contraction phase. Spectral broadening on the red side provides a seed for Raman amplification,
that is, the blue components of the pulse pump the red components through
self-induced SRS. This is clearly seen in Figure 5.21 where the dominant spectral peak
moves continuously toward the red side because of such a Raman-induced frequency
shift [153]. In the time domain, energy in the red-shifted components appears in the
form of a Raman pulse that lags behind the input pulse because the red-shifted components
travel slowly in the anomalous-GVD regime. The use of Eq. (2.3.43) becomes
questionable for pulses of widths 100 fs or less because it does not take into account
the shape of the Raman-gain spectrum shown in Figure 8.2. Equation (2.3.36) should
be used for such ultrashort pulses. This equation is used in Chapter 12 in the context
of supercontinuum generation.
Intrapulse Raman scattering can occur even for picosecond input pulses as long as
the soliton order N is large enough to broaden the input spectrum (through SPM) to
widths ∼1 THz. Indeed, in the first experimental demonstration of this phenomenon,