Nonlinear Fiber Optics - 4 ed. Agrawal

300 Chapter 8. Stimulated Raman Scattering
Figure 8.12 shows the pump and Raman spectra at z = 2L W (top row) and 3L W (bottom
row). The asymmetric nature of these spectra is due to XPM-induced chirp. The highfrequency
side of the pump spectra exhibits an oscillatory structure that is characteristic
of SPM (see Section 4.1). In the absence of SRS, the spectrum would be symmetric
with the same structure appearing on the low-frequency side. As the low-frequency
components occur near the leading edge of the pump pulse and because the pump is
depleted on the leading side, the energy is transferred mainly from the low-frequency
components of the pump pulse. This is clearly seen in the pump spectra of Figure
8.12. The long tail on the low-frequency side of the Raman spectra is also partly for
the same reason. The Raman spectrum is nearly featureless at z = 2L W but develops
considerable internal structure at z = 3L W . This is due to the combination of XPM
and pump depletion; the frequency chirp across the Raman pulse induced by these
effects can vary rapidly both in magnitude and sign and leads to a complicated spectral
shape [121].
The temporal and spectral features seen in Figures 8.11 and 8.12 depend on the peak
power of input pulses through the lengths L G and L NL in Eqs. (8.3.16) and (8.3.17).
When peak power is increased, both L G and L NL decrease by the same factor. Numerical
results show that because of a larger Raman gain, the Raman pulse grows faster
and carries more energy than that shown in Figure 8.11. More importantly, because
of a decrease in L NL , both the SPM and XPM contributions to the frequency chirp are
enhanced, and the pulse spectra are wider than those shown in Figure 8.12. An interesting
feature is that the Raman-pulse spectrum becomes considerably wider than
the pump spectrum. This is due to the stronger effect of XPM on the Raman pulse
compared with that of the pump pulse. The XPM-enhanced frequency chirp for the
Raman pulse was predicted as early as 1976 [114]. In a theoretical study that included
XPM but neglected group-velocity mismatch and pump depletion, the spectrum of the
Raman pulse was shown to be wider by a factor of two [115]. Numerical results that
include all of these effects show an enhanced broadening by up to a factor of three,
in agreement with experiments discussed later. Direct measurements of the frequency
chirp also show an enhanced chirp for the Raman pulse compared with that of the pump
pulse [130].
8.3.4 Experimental Results
The spectral and temporal features of ultrafast SRS have been studied in many experiments
performed in the visible as well as in the near-infrared region. In one experiment,
60-ps pulses from a mode-locked Nd:YAG laser operating at 1.06 μm were propagated
through a 10-m-long fiber [116]. When the pump power exceeded the Raman threshold
(∼1 kW), a Raman pulse was generated. Both the pump and Raman pulses were
narrower than the input pulse as expected from the results shown in Figure 8.11. The
spectrum of the Raman pulse was much broader (spectral width ≈2 THz) than that
of the pump pulse. The XPM-enhanced spectral broadening of the Raman pulse was
quantified in an experiment in which 25-ps pulses at 532 nm were propagated through a
10-m-long fiber [123]. Figure 8.13 shows the observed spectra at four values of pumppulse
energies. The Raman spectral band located at 544.5 mm has a width about three