Nonlinear Fiber Optics - 4 ed. Agrawal

8.3. SRS with Short Pump Pulses 299
0.06
0.02
z = 2L W
Intensity
0.04
0.02
Intensity
0.01
0
0
−10 0 10
−10 0 10
Frequency, (ν − ν p
)T 0
Frequency, (ν − ν s
)T 0
Intensity
0.04
0.03
0.02
0.01
Intensity
0.02
0.01
z = 3L W
0
0
−10 0 10
−10 0 10
Frequency, (ν − ν p
)T 0
Frequency, (ν − ν s
)T 0
Figure 8.12: Spectra of pump (left column) and Raman (right column) pulses at z = 2L W and
3L W under conditions of Figure 8.11.
widths and pump wavelengths by using the scaling of Eqs. (8.3.5) and (8.3.15). The
choice L W /L G = 12 implies that
√ πgs P 0 L W ≈ 21, (8.3.18)
and corresponds to a peak power 30% above the Raman threshold.
Several features of Figure 8.11 are noteworthy. The Raman pulse starts to build up
after one walk-off length. Energy transfer to the Raman pulse from the pump pulse is
nearly complete by z = 3L W because the two pulses are then physically separated owing
to the group-velocity mismatch. As the Raman pulse moves faster than the pump pulse
in the normal-GVD regime, the energy for SRS comes from the leading edge of the
pump pulse. This is clearly apparent at z = 2L W where energy transfer has led to a
two-peak structure in the pump pulse as a result of pump depletion—the hole near the
leading edge corresponds exactly to the location of the Raman pulse. The small peak
near the leading edge disappears with further propagation as the Raman pulse walks
through it. The pump pulse at z = 3L W is asymmetric in shape and appears narrower
than the input pulse as it consists of the trailing portion of the input pulse. The Raman
pulse is also narrower than the input pulse and is asymmetric with a sharp leading edge.
The spectra of pump and Raman pulses display many interesting features resulting
from the combination of SPM, XPM, group-velocity mismatch, and pump depletion.