Nonlinear Fiber Optics - 4 ed. Agrawal

348 Chapter 9. Stimulated Brillouin Scattering
Transmitted Power (kW)
1
0.8
0.6
0.4
0.2
10 ns
20 ns
(a)
Stokes Power (kW)
1
0.5
10 ns
20 ns
(b)
0
0 20 40 60 80
Time (ns)
0
0 20 40 60 80
Time (ns)
Figure 9.10: (a) Transmitted pump pulses and (b) reflected Stokes pulses when Gaussian-shape
pump pulses with 10 or 20 ns width are launched into a 1-m-long fiber. Dashed curves show for
comparison the input pump pulse in each case.
Several other features of Figure 9.9 are noteworthy. The Stokes pulse is far from
being Gaussian and exhibits a sharp leading edge, followed by a much shallower trailing
edge. The width of the Stokes pulse is also shorter than the 15-ns width of input
pump pulses. Transmitted pump pulses exhibit a sharp trailing edge and are also reduced
in width. In the case of 1-kW peak power, the sharp trailing edge is followed
by several secondary peaks of much reduced amplitude. All of these features can be
understood by recalling that (a) the Stokes pulse builds up in the backward direction
and is thus amplified mainly by the trailing edge of the pump pulse; (b) the round-trip
time for a 1-m-long fiber is about 10 ns; and (c) the length of a 15-ps pump input pulse
is about 3 m.
The width of the pump pulse also plays a critical role. Figure 9.10 compares (a)
transmitted pump pulses and (b) reflected Stokes pulse for Gaussian-shape pump pulse
with 1-kW peak power as the pump width is reduced from 20 ns to 10 ns. Transmitted
pump pulses have similar shapes in both cases, although Stokes pulses exhibit different
features. The important point is that, as the pump pulse becomes shorter, less and less
energy is transferred to the Stokes pulse. SBS eventually ceases to occur for pump
pulse widths smaller than the phonon life time.
The experiments performed using a Q-switched Nd:YAG laser exhibit features similar
to those seen in Figures 9.9 and 9.10. Figure 9.11 shows the reflected Stokes pulse
(dotted curve) and the transmitted pump pulse (solid curve) for several peak powers
when 14- and 50-ns pump pulses at the 10-Hz repetition rate were transmitted through
a 0.5-m-long optical fiber [93]. The experimental results agree reasonably well with
the numerical predictions based on Eqs. (9.4.5)–(9.4.7).
An interesting question is whether Eqs. (9.4.5)–(9.4.7) permit solitary-wave solutions
such that each pump pulse generates the Stokes field A s in the form of a backwardpropagating
soliton. It turns out that, under certain conditions, the pump and Stokes
waves can support each other as a coupled bright–dark soliton pair [95]–[97], similar