Nonlinear Fiber Optics - 4 ed. Agrawal

352 Chapter 9. Stimulated Brillouin Scattering
4
(a)
3.0
(b)
Index Change (×10 −8 )
2
0
−2
Group Index, n g
2.5
2.0
1.5
−4
−6 −4 −2 0 2 4 6
Detuning, δ
1.0
−6 −4 −2 0 2 4 6
Detuning, δ
Figure 9.13: (a) SBS-induced index change and (b) the resulting group index at a pump power
of1W.
standard fiber when the pump power was large enough to provide a 30-dB gain. In the
other experiment [99], 15-ns Stokes pulses were delayed by 20 ns when they were amplified
by 40 dB or so in a 0.5-km-long fiber. These numbers agree with the theoretical
delay expected from Eq. (9.4.23). In both experiments, observed changes in the group
velocity were relatively small because the transit time (about 500 ns for a 1-km-long
fiber) changed by a small fraction. The use of shorter fibers with higher pump powers
should allow one to observe larger relative changes in the group velocity.
The slowing down or speedup of optical pulses in the vicinity of a laser-induced
resonance has attracted considerable attention as it can be used to make an optical
buffer [100]. However, most experiments make use of atomic vapors that are not suitable
for a practical device. The use of SBS in optical fibers has the potential of realizing
a compact device in which pulses can be delayed by an amount that is externally controllable.
9.4.4 Relaxation Oscillations
The dynamic response of SBS has many interesting features even for pump pulses that
are much wider than T B so that the acoustic dynamics plays little role. It turns out that
the Stokes power does not approach its steady-state value monotonically but exhibits
relaxation oscillations with a period 2T r , where T r = L/v g is the transit time for a fiber
of length L [101]. An example of such oscillations is seen in Figure 9.3 for 1-μs-wide
pump pulses. In the presence of external feedback, relaxation oscillations can turn into
stable oscillations [102], i.e., both the pump and Stokes waves can develop self-induced
intensity modulation.
Even though the group velocity v g is nearly the same for the pump and the Stokes
waves, their relative speed is 2v g because of their counterpropagating nature. Relaxation
oscillations occur as a result of this effective group-velocity mismatch. A simple
way to obtain the frequency and the decay time of relaxation oscillations is to perform a