2.6. NONLINEAR OPTICAL EFFECTS 61
Figure 2.17: Brillouin-gain spectra measured using a 1.525-μm pump for three fibers with dif-
ferent germania doping: (a) silica-core fiber; (b) depressed-cladding fiber; (c) dispersion-shifted
fiber. Vertical scale is arbitrary. (After Ref. [78];©c1986 IEE; reprinted with permission.)
shiftνB= 11 .25 GHz is in agreement with Eq. (2.6.2). The Brillouin shift is reduced
for fibers (b) and (c) of a higher germania concentration in the fiber core. The double-
peak structure for fiber (b) results from inhomogeneous distribution of germania within
the core. The gain bandwidth in Fig. 2.17 is larger than that expected for bulk silica
(∆νB≈17 MHz atλp= 1. 525 μm). A part of the increase is due to the guided nature
of acoustic modes in optical fibers. However, most of the increase in bandwidth can
be attributed to variations in the core diameter along the fiber length. Because such
variations are specific to each fiber, the SBS gain bandwidth is generally different for
different fibers and can exceed 100 MHz; typical values are∼50 MHz forλpnear
1.55μm.
The peak value of the Brillouin gain in Eq. (2.6.5) occurs forΩ=ΩBand depends
on various material parameters such as the density and the elasto-optic coefficient [73].
For silica fibersgB≈ 5 × 10 −^11 m/W. The threshold power level for SBS can be esti-
mated by solving Eqs. (2.6.3) and (2.6.4) and finding at what value ofIp,Isgrows from
noise to a significant level. The threshold powerPth=IpAeff, whereAeffis the effective
core area, satisfies the condition [74]
gBPthLeff/Aeff≈ 21 , (2.6.6)whereLeffis the effective interaction length defined as
Leff=[ 1 −exp(−αL)]/α, (2.6.7)andαrepresents fiber losses. For optical communication systemsLeffcan be approx-
imated by 1/αasαL 1 in practice. UsingAeff=πw^2 , wherewis the spot size,
Pthcan be as low as 1 mW depending on the values ofwandα[77]. Once the power
launched into an optical fiber exceeds the threshold level, most of the light is reflected
backward through SBS. Clearly, SBS limits the launched power to a few milliwatts
because of its low threshold.
The preceding estimate ofPthapplies to a narrowband CW beam as it neglects the
temporal and spectral characteristics of the incident light. In a lightwave system, the