Page 459 - High Power Laser Handbook

426 Fi b er L a s er s Intr oduction to Optical Fiber Lasers 427

1.0

0.8

0.6
L eff /L
0.4

0.2

0.0
0 10 20 30 40 50
Total amplifier gain (dB)
Figure 15.12 Effective amplifier length for a counterpumped fiber amplifier.

In a counterpumped fiber amplifier with length L where signal
gz
growth is more or less exponential as f(z) = e , the effective nonlinear
length can be estimated as
L eff = 1 − e − gL ≈ 4 343
.
(
L g G dB) (15.17)

which is plotted in Fig. 15.12. G(dB) is the total gain expressed in
decibels. The approximation applies when G > 10 dB. Because the
total gain can be as high as 40–50 dB, the effective nonlinear length
can be a small fraction of the total amplifier length.
Using the peak Brillouin gain g = 5 × 10 m/W and an acoustic
–11
B
spectral bandwidth ∆ν = 100 MHz for transform-limited gaussian
a
pulses with ∆ν ∆τ = 0.44, where ∆ν and ∆τ are the full-width, half-
s
s
maximum (FWHM) pulse spectral and temporal widths, respectively,
we obtain P *L /A = 1.85 × 10 /∆τ MW/m, where pulse width is
–3
eff
eff
cr
expressed in seconds. P *L /A as a function of pulse duration is
cr
eff
eff
plotted for SBS in Fig. 15.13. For example, for L = 1 m and A =
eff
eff
2
–6
1000 µm , P = 1.85 × 10 /∆τ W/m; the critical power is inversely
cr
proportional to the pulse width. For optical fibers with inhomoge-
neous transverse doping profile, which produces varying acoustic
properties across the core, the overall Brillouin gain seen by the
guided mode requires spectral and spatial integration over the core.
This has been shown to lead to SBS suppression compared with a
homogeneously doped fiber core, due to a reduction of overall peak
Brillouin gain as a result of the spectrally varying Brillouin gain peak
across the fiber core. 18,19