Page 458 - High Power Laser Handbook

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

15.2.3 Power Scaling of Fiber Lasers

Nonlinear Limits

Stimulated Brillouin Scattering In stimulated Brillouin scattering
(SBS), a pump photon is annihilated to produce a Stokes photon and
17
an acoustic phonon through the electrostriction process. This pro-
cess is further stimulated by the presence of the generated Stokes
photons and acoustic phonons in the fiber. In an optical fiber, momen-
tum conservation requires that the scattered Stokes photons can only
propagate in the opposite direction to the pump photons. Energy
conservation and momentum conservation requires
ν ν = − ν , k = − k k (15.13)
a p s a p s
where ν , ν , and ν are frequencies for pump, Stokes, and acoustic
a
s
p
waves, respectively, and k , k , and k are wave vectors for pump,
p
s
a
Stokes, and acoustic waves, respectively. The acoustic frequency
ν is around 11 GHz in silica fibers at 1.55 µm, and the acoustic
a
velocity in silica is v = 5.944 km/s. The phonon lifetime is less
a
than 10 ns, giving a phonon travel distance of less than 60 µm. The
SBS threshold is a strong function of the spectral bandwidth of
optical pulses:
A ∆ν
P = 21 eff s (15.14)
cr
gL ∆ν a
Beff
where g is peak Brillouin gain, A is the effective mode area, L is
eff
eff
B
the effective nonlinear length, ∆ν is the acoustic spectral band-
a
width, and ∆ν is the signal spectral bandwidth. The peak Brillouin
s
–11
gain is typically 3–5 × 10 m/W in a silica fiber and is almost inde-
pendent of wavelength. The acoustic bandwidth ∆ν is typically
a
around 10–1000 MHz. The effective mode area A for a mode with
eff
a spatial electric field distribution of E(x, y) is defined as
(∫∫ ∞ −∞ Ex y) 2 dxdy ) 2
(,
A eff = 4 (15.15)
(,
∫∫ ∞ −∞ Ex y) dxdy
The effective length for an amplifier with a maximum output power
P and power distribution P(z) = P f (z) is
0
0
L
=
()
L eff ∫ f zdz (15.16)
0