Page 460 - High Power Laser Handbook

428 Fi b er L a s er s Intr oduction to Optical Fiber Lasers 429

1.E+09
Raman
1.E+08
SPM
P cr L eff /A eff (MW/m) 1.E+06
1.E+07

1.E+05

Brillouin
1.E+04

1.E+03
1.E−15 1.E−12 1.E−09 1.E−06
Pulse duration (s)
Figure 15.13 Nonlinear thresholds for stimulated Brillouin scattering (SBS),
stimulated Raman scattering (SRS), and self-phase modulation (SPM).

Stimulated Raman Scattering In stimulated Raman scattering (SRS), a
pump photon is annihilated, and a Stokes photon and an optical pho-
non are generated. This effect was discovered in 1928, well before the
advent of lasers, by using focused sunlight and an optical grating to
measure air-scattered light that is in the forward direction. Energy is
conserved as in SBS; however, momentum is not conserved. Due to
the amorphous nature of silica glass, a broad Stokes band of more
than 40 THz and peaked at ~13 THz from the pump is typically seen
in optical fibers. The peak Raman gain is around 1 × 10 m/W.
–13
Unlike SBS, the peak Raman gain g scales inversely with pump
R
wavelength λ .
p
The SRS threshold is determined by
A
P = 16 eff (15.18)
cr
gL
Reff
which is plotted in Fig. 15.13 for g = 1 × 10 m/W at a wavelength
–13
R
8
of 1 µm, where P *L /A = 1.6 × 10 MW/m. For example, for L = 1 m
eff
eff
cr
eff
and A = 1000 µm, we obtain P =160 kW; the critical power is inde-
eff
cr
pendent of pulse width.
Self-Phase Modulation Self-phase modulation (SPM) arises from the
nonlinear phase dependence on local intensity during pulse propaga-
tion. The time-dependent phase change leads to the generation of