Theoretical study of stimulated Raman scattering in long
tapered fiber amplifier
Chen Shi (史 尘)
1
, Xiaolin Wang (王小林)
1,2,3,
*, Pu Zhou (周 朴)
1,2,3
,
and Xiaojun Xu (许晓军)
1,2,3
1
College of Optoelectronic Science and Engineering, National University of Defense Technology,
Changsha 410073, China
2
Hunan Provincial Key Laboratory of High Energy Laser Technology, Changsha 410073, China
3
Hunan Provincial Collaborative Innovation Center of High Power Fiber Laser, Changsha 410073, China
*Corresponding author: chinawxllin@163.com
Received June 27, 2017; accepted September 22, 2017; posted online October 16, 2017
A model that is based on the propagation equation and coupled mode theory is introduced in order to describe
stimulated Raman scattering (SRS) effects in long tapered fiber amplifiers. Based on the presented model, fiber
amplifiers with uniform and long tapered fibers are theoretically and numerically simulated. It can be drawn
from the results of our simulations that the long tapered fiber has the advantage in suppressing SRS when ap-
plied in fiber laser amplifiers. Our results can provide guidance in the designing of system configuration in long
tapered-fiber-based fiber laser systems.
OCIS codes: 060.2320, 060.4370, 290.5910.
doi: 10.3788/COL201715.110605.
For the advantage of high slope efficiency, good beam
quality, superior thermal management property, and com-
pactness, fiber lasers are widely used in the field of laser
marking, material processing, medical, communication,
and many other industrial applications
[1–3]
. Compared with
the traditional fiber laser oscillator, the master oscillator
power amplifier (MOPA) system, which can boost the
progress of fiber laser power scaling, offers an effective
way to acquire a high power fiber laser source with excellent
beam quality by employing a cascaded structure
[4–6]
.In
comparison with a traditional uniform large-mode-area
(LMA) active fiber, the long tapered double clad fiber
(T-DCF) shows numerous unique advantages when being
employed as gain medium of an optical amplifier, such as
LMA, higher pump absorption, suppression to nonlinear
effects, maintaining good beam quality, and so on
[7]
. Some
experimental and theoretical studies on long T-DCF-based
fiber lasers have already been presented by earlier research-
ers, including the continuous-wave (CW) regime
[8–11]
,pulsed
regime
[12,13]
, mode propagating properties
[14,15]
, and so on.
However, among these previous researches, there is hardly
a systematic analysis for nonlinearities in long T-DCF-
based fiber laser systems. The stimulated Raman scattering
(SRS) effect is one of the dominant nonlinear effects in high
power fiber lasers, which usually sets the upper limit of the
power scalability of the whole system
[16]
. In order to fully
understand the performance of long T-DCF-based fiber la-
sers, the analysis of the SRS effect in long T-DCF is needed.
Consider the fiber amplifier, which launches under the
CW regime. By ignoring self-phase modulation (SPM),
cross-phase modulation (XPM), four-wave mixing
(FWM), and stimulated Brillioun scattering (SBS), the
propagation equation of uniform fiber amplifier can be
written as
∂b
λ
p
j
∂z
− iβ
λ
q
j
b
λ
p
j
¼
b
λ
p
j
2
X
p≠q;j;k
b
λ
q
k
A
ðj;k;p;qÞ
eff
g
R
ðω
p
− ω
q
Þ; (1)
where b represents the complex amplitude of the corre-
sponding eigenmode and wavelength. The subscript of
b ðj; kÞ stands for different boundary modes, while the
superscript (p, q) stands for different signal wavelengths.
β is the propagating constant of the corresponding b. A
eff
is the effective area between different modes in different
wavelengths, and it is defined as follows:
A
ðj;k;p;qÞ
eff
¼
hjψ
λ
p
j
j
2
i·hjψ
λ
q
k
j
2
i
hjψ
λ
p
j
j
2
·jψ
λ
q
k
j
2
i
; (2)
where ψ is the normalized modal distribution of the cor-
responding boundary mode. The symbol h·i means inte-
grating over the infinite transverse cross section. g
R
is the
Raman gain, which can be calculated using
[17]
g
R
ðΔωÞ¼
4
3
γf
R
Im½
~
h
R
ðΔωÞ; (3)
where γ is the nonlinear parameter. f
R
¼ 0.18 is the frac-
tional Raman contribution in silicon-based fibers.
~
h
R
is
the frequency domain Raman response function, and it
can be expressed as
~
h
R
ðΔωÞ¼
1
2i
τ
2
1
þ τ
2
2
τ
1
τ
2
2
1
ð1∕τ
2
Þ − i½Δω þð1∕τ
1
Þ
−
1
ð1∕τ
2
Þ − i½Δω − ð1∕τ
1
Þ
; (4)
COL 15(11), 110605(2017) CHINESE OPTICS LETTERS November 10, 2017
1671-7694/2017/110605(5) 110605-1 © 2017 Chinese Optics Letters