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大功率连续波光纤放大器中拉曼噪声增强的受激拉曼散射
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考虑到种子拉曼噪声,研究了大功率连续波(CW)光纤放大器中的受激拉曼散射(SRS)。 结果表明,播种的拉曼噪声作为种子光的一部分,即使在强度比种子信号光弱得多的情况下,也应增强大功率连续波光纤放大器中的SRS。 给出了双向抽运光纤放大器拉曼阈值的解析公式,并考虑了种子拉曼噪声,其预测结果与数值结果吻合良好。 还表明,共泵浦放大器的拉曼阈值最低,当有源光纤的泵浦吸收大于8.7时,双向泵浦比双向泵浦更有利于SRS抑制。这些结果将为大功率连续波光纤放大器的设计提供指导。
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Optik
144
(2017)
163–171
Contents
lists
available
at
ScienceDirect
Optik
j
ourna
l
ho
me
pa
ge:
www.elsevier.de/ijleo
Original
research
article
Raman-noise
enhanced
stimulated
Raman
scattering
in
high-power
continuous-wave
fiber
amplifier
Hanyuan
Ying
a,b,c
,
Jianqiu
Cao
a,b,c,∗
,
Yu
Yu
a,b,c
,
Meng
Wang
a,b,c
,
Zefeng
Wang
a
,b,c
,
Jinbao
Chen
a
,b,c,∗
a
College
of
Optoelectronic
Science
and
Engineering,
National
University
of
Defense
Technology,
Changsha,
Hunan,
410073,
China
b
Hunan
Provincial
Key
Laboratory
of
High
Energy
Laser
Technology,
Changsha,
Hunan,
410073,
China
c
Hunan
Provincial
Collaborative
Innovation
Center
of
High
Power
Fiber
Laser,
Changsha,
Hunan,
410073,
China
a
r
t
i
c
l
e
i
n
f
o
Article
history:
Received
19
March
2017
Received
in
revised
form
23
June
2017
Accepted
23
June
2017
Keywords:
Fiber
amplifiers
Stimulated
Raman
scattering
Pumping
a
b
s
t
r
a
c
t
The
stimulated
Raman
scattering
(SRS)
in
high-power
continuous-wave
(CW)
fiber
ampli-
fier
is
investigated
with
the
seeded
Raman
noise
taken
into
account.
It
is
revealed
that
the
seeded
Raman
noise,
as
a
portion
of
seed
light,
should
enhance
SRS
in
high-power
CW
fiber
amplifier
even
when
it
is
much
weaker
than
the
seeded
signal
light.
The
analytic
formula
for
predicting
the
Raman
threshold
of
bi-directional
pumping
fiber
amplifier
is
given
with
the
seeded
Raman
noise
taken
into
account,
and
the
predictions
agree
well
with
the
numer-
ical
results.
It
is
also
revealed
that
the
co-pumping
amplifier
suffer
from
the
lowest
Raman
threshold,
and
the
counter-pumping
one
is
more
beneficial
to
the
SRS
suppression
than
the
bi-directional
pumping
one
when
the
pump
absorption
of
active
fiber
is
larger
than
8.7
dB.
These
results
will
provide
guidance
for
the
design
of
high-power
CW
fiber
amplifier.
©
2017
Elsevier
GmbH.
All
rights
reserved.
1.
Introduction
High-power
fiber
lasers
have
attracted
much
attention
because
of
their
advantages
such
as
compactness,
reliability,
high
efficiency,
good
beam
quality,
etc.
Particularly
with
the
rapidly
power
up-scaling
in
recent
years,
they
can
meet
various
requirements
of
academic
and
industrial
applications
[1–3].
In
2009,
a
10-kW
single-mode
fiber
laser
was
demonstrated
with
the
master
oscillator
power
amplification
(MOPA)
configuration
[4].
Nowadays,
the
MOPA
configuration
consisting
of
a
seed
fiber
oscillator
and
a
fiber
amplifier
is
most-widely
used
in
high-power
fiber
laser
system,
where
the
fiber
amplifier
plays
the
most
important
role
for
the
power
scalability
of
MOPA
fiber
laser
system.
One
fundamental
issue
limiting
the
power
scalability
of
MOPA
fiber
laser
system
is
the
stimulated
Raman
scattering
(SRS)
in
the
high-power
fiber
amplifier
[2,5,6].
It
has
been
revealed
that
when
the
signal
power
is
beyond
some
threshold
(generally
named
as
the
Raman
threshold),
SRS
should
be
present
and
preventing
the
further
increment
of
signal
power.
A
number
of
studies
were
carried
out
with
the
purpose
of
estimating
the
threshold.
At
present,
two
typical
formulas
given
by
J.
R.
Smith
[7]
and
C.
Jauregui
et
al.
[8]
are
most
widely
used,
which
are
induced
with
the
case
of
passive
fiber
and
show
that
the
threshold
is
mainly
determined
by
the
mode
area,
effective
fiber
length
and
Raman
gain.
The
Raman
threshold
of
fiber
amplifier
(also
defined
as
the
pump
power
threshold
corresponding
to
the
presence
of
SRS
effect
[9])
was
also
investigated
∗
Corresponding
authors
at:
College
of
Optoelectronic
Science
and
Engineering,
National
University
of
Defense
Technology,
Changsha,
Hunan,
410073,
China.
E-mail
addresses:
jq
cao@126.com
(J.
Cao),
kdchenjinbao@aliyun.com
(J.
Chen).
http://dx.doi.org/10.1016/j.ijleo.2017.06.098
0030-4026/©
2017
Elsevier
GmbH.
All
rights
reserved.
164
H.
Ying
et
al.
/
Optik
144
(2017)
163–171
in
Refs.
[5,9]
with
the
gain
of
active
fiber
taken
into
account.
All
these
studies
were
carried
out
based
on
an
assumption
that
the
SRS
light
be
induced
by
the
spontaneous
Raman
noise
with
a
constant
small
power
[7–9].
However,
such
an
assumption
may
not
be
so
coincident
to
the
practical
case
of
fiber
amplifier
in
the
high-power
MOPA
fiber
laser
system.
The
reason
is
that
seeded
Raman
noise,
as
a
portion
of
the
seed
light
output
from
the
seed
fiber
oscillator
of
MOPA
fiber
laser
system,
was
not
taken
into
account
in
these
studies.
It
should
be
noted
that
because
of
the
high-power
(hundreds-of-
to
kilo-Watt)
of
seed
fiber
oscillator,
the
seeded
Raman
noise
may
be
mainly
induced
by
SRS
rather
than
uniquely
by
the
spontaneous
Raman
scattering
in
the
seed
fiber
oscillator.
However,
because
it
is
generally
much
smaller
than
the
seeded
signal
light,
we
still
call
it
as
the
“seeded
Raman
noise”
here.
Such
a
seeded
Raman
noise
may
be
too
weak
to
be
observed
with
the
spectrum
measurement,
especially
when
the
signal-to-noise
ratio
of
the
spectrum
measurement
is
not
high
enough
(e.g.,
around
30
dB
[10,11,13–15]),
but
may
be
much
larger
than
the
initial
power
of
Raman
noise
used
in
these
studies
of
Refs.
[7–9].
Taking
a
200-W
seed
fiber
oscillator
for
example,
the
seeded
Raman
noise
will
be
0.2
mW
with
a
60-dB
Raman
suppression
of
seed
fiber
oscillator,
which
can
be
much
larger
than
the
value
(estimated
to
be
around
10
−7
W
with
Eq.
(15)
of
Ref.
[9])
used
in
Refs.
[7–9].
Then,
such
a
large
seeded
Raman
noise
will
make
the
Raman
threshold
predictions
of
formulas
given
in
Refs.
[7–9]
not
effective.
Actually,
some
recent
experimental
studies
also
implied
that
the
effect
of
seeded
Raman
noise
should
not
be
neglected.
For
example,
the
3-kW
Raman
fiber
laser
reported
in
Ref.
[10]
demonstrated
that
the
seeded
Raman
noise
can
be
strong
enough
as
the
Raman
seed
of
the
multi-kW
Raman
fiber
amplifier,
which
suggests
that
the
effect
of
seeded
Raman
noise
on
SRS
in
the
fiber
amplifier
should
be
considerate.
Besides,
the
experimental
study
in
Ref.
[11]
also
revealed
that
the
Raman
threshold
of
fiber
amplifier
should
be
varied
with
the
seed
light
power.
It
should
be
noted
that
the
seeded
Raman
noise
output
from
the
seed
fiber
oscillator
may
increase
monotonously
with
the
seed
light
power
[10,12].
Then,
besides
the
seeded
signal
light,
the
seeded
Raman
power
(i.e.,
the
power
of
seeded
Raman
noise)
may
still
be
a
factor
affecting
the
Raman
threshold
of
fiber
amplifier.
Now,
how
seriously
will
the
seeded
Raman
power
affect
the
SRS
effect
in
the
fiber
amplifier?
What
is
the
relationship
between
the
seeded
Raman
power
and
the
Raman
threshold
of
the
fiber
amplifier?
These
questions
are
of
great
importance
for
designing
multi-kW
fiber
amplifier,
but
not
so
clearly
currently
and
need
to
be
further
investigated.
In
this
paper,
the
SRS
effect
in
the
multi-kW
CW
fiber
amplifier
is
investigated
with
the
seeded
Raman
noise
taken
into
account.
In
Section
2,
the
numerical
research
will
be
carried
out,
where
the
numerical
model
will
be
introduced
and
preliminary
numerical
results
will
be
given.
In
Section
3,
the
analytic
formula
of
Raman
threshold
will
be
deduced,
and
it
will
be
validated
by
comparing
the
theoretical
results
with
the
numerical
ones.
In
Section
4,
the
conclusions
will
be
summarized
and
pertinent
discussions
will
be
given.
2.
Numerical
model
The
numerical
model
used
here
is
the
rate-equation
model
taking
SRS
into
account,
i.e.,
N
2
(
z
)
N
=
P
ap
P
+
p
(
z
)
+
P
−
p
(
z
)
p
+
s
as
P
s
(
z
)
s
+
r
ar
P
r
(
z
)
r
P
ap
+
ep
P
+
p
(
z
)
+
P
−
p
(
z
)
p
+
s
(
as
+
es
)
P
s
(
z
)
s
+
r
(
ar
+
er
)
P
r
(
z
)
r
+
hcA
c
(1)
±
dP
±
p
(
z
)
dz
=
−
p
ap
N
−
ap
+
ep
N
2
(
z
)
P
±
p
(
z
)
−
˛
p
P
±
p
(
z
)
(2)
dP
s
(
z
)
dz
=
−
s
[
as
N
−
(
es
+
as
)
N
2
(
z
)]
P
s
(
z
)
−
˛
s
P
s
(
z
)
−
r
s
g
r
A
eff
P
r
(
z
)
P
s
(
z
)
+
2
s
es
N
2
(
z
)
hc
2
3
s
s
(3)
dP
r
(
z
)
dz
=
−
r
[
ar
N
−
(
er
+
ar
)
N
2
(
z
)]
P
r
(
z
)
−
˛
r
P
r
(
z
)
+
g
r
A
eff
P
s
(
z
)
P
r
(
z
)
+
2
r
er
N
2
(
z
)
hc
2
3
r
r
(4)
where
the
subscript
p,
s,
and
r
represent
the
parameters
of
pump
light,
signal
light
and
first-order
Raman
Stokes
light
(called
as
the
Raman
light
in
the
following
part),
respectively.
The
quantity
z
represents
the
coordinate
along
the
fiber
axial.
The
quantity
N
is
the
dopant
concentration
(per
unit
volume),
N
2
is
the
population
destiny
of
the
upper
level.
The
wavelengths
of
signal
light,
pump
light
and
Raman
light
are
marked
as
s
,
p
,
and
r
,
respectively.
p
is
the
overlap
factor
between
the
pump
light
and
the
doped
area,
while
s
is
the
overlap
factor
between
the
signal
light
and
the
doped
area.
The
plus
and
minus
superscripts
respectively
represent
propagation
along
the
positive
or
negative
direction
of
z
coordinate,
and
thus,
P
p
+
represents
the
co-pumping
power
and
P
p
−
represents
the
conter-pumping
power.
A
eff
represents
the
effective
mode
area
and
is
roughly
equal
to
the
cross-section
area
of
the
core,
and
the
positive
coefficient
˛
p
,
˛
s
and
˛
r
characterize
the
loss
of
active
fiber
at
the
wavelengths
of
pump
light,
signal
light
and
Raman
light,
respectively.
The
coefficients
ep
,
es
,
er
and
ap
,
as
,
ar
represent
the
emission
and
absorption
cross
sections
of
active
fiber
at
the
pump,
signal,
and
Raman
wavelength,
respectively.
h
is
Plank’s
constant,
c
is
the
velocity
of
light
in
vacuum,
is
the
spontaneous
lifetime,
g
r
is
the
gain
coefficient,
A
c
is
the
active
core
area
and
n
is
the
refractive
index
of
the
core.
r
and
s
represent
the
bandwidth
of
Raman
and
signal
light,
respectively.
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