Toward high-power nonlinear fiber amplifier 3
Figure 1. The basic system setup of the NFA.
The emission spectrum of Yb-doped fiber (from 970 nm
to 1200 nm) can be divided into discrete spectral channels
with width of 1λ. The subscript k represents the kth channel
but p, s
1
and s
2
represent the pump and two signal waves
specially. The superscript ± corresponds to positive and
negative directions, respectively. N (z) is the Yb ions concen-
tration distribution along the fiber, for passive fiber N (z) =
0; N
2
(z) is the excited state population; P
si
represents the
signal power; P(z, λ
k
) is the power of laser λ
k
; σ
a
and σ
e
are
Yb absorption and emission cross sections, respectively
[41]
.
Γ is the overlapping factor between the pump (ASE signal)
and the fiber doped area. g
R
is the Raman gain coeffi-
cient; α is the loss coefficient. 2hv1v is the Raman noise
and the factor 2 corresponds to two polarization states. h
is the Planck constant; v is frequency; 1v is bandwidth
of the signal. For spontaneous Raman noise we assume
the bandwidth equals the gain bandwidth that is about
40 THz.
The boundary conditions can be described by the follow-
ing equations:
P
+
(0, λ
k,si
) = R
1
(λ
k,si
)P
−
(0, λ
k,si
) + P
+
0
(λ
k,si
), (6)
P
−
(L , λ
k,si
) = R
2
(λ
k,si
)P
+
(L , λ
k,si
) + P
−
0
(λ
k,si
), (7)
where R
1
and R
2
refer to the reflectivity in the left and
right side, respectively. Then this model can be numerically
calculated by the finite-difference method
[42]
.
3. Numerical analysis of nonlinear fiber amplifier
3.1. Power scaling potential of NFA
SRS is a main restriction for the power scaling of wide band-
width YDFA. There is still not a straightforward technique
that can suppress SRS effectively without introducing any
drawback in YDFA. In this section we would like to show
the advantage of the NFA in the potential of suppressing
SRS by using a numerical example. The parameters used
in the calculation are shown in Table 1. It is a co-pumping
scheme with power of 8000 W. The gain fiber is 20/400 µm
(core/inner diameter) double cladding YDF.
Firstly, we calculate a traditional case of only the 1070 nm
laser in the seed. The seed power is 200 W. The power
distribution along the fiber is shown in Figure 2. It can be
found in this case that the signal power can reach more
Figure 2. The power distribution of pump, signal, and Raman waves in
forward and backward propagating directions. It can be found that Raman
Stokes wave (1120 nm) has arisen in both directions, and the power is
642 W and 387 W for forward and backward directions, respectively.
Table 1. The parameters of the calculated fiber amplifier.
Parameter Value Unit Parameter Value Unit
λ
p
976 nm λ
s1
1070 nm
λ
s2
1120 nm λ
s3
1180 nm
d
core
20 µm d
inner-clad
400 µm
P
p
8000 W τ 0.84 ms
P
+
0
(s1) 200 W Γ
k
0.8 —
L 17 m α 2 × 10
−3
m
−1
1v
1
0.3 THz 1v
2
0.3 THz
1v
3
40 THz N
0
4.33 × 10
25
m
−3
g
R
0.5 × 10
−13
m/W g
R1
0.48 × 10
−13
m/W
than 6000 W if other nonlinear effects or thermal effects are
ignored. However, such a system is unpractical for Raman
Stokes wave (1120 nm) that can be found in both directions.
Especially in the backward direction, the power of 1120 nm
laser in the fiber core is about 387 W, which is a big hidden
danger for the high-power laser system. From this point of
view, SRS is a limitation of the traditional Yb-doped fiber
amplifier system. For comparison, we would like to give
an example with similar condition for the NFA. The only
change is that a 10 W 1120 nm laser is added in the seed. The
1120 nm laser corresponds to the first-order Stokes wave of
1070 nm laser. The other parameters of the amplifier are the
same as that shown in Table 1.
Figure 3 is the calculated results of the NFA. In this am-
plifier, the 1070 nm laser is firstly amplified by the ytterbium
gain, and as the 1120 nm laser propagates in the fiber core,
it reaches the Raman threshold and begins to dominate the
following amplification
[34]
. Finally, the power of 1070 nm
laser is all transferred to the Stokes wave (1120 nm) at the
output end. It can be found in Figure 3(b) that the sum of the
laser power of 1070 nm and 1180 nm is less than 5 W. At the
backward output end, seen in Figure 3(c), the total output