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ISTANBUL UNIVERSITY –
JOURNAL OF ELECTRICAL & ELECTRONICS ENGINEERING
YEAR
VOLUME
NUMBER
: 2004
: 4
: 2
(1111-1122)
Received Date : 09.09.2001
Accepted Date: 15.06.2004
GAIN AND NOISE FIGURE PERFORMANCE OF
ERBIUM DOPED FIBER AMPLIFIERS (EDFA)
A.Cem ÇOKRAK 1 Ahmet ALTUNCU
2
1,2 Dumlupınar Üniversitesi, Mühendislik Fakültesi, Elektrik-Elektronik Mühendisliği Bölümü,
Tavşanlı Yolu 12.km 43100 KÜTAHYA
E-mail: altuncu@dumlupinar.edu.tr
ABSTRACT
Fiber loss is a fundamental limitation in realising long haul point-to-point fiber optical
communication links and optical networks. One of the advanced technologies achieved in recent years
is the advent of erbium doped fiber amplifiers (EDFAs) that has enabled the optical signals in an
optical fiber to be amplified directly in high bit rate systems beyond Terabits. In this study, an EDFA
simulation program has been written in Matlab to characterize Gain, Noise Figure and ASE power
variations of a forward pumped EDFA operating in C band (1525-1565 nm) as functions of Er3+ fiber
length, injected pump power, signal input power and Er3+ doping density. The program solves the rate
and propagation equations numerically and shows the results graphically. Thus, Gain and Noise
Figure performance of an EDFA given with its physical parameters can be graphically obtained or
the required physical parameters of an EDFA with desired operating performance can easily be
optimised.
Keywords: : Optical Amplifiers, EDFA, Erbium Doped Fiber, Gain, Noise Figure..
1. INTRODUCTION
One of the most important factors limiting the
transmission distance in fiber optical
communication systems is the optical power loss
caused by scattering and absorption mechanisms
in optical fiber [1]. Electrical repeaters, which
require optical-electrical signal conversion, have
previously been used to compensate the power
losses increasing with distance. The use of such
repeaters in optical communication systems have
made the systems more complex and increased
their installation costs. The optical amplifiers,
that were developed in 1980s and came partially
into the use commercially in 1990s, enable the
optical signals to be directly amplified optically.
The most significant types of optical amplifiers
are semiconductor laser amplifiers, Raman and
Brillouin amplifiers, and rare-earth doped fiber
amplifiers.
The fiber amplifiers operating at specific
wavelengths from visible to infrared light region
(up to 3 mm) can be made using different rare
earth ions such as Erbium (Er
3+), Holmium
(Ho3+), Neodmium (Nd3+), Prasedmium (Pr3+),
Samarium (Sa3+), Thulium (Tm3+) and Ytterbium
(Yb3+). However, the most interesting element
listed above is erbium. Because, Erbium Doped
Fiber Amplifiers (EDFA) made by doping the
silica fiber with erbium ions can operate in a
broad range within the 1550 nm window at
which the attenuation of silica fiber is minimum
Gain And Noise Figure Performance Of Erbium Doped Fiber Amplifiers (EDFA)
A.Cem ÇOKRAK, Ahmet ALTUNCU
1112
and therefore it is ideal for the optical fiber
communication systems operating at this
wavelength range. According to the research
performed in recent years, it is known that the
pumping of erbium doped fiber at 980 nm or
1480 nm is the most efficient way [3]. High gain
(30∼50 dB), large bandwidth (≥ 90 nm), high
output power (10∼20 dBm) and low noise figure
(NF=3∼5 dB) can be obtained using an erbium
doped fiber amplifier optimised for 1.55 µm
range. The amplification that could previously be
made within C band (1525-1565 nm) has now
extended to L band (1570-1620 nm) by
codoping the active fiber with Erbium (Er3+), and
Ytterbium (Yb3+). On the other hand, Thulium
(Tm3+) doped Raman fiber amplifiers have
enabled to operate within the S band (1480-1520
nm).
2.THE STRUCTURE OF EDFA AND
ITS PUMPING REQUIREMENTS
The structure of a typical EDFA is shown in
figure 1. EDFAs consist of optical couplers to
combine pump and signal lights injected to
active fiber, unidirectional optical isolators,
pumping lasers, polarisation couplers to combine
pump sources and optical bandpass filters to
reduce out of band noise. The gain characteristics
of EDFAs depend mainly on their pumping
schemes. EDFAs can be pumped at 980 nm or
1480 nm, and with different configurations:
backward, forward or bi-directional. The
pumping at 980 nm provides lower noise figure
than pumping at 1480 nm. Therefore pre-
amplifier version of EDFA chooses 980 nm for
pumping wavelength. On the other hand, 1480
nm pumping has higher quantum efficiency and
so provides higher output power at a lower cost
and therefore it is preferred for booster amplifier
operations. In forward pumping, both of the
signal and pump lights propagate in the same
direction through the fiber whereas in the
backward pumping they propagate in the
opposite direction.
The forward pumping direction provides the
lowest noise figure. In fact, the noise is sensitive
to the gain and the gain is the highest when the
input power is the lowest. Backward pumping
provides the highest saturated output power [2].
Bi-directional pumping scheme has a higher
performance than the other two by combining the
lowest noise figure and the highest output power
advantageous although it requires two pump
lasers. In addition, in this scheme the small
signal gain is uniformly distributed along the
whole active fiber.
Figure 1. A bidirectionally pumped EDFA structure
Gain And Noise Figure Performance Of Erbium Doped Fiber Amplifiers (EDFA)
A.Cem ÇOKRAK, Ahmet ALTUNCU
1113
3. EDFA THEORY
In this section, the rate and propagation
equations characterizing an EDFA operating in C
band and pumped at 1480 nm are given. The
simulation of EDFA requires the simultaneous
calculation of the rate equations, which define
the transitions between energy levels, and the
propagation equations, which characterize signal,
pump and ASE power variations along the active
fiber.
The performance of absorbing injected pump
light and then emitting it as the signal light by
stimulation are known as absorption cross
section and emission cross section or in a
different way as loss and gain coefficients,
respectively. A typical absorption and emission
spectra of an erbium doped silica fiber is shown
in figure 2. In erbium, the absorption is higher at
1480 nm whereas the emission is higher at 1535
nm. The signal and pump powers along the fiber
vary due to absorption, spontaneous emission
and stimulated emission processes.
Figure 2. A typical absorption and emission spectra of erbium doped fiber (EDF) [2]
3.1 Rate Equations
In pumping at 980 nm, it is required to form a system model with three energy levels. When the
excited state absorption (ESA) is considered, a forth level should also be included. If the pumping is
performed at 1480 nm, a simple system model with two energy levels can be used. In figure 3, erbium
ion transitions of an EDFA pumped at 1480 nm was given. From figure 3, time dependent population
rates in level 2 and 1 can be given as:
221212111212
2n)AWR(n)WR(
dt
dn ++−++= d
t
dn
d
t
dn 21 −= (1)
Figure 3. Erbium ion levels
R
12
R
21 W
21 W12
A21
4I13/2
Level 2:
n2 density
4I15/2
Level 1:
n1 density
R12 :Pump absorption rate
W12 :Signal absorption rate
R21 :Pump emission rate
W21 :Signal emission rate
A21 :Spontaneous emission rate
Gain And Noise Figure Performance Of Erbium Doped Fiber Amplifiers (EDFA)
A.Cem ÇOKRAK, Ahmet ALTUNCU
1114
Here, nt (ion/m3) is called total ionic population and is equal to the total of populations in two energy
levels ( 21 nnnt+= ). In steady state, ( 0dt/dn2
=
), the ratio of level 1 and level 2 population to the
total population can be written as:
)AWWR(R
)AW(R
n
n
2112211221
212121
t
1
++++
++
= )AWWR(R
)W(R
n
n
2112211221
1212
t
2
++++
+
=
(2)
Expressing the absorption and emission rates in terms of pump and signal powers makes the
population equations more meaningful.
p
p
p
ijp
ij h
)r(P
R
ν
Ψσ
= ; i, j=1,2 (pump)
s
s
s
ijs
ij h
)r(P
W
ν
Ψσ
= ; i, j=1,2 (signal)
(3)
Here, )(
s,p
ij
νσ
is absorption and emission cross-section for pump and signal (absorption for ij = 12,
emission for ij = 21), h
ν
p,s is photon energy and
Ψ
p,s(r,
θ
) is normalized line shape function. The
threshold power at pumping wavelength and saturation power at signal wavelength is given by:
p
12
21
2
pp
qu
Ah
P
σ
πων
= s
12
21
2
ss
sat
Ah
P
σ
πων
= (4)
The pumping of erbium doped fiber causes to amplify not only signal but also spontaneous emission.
Spontaneous emission (SE) is a noncoherent, randomly polarized optical wave having a wide
bandwidth and is propagated in both directions in the fiber. The spontaneous emission amplified
simultaneously with the signal consists of noise produced in the amplifier and is therefore called
Amplified Spontaneous Emission (ASE). ASE simply causes decrease in amplifier gain and increase
in noise figure. Therefore, forward and backward ASE powers should also be included into the rate
equations. Thus, the rate equations can be rewritten as :
t
sat
saas
s
21
s
12
qu
pp
p
12
p
21
sat
saas
qu
pp
p
12
p
21
1n
P
)PPP(
1
P
P
11
P
)PPP(
P
P
1
n
++
++
++
++
+
+
=−+
−+
ψ
σ
σ
ψ
σ
σ
ψ
ψ
σ
σ
1t2 nnn
−
=
(5)
3.2 Propagation Equations :
The amplification of optical signals in EDFA is also defined with propagation equations which is
directly related to Er doped fiber characteristics. The propagation equations, which give the signal,
pump and ASE variations along the fiber, depend also on the pumping scheme. For forward pumping,
the pump, signal and bi-directional propagating ASE noise power can be defined as [3]:
[]
±±
=
+
−
∫−+= pppp
a
0r
1
p
122
p
21
pPrdr)r(P.nn2
dz
dP
αΨσσπ
(6)
Gain And Noise Figure Performance Of Erbium Doped Fiber Amplifiers (EDFA)
A.Cem ÇOKRAK, Ahmet ALTUNCU
1115
[]
++
=
+
−
∫−+= ssss
a
0r
1
s
122
s
21
sPrdr)r(P.nn2
dz
dP
αΨσσπ
(7)
()
[]
±
=
±±
±
∫−+±= as
a
0r
sa1
s
12osa2
s
21
aPrdr )r(PnP2Pn2
dz
dP
αΨσΨσπ
∓ (8)
Here,
α
p and
α
s are the fiber loss for the pump and signal, respectively. In short fibers, these losses are
in negligible. However, they should be taken into account for long fibers specifically distributed
erbium doped fibers (DEDF) [4]. The propagation equations given (6-8) are the non-linear differential
equations and their solution can only be obtained using numerical techniques. In (6-8), 2π values is
a result of integration by θ. The integration in (6-8) characterizes the light intensity variations in
optical fiber with coordinate r. Rather than performing integration for radius r, the pump and signal
overlap ratio with fiber core can be used. Thus, equations (7-9) can be given using the overlap ratio
(Γ) as [5] :
++
+
−−−= pp2
p
211
p
12pp
pP)nn(P
dz
)t,z(dP
ασσΓ
(9)
ss1
s
122
s
21ss
sP)nn(P
dz
)t,z(dP
ασσΓ
−−=
(10)
±±
±
±−±= as0s2
s
211
s
122
s
21sa
aPPn2)nn(P
dz
)t,z(dP
αΓσσσΓ
∓
(11)
3.3 Gain and Noise Figure
Gain of an erbium-doped fiber with a length of L is the ratio of the signal power at the fiber output to
the signal power injected at the fiber input as:
)0(P
)L(P
G
s
s
= (12)
ASE noise generated during amplification process is added to the signal leading to decrease in signal
to noise ratio (SNR) at the amplifier output. SNR reduction ratio from input to output of the amplifier
is defined as Noise Figure (NF), which is also used for electronic amplifiers:
out
in
)SNR(
)SNR(
NF = (13)
Noise Figure can also be expressed in terms of gain and spontaneous emission factor (nsp) (or
population inversion factor) [3]:
spsp n2
G
)1G(
n2NF ≈
−
= (14.a)
12
2
nn
n
nsp −
= (14.b)
The power spectral density of spontaneous emission induced noise )(
ν
sp
S is a function of
frequency and follows the emission spectrum of Er3+ ions :
ν
ν
hn)1G()(S spsp −=
ν∆
ν
+
=a
sp
P
)(S (15)
Gain And Noise Figure Performance Of Erbium Doped Fiber Amplifiers (EDFA)
A.Cem ÇOKRAK, Ahmet ALTUNCU
1116
Using equation (15), EDFA noise figure can be expressed in terms of forward propagating ASE power
( +
a
P ) [5] :
ν∆ν
Gh
P2
NF a
+
= (16)
Here,
ν
∆ is the bandwidth of the optical bandpass filter and
ν
his the photon energy. As it can be
seen from (16), EDFA noise figure depends directly on forward ASE power and gain. Noise Figure
increases with increasing ASE power, on the other hand, decreases with increasing gain.
4. EDFA SIMULATION PROGRAM
In this study, the rate and propagation equations characterizing a forward pumped C band EDFA were
numerically solved in Matlab environment and the results were graphically simulated. After entering
the required parameters for a desired amplifier in main menu and sub menus of the program, gain,
noise figure and ASE power variations can be obtained as a function of four fundamental fiber
parameters namely : fiber length, pump power, signal input power and erbium doping density. Thus,
gain-NF performance for typical parameters of a given EDFA can be simulated or the required fiber
parameters and signal/pump power values can be optimized for a desired EDFA gain-NF
performance. The main menu and some of the submenus of the simulation program are shown in
figure 4.
Figure 4. The main and sub menus of the simulation program.
Gain And Noise Figure Performance Of Erbium Doped Fiber Amplifiers (EDFA)
A.Cem ÇOKRAK, Ahmet ALTUNCU
1117
5. TYPICAL EDFA CHARACTERISTICS OBTAINED WITH SIMULATION
Table 1 shows the typical EDFA parameters used in the simulation program.
Table 1. The typical EDFA parameters used in the simulation program.
Parameter Sembol Value Unit
Fiber radius a 2 µm
Pump-fiber core overlap ratio Γp 0.4 -
Signal-fiber core overlap ratio Γs 0.4 -
Power for effective bandwidth P0 1 µW
Pump absorption cross section p
12
σ
0.75 10-25 m
2
Signal absorption cross section s
12
σ
2.40 10-25 m
2
Pump emission cross section p
21
σ
0.19 10-25 m
2
Signal emission cross section s
21
σ
3.80 10-25 m
2
Pump wavelength λp 1480 nm
Signal wavelength λs 1550 nm
Cut-off wavelength λc 1400 nm
Background loss at pump wavelength αp 0.25 dB/km
Background loss at signal wavelength αs 0.25 dB/km
5.1 Pump power variation
The attenuation of different pump powers applied to the input of erbium doped fiber is given in figure
5 for a certain length of fiber, a constant erbium doping density and signal input power. 10, 20, 30, 40
and 50 mW pump powers were applied to a 50 m Er-doped fiber with a 140 ppm doping concentration
for a signal input power of –30 dBm and the pump power variations along the active fiber were
obtained. As it can be seen from figure 5, the pump power rapidly attenuates with fiber length which
results mainly from two mechanisms namely erbium absorption and background loss of silica fiber.
The fiber background loss, which is less effective in a short distance, causes much higher pump power
depletion in a longer fiber. Due to excessive pump depletion in longer distances, the gain obtained
from an amplifier begins to decrease after a maximum level.
Figure 5. The attenuation of pump power along an erbium doped fiber
Gain And Noise Figure Performance Of Erbium Doped Fiber Amplifiers (EDFA)
A.Cem ÇOKRAK, Ahmet ALTUNCU
1118
5.2 Gain Characteristics
The variation of gain with fiber length is shown in figure 6.a for different pump powers having a
constant signal input power and erbium doping density. In this figure, the gain obtained from an
amplifier for eight different pump power levels were given for a 100 m long EDF with 315 ppm
doping density when a signal input power of 100 µW was applied to the active fiber. As it is shown,
the gain increases up to a certain length of fiber, and then begins to decrease after a maximum point.
The reason for the decrease in gain is insufficient population inversion due to excessive pump
depletion and getting higher losses than the provided gain at the signal wavelength due to high total
loss of Erbium doped fiber (fiber background loss+Er absorption loss).
Figure 6.b shows the variation of gain with pump power for different fiber lengths, a constant signal
input power and Er doping density. In this simulation, a 100 µW signal power was applied at the input
of an EDFA with 70 ppm doping density for six different fiber lengths and the pump power supplied
was increased from 0 mW to 100 mW. It is seen that the gain of the EDFA increases with the
increasing pump power and then goes to saturation after a certain level of pump power. From the
figure, it is shown that, the gain of the EDFA sharply increases with increasing pump power; after a
certain level of gain, the increase in gain becomes smaller when the population inversion is provided
for all the erbium ions in the fiber and therefore amplifier goes to saturation. As a result, the gain
efficiency defined in terms of dB gain per unit mW pump power reduces for high pump powers. In
addition, a higher gain can be obtained if a longer erbium doped fiber is used with sufficient pumping.
Figure 6. The variation of gain with a) Fiber length and b) Pump power
Figure 7.a shows how the gain varies as a function of signal input power for different pumping powers
at a constant fiber length and erbium doping density. In this work, six different pump powers were
applied to a 50 m long EDFA with a doping density of 140 ppm and the signal power was increased
from –30 dBm to 10 dBm. From the figure, it is seen that EDFA gain decreases with increasing signal
input power. The reason of this is the easier saturation of the EDFA at higher signal powers for a
constant pump power.
Gain And Noise Figure Performance Of Erbium Doped Fiber Amplifiers (EDFA)
A.Cem ÇOKRAK, Ahmet ALTUNCU
1119
Figure 7. The variation of gain with a) Signal input power and b) Erbium ion density
The gain variation as a function of erbium doping density is shown in figure 7.b for a 50 m long fiber
and a constant signal input power. The simulation was realised for the pump powers varying from 10
mW to 100 mW. It is seen that for a sufficiently large pump power, the gain linearly increases with
increasing erbium ion density and stays constant after a certain level. Since the amplifier reaches the
population inversion, the variation in maximum gain is small despite occuring a high increase in pump
power. In the trace obtained for 10 mW pump power, the gain reduces sharply in highly doped fiber
due to insufficient pumping. At high pump levels, invariation of the gain with erbium doping density
can be explained such that the extra gain provided in the EDFA spends by the increasing erbium
absorption.
5.3 Noise Figure Characteristics
The variation of noise figure as a function of fiber length is shown in figure 8.a for different pumping
powers at a constant signal input power and erbium ion density. This graph was obtained in a 100 m
long fiber with 350 ppm doping density and using an input signal power of 100 µW. For a pump
power of 15 mW, the increase in noise figure from 70 m can be clearly noticed. The reason for this
increase is the decreasing gain with sharp pump depletion.
Figure 8. The variation of noise figure with a) Fiber length and b) Pump power
Gain And Noise Figure Performance Of Erbium Doped Fiber Amplifiers (EDFA)
A.Cem ÇOKRAK, Ahmet ALTUNCU
1120
Figure shows the noise figure variations as a function of pump power for different fiber lengths at a
constant signal input power and doping density. In the simulation performed for six different fiber
length, a 100 µW signal input power was applied to an EDFA with an erbium doping rate of 70 ppm
and the pump power was increased from 0 mW to 100 mW. In an amplifier having these parameters,
it can be seen from the graph that the noise figure decreases with increasing pump power. The high
gain in an active fiber with the total population inversion provided causes the spontaneous emission to
stay in low levels. The noise figure of the EDFA varies linearly with ASE power and inversely with
the amplifier gain. Therefore, the noise figure of an EDFA can be reduced to a minimum level by
increasing the gain.
In figure 9.a, the variation of noise figure is given as a function of signal input power for a constant
fiber length and erbium ion density. In this simulation, a 50 m long EDFA with an erbium ion density
of 140 ppm was used. The graph shows that the NF of the EDFA increases with increasing signal
input power. The variation of noise figure as a function of erbium ion density is given in figure 9.b for
a constant fiber length and signal input power. These graphs were obtained using a 50 m long erbium
doped fiber and 1 µW signal input power. From figure 9.b, it is seen that, NF remains constant from
approximately 30 ppm even if the pumping power would be increased. The noise figure at 0 ppm
density has not started from 0 dB due to some inability of the EDFA model used here. Beyond 30 ppm
and for a 10 mW pumping power, insufficient pumping occurs and the noise figure sharply increases
due to not to have population inversion. The pump powers of 20 mW or beyond is sufficient to obtain
nsp=1 .
Figure 9. The variation of noise figure with a) Signal input power and b) Erbium ion density
5.4 ASE Power Characteristics
The variation of ASE power in EDFA with fiber length is shown in figure 10.a for the pump powers
from 10 mW to 50 mW and for a constant signal input power and erbium doping density. This graph
was obtained by applying 1 µW signal input power to a 50 m long EDF with a doping density of 140
ppm. The ASE power propagates in an EDFA in forward and backward directions. The one shown in
the graph is the forward ASE which is the parameter taken into account in the NF calculations. As can
be shown, the ASE power increases with increasing fiber length due to the gain provided inside EDFA
and reaches to larger values for high pumping powers.
Gain And Noise Figure Performance Of Erbium Doped Fiber Amplifiers (EDFA)
A.Cem ÇOKRAK, Ahmet ALTUNCU
1121
Figure 10. The variation of ASE power with a) Fiber length and b) Pumping power.
Figure 10.b shows the ASE power variation as a function of pump power for different fiber lengths, at
a constant signal input power and erbium doping density. This graph was obtained for a five different
fiber lengths having 245 ppm doping density and by applying a signal input power of 1 µW and
increasing the pump power from 0 mW to 100 mW. As it can be shown, ASE power increases
significantly with the increasing pump power. The main reason of that is to amplify not only the
signal but also the spontaneous emission. The saturation of gain by the increasing pump power leads
to reach the ASE power to a maximum level. This level is limited with erbium doping density.
The ASE power variations as a function of signal input power is shown in figure 11.a for a constant
fiber length and erbium ion density. In this simulation, a 50 m long EDF with an erbium density of
140 ppm was used and the pump power was increased from 10 mW to 100 mW. As it is expected,
higher stimulated emission and less spontaneous emission occur with increasing signal input power
and therefore ASE power decreases.
Figure 11. The variation of ASE power with a) Signal input power b) Erbium ion density
In figure 11.b, the ASE power variation is shown
as a function of erbium ion density for a constant
fiber length and signal input power. The
simulation was realised for six different pump
powers by applying 1 µW signal input power to a
50 m long EDFA. As it can be seen, ASE power
sharply increases from a doping density of ∼100
ppm and remains nearly constant at beyond ∼250
ppm. Higher gains provided by injecting higher
pumping powers cause the ASE generated in the
EDFA to be high.
6.RESULTS
In this study, the rate and propagation equations
characterizing an EDFA operating in C band and
pumped at 1480 nm in forward direction was
numerically solved and the results were
Gain And Noise Figure Performance Of Erbium Doped Fiber Amplifiers (EDFA)
A.Cem ÇOKRAK, Ahmet ALTUNCU
1122
graphically displayed. By entering the necessary
parameters of an EDFA to be simulated into the
main and sub menus of the simulation program;
gain, noise figure and ASE power variations
were obtained as functions of fiber length, pump
power, signal input power and erbium doping
density. In this way, the gain and NF
performance could be simulated for the given
EDFA parameters or the required fiber
parameters and signal/pump power values could
be optimised for a desired EDFA Gain-NF
performance.
According to our results, it was seen that the
pump power applied to EDFA sharply reduces
due to absorption in erbium doped fiber; in
addition, gain and NF is strongly dependent on
the fiber length, pumping power, signal input
power and erbium ion density. When the EDFA
is supplied with sufficient pump power, it was
shown that EDFA could be operated in saturation
regimes leading to maximum gain and minimum
NF. Due to the flexibility of the simulation
program, it is possible to simulate EDFAs
operating at 980 nm by using a few different
parameters. These simulations can also be
performed for distributed erbium doped fiber
amplifiers (DEDFA) by activating the
background loss coefficients.
REFERENCES
[1] Agrawal G.P., Fiber optic communication
systems, John Wiley & Sons, New York, 1997
[2] Giles C.R., Desurvire E., “Modelling
Erbium-Doped Fiber Amplifiers”, Journal of
Lightwave Technology Letters, Vol. 9, No 2,
271-283, 1991
[3] Deservire E., “Erbium doped fiber amplifiers
: principles and applications”, John Wiley &
Sons, New York, 1994
[4] Altuncu A., Siddiqui A.S., Ellis A.,
Newhouse M.A., Antos A.J. " Gain and noise
figure characterisation of a 68 km long
distributed erbium doped fibre amplifier ",
Electronics Letters, Vol.32, No.19, 1800-1801,
1996.
[5] Giles C.R., Desurvire E., “Propagation of
Signal and Noise in Concatenated Erbium-Doped
Fiber Optical Amplifiers”, Journal of Lightwave
Technology Letters, Vol 9, No 2, 147-154, 1991
