Thulium Doped Fiber Amplifier (TDFA) for S-band WDM
Systems
Fady I. El-Nahal
Department of Electrical Engineering
Islamic University of Gaza
Gaza, Gaza Strip, Palestine
Abdel Hakeim. M. Husein
Physics Department
Al-Aqsa University
Gaza, Gaza Strip, Palestine
Abstract— A comprehensive numerical model based on solving rate equations of a thulium-doped silica-based fiber amplifier
is evaluated. The pump power and thulium-doped fiber (TDF) length for single-pass Thulium-Doped Fiber Amplifiers (TDFA)
are theoretically optimized to achieve the optimum Gain and Noise Figure (NF) at the center of S-band region. The 1064 nm
pump is used to provide both ground-state and excited state absorptions for amplification in the S-band region. The theoretical
result is in agreement with the published experimental result.
Keywords-component; Thulium-Doped Fiber Amplifiers, Rate Equations, Gain, Noise Figure
I.
1. Introduction
The increase demands on the capacity of WDM
transmission system now require newly developed
transmission windows beyond the amplification bandwidth
supported by erbium-doped fiber amplifiers (EDFA’s).
Thulium-doped fiber amplifier (TDFA) provides high-power
optical amplification in the S+ (1450–1480 nm) and S-bands
(1480–1530 nm) [1-3], hence the TDFA is expected to
complement C- (1530–1560 nm) and L-band (1560–1580 nm)
amplification based on EDFAs in high-capacity dense
wavelength division multiplexed (DWDM) systems [4, 5]. The
additional bandwidth, modularity, inherent higher pumping
efficiency, and lower nonlinear signal degradation (compared
with alternatives such as S-band Raman amplification [6,7]
offered by TDFA enables applications such as coarse
wavelength-division multiplexing (CWDM) and fiber to the
home (FTTH).
The TDFA length and Pump power are the important
parameters that determine the achievable gain and NF in
TDFA [8]. In this paper, we detail the observation and
modeling of TDFA where TDFA gain and NF are optimized
by solving the rate equations.
2. Configuration of the TDFA
The basic architecture used to model TDFA in the WDM
system consists of 16 input signals (channels), an ideal
multiplexer, a pump laser , pump coupler, Thulium-doped
fiber (TDF), Optical spectrum analyzer and dual port WDM
analyzer. The input of the system is 16 equalized wavelength
multiplexed signals (channels) in the wavelength region of 80
nm (1450 nm-1530 nm) with 5 nm channels spacing. The
power of each channel is -20 dBm. The pumping at 1064 nm
is used to excite the doped atoms to a higher energy level. The
TDF used is a glass based one with thulium density of
15.6×10-24 m2, core radius is 1.3μm, doping radius is 1.3 μm
and Numerical aperture (NA) is 0.3. The simulation done with
maximum number of iterations is 150 and relative error is
5×10-4.
3. Theory of the TDFA
The rate equations describe the interaction between signal,
pump, and ASE light in the TDFA. The rate equations are
used to analyze theoretically the populations in the energy
levels of Tm3+ ions under 1064 nm pump and signal power
conditions. The absorption and stimulated emission cross
sections define the absorption coefficient for pump light and
gain coefficient for signal light [9]. The transition cross-
sections of thulium are shown in Fig. 1 [8]. The transition
cross-sections were calculated in fluoride based TDF [10]. The
Judd–Ofelt analysis shows that the transition strengths
obtained were consistent with those for silica.
Figure 1. Absorption and emission cross-sections spectra of the fluoride-
based TDFA.
Open Journal of Applied Sciences
Supplement：2012 world Congress on Engineering and Technology
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An analysis of a six energy levels system is shown in
Figure 2, where the energy levels of trivalent thulium ion in
fluoride glass are displayed. The absorption and emission
transitions are shown in fig. 2(a) and (b), respectively for the
TDFA with 1064 nm pump wavelength. For S-band
amplification, the main transition is from
3
4
H o
3
4
F energy
levels. Pumping at 1064 nm range takes benefit of the excited
state absorption (ESA)
3
4
F at the level to excite electrons to
the upper energy state. On the other hand, as 1064 nm is the
main source of excitation, ground state absorption (GSA) of
1064 nm and /or WDM signals at the
3
6
H ground state must
be nonzero in order to populate
3
5
H energy level and then
relaxed to the
3
4
F energy level by non-radiative decay [11]. By
exciting the TDFA at a fixed level (at 1064 nm), increasing the
input WDM signals power further populates the lower energy
state (3
4
F), from which the excited ions are raised to the upper
energy state (
3
4
H ) because of excess pump power [11]. The
pumping transition
3
4
F o
1
4
G is (ESA). The energy level of
the 3
2
F and3
3
F are very close nearly the same and can be
regarded as one level for simplicity. So the
3
4
F energy level
ions are re-exited to the
3
2
F energy level and experience non-
radiative decay to the
3
4
H energy level via exited state
absorption [12, 13].
Figure. 2. Energy levels with pumping mechanism 1064 nm of trivalent
ion (Tm3+) in fluoride glass. (a) Pump absorption, (b) signal and ASE
emission transitions.
The Thulium doped fiber ions can be considered
homogeneously broadened in amplification system and also
characterized by the variables
01234
,,,,NNNNN and
5
Nwhich are used to represent population ions in the
3
6
H ,
3
4
F
,
3
5
H
,
3
4
H
,
3
2
F
, and 1
2
G
energy levels, respectively. For
simplicity,
31
J
and 32
J
are ignored because they are very small
compared with
30
J
.
51
J
and
53
J
are also ignored because
they are small compared with
50
J
and
52
J
.
20
J
and 4
J
j (j =
0,1,2) are very small and can be disregarded because
21
J and
43
J
are multiphonon decay. On the basis of the energy level
diagram as in Fig. 2. The rate equation for Tm3+ population
density can be written as follows [14]:
0
1010130 350 5
JJJ 
p
dN WNN NN
dt
(1)
1
102121 23
() JJ 
ps s
dN WWN NWN
dt
(2)
2
1021 2525
JJ 
nr
p
dN WNN N
dt
(3)
3
130 33434
() JJ 
sps
dN WNWW NN
dt
(4)
4
2143 4
J 
nr
p
dN WN N
dt
(5)
5
3 350525
()
JJ 
p
dN WN N
dt
(6)
5
1
¦ ti
i
NN (7)
where
11 3
,, and
pp p
WW W
are transition rates of
3
6
H
o
3
5
H,
3
4
H
o
3
2
F, and
3
4
F
o
1
4
G
pumping transition.
The signal of the central S-band is 1470 nm as signal
stimulated absorption and emission is described by transition
rate s W. The non-radiative transition rate from
3
2
F o
3
4
F and
from
3
5
H
o
3
4
F
energy levels are defined as
43 21
, and JJ
nr nr
,
respectively.
ij
J
is the radiative rate from level
i
to level
j
.
Others radiative transitions are not included in the rate
equations because they have an ignorable effect on the S-band
ampliation. For simplicity,
31
J and 32 J are ignored because
they are very small compared with 30 J
.
51
J
and
53
J
are also
ignored because they are small compared with 50
J
and 52
J
.
20
J
and 4j
J
(j = 0,1,2) are very small and can be disregarded
because
21
J and 43 J are multiphonon decay [15, 16]. Rate
equations can be solved by considering the steady state regime
where the populations are time independent,
0 , (i = 0, 1, 2,......., 5)
i
dN
dt
. The average thulium ion
concentration in the core t Nis calculated by [17]
2
0
2()
t
NNrrdr
b
f
³
(8)
where b is the doping radius , i.e. the half of the
concentration profile FWHM. In general, the variable i N is
functions of position r, z and time t. N(r) is the thulium ions
concentration profile.
2
N
and
4
N
are very small compared to
other i Nvalues. Therefore the total population density t Nis
expressed as:
0135t
NNNNN  (9)
The transition rates, which describe the interaction of the
electromagnetic field with the Tm3+ ions for a TDFA can be
written as [14]:
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1
1
a
pp
p
p
P
Wh
V
Q
(10)
2
2
a
pp
p
p
P
Wh
V
Q
(11)
3
3
a
pp
p
p
P
Wh
V
Q
(12)
a
ss
s
s
P
Wh
V
Q
(13)
where
p
P is the pump power intensity and s P is the signal
power intensity.
1
a
p
V
, 2
a
p
V
, and
3
a
p
V
are
3
6
H o
3
5
H ,
3
4
H o
3
2
F ,and
3
4
F o
1
4
Gstimulation absorption
cross sections where the Tm3+ ions are excited homogeneously
across the fiber cross-section. So;
30 3
1 l JW (14)
10 1
1l JW (15)
where
3
W
and
1
W
are the lifetimes of the
3
4
F
and
3
4
H
levels, respectively. h is the Planck constant,
p
Q is pump light
frequency and
s
Q is signal light frequency. The light wave
propagation equations along the thulium fiber in the z-
direction can be recognized as follows [8]:
1021 13
()
p
ppppp p
dP NNNPP
dz
VVV D *
(16)
31010
()
s
ea s
ss ss
dP NNNPP
dz
VVVD *
(17)
31010 3
()2
s s
ea e ASE
ASEsASE ASEASE
dP NNNPhNP
dz
VVVXXVD r*r*'m
(18)
where D is the background scattering loss which assumed
to constant for all wavelength.
ASE
Pis the amplified
spontaneous emission (ASE) at S- band in forward (+) and
backward (-) directions a along the fiber.
01
V is transition
cross section from background level 0 N to the first level 1 N
for 1800 nm wavelength.
,,spASE
*
is the overlapping factor
between each radiation and the fundamental mode for the
signal, the pump, and ASE respectively, * can be given by
[15,18]:
2
2
0
2
1
b
w
e

*  (19)
where
0
w is the model field radius and b is the thulium
ion-dopant radius.
01.5 6
1.237 1.429
(0.761 )wa VV 
(20)
where a is the core diameter, V is the normalized
frequency. In eq. (17) the term
01 0
N V is ignored because the
01
V
is very small, so eq. (17) becomes as:
31
()
s
ea s
psss
dP NNPP
dz
VV D
*
(21)
The gain (G) is given by integration eq. (21) along z-
direction from 0 to L;
103 1
()10logexp[() ]exp()
s
ea
ss
GdBNN LL VV D
ªº *
¬¼
(22)
where L is the length of the TDFA. The gain in decibel (dB)
From a practical point of view, the noise figure (NF)
characteristic is very important in an optical amplifier's
performance. The rate equation analysis predicts a low-noise
characteristic in the optical amplification. Therefore, the NF
was calculated using fiber by an optical method [19]. NF is
given by
out
ASE s
P( ) 1
NF GGh
O
Q'Q

(23)
where
out
ASE s
P(Ȝ is the output ASE spectral density (W/Hz)
at the signal wavelength. For each signal wavelength, the NF
in dB is given by:
out
ASE s
10
P()
1
NF(dB)10xlogGGh
O
Q'Q
ªº

«»
¬¼
(25)
4. Results and Discussions
The proposed system amplifies a set of 16 channels in the
S-band going from 1450 nm to 1525 nm. The parameters used
in the simulation are listed in table 1.
Table 1: Parameters used in the simulation [12]:
Parameter Value
Thulium ion density 1.68e+025 1/m3
Numerical aperture 0.4
Fiber Length 2.5, 7.5, 10 m
Core radius 1.3µm
Optimization of the length of the thulium-doped fiber
(TDF) is one of the most important issues for optical networks
that need to be considered for designing a TDFA in order to
obtain the best gain with the lowest noise figure. The gain and
noise figure of the TDFA are dependent on the TDF length
and the operating pump power. The TDF length is selected
carefully, when the TDF length is too short, the TDFA will be
saturated at a low pump power and this does not provide a
high gain. For a short TDF, the total population is very low
and therefore the TDF is fully inverted by a low amount of
pump power. When this low amount of pump power is used
then the optimized TDF length is short. The length of the TDF
is optimized by calculating the gain as a function of TDF
length for various operating pump powers. The input signal
power and wavelength is fixed at í20 dBm and 1470 nm,
respectively and the pump power is varied from 1000 mW to
2000 mW. Three different amplifier lengths are simulated (2.5
m, 7.5 m, 10 m) and the gain and NF curves are plotted in
Figure 3. It is clear from the results that the gain increases
with increasing the pump power for L = 7.5m and 10 m and it
stays almost constant at L =2.5 m. However, the best gain is
achieved at L = 7.5 m. For the NF results, it is clear that
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increasing the pump power and the fiber length has a little
impact on the NF.
Although the 10 m long TDFA design provides the highest
gain (16.7 dB) at pump power of 2000 mW. However the use
of a high pump power is in conflict with the main objective of
the TDFA design which requires a smaller pump power
especially for long haul applications. For this reason, a very
(a) Gain
(b) NF
Figure 3. Gain and Noise Figure (NF) versus pump power at different
lengths L=2.5m, 7.5m and 10 m.
long TDF is not recommended to be considered as a reference
TDF length during the design of single pass TDFAs. In the
optical network, an amplifier is mainly designed to obtain a
gain as high as possible with a low noise figure using a
minimum pump power. So the optimum length is 7.5 m with
optimum pump power of 1500 mw, where a gain of 15.4 dB
and NF of 2.9 dB are achieved.
5. Conclusion
This paper has described in detail the relation between the
operating 1064 nm pump power and TDFA length for single-
pass TDFA. The simulation results are based on the rate
equations to determine the gain and noise figures for TDFA.
The simulated model was also used for optimizing of the
TDFA parameters: fiber length, pump wavelength and pump
power. The theoretical results obtained here is in agreement
with the published experimental result. It is found that the
optimum TDFA length is 7.5 m with optimum pump power of
1500 mW. The results show that silica-based TDFA amplifiers
are interesting comparing to its competitors within the S-band
optical amplifiers, namely the fluoride-fiber based TDFA and
the Raman amplifiers.
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