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Antioxidant and antimicrobial compounds

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ARTICLE IN PRESSOpticsOptik
Optik 121 (2010) 1257–12620030-4026/$ - se
doi:10.1016/j.ijl
Correspond
E-mail addrwww.elsevier.de/ijleoA theoretical study of double-pass thulium-doped fiber amplifiers
S.D. Emamia,, S.W. Haruna, F. Abd-Rahmand, H.A. Abdul-Rashidb, S.A. Daudb,
Z.A. Ghanic, H. Ahmada
aPhotonics Research Center, University of Malaya, 50603 Kuala Lumpur, Malaysia
bFaculty of Engineering, Multimedia University, 63100 Cyberjaya, Malaysia
cFaculty of Applied Science, University Technology MARA, 40450 Shah Alam, Malaysia
dFaculty of Engineering and Science, Universiti Tunku Abdul Rahman 53300 Setapak, Malaysia
Received 1 September 2008; accepted 12 January 2009Abstract
An efficient fluoride-based thulium-doped fiber amplifier (TDFA) is theoretically demonstrated using a double-pass
scheme. A reflector is incorporated in the double-pass TDFA to allow double propagation of the test signal in the gain
medium and thus improve the gain of the TDFA. The small signal gain improvement of more than 15 dB is obtained in
the 1465 nm region. A gain as high as 42 dB is obtained in this region with 300mW of 1050 nm pump using 20m of
thulium-doped fiber. However, a noise figure penalty of approximately 1 dB is also obtained in this wavelength region.
Differential equations are solved using the Runge–Kutta method in the theoretical analysis. The theoretical result is in
agreement with the experimental result.
r 2009 Elsevier GmbH. All rights reserved.
Keywords: Thulium-doped fiber amplifier; S-band amplifier; Double pass1. Introduction
Due to the tremendous increase in communication
traffic in recent years, more and more efforts in research
have been directed towards developing highly efficient
broad-band fiber amplifiers that will fully exploit the low-
loss band of silica fibers in the 1450–1630nm range, which
has a loss of only 0.25dB/km in order to increase the
transmission capacity of wavelength-division multiplexing
(WDM) networks [1,2]. These broad-band amplifiers must
be able to amplify the new short wavelength band (S-band)
in addition to the existing C- and L-bands. Thulium-doped
fluoride fiber amplifiers (TDFFAs) are a promising
candidate for the S-band amplification because thee front matter r 2009 Elsevier GmbH. All rights reserved.
eo.2009.01.017
ing author.
ess: S.D.Emami@gmail.com (S.D. Emami).amplification bandwidth of the TDFA is centered at
1470nm [3], which falls within the S-band. However, its
power conversion efficiency and its spectral gain char-
acteristics are crucial issues that need to be addressed [4–6].
Several studies dealing with gain enhancement have been
reported [7–10], leading to an improvement of pumping
efficiency through an up-conversion pumping scheme.
In this paper, an efficient TDFFA is demonstrated
theoretically using a double-pass scheme. The thulium-
doped fluoride fiber is pumped by a 1050 nm laser
diode using a forward pumping scheme. A reflector
is used at the output end of the amplifier to allow a
double propagation of the forward amplified sponta-
neous emission (ASE) and the optical signal in the
thulium-doped fiber. Differential equations involved in
the theoretical analysis are solved using the Runge–
Kutta method [11,12].
ARTICLE IN PRESS
S.D. Emami et al. / Optik 121 (2010) 1257–126212582. Configuration and modeling of the TDFA
Fig. 1 shows the configuration of the double-pass
TDFA, which consists of a fluoride-based TDF, a
WDM coupler, a pump laser, an optical circulator and a
reflector. The TDF used is 20m long and has a Tm ion
concentration of 2000 ppm. The pump light and the
input signal are combined using a WDM coupler.
A 1050 nm laser diode is used as the pump. Both the
forward ASE and the signal are reflected back into the
system by a reflector. An optical circulator is then used
to route the output and to prevent the backscattered
light from entering the transmitter.
Fig. 2 shows the energy level diagram of trivalent
thulium ion in fluoride glass. Figs. 2 (a) and (b) show the
absorption and emission transitions, respectively, in
the TDFA with 1050 nm pump. As shown in the figure,
the main transition used for S-band amplification is
between 3H4 and
3F4 levels, which emit photons at
1460 nm region. This amplification is made possible by
an up-conversion pumping method, which forms a
population inversion between 3H4 and
3F4 levels. When
the TDF is pumped with 1050 nm laser, the ground-state
ions in the 3H6 energy level can be excited to the
3H51050nm
Signal
WDM
coupler
Pump
TDF (2000ppm, 20 m)
OSA
reflector
Port 2
Fig. 1. Configuration of the double-pass TDFA.
3H6
1G4
N0
3H4
3H5
3F4
3F2,
N5
N4
N3
N2
N1
A30
A52 A50
8 µm(ASE)
A10
σ03 ,σ03
σ13
σ31
A21
A43
(1050 nm)
(1050 nm)
σp02
(1050 nm)
σp14
σp35
σ10 ,σ01
1.8 μm (ASE)
Fig. 2. Energy level diagram of thulium ion.energy level and then relaxed to the 3F4 energy level by
non-radiative decay. The 3F4 energy level ions are then
re-excited to the 3F2 energy level and experience non-
radiative decay to the 3H4 energy level via excited-state
absorption. The 1050 nm pump alone can provide both
the ground-state and excited-state absorptions.
The difference between the 3F2 and
3F3 energy levels is
very small and therefore they can be treated as one level
for simplicity [13]. We substitute N0, N1, N2, N3, N4 and
N5 variables for ion populations of
3H6,
3F4,
3H5,
3H4,
3F2 and
1G2 respectively. According to Fig. 2, the rate
equations can be established as follows:
dN0
dt
¼  ðWp02 þW 18a þW 8aÞN0 þ ðA10 þW 18eÞN1
þ ðA30 þW 8eÞN3 þ A50N5 (1)
dN1
dt
¼ ðW 18aÞN0  ðA10 þWp14 þW sa þW 18eÞN1
þ ðA20ÞN2 þ ðW seÞN3 (2)
dN2
dt
¼ ðWp02ÞN0  ðA
nr
21ÞN2 þ ðW 52ÞN5 (3)
dN3
dt
¼ ðW 8aÞN0 þ ðW saÞN1  ðA30 þWp35 þW se
þW 8aÞN3 þ ðA43ÞN4 (4)
dN4
dt
¼ ðWp14ÞN1  ðA
nr
43ÞN4 (5)
dN5
dt
¼ ðWp35ÞN3  ðA50 þ A52ÞN5 (6)
X
i
Ni ¼ r (7)
where Wp02, Wp14, Wp35 are transition rates of 1050 nm
pump. Signal stimulated absorption and emission are
described by Wsa and Wse, respectively. The transition
rates of amplified spontaneous emission at 800 nm
(3H4-
3H6) and 1800 nm (
3F4-
3H6) are governed by
W8 and W18 respectively. Non-radiative transition rate
from 3F2 to
3F4 and from
3H5 to
3F4 are defined as A43
nr
and A21
nr. Aij is the radiative rate from level i to level j.
The average concentration of thulium in the core is r
and is quantified by [12]
r ¼
2
b2
Z 1
0
nðrÞrdr
(8)where b is doping radius and N(r) is thulium
concentration profile. Interaction of the electromagnetic
field with ions or transition rate (Wij) can be written as [11]
Wp02;p14;p35 ¼ lP1sp02;p14;p35
PþP1
hcAeff
 
(9)
ARTICLE IN PRESS
S.D. Emami et al. / Optik 121 (2010) 1257–1262 1259W 8a;8e;18a;18e ¼ l
8;18
ASEs03;30;01;10
P8;18þASE þ P
8;18
ASE
hcAeff
 !
(10)
W 8a;8e;18a;18e ¼ l
8;18
ASEs03;30;01;10
P8;18þASE þ P
8;18
ASE
hcAeff
 !
þ lsssa;se
PþS þ P

s
hcAeff
 
(11)
where sp02, sp14, and sp35 are the
3H6-
3H5,
3F4-
3F2,
and 3H4-
1G4 absorption cross sections of 1050nm
forward pumping, respectively. The stimulated absorption
and emission cross section of ASE at 800 and 1800nm are
denoted by s8a, s8e, and s18e, respectively. Pp
1+ is the
spectral power radiation of 1050nm pump. Ps is the signal
power and PASE, PASE8, and PASE18 are the S-band ASE,
800nm ASE and 1800nm ASE in the forward direction
(+) and backward () direction along the fiber. The
equation to calculate W8a, W8e, W18a and W18e of single-
pass TDFA are modified by integrating the reflected
backward signal power Ps of double-pass TDFA. The
lightwave propagation equations along the thulium fiber
(in the z direction) can be established as follows [11,12]:
dPASE
dz
¼  GðlASEÞðsseN3  sseN1 þ sp01N0Þ  PASE
 GðlASEÞ2hnDnsseN3  aPASE (12)
dP8ASE
dz
¼  Gðl8Þðs30N3  s03N1Þ  P8ASE
 Gðl8Þ2hnDns30N3  aP8ASE (13)
dP18ASE
dz
¼  Gðl18Þðs10N1  s01N0Þ
 P18ASE  Gðl18Þ2hnDns10N1  aP
18
ASE (14)Table 1. Initial condition.
Initial condition Operating wavelength
PP1ðz ¼ 0Þ ¼ PP1
l ¼ 1050
PSðz ¼ 0Þ ¼ PS
–
PþASEðz ¼ 0; vÞ ¼ P

ASEðz ¼ l; vÞ ¼ 0
1460olo1050
P8þASEðz ¼ 0; vÞ ¼ P
8
ASEðz ¼ l; vÞ ¼ 0
1460olo1050
P18þASEðz ¼ 0; vÞ ¼ P
18
ASEðz ¼ l; vÞ ¼ 0
1460olo1050dPþP1
dz
¼  GðlP1Þðsp02N0 þ sp14N1 þ sp02N3Þ
 PþP1  aP

P1 (15)
dPs
dz
¼ GðlsÞðsseN3  ssaN1  sp01N0Þ  Ps  aP

s
(16)
where a is background scattering loss, which is assumed to
be constant for all wavelengths. lASE, lASE8 and lASE18 are
the signal wavelengths, 800nm ASE and 1800nm ASE,
respectively. Overlapping factors between each radiation
and fiber fundamental mode, G(l) can be expressed as
[12,14]
GðlÞ ¼ 1 eð2b
2=w2
0
Þ (17)
W 0 ¼ a 0:761þ
1:237
V1:5
þ
1:429
V6
 
(18)
where w0 is mode field radius defined by Eq. (18), a is core
diameter, b is thulium ion dopant radius and V is
normalized frequency.3. Numerical calculations
In order to solve the population rate in steady-state
condition, the time derivatives of Eqs. (1)–(6) are set to
zero [15]. All the equations used for pump and signal
powers, Eqs. (12)–(17), are first-order differential
equations. The Runge–Kutta method is used to solve
the differential equations. In the numerical modeling, we
initially assume all the population to be at the ground
level (3H6). Table 1 shows the initial conditions, which
are set on pump power, signal power and ASE spectrum
at S-band, 800 and 1800 nm wavelength [16]:Explanation
Initial condition for 1050 nm pump at Z ¼ 0
Initial condition for signal pump at Z ¼ 0
Initial condition for PASE at s-band for Z ¼ 0 and Z ¼ L
Initial condition for PASE at 800 nm for Z ¼ 0 and Z ¼ L
Initial condition for PASE at 1800 nm for Z ¼ 0 and Z ¼ L
ARTICLE IN PRESS
S.D. Emami et al. / Optik 121 (2010) 1257–12621260The thulium-doped fiber with length L is divided into
L segments along the z direction, as shown in Fig. 3. We
solve for the pump, signal and ASE power propagating
in the first segment (segment 0) by using the above initial
conditions. For the following segments (segment
1–L1), the power for all the pump, signal and ASE
at one end of a segment is used as the input for the next
segment [17]. Relaxation method is used to achieve an
accuracy of 0.01% for all the pump, signal and ASE
powers [16].
The spectroscopic parameters used in our analysis are
carefully chosen from the literature [6,11,18] and are
summarized in Table 2. The spectral emission cross
section at S-band of thulium ion [8] and the spectral
absorption cross section at S-band can be estimated by
the modified McCumber’s relation [14]:
saðnÞ ¼
seðnÞ
Zpeak
expð
hðn npeakÞ
kBT
 
(21)I=0 1 2
Z=L
P(0) P(2) P(L)P(L-1)P(1)
Z=0
L-1L-2L-3
Fig. 3. Schematic of the fiber model.
Table 2. Parameter used in the numerical simulation.
Parameter Unit
Thulium concentration 1/m3
Numerical aperture
Fiber length m
Background lost dB/m
Effective area m2
Division along fiber
800 nm ASE bandwidth nm
1800 nm ASE bandwidth nm
ASE bandwidth nm
1050 nm Pump absorption cross section
Section m2
1050 nm Pump absorption cross section m2
1050 nm Pump absorption cross section m2
1650 nm Pump absorption cross section m2
Signal absorption cross section m2
Signal stimulated emission cross section m2
800 nm transition cross section m2
1800 nm transition cross section m2
Radiative decay rate 1/s
Radiative decay rate 1/s
Radiative decay rate 1/s
Radiative decay rate 1/s
Non-radiative decay rate 1/s
Non-radiative decay rate 1/sZpeak ¼
speake
speaka
. (22)
where kB is the Boltzmann constant and T is tempera-
ture. As observed experimentally, the absorption cross
section peak is approximately 70% of the emission peak
[6]. Fig. 4 shows the emission cross section spectrum andSymbol Value
r 1.68 1025
NA 0.3
L 20
a 1.68 1025
Aeff 2.096 10
12
12
Dn8 10
Dn18 100
Dn 2
sp02 1.1 10
27
sp14 8.2 10
25
sp35 2.5 10
27
sp01 2 10
26
ssa Fig
sse Fig
s03, s30 6.2 10
25
s01, s10 5.2 10
25
A10 172.4
A30 702.8
A50 676.3
A52 492.9
A43
nr 52976
A21
nr 165626
Fig. 4. Gain and noise figure characteristics for both single-
pass and double-pass TDFAs.
ARTICLE IN PRESS
S.D. Emami et al. / Optik 121 (2010) 1257–1262 1261the absorption cross section spectrum from Eq. (21) of
the thulium-doped fiber in fluoride host.Fig. 6. Noise figure vs pump power and input signal power for
the double-pass TDFA.4. Results and discussion
The model is numerically resolved using a Runge–-
Kutta method. Here we first compare the gain and noise
figure characteristics between the single-pass and dou-
ble-pass TDFA as shown in Fig. 4. For comparison, the
1050 nm pump and input signal powers are set at
250mW and 30 dBm, respectively. As shown in the
figure, the gain is higher in a double-pass amplifier
compared to the single-pass amplifier. The double-pass
amplifier achieves a maximum gain of 32 dB at 1465 nm,
which is 15 dB higher than the single-pass TDFA. The
gain enhancement is attributed to the longer effective
length in the double-pass TDFA. With the double-pass
configuration, the effective TDF amplification length is
twice the TDF length of the single-pass configuration,
where the signals make one round-trip in the fiber.
Therefore, the gain is higher in the double-pass
amplifier. However, the noise figure is higher in the
double-pass amplifier compared to the single-pass as
shown in Fig. 5. For instance, a 1 dB of noise figure
penalty is observed at 1470 nm in the double-pass
amplifier compared with the single-pass amplifier. This
increase in the noise figure is due to the counter-
propagating ASE at the input part of the TDFA, which
reduces the population inversion at the input part of the
fiber and subsequently increases the noise figure [19]. As
shown in Fig. 4 we compare our result with experi-
mental work of J.A. Camrlo in 2003 that represent the
double-pass single pump 1050 nm pump power with the
same setup [20]. The theoretical gain and noise figure is
in agreement with the experimental results.
Figs. 5 and 6 show the gain and noise figures of the
double-pass TDFA, respectively, with variations ofFig. 5. Gain vs pump power and input signal power for the
double-pass TDFA.1050 nm pump power from 0 to 300mW and variations
of input signal power from 40 to 0 dBm. The TDF
length and input signal wavelength is set at 20m and
1460 nm, respectively. As shown in Fig. 6, the gain
gradually decreases with the increment of input signal
power. This is due to the pump being unable to replenish
the inversion as fast as the input signal is depleting it.
The gain also increases with pump power and finally
saturates at a certain pump power. The saturation pump
power reduces with the increase of input signal power as
shown in Fig. 6. The maximum gain of 42 dB is obtained
at an input signal power of 40 dBm with a pump
power of 300mW. The noise figure can be reduced
(improved) by either increasing the pump power or
reducing the input signal power as shown in Fig. 6. The
noise figure at a particular wavelength is calculated by
the equation NF ¼ 1/G+PASE/(G h nDn) where
G and PASE is gain and ASE power, respectively. This
equation shows that the noise figure reduces as the gain
increases which is in agreement with our results.5. Conclusion
In this paper an efficient fluoride-based thulium-
doped fiber amplifier (TDFA) in a double-pass config-
uration is demonstrated theoretically. The double-pass
TDFA incorporates a reflector to allow double propa-
gation of the test signal in the thulium gain medium and
thus improves the TDFA gain. The theoretical analysis
uses the Runge–Kutta method to solve the differential
equations. The proposed TDFA shows a small signal
gain improvement of more than 15 dB in the 1465 nm
region, with a gain as high as 42 dB obtained in this
region at a 1050 nm pump power of 300mW and a 20m
of thulium-doped fiber. However, a noise figure penalty
of about 1 dB is also obtained at this wavelength region
ARTICLE IN PRESS
S.D. Emami et al. / Optik 121 (2010) 1257–12621262compared to a single-pass configuration, due to the
reduction in the population inversion by the counter-
propagating ASE. The theoretical results are in agree-
ment with the experimental results.References
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Antioxidant and antimicrobial compounds From the marine algae padina antillarum

A theoretical study of double-passthulium-doped fiber amplifiers

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